- 1 -
2009 ASSESSMENT OF THE DELAWARE BAY
BLUE CRAB (Callinectes sapidus) STOCK
Richard Allen Wong
Delaware Division of Fish and Wildlife
Department of Natural Resources & Environmental Control
89 Kings Highway
Dover, DE 19901
December 8, 2009
- 2 -
- 3 -
EXECUTIVE SUMMARY
The blue crab (Callinectes sapidus) is the most valuable commercial fishery species in
the State of Delaware. Harvest occurs from a residential Delaware Bay stock, which supports
fisheries in both Delaware and New Jersey. Between 1978 and 1995, bay-wide blue crab
commercial landings increased by 1,175% peaking at over 5.7 million kg (12.7 million lb).
Following a sharp decline in landings in 1996, the State of Delaware began efforts on a fishery
management plan and quantitative stock assessment to monitor the status of the stock. The
stock supported historically high levels of harvest for an extended period averaging 4 million
kg*y-1 (8.8 million lb) from 1988-2002. Landings again dropped significantly to less than 2 million
kg*y-1 (4.3 million lb) in 2003 and 2004 concomitant with a detected decline in stock abundance.
Depressed abundance was observed through yearly stock assessments for five years from
2002 to 2006. Some concern for the stock was raised given low adult abundance yet a rebound
in harvest to prior high levels of 3.4 million kg*y-1 (7.5 million lb) in 2005 and 2006. Recruitment
improved in 2006 and 2007, fueling an increase in 2007-2008 baywide landings to an above-
average level of 3.8 million kg (8.4 million lb).
This report provides results of the eleventh comprehensive stock assessment of the
Delaware Bay blue crab stock. The assessment employs a catch-survey population model that
simulates stock dynamics through time using two discrete groups of pre-recruited and fully
recruited individuals (Collie and Sissenwine 1983). The CSA model produces absolute
estimates of stock abundance and annual instantaneous rates of total mortality Z. Estimates of
abundance and total mortality were combined with known harvest to calculate a range of annual
exploitation rates µ. This range of µ was employed to generate upper and lower bounds of
- 4 -
annual F rates. Stock status was assessed relative to F-based benchmarks (Frep =1.3, Fmax
=1.0, F0.1 =0.6, F = M = 0.8), and from an index-based measure of spawning stock biomass
(Helser and Kahn 1999). Separate combined-sex, male, and female CSA analyses were
completed.
Four different model configurations of varying error component weightings were explored
based on work by Kahn and Helser (2005). The four model configurations consisted of an
observation error-only model and three models with varying weightings of observation and
process error residuals. A preferred model was chosen that emphasized the fit to observed
abundance indices while minimizing the effect of process error. The mixed-error model with the
smallest process error weighting provided the best fit to observed indices by minimizing the
influence of the model difference equation in the prediction of indices. Reducing the influence of
the model difference equation was helpful since the model could not account for the effect of
density dependent mortality on pre-recruits apparent in recurring residual patterns.
The Delaware Bay blue crab stock can fluctuate wildly. Since 1978, model estimates of
annual blue crab abundance have ranged from 29 to 614 million, with a mean and median of
155 and 135 million crabs. Most of the fluctuation is caused by great variability in pre-recruit
numbers. Time series estimates of pre-recruit abundance ranged from 15 to 544 million, with a
mean and median of 124 and 95 million recruits. Pre-recruit abundance dropped to 35 million
crabs in 2008, among the lowest of the time series. Full recruit abundance ranged between 9
and 70 million crabs, with a mean and median of 31 million individuals. Terminal year full-recruit
abundance was 23 million, representing a substantial decline from 37 million crabs in 2007.
Terminal year (2007-2008) fishing mortality rate on the combined-sex stock was F =
- 5 -
0.64, below all said reference points. Terminal F rose considerably from the prior year F =0.44.
The lower and upper bounds of terminal year F ranged from 0.35 to 1.22. The most-recent 3
year mean F was 0.71, approximately equal to benchmarks F0.1 and 0.8*M, with lower and upper
3 year means of 0.39 and 1.23. The 30 year mean F was 0.51 with upper and lower means of
0.28 and 0.78.
Additional fishery-independent indices of relative abundance portray a gradual recovery
in stock abundance after bottoming in 2002-2003. Low young-of-the-year abundance began in
2000 and continued with below-median YOY index values in four of the six ensuing years,
bottoming in 2002. Above-average winter mortality in winter 2002-2003 likely exacerbated the
effects of the weak 2002 year class. Depressed CPT values of recruits (medium crabs), large
crabs, and spawning stock were observed from 2003-2006. Harvest was depressed in 2003
and 2004 concomitant with the deterioration in stock abundance. Harvest rebounded
considerably in 2005 and 2006 amidst the ongoing low levels of recruitment and adult
abundance likely prolonging the depression in stock abundance. In 2006, YOY recruitment
spiked spurring a recovery to above-average values in medium and spawner indices in 2007. In
2008, however, the YOY index was very poor, which may act to stall the observed recent stock
recovery.
Despite low levels of abundance from 2003-2006, the stock still persisted at or above its
spawning stock biomass threshold. The stock exhibits very strong resiliency at low spawning
abundances and depensation at high abundances given a Ricker stock-recruitment relationship.
An example of its resiliency was seen in a large spike in YOY abundance in 2006 after only
small incremental increases in low SSB beginning in 2004. Spawning stock levels observed in
2008 should yield near optimal recruitment in 2009 given the S-R relationship.
- 6 -
In the terminal model year we observe low blue crab abundance and high fishing
mortality rates. Terminal estimates of absolute abundance are below-average for both pre-
recruits and full-recruit crabs. Recent fishing mortality rates are at high levels above time series
norms and near upper management thresholds. Furthermore, a weak year class was observed
in terminal year 2008 which forecasts poor fishery recruitment into exploitable stages in 2009.
On the other hand, the stock has shown very high resiliency/productivity at observed low
abundance levels. The standing spawning stock in 2008 is at a level that should produce robust
juvenile recruitment in 2009. This is encouraging for a rebound in year class strength in 2009
and exploitable abundance in 2010.
This work portrays a highly resilient stock under substantial exploitation pressure. Stock
status in the terminal year in terms of abundance and F is below-average, yet these metrics
should rebound in the near future given an expected recovery in recruitment.
- 7 -
Executive Summary .................................................................................................................... - 3 -
Background ................................................................................................................................. - 9 -
Life History ................................................................................................................................ - 10 -
Distribution ....................................................................................................................... - 10 -
Early Life History .............................................................................................................. - 11 -
Age and Growth ............................................................................................................... - 12 -
Maximum life span........................................................................................................... - 16 -
Reproduction and Maturity .............................................................................................. - 16 -
Predator Prey Interactions ............................................................................................... - 17 -
Natural Mortality ............................................................................................................... - 18 -
Unit Stock Definition ........................................................................................................ - 19 -
Fishery Description ................................................................................................................... - 20 -
Overview .......................................................................................................................... - 20 -
Commercial Fishery Harvest ........................................................................................... - 21 -
Sex-specific harvest ................................................................................................... - 24 -
Recreational Fishery........................................................................................................ - 25 -
Data Sources ............................................................................................................................ - 26 -
Harvest ............................................................................................................................ - 26 -
Commercial Landings ................................................................................................. - 26 -
Recreational harvest ................................................................................................... - 27 -
Fishery-Independent Data ............................................................................................... - 28 -
Indices of Abundance ................................................................................................. - 28 -
Instantaneous Natural Mortality Rate .............................................................................. - 29 -
Methodology .............................................................................................................................. - 29 -
Population Model ............................................................................................................. - 29 -
Model Inputs ............................................................................................................... - 33 -
External-Model Calculations of Fishing Mortality ............................................................ - 36 -
External Indices of Relative Abundance ......................................................................... - 37 -
Index-Based Stock–Recruitment Model .......................................................................... - 38 -
Results ...................................................................................................................................... - 38 -
Error-weighting Model Selection ..................................................................................... - 39 -
Combined-Sex Model ...................................................................................................... - 41 -
Model Outputs ............................................................................................................ - 41 -
Mortality Rates ............................................................................................................ - 42 -
- 8 -
Indices of Relative Abundance........................................................................................ - 43 -
Index-Based Stock Recruitment Model ........................................................................... - 44 -
Discussion ................................................................................................................................. - 45 -
Stock Status .................................................................................................................... - 47 -
Acknowledgments ..................................................................................................................... - 49 -
References Cited ...................................................................................................................... - 51 -
Tables ....................................................................................................................................... - 61 -
Figures ...................................................................................................................................... - 70 -
Appendix I ................................................................................................................................. - 89 -
- 9 -
BACKGROUND
The blue crab (Callinectes sapidus) is the most valuable commercial fishery resource in
the State of Delaware. Its landings value is more than two times greater than all of Delaware‟s
commercial fisheries combined. Given its importance, the State of Delaware monitors
commercial blue crab landings and relative stock abundance to complete a yearly quantitative
stock assessment with federal funding provided by the Atlantic Coastal Fisheries Cooperative
Management Act. This report represents the eleventh comprehensive assessment of the
Delaware Bay blue crab stock, providing estimates of stock size and fishing mortality rates from
1978 to 2008.
The Delaware Bay Blue Crab Fishery Management Plan was prepared by the State of
Delaware in cooperation with the State of New Jersey in 1999 amidst an uneasy period of ten-
plus years of increasing commercial effort and harvest in the bay. A sharp decline in landings in
1996 after a historically unprecedented peak in 1995 was feared to be a potential signal of stock
decline due to overfishing (Helser and Kahn 1999). A quantitative assessment employing a
stage based, catch-survey approach (Collie and Sissenwine 1983; Conser and Idoine 1992) was
completed in 1999 revealing fishing mortality rates (F) on the stock to be near the upper
management target (Fmax) indicating a fully-exploited stock (Helser and Kahn 1999). Annual
fishing mortality rates had exceeded the management threshold Frep in several years between
1985 and 1995, prompting management recommendations to prevent further fishery expansion
(DDFW 1999).
Updates and improvements to the quantitative assessment have occurred annually since
1999. A stochastic decision-based framework that incorporated statistical uncertainty
- 10 -
associated with both terminal year F and the derived biological reference point, in order to
generate an overfishing probability was included in the 2000 assessment (Helser 2000; Helser et
al. 2001). In 2003, an alternative method for calculating fishing mortality was explored, based on
a derivation of the catch equation using model-estimated stock size and known harvest to
calculate annual F (Kahn 2003). The 2005 assessment included a reanalysis of historic
landings allowing the indices of abundance to occur at the start of the harvest year (Wong and
Kahn 2005). Assessments from 2006 to 2008 explored sex-specific growth rates, indices of
abundance, and landings for modeling population dynamics of male and female segments of the
Delaware Bay stock separately (Wong 2006; 2007; 2008).
This report represents the eleventh comprehensive assessment of the Delaware Bay
blue crab stock. A continued investigation of harvest, abundance, and population dynamics is
covered in the report. Stock status is assessed by measuring model outputs relative to F-based
benchmarks and by examining current trends observed in several fishery independent relative
abundance indices.
LIFE HISTORY
Distribution
The blue crab (Callinectes sapidus) is a member of the swimming crab family Portunidae,
and inhabits primarily estuarine habitats throughout the western Atlantic, Gulf of Mexico, and
Caribbean, from Nova Scotia (although rare north of Cape Cod) to northern Argentina, and
along western South America as far south as Ecuador (Williams 1979). Its range overlaps with
the closely related lesser blue crab (C. similis) in Delaware Bay. However, the primary
- 11 -
distribution of the lesser blue crab is south of Cape Hatteras, NC (Gosner 1978), making it only
an occasionally observed species in Delaware Bay.
Early Life History
Blue crab spawning occurs in the summer months in lower Delaware Bay with peak larval
abundance occurring in August (Dittel and Epifanio 1982). Larvae are exported from the estuary
into the coastal ocean where they undergo a 3-6 week, seven stage zoeal development in
surface waters (Epifanio 1995; Nantunewicz et al. 2001). Quantitative models describe an initial
southward transport of zoeae along the inner continental shelf within the buoyant estuarine
plume after exiting the estuary (Epifanio 1995, Garvine et al. 1997). Northward transport back
toward the estuary is provided by a wind-driven band of water flowing northward along the mid-
shelf. Across-shelf transport into settlement sites in Delaware Bay is accomplished by coastal
Ekman transport tied to discrete southward wind events (nor‟easters) in the fall. These discrete
wind events may have a large effect on larval recruitment and settlement success in the bay and
strongly influence year class strength through juvenile and adult stages.
A single megalopal stage follows the seven stages of zoeal development. Megalopae
settle in lower Delaware Bay during the late summer and early fall where they utilize extensive
detritus beds as nursery habitat (DDFW 1998). Early crab stages (5-10 mm carapace width
(CW)) of both sexes begin an up-estuary migration to shallow areas of low to intermediate
salinity (Olmi 1995). Larger juvenile males tend to utilize lower salinity, more upper estuary
nursery areas, while juvenile females remain in the mid- to lower estuary during summer and fall
months (Miller et al. 1975). By winter, juveniles of both sexes appear to utilize middle to upper
- 12 -
bay winter habitats and are not found in lower bay areas with overwintering adult females
(DDFW 1999). Both immature and mature crabs overwinter in a quiescent state in the sediment.
Age and Growth
Blue crab growth is discontinuous, occurring only during stepwise molting events
(ecdysis). Growth during each molt (molt increment) and molt frequency are therefore the sole
components of growth rate. Molt frequency decreases with size, ranging from 3-5 days as
larvae to 20-50 days for large adults during the growing season (Guillory, unpublished). Molt
frequency also decreases during the winter, with cessation in molting occurring below 13C for
juveniles (Guillory, unpublished). Number of molts is determinate at about 25 over a lifetime
(Newcombe et al. 1949; Van Engel 1958), so maximum size is ultimately a function of the
cumulative incremental growth per molt (Leffler 1972). Females exhibit a terminal molt at
maturation (pubertal molt), and are estimated to have fewer post-megalopal stage molts (18)
than males (20) (Newcombe et al. 1949). Post-puberty ecdysis in females has been
documented, but is considered a very rare occurrence (Guillory et al. 2001). According to
several watermen in Delaware Bay mature females (sooks) have occasionally been found in
peeler condition, but had always died in the molt when held in captivity (Kahn 2003).
Blue crab growth in Delaware Bay is described in earlier assessments from modal
progression analyses of size distributions observed in monthly sampling by the Delaware
Division of Fish and Wildlife‟s (DDFW) juvenile crab and finfish trawl survey. The following
description of growth is taken from Helser and Kahn (1999) and Coakley‟s (2004) examinations
of monthly width-frequency distributions during the periods of 1979-1981 and 1980-1981,
respectively.
- 13 -
New recruit blue crabs appear in trawl samples in August. In Coakley‟s (2004) width-
frequency analysis, mean cohort sizes of new recruits in August of 1980 and 1981 were 24.2 ±
7.9mm and 29.5 ± 8.1mm, with individuals ranging in size from about 5 to 50 mm CW. The age
1+ crabs in August of 1980 and1981 (the previous year‟s recruits) had mean cohort carapace
widths of 137.8 ± 17.5 mm and 130.0 ± 32.4 mm, and individuals ranged in size from about 75 to
190 mm CW. Similarly, Helser and Kahn (1999) reported the August size range of age 1+ crabs
from 65 to 175 mm CW in 1979 (Figure 1). According to Helser and Kahn (1999), new recruits
reach an upper size range of 80-90 mm CW during their first September, already overlapping
with sizes of small age 1+ crabs (Figure 1). By October, largest sizes of new recruits reach 100
mm CW (Helser and Kahn 1999) (Figure 1). By the following May, fast growing new recruits are
near 100 mm CW or higher, mixing in size with age 1+ crabs (Helser and Kahn 1999) (Figure 1).
By July (at approximately one year of age), the mode for age 0 is roughly 60 mm, although
some have probably passed 120 mm (Helser and Kahn 1999). By their second August, when
the new year class appears, the new age 1 crabs have merged with older crabs with a mode of
135 – 150 mm CW, and by September, nearly all age 1 crabs have reached a size greater than
100 mm (Helser and Kahn 1999) (Figure 1). In October of 1980, sizes of new recruits and older
crabs were mixed forming a single broad size distribution (Helser and Kahn 1999) (Figure 1). In
June of the following year (1981), there was virtually a unimodal distribution with a mode of 80
mm and by July 1981 crabs had grown larger to a mode of about 115 mm CW (Helser and Kahn
1999) (Figure 1). By August 1981, the large majority of age 1+ crabs were 120 mm or greater, as
new recruits again appeared in the survey (Helser and Kahn 1999) (Figure 1).
Helser and Kahn (1999) further generalized their growth observations using size stages,
small, medium, and large, as growth milestones. Recruits begin to reach the medium stage (60-
- 14 -
119 mm CW) in October, and the large stage (>119 mm) by the following June (Figure 1). By
July, hard crab landings usually increase as more age 0 animals recruit into the legal size (127
mm in DE, 120 in NJ). The overwhelming majority of the cohort reaches the large stage by the
end of their second October, with new recruits overwintering as mediums. This proportion varies
among years. Kahn et al. (1998) substantiated this description of blue crab growth using life-
stage-specific indices of abundance to predict later life stages.
Von Bertalanffy (LVB) growth parameters were estimated by Helser and Kahn (1999)
from the modal analyses of monthly width-frequency data using MULTIFAN (Fournier et al.
1991). Three sets of LVB growth parameters were produced from three separate linear time
series of trawl data, each consisting of 21 monthly size distributions. Three cohorts were able to
be detected in the analysis. The final sets of growth trajectories did not necessarily represent
the best model fit to the data among numerous runs (Helser and Kahn 1999), as interpretation
was needed to weigh model fit with realistic biological outcomes (ostensibly due to the quick
growth and ambiguity in discerning cohorts at larger sizes). The predicted growth trajectories of
crab carapace width as a function of age for the three sets of parameters are shown in Figure 2.
Growth scenario 1 (K=0.75, L =234.7) was accepted for the purposes of their subsequent yield
per recruit analysis.
Subsequent examinations of monthly width frequency distributions from the DDFW trawl
survey revealed expected differences in growth between male and female blue crabs (Figure 3)
(Wong 2006). Wong (2006) estimated non-seasonal and seasonal LVB parameters from sex-
specific datasets of width frequency distributions across 26 months from 1996-2000 using a
version of the Elefan method (Pauly 1987) from the Length Frequency Distribution Analysis
software (LFDA). Seasonal growth was described by the equation: L(t) =Linf*(1-EXP(-(k*(t -
- 15 -
t0)+(C*k/2 )*Sin(2 )*(t-ts)-(C*k/2 )*Sin(2 )*(t0-ts)) (Hoenig and Hanumara 1982). Allowing for
seasonal depressions in growth in the LVB curve was helpful in better fitting the male size
frequency data (C =0.975), but did not necessarily improve the fit to the female data (C =0.1).
Two sets of sex-specific growth parameters are presented below, representing the best
realizations of growth from the data:
Although there was model convergence around these estimates in fitting the given data,
the accuracy of the estimates could not be evaluated. Given fast growth and the fairly rapid
disappearance of size distinguishable cohorts, other methods aside from size frequency analysis
should be explored to produce alternative growth curves for the stock.
While males and females exhibited similar early growth rates based on the seasonal
growth curves, males clearly attained a larger maximum size than females (Figure 3). Of
158,849 blue crabs captured in the DDFW 16 ft. trawl survey since 1978 the maximum size
observed was 230 mm CW (n=2, unidentified sex) with only six total specimens greater than or
equal to 200 mm. Since the onset of sex identification of crabs by DDFW in 1995, only one
female was observed greater than 180 mm, while 14 males were greater than 180 mm,
suggesting that the two 230 mm specimens were most likely males.
Males 1 Males 2 Females 1 Females 2
Linf 261.077 203.96 191.767 167.231
k 0.576 0.562 0.703 0.675
T0 -0.02 -0.74 -0.18 -0.6
C 0.975 0.922 0.1 0.036
Ts -0.137 0.141 0.19 -0.2
Score 0.17136 0.158 0.177 0.1846
- 16 -
Maximum life span
Van Engel (1958) indicated the general lifespan to be two to three years. Kahn (2003)
postulated that rapid growth and early maturation (1 year) of blue crabs are not consistent with
longer lived decapod crustaceans such as snow crabs, king crabs, and American lobsters.
Helser and Kahn (1999) assumed a four year maximum age for the mixed-sex Delaware Bay
stock. Mature females initially tagged in the Chesapeake (Rugolo et al. 1998) and in North
Carolina (Fischler 1965) were returned by fishermen after several years, possibly indicating a
lifespan of up to 8 years (Rugolo et al. 1998; Miller and Houde 1998). However, possible biases
related to public-generated tag returns are often cited with respect to these cases (Kahn 2003).
Recent fishery-independent tag-recapture work in the Chesapeake indicated at least a 4 year
lifespan for females, given an at-large period of 3 years for a tagged mature female (Lambert et
al. unpublished; pers. comm. R. Aguilar, Smithsonian Environmental Research Center).
Reproduction and Maturity
Females mate immediately after their pubertal molt into sexual maturity, usually late in
their first year (summer). Females then store the sperm over the winter and produce eggs in the
following summer at the end of their second year. Prager et al. (1990) estimated fecundity per
batch as over 3x106 eggs. Females may spawn twice in their first year of spawning (Churchill
1921; Van Engle 1958). Some researchers believe it is possible for females to spawn into their
fourth summer as age 3 (Kahn 2003). However, Cole and Beck (1975) observed evidence of
previous spawning (i.e. presence of nemertean egg parasite) on only 4.5% of overwintering
females in Delaware Bay.
- 17 -
Maturation by carapace width of Delaware Bay blue crabs was estimated from a sample
of 1,335 female crabs collected from the commercial catch between 1995 and 1997 (Helser and
Kahn 1999). Female blue crabs were categorized as either mature or immature, based on the
shape of the crab‟s apron, and modeled as a binary response using a logistic regression model
(Agresti 1990):
logit (P) = log (P/(1-P)) = α + β*CW + ε
where: P = Pr(Y=1|X) is the response probability, CW = carapace width (mm) and α, β
are parameter estimates. Observed maturity by carapace width and the predicted maturity ogive
are shown in Figure 4 (Helser and Kahn 1999). Results were similar to those of Rothschild et al.
(1992) who found very few mature crabs with carapace widths of less than 100 mm, and nearly
all crabs were fully mature by 140 mm.
Predator Prey Interactions
Juvenile and adult blue crabs hold an important ecological role as opportunistic benthic
omnivores, with major food items including bivalves, fish, crustaceans, gastropods, annelids,
nemertean worms, plant material, and detritus (Guillory et al. 2001). Post-settled blue crabs
have been shown to have a key effect on infaunal community structure, particularly through
major predation on bivalves such as the eastern oyster (Crassostrea virginica) (Eggleston 1990),
Mercenaria mercenaria (Sponaugle and Lawton 1990), Rangia cuneata (Darnell 1958), Mya
arenaria (Blundon and Kennedy 1982; Smith and Hines 1991; Eggleston et al. 1992), and other
- 18 -
bivalve species (Blundon and Kennedy 1982), and through indirect mortality on infaunal species
from mechanical disturbance of sedimentary habitats caused by foraging (Virnstein 1977).
Fish appear to be the primary predators on blue crabs, with more than 60 fish species
listed as known predators (Guillory et al. 2001). Blue crabs are known to be a common
component of both juvenile and adult striped bass in Chesapeake Bay, albeit with great
variability in relative importance among studies (Speir 2001). Although there have been recent
investigations on the potential negative effect of the recovered striped bass stock on the
Chesapeake Bay blue crab stock, no connection with decreasing blue crab population numbers
has been supported (Booth and Martin 1993; Speir 2001).
Another very important source of predation on blue crabs occurs from cannibalism, as
cannibalized blue crabs make up as much as 13% of the diet (Darnell 1958). Cannibalism
appears to increase with increasing crab predator size and is heaviest during the period of
juvenile recruitment (Mansour 1992). Peery (1989) demonstrated that size specific cannibalism
occurs, with small crab predators preying on small juveniles, and large crabs selecting the upper
size range of juveniles. However, with high abundance of small juveniles, large blue crab
predators also cannibalized small sizes, suggesting strong density-dependent regulation of
juveniles (Peery 1989).
Natural Mortality
A high rate of natural mortality is assumed to occur on the Delaware Bay stock given the
presumably short, 3-4 year life span of individuals. A range of instantaneous natural mortality
- 19 -
rates (M) for the stock was explored in previous DDFW assessments, varying from 0.375 to 1.1.
Helser and Kahn (1999) adopted M =0.8 as the input for natural mortality rate for the CS
assessment model assuming the maximum age between 3 and 4 for Delaware Bay blue crabs
and using the convention, ln(5%)/maximum age. This M was maintained in the yearly
assessments from 1999-2007 excluding 2004. Coakley (2004) chose M =0.75 for the final
model output after testing sensitivity of model outputs to ranging M values from 0.375 to 0.75
(based on maximum ages of 4, 6, and 8). Rugolo et al. (1997) employed the 5% max age
convention, assuming a maximum longevity of eight years based on aforementioned tag returns
in Chesapeake Bay, yielding M =0.375. Helser and Kahn (1999) also investigated natural
mortality by regressing an apriori length-based estimate of total mortality (Z) as a function of
fishing effort (Gulland 1983). Natural mortality (M) was calculated as 0.84 to 1.1, albeit with
some recognized uncertainty in both measures of fishing effort and the length-based estimates
of Z.
Unit Stock Definition
The unit stock of this assessment is defined as all blue crabs that spawn in and utilize
the tidal and non-tidal waters of Delaware Bay. The significant stock-recruitment relationship
observed in Delaware Bay, estuary-retentive coastal circulation patterns for larval transport, and
the considerable distance of Delaware Bay to other large estuaries suggests the stock is the
primary source of its own recruits. However, some degree of stock mixing between estuaries
along the mid-Atlantic and south-Atlantic Bights occurs, given the larval emigration into the
coastal shelf before re-entering the estuary to settle. Electrophoretic allozyme analysis of blue
crabs (N=750) from 16 near-shore locations from New York to Texas indicated substantial gene
- 20 -
flow among sites, however, with genetic structuring occurring (McMillen-Jackson et al. 1994).
FISHERY DESCRIPTION
Overview
The Delaware Bay blue crab stock is harvested by commercial and recreational fisheries
of Delaware and New Jersey. On average, 2.8 million kg (6.2 million lb) of blue crabs are
harvested annually from the Delaware Bay by commercial and recreational crabbers since 1973,
with 52% of the total weight landed in the State of Delaware (DNREC data; NMFS data) (Table
1; Figure 5). The commercial fishery is responsible for the majority of total annual harvest.
Recreational harvest estimates were about 4% and 20% of the hard crab pot landings in
Delaware and New Jersey.
Total annual Delaware Bay blue crab landings increased by 1,175% from 1978 to 1995
causing concerns of overfishing and the development of fishery restrictions in both states. Total
landings peaked at 5.4 million kg (11.9 million lb) in 1995, remained high for the next seven
years (averaging 3.7 million kg), and then declined considerably in 2003 and 2004 (1.7, 2.3
million kg). Recent landings have rebounded again to historical high levels, averaging 3.4
million kg*y-1 from 2005-2007, and reaching 4.1 million kg in 2008 (Table 1).
Differing size regulations exist between states. The commercial fishery minimum size for
male hard crabs is 5” (127 mm) CW in Delaware and 4 ¾” (120 mm) CW in New Jersey.
Female hard crabs must be mature for commercial sale in Delaware with no minimum size limit,
whereas female hard crabs must be both mature and greater than 4 ½” (114.3 mm) CW in New
Jersey. Gravid (sponge) females are protected from harvest in both states. Recreational size
- 21 -
limits and female maturity requirements are the same as commercial regulations in Delaware.
Both male and female hard crabs carry a uniform minimum size limit of 4 ½” CW in New Jersey
for recreational harvest. The recreational harvest limit is one bushel per person per day in both
states.
Commercial Fishery Harvest
Blue crabs easily make up the highest value commercial fishery in the State of Delaware,
with a 2008 ex-vessel value of 5.3 million dollars, and a combined New Jersey and Delaware
value of 10.6 million dollars. The majority of the commercial landings occur in the warmer
months from May to September (75% of annual total) with a peak in August, during the period
when the pot fishery traditionally harvests mostly male hard crabs (Figure 6). Four distinct
market categories are recognized in Delaware: large male hard crabs (#1 crabs, a.k.a. jimmies),
small male hard crabs (#2 crabs), female hard crabs (#3 crabs), and peelers (crabs about to
molt). Helser and Kahn (1999) assumed peeler landings to be entirely immature females about
to molt into maturity.
Commercial landings are prosecuted by two fisheries, a winter dredge fishery and a
spring-to-fall pot fishery that harvests the lion‟s share of annual landings. Ninety-one percent of
Delaware and New Jersey Delaware Bay commercial hard crab landings (kg) are annually
harvested by pots (2003-2008) (Tables 2, 3).
The pot fishery typically begins in April or May with increasing activity of mature,
overwintering females prior to June egg production known as the “sook run”. Substantial spring
landings composed mostly of #3 crabs (female hard crabs) occur in May based on this sook run
- 22 -
(Figure 6). As sooks produce eggs and become sponge crabs, they are protected from harvest
resulting in the movement of crabbing effort further up-bay and away from higher salinity areas
inhabited by gravid females. Landings of mature males increase in July and peak in August or
September as new recruits enter the fishery. In the 1990s, increased targeting of females during
their migration down bay in September and October was noted, ostensibly driven by added
Asian export and western U.S. demand (Cole 1998); however, this trend has not continued in
recent years. By November, the pot fishery season has ended.
Peelers make up 3.8% of annual pot landings (numbers) in Delaware (2003-2008).
Significant peeler landings occur in June, or some years in May, occurring primarily around the
new and full moons. Peelers are typically held until molting occurs and sold as soft crabs for
their high market value, and to a lesser degree as fishing bait. In the 1990s, crab pots began to
be modified with 1” mesh (previously 1 ½”) to target peelers. Peeler pots are baited with a
mature male (jimmy) to attract females seeking males for protection during ecdysis and for
mating immediately after the molt. Total (combined Delaware and New Jersey) peeler landings
peaked in 1995 at 6.15 million peelers (580,959 kg) and have since declined to 1.14 million
crabs (107,434 kg) in 2008.
In an effort to curb fishing effort in 1994, both Delaware and New Jersey limited entry into
their commercial crab pot fisheries by capping the number of annual pot licenses sold at the
1994 level, specifying future license targets of 82 and 312 annual licenses for the bay. Pot
fishery licenses have declined by 40% in New Jersey through attrition since peaking in 1994
(Table 4). Delaware pot licenses have remained at the 1994 level. If or when annual licenses
eventually fall to 82 in Delaware, a special lottery will be held to increase the license total to 100.
The pot fishery season is restricted to March 1 to November 30 in Delaware, and from April 6 to
- 23 -
December 4 in New Jersey (Delaware Bay only). Commercial crabbers are limited to 600 pots in
New Jersey. In Delaware, crabbers can renew a commercial license for up to 200 pots in
increments of 50. A Delaware vessel with three crab pot licenses assigned to it can fish a
maximum 500 pots.
The commercial dredge fishery is smaller in comparison to the pot fishery and operates
during a shorter, three to four month winter season. Commercial crab dredging is permitted from
December 15 to March 30 in Delaware, and November 15 to April 15 in New Jersey (Delaware
Bay only). The fishery is further restricted to specific portions of Delaware Bay and by gear
limitations on overall dredge length and numbers (2) per vessel. Twenty-three percent of the
Delaware dredge landings occur in December. Peak dredge landings (40%) occur in January,
and taper to 27% and 10% in February and March.
The dredge fishery primarily lands mature females (sooks) that have overwintered in
aggregations in the higher salinity areas of the lower bay. Unlike the pot fishery, males only
make up a small component (10% weight) of the annual dredge harvest (DDFW data). Market
grade composition does not change considerably across the relatively short dredge season.
In the late 1990s, New Jersey capped Atlantic coast commercial dredge fishery licenses
to the number of 1993 licenses (338). Annual dredge licenses have been well below this limit
since its cap inception. In 1997, New Jersey began issuing dredge licenses by water body.
Since 1997, New Jersey dredge licenses in Delaware Bay have fluctuated between 80 and 94
without trend (Table 4). Delaware dredge licenses have remained fairly constant since 1994
(Table 4).
- 24 -
Annual commercial landings are affected by severe winters in this region (Helser and
Kahn 1999). Unusually cold or stormy winters cause sharp decreases in dredge landings as
seen in 1978 and 1979. In severe winters, the commercial dredge fishery catches greater
proportions of dead adults indicating higher overwintering mortality. In 1996, the Delaware
Division of Fish and Wildlife (DEDFW) observed >30% mortality in commercial dredge catch
samples. Overall landings in the subsequent year (1997) declined by 40%.
Sex-specific harvest
Male and female components of the harvest were determined based on sex- and size-
based fishery market grades. For reference, large male hard crabs are sorted by the fisherman
in Delaware into market grade 1; small males are sorted as 2‟s; females are graded as 3‟s.
Market grades 1 and 2 were therefore assumed to be composed of 100% males for this
assessment. Market grade 3 and peelers were assumed to be 100% females. Fish house
sampling in 2006 corroborated these hard crab sex-ratios. The peeler fishery in Delaware
predominantly targets females during relatively short-lived pulses in the spring and summer.
Although the male proportion of peeler landings is likely minor compared to females, the true
ratio is unknown and in need of future investigation.
Market grade information of New Jersey landings was available beginning in 1999,
consisting of male, female, mixed, and peeler categories. Prior to 1999, all hard crabs were
recorded as mixed. Mixed NJ landings prior to 1999 were divided into male and female
components based on the Delaware sex-ratio observed in that specific year, gear, and month
combination. The year/gear/month DE and NJ sex-ratios were very similar from 1999 to current.
- 25 -
Gaps in sex-ratio data were filled with gear/month sex-ratios across years (1999-2006) observed
in NJ landings.
Most of the commercial harvest is composed of male crabs. Annual harvest is 64.7%
males in numbers and 60.4% males in weight in Delaware Bay since 2003. Males and females
were generally harvested in equal proportions until 1998 when the ratio of males became
consistently higher than females in Delaware Bay harvest (Figure 7).
Recreational Fishery
Estimates of recreational blue crab harvest in Delaware Bay are limited. Cole et al.
(1997), utilizing a bus route design on land to quantify effort and a riverine boat sampling
program to determine catch rates, estimated 135,193 and 130,464 crabs landed in 1996 and
1997 by Delaware-only recreational crabbers. This was 1.7% and 1.2% of the hard crab
landings harvested by the Delaware commercial pot fishery in those years. Fifty-four percent of
the recreational landings were captured by commercial style crab pots, while 46% were captured
by traditional, shore-based gears, presumably traps, lines, hand nets, etc. Most of the harvest
occurred on the weekends, and in August and September.
An estimate of recreational harvest in NJ in 2005 was 1.9 million crabs (ORC Macro
2006), equal to 20% of the NJ commercial non-dredge hard crab harvest occurring during that
same period (May-Oct). In 2005, ORC Marco estimated that 1,925,425 (CV =20.5) hard crabs
were harvested in New Jersey by recreational crabbers using a telephone and intercept survey
design (ORC-Macro 2006). Most of the effort (69% of total) and harvest (65%) occurred during
the Jul-Aug period of the May-Oct survey. Seventy-four percent of the harvest was captured by
- 26 -
boat rather than by land crabbers. Nearly 75% of the harvest was composed of males, while
79% of the female harvest was mature. The total 2005 recreational harvest in NJ equalled 20%
of the NJ commercial (non-dredge gears) hard crab landings occurring from May-Oct.
In 2008, ORC Macro estimated Delaware-only recreational harvest to be 416,381
(numbers), equal to 4.3% of the Delaware commercial pot hard crab harvest. The sex-ratio was
6:1 males to females. Seventy percent of the female harvest was mature. Sixty-eight percent of
the harvest was caught by boat crabbers. All harvest was composed of hard crabs (no peelers).
Other estimates of recreational hard crab harvest are widely variable (expressed as
percentages of commercial production): 5.9% in Galveston Bay, TX (Benefield 1968); <4% in
Mississippi (Herring and Christmas 1974); 20% in Alabama (Tatum 1982); and 4.1% in
Louisiana (Guillory 1998).
DATA SOURCES
Harvest
Commercial Landings
Commercial fishery blue crab landings from Delaware and New Jersey were utilized in
the assessment covering the period 1978-2008. Annual Delaware landings were compiled from
multiple data sources: annual reports assembled by DDFW for the period 1978-1984; landings
data collected by a DDFW fishery-dependent dockside intercept survey for the period 1985-
2002; and mandatory, monthly, logbook reports submitted by commercial fishermen to the State
of Delaware for the period 2002-2008. Fisherman logbook reports and the DDFW dockside
intercept survey occurred simultaneously from 1985 to 2003. The DDFW survey suggests
- 27 -
possible under-reporting in fishermen logbook reporting from 1989 to 1994. However, good
agreement between fishermen logbook landings and survey landings began in 1995,
contributing to the decision to eliminate the DDFW survey in early 2003 (Figure 8). New Jersey
landings data were taken from the National Marine Fisheries Service commercial landings
statistics database from 1978 to 2000 and directly from fisherman logbook reports compiled by
the New Jersey Bureau of Marine Fisheries for 2001-2008.
Commercial landings reported in bushels were converted to numbers for use in the
assessment model. Bushels-to-numbers conversions were based on DDFW at-sea sampling of
pot and dredge landings in 1996 (unpublished DDFW data) (Table 5). Numbers per bushel by
market grade and gear (pot or dredge) were calculated from this DDFW sampling. Converting
bushels of unspecified market grade landings to numbers for the assessment required creating
conversions based on the known DDFW at-sea conversions weighted by empirical market grade
compositions observed in Delaware logbook landings.
Recreational harvest
Recreational harvest was estimated as a percentage of the annual, commercial non-
dredge, hard crab landings. A harvest proportion of 2.5% of the commercial non-dredge hard
crab landings was continued from earlier assessments to estimate yearly Delaware recreational
harvest from 1973 to 2007 (Helser and Kahn 1999). The 2008 recreational harvest estimate of
416,318 (approximately 4% of the commercial hard crab pot landings) was used in lieu of the
2.5% proxy. Annual recreational harvest in New Jersey was calculated as 20% of the
commercial non-dredge May-Oct hard crab landings based on the findings of the 2005 ORC-
Macro Delaware Bay blue crab recreational fishery survey (ORC-Macro 2006).
- 28 -
Fishery-Independent Data
Indices of Abundance
The Delaware Division of Fish and Wildlife has operated a blue crab and juvenile finfish
trawl survey in Delaware Bay since 1978. The 16 foot trawl is equipped with 1.5 inch mesh with
a 0.5 inch cod end liner. Fixed sites are sampled on the western inshore areas of the bay into
the Delaware River. Sites are sampled monthly from April through October with ten minute tows
against the tide. Blue crabs are measured in 5 mm increments, sexed, and counted.
Indices of pre-recruited and fully-recruited blue crabs were used in the assessment
model. Trawl data used for these indices were taken from the lower 26 stations that have been
sampled continuously since 1978 (Figure 9), and restricted to the August-September sampling
period (Helser and Kahn 1999). The index of pre-recruits was composed of the geometric mean
catch per tow (GM CPT) (in numbers) of blue crabs less than 120 mm CW. The index of fully-
recruited blue crabs was composed of blue crabs greater than or equal to 120 mm CW.
Other stage-specific indices of abundance have been developed from the trawl survey
for monitoring the stock yet not used in the population model. A YOY index is developed from
the GM CPT of small crabs (< 60 mm CW) in September-October. A second index, termed the
recruitment index in previous assessments, uses the GM CPT of medium crabs (60 mm CW –
119 mm CW) in the April – August period. An index of large crabs (GM CPT of crabs ≥ 120 mm)
was also developed based over the entire survey year (Apr-Oct).
Kahn et al. (1998) also developed measures of spawning stock biomass from the trawl
- 29 -
survey. The index of spawning stock consists of the arithmetic mean CPT (AM CPT) of large
crabs (≥ 120 mm) in spring tows (April and May). A similar, female only, biomass-based index
consists of the arithmetic mean tow weight (kg). Individual weights were calculated from
carapace widths using the female width-weight model from Rothschild et al. (1992):
Weight = (3.4865 X 10-3 * CW2.116) /1000.
Instantaneous Natural Mortality Rate
A constant instantaneous natural mortality rate of M =0.8 was utilized in the current
assessment model consistent with previous DDFW assessment methodology from 1999-2003,
and 2005-2006. A previous exploration of M included the regression of an apriori length-based
estimate of total mortality (Z) as a function of fishing effort by Helser and Kahn (1999) as per
Gulland (1983). Natural mortality (M) was calculated as 0.84 to 1.1, albeit with recognized
uncertainty in both measures of fishing effort and the length-based estimates of Z. Coakley
(2004) used a constant natural mortality rate of M =0.75 in the 2004 DDFW assessment.
Rugolo et al. (1997) estimated M =0.375, assuming a maximum longevity of 8 years based on
reportedly controversial tag returns in Chesapeake Bay.
METHODOLOGY
Population Model
The catch-survey population model simulates stock dynamics through time using two
size groups: pre-recruits and fully recruited blue crabs (Collie and Sissenwine 1983). Minimum
- 30 -
data requirements for the model include: 1) annual indices of population abundance (in
numbers) for each size stage (i.e., pre-recruit and fully-recruited sizes); 2) relative selectivities of
size stages to the survey gear; 3) annual total harvest in numbers; and 4) an estimate of
instantaneous natural mortality rate. The analysis was executed using the Collie-Sissenwine
Analysis (CSA) version 3.04 application from the NFT toolbox (version 2.11A). The catch-survey
model is based on the first order difference equation:
e )C - R + N(= N-M
yy0y01+y0, ,, (1)
which relates the fully-recruited stock size at the beginning of the year (N0,y+1), to the fully-
recruited stock size at the beginning of the previous year (N0,y), plus recruitment in the previous
year (R0,y), minus the catch (Cy), all discounted for natural mortality, M.
The above equation assumes that a pre-recruit is any crab smaller than the minimum
size vulnerable to the fishery at the beginning of the model year that will also become fully-
vulnerable to the fishery by the beginning of the next model year. The term, recruit, will be used
synonymously in place of pre-recruit for the remainder of this report. Helser and Kahn (1999)
defined recruit blue crabs to be less than 120 mm and fully-recruited crabs as greater than or
equal to 120 mm. The model year runs from September 1 to August 31. Helser and Kahn
(1999) offered three reasons for the size definitions and survey year: 1) current commercial
regulations specify a 120 mm and 127 mm minimum carapace width for hard crabs in New
Jersey and Delaware, respectively; 2) width frequencies indicate that the large majority of
recruits, which appear in the research surveys during August-September, have grown to the
fully-recruited size (120 mm) by the following year; and 3) Kahn et al. (1998) demonstrated a
significant positive correlation between large blue crab indices (defined as > 120 mm) in a given
year and pre-recruit size (< 60 mm) crab indices during the previous year. The catch-survey
model is predicated on the basis that a “signal” exists between recruit and fully-recruited sizes.
- 31 -
Given a September 1 to August 31 model year, the current model difference equation is
as follows:
e)] C - e)R + N[(= NM-0.
yM-0.
0y0y1+y0,2575 (3)
with the midpoint of harvest occurring at a point 75% into the survey year.
Survey indices of abundance are related to absolute stock sizes by
eNq = nt
0yny (4)
and
eRq = rt
0yry (5)
where r’y and n’
y are the observed research indices of recruit and fully-recruited blue crabs, q is
the catchability coefficient of the research survey gear, and eη t and eδ t are lognormally
distributed random variables, which represent survey measurement errors for the recruits and
fully-recruited indices, respectively. In essence, these errors represent the difference between
the observed survey indices of recruits and fully-recruited animals and the expected indices
predicted within the nonlinear least squares (NLLS) framework by the DeLury difference
equation. Another source of error, called process error, arises from the DeLury equation itself,
which is the difference between calculated indices of fully-recruited animals and the expected
value of the fully-recruited indices again predicted within the NLLS framework from the catch-
survey model.
Substituting the above equations into the model difference equation and including the
- 32 -
lognormally distributed process error (eε t):
e e]Cq - e)s/r+n[( = ntM-0.
1-ynM0.
r1-y1-yy2575 (6)
where
q / q = s nrr (7)
is the relative selectivity of recruits to the fully-recruited blue crab, set equal to unity. The
research survey uses a 1.5 inch mesh with a 0.5 inch codend liner (shrimp trawl) and it is
unlikely that small blue crabs of recruit size observed in the survey would escape at a rate
different from that of fully-recruited crabs.
Thus, the above equation is a statistically estimable function with 2Y parameters to be
estimated; ny for all years Y, ry for all years except the last year, and qn. Estimates of these
parameters (θ) are obtained by minimizing the least squares objective function (S):
2y
1-Y
y=1
2y
Y
y=1
2y
Y
2y=
+ + = )S( ˆ (8)
where λε and λδ are relative weights for the process error and recruit measurement error,
respectively (relative to the measurement error for indices of the fully-recruited size). Conser
(1995) describes an approach to weighting process and measurement errors within the least
squares objective framework that is implemented in this analysis to evaluate model sensitivity.
Four different model configurations were analyzed as in Kahn and Helser (2005), an
observation error-only (OE) model recommended by Collie and Kruse (1998) and three
configurations of a mixed error model, with the following weights of process error relative to
observation error: 1.0 equal weighting (EW), 0.5 (PE0.5), and 0.1 (PE0.1). The OE model
estimates q (catchability coefficient), the time series of the recruit index (except the last year‟s
value), and the full recruit index in the first year, for Y + 1 parameters. Model predicted full
- 33 -
recruit index values are calculated by the model difference equation (Eq. 6). All error
components were weighted equally. The mixed error models estimate q, all full recruit index
values, and all recruit index values except the last years‟, for 2Y parameters. Process error is
the difference between the full recruit index calculated by (Eq. 6) without the process error term
(i.e., deterministically with no error) and the full recruit index as calculated by (Eq. 6) with the
process error term included.
Given estimates of ny , ry, and qn from the nonlinear least squares minimization and the
value of relative selectivity, sr, population abundances for the recruit and fully-recruited blue
crabs are
Ny = ny /q
and
Ry = ry / sr q.
Annual estimates of spawning stock biomass were based on model estimates of
population abundance in numbers multiplied by the annual mean weight of adults observed in
the full recruit index of the DDFW trawl survey. Mean weights were converted from empirical
mean size (CW) of full recruits using the mixed-sex width-weight model,
Weight = (8.1636 X 10-3 * CW 2.43) / 1000,
from Rothschild et al. (1992)
Model Inputs
Indices
Annual indices of recruit and full-recruit blue crab abundance were constructed from the
- 34 -
DDFW juvenile finfish and blue crab trawl survey data. The combined-sex indices covered
years 1978-2008. Average weights of recruits and full-recruits were required by the NFT CSA
model. Average weight was based on empirical carapace width (CW) data from the survey and
the width-weight models from Rothschild et al. (1992):
Combined-sex: Weight = (8.1636 X 10-3 * CW 2.43) / 1000
Female: Weight = 0.0034865 * CW 2.1165
Male: Weight = 0.00022105 * CW 2.7208.
Model inputs are shown in Table 6.
Harvest
Annual harvest occurring over the model year (September to August) was also required
for the model (Table 6). Discard landings were input as nil given lack of discard sampling. The
discard component is likely minor given the pot fishery harvest practices. Average weight of the
harvest was calculated from the annual harvest weight divided by the total numbers of crabs
harvested. Combined-sex harvest inputs covered „model‟ years 1978-2007.
Methodological changes in quantifying baywide harvest occurred in 2005. A complete
re-analysis of historical Delaware and New Jersey landings was undertaken in 2005 in order to
synchronize annual harvest to a September-August model year, consistent with the timing of the
survey indices. Also prior to the 2005 assessment, New Jersey logbook-reported landings had
been inflated by 1.4 for hard crabs and by 2.3 for peelers on an annual basis, based on the
assumption of under-reporting in logbook records. Lower landings were observed in Delaware
fishermen logbooks versus the DDFW dockside intercept survey during the early years of those
overlapping methods. In the latter years of the dockside survey, however, both methods
- 35 -
produced very similar annual landings. In the 2005 assessment, New Jersey reported landings
were not expanded, given: better confidence in new, updated landings datasets provided by NJ
DEP; the uncertainty in assuming under-reporting of New Jersey landings based on logbook
versus survey differences in Delaware landings primarily based on the early part of the DDFW
dockside intercept survey; the inability to account for changes in under-reporting through time in
New Jersey; and based on recommendations from NJ Bureau of Marine Fisheries personnel
after extensive discussions (personal communication; T. Baum et al.). In addition to the uniform
expansion of New Jersey landings across years in previous assessments, some individual years
were also further increased to address abnormally low landings values. Delaware landings from
analogous time periods and gears were used as appropriate scalars in these situations. Given
new, updated landings datasets, these spot corrections to New Jersey landings were not
conducted in the 2005 assessment. Another methodological convention used in previous
assessments was the lagging of December dredge fishery landings, so that each December
harvest was counted towards the following calendar year. Ultimately, the updated landings
analysis for the current assessment produced slightly different landings totals from previous
assessments, although they are very similar in trend when viewed in the same time step (e.g.
calendar year) (Figure 10).
Instantaneous Natural Mortality Rate, M
Instantaneous natural mortality rate was fixed at M = 0.8, consistent with 1999-2003,
2005-2008 assessment methodology.
- 36 -
External-Model Calculations of Fishing Mortality
Annual instantaneous fishing mortality rate (F) was calculated from instantaneous total
mortality rate (Z), exploitation rate ( ), and annual percent mortality (A), derived from model
estimates of annual stock size. Total mortality (Z) is expressed as the log survival ratio:
N
R + N = Z
1+y0,
0y0y
eyN,R+ log (8)
A range of annual exploitation rates, , was calculated using the input catch in numbers divided
by exploitable stock size. Three estimates of exploitable stock size were calculated, providing
theoretical upper and lower bounds of exploitable abundance to account for the considerable yet
unknown amount of recruitment into the fishery occurring within the year due to fast growth of
pre-recruits (Kahn and Helser 2005). Given this unknown level of within-year recruitment, upper
and lower bounds around an estimate of exploitable stock size were created for calculating
exploitation rates and fishing mortality rates.
The best approximation of annual exploitable stock size, based on the method detailed
by Collie and Kruse (1998) was assumed to be R + N, decremented by natural mortality over the
time period until the harvest occurs
SC TTMeNR
harvest =
(a*)(
,
where R and N are the absolute abundances of pre-recruits and post-recruits, M =instantaneous
natural mortality rate, Tc = time when the harvest occurs, Ts = time when the survey occurs.
Maximum annual stock size was assumed to be R + N. Using a maximum estimate of
annual stock size yields a lower bound of exploitation rate,
- 37 -
)(b
NR
harvest= .
Minimum exploitable stock size was defined as the annual catch plus all post-recruits
surviving to the next survey year. Using a minimum estimate of annual stock abundance in the
following equation,
)( 1
c
tNcatch
harvest =
results in an upper bound of exploitation rate.
Fishing mortality is calculated by solving the catch equation for F,
F = Z/A,
where and Z are as defined and A is the total annual mortality as a percent,
At = (1 – Nt+1/ (Rt + Nt)) = (1 – e (–Z)).
External Indices of Relative Abundance
Stage-specific indices of abundance, other than the pre-recruit and full recruit indices
used in the population model, were analyzed to further describe population trends (Table 7).
These indices were drawn from the DDFW juvenile finfish and blue crab trawl survey and are
described in the previous section, Data Sources; Fishery-Independent Data; Indices of
Abundance.
- 38 -
Index-Based Stock–Recruitment Model
The index of recruits lagged by one year (see Data Sources; Fishery-Independent Data;
Indices of Abundance) was plotted as a function of the index of spawning stock biomass.
Recruits are defined as the medium crabs in April-August of the year following birth. Two stock
recruitment models were fit to the data by Helser and Kahn (1999). One model was a null model
with no density-dependent mortality (Fogarty et al. 1992). This is a simple regression of
recruitment on spawners with a linear term, a quadratic term and no intercept. The quadratic
term in the regression analysis was highly significant (p < 0.01) and substantially improved the
model fit (r2 = 0.62; p = 0.0002) over a model based on just the linear term (r2 = 0.38; p < 0.002).
Helser and Kahn (1999) rejected the null model of no compensation based on the linear
regression of recruitment on spawning stock. The standard Ricker model was then fit with an
additive normal error structure using the Marquardt algorithm in SAS. Based on the alternative
hypothesis of compensatory mortality for blue crabs, PROC NLIN in SAS was employed to fit the
nonlinear Ricker model, R = A*SSB*exp(B*SSB), where R is the estimate of recruitment, SSB is
the index of spawning stock biomass and A and B are model parameters. The coefficient of
determination, R2, is calculated as R27 of Kvalseth (1985): 1 - (residual SS/ uncorrected total
SS).
An index-based benchmark was determined from the S-R curve, equal to the SSB that
produces half of the maximum recruitment, termed the SSB50. This level of SSB has been
recommended as a measure of recruitment overfishing (Mace 1994).
RESULTS
- 39 -
Error-weighting Model Selection
An examination of error residuals revealed similar residual patterns across all four error-
weighting model configurations, revealing a difficulty of the model difference equation in
predicting observed index values in recurring circumstances. One noticeable residual pattern
was the under-prediction of recruits corresponding to years when very large observed recruit
index values occurred (Figure 11; Appendix I). Typical over-prediction of full recruit indices in
the year following large observed pre-recruit indices also occurred (Figure 12; Appendix I).
Another major source of residuals occurred when a low pre-recruit index and significant harvest
took place in the same year, yet a substantial full recruit index value was observed in the
ensuing year. This was particularly evident in 1990, when a weak, observed, recruit index and
considerable harvest occurred, yet the 1991 observed full recruit index was robust. Given the
model difference equation, low recruitment of individuals into the full recruit stage was expected
in the ensuing year.
These noticeable residuals fall into a larger, systemic pattern of a negative correlation
between recruit and full recruit index residuals. Observed full recruit index residuals are
negatively related to the previous year‟s recruit index residual (Figure 13). Typically, an
underestimated recruit index in a given year leads to the overestimation of the next year‟s full-
recruit index, and vice-versa. This is a somewhat natural consequence of the model difference
equation, since the model‟s calculation of full recruit abundance is based directly on the previous
year‟s recruit and full recruit abundance. However, it also indicates an inability of the model
difference equation to completely describe recruitment from one stage to the next, emblematic of
the model equation‟s inability to account for density dependent recruitment.
- 40 -
Recruit and full-recruit residuals were most pronounced in the observation error-only
(OE) and the equal-weight mixed error (EW) models, and were dampened as process error was
downweighted across the mixed error models. In this analysis of models, the model difference
equation is most heavily involved in the final convergence in the OE model, and declines in
importance as process error is downweighted across the mixed error models (EW, PE0.5, and
PE0.1). As influence of the model equation is reduced, there are less model constraints on
predicting the observed indices, allowing better agreement between observed and predicted
indices. One consequence to the increasing fit of predicted indices to observed indices is the
decreasing estimate of q across the sequence of models from OE to PE0.1, from 0.0741 to
0.0387. As predicted indices more closely match observed indices, the difficulty in balancing the
aforementioned scenario of high full recruits following low recruitment minus substantial harvest
in the previous year is intensified. In order for the model to account for the unusually high
survival between years in this circumstance, the model minimizes the relative contribution of
harvest removals by amplifying stock size (i.e. decreasing q) in order to best fit the observed full
recruit index and minimize the residual.
The mixed error PE0.1 model was chosen as the preferred model configuration, given
the best fit to the observed survey indices. Higher priority was given to fitting the observed
indices in lieu of minimizing process error, given the high degree of confidence in the survey
indices as measures of relative stock abundance (Kahn et al. 1998). As discussed above,
reducing the influence of the model equation in the prediction of observed indices was helpful
given the aforementioned model equation difficulties in rectifying very low recruit index values
preceding relatively high full recruit indices. Consequently, assigning less weight to process
error residuals across the mixed error models reduced the influence of the model difference
equation, achieving a tighter fit to the observed data. Although no process error was generated
- 41 -
in the OE model, the sole predicted full recruit index was calculated entirely from the model
difference equation, which explains why the OE model provided the poorest fit the observed
indices. This approach in selecting the preferred model assumes that the survey indices contain
less error than the difference equation (Eq. 6). The remainder of the report presents results
from this model (PE0.1).
Combined-Sex Model
Model Outputs
Estimates of total, annual blue crab abundance from model years 1978 to 2008 ranged
from 29 to 614 million, with a mean and median of 155 and 135 million (Table 8; Figure 14).
Most of the fluctuation is caused by large annual variability in recruit numbers. Estimates of
annual recruit abundance ranged from 15 to 544 million across the assessment time period, with
a mean and median of 124 and 95 million recruits (Figure 15). Terminal year recruitment in
2008 was 35 million, the fifth lowest estimate since 1978. Full recruit abundance ranged
between 9 and 70 million crabs, with a mean and median of 31 million individuals (Figure 16). In
the earliest years of the assessment from 1978 to 1987 full-recruit abundance was low, falling
below the median in 9 of 10 years. Full-recruit abundance then stayed at or above the median
for 14 straight years until 2001 (Figure 16). A 5 year decline occurred from 1999 until 2003,
followed by a two-year increase in 2004-2005. Full-recruit abundance dropped to the second
lowest value in the assessment time series at 10 million crabs in 2006, punctuating a prolonged
5 year period of below-median low abundance. A temporary spike in full recruit abundance
occurred in 2007 to 37 million crabs followed by another low abundance value of 23 million in the
terminal year of 2008. Full recruit biomass ranged from 1.4 to 9.7 million kg, with a mean and
- 42 -
median of 4.4 and 4.2 million kg (Figure 17). Terminal year 2008 full-recruit biomass was 3.2
million kg.
Model CVs of estimated recruit and full recruit parameters were between 23.9% and
27.2%. The CV associated with the estimate of the catchability coefficient q improves with each
additional year of data; from 40.4% in 2005, 33.0% in 2007, and 30.9% in 2008. Terminal year
estimate of q was 0.0387, an increase from the prior estimate of 0.0371 in 2007, 0.0365 in 2006
and 0.0329 in 2005. Bootstrap CVs of annual recruit abundance ranged from 15.7% to 30.9%.
Full-recruit abundance bootstrap CVs ranged from 17.1% to 33.8%. The bootstrap CVs for Z
ranged from 12.4% to 44.8%. The bootstrap CV for the estimate of q was 14.4%. Bootstrap
means of all estimated parameters and output results are shown in the final NFT model output
report (see Appendix I).
Mortality Rates
Instantaneous total mortality rates (Z) across the assessment time series were variable
ranging between 0.50 and 2.66, with an average and median of 1.52 and 1.47 (Table 8; Figure
18). Terminal Z was 2.00, continuing a trend of at- or above-median Z since 1997. Average
annual survival rate (1-A) was 25.2% and ranged from 7.0 to 60.5 % across the time series.
Total mortality appears to be strongly, positively related to recruit abundance (Figure 19).
Exploitation rates are widely variable given the range in annual exploitable stock sizes
(Figure 20). The upper bound and Collie-Kruse estimates of exploitable stock size were most
variable due to dramatic fluxes in recruit abundance, whereas the lower bound estimates which
do not use prior year recruit abundance in calculating exploitable stock were fairly stable across
- 43 -
the time series. The lower bound, Collie-Kruse, and upper bound exploitation rates averaged
15%, 27%, and 38% over the 1978 to 2007 period (Table 8; Figure 21). Terminal year
exploitation rates (LB 15%, CK 28%, UB 53%) were above time series norms.
Estimates of fishing mortality rate rose in terminal model year 2007 well above time
series norms. The range of upper bound Fs were between 0.23 in 1978 and 1.79 in 2005,
averaging 0.78 across the time series with terminal UBF=1.22 (Table 8). The lower bound F
ranged between 0.08 in 1980 and 0.58 in 2005 averaging F =0.28 with terminal LBF=0.35 (Table
8). The Collie-Kruse F was generally between the upper and lower bound estimates except
when it exceeded the upper bound in 1982, 1983, 1987, 1988, 1990, and 1991 (Figure 22). The
Collie-Kruse and lower bound estimates of fishing mortality fluctuate similarly (Figure 22). Peak
Collie-Kruse F occurred in 2005 at F =1.05; the time series average was 0.51; terminal
CKF=0.64. Annual F calculated from Z – M was highly erratic, achieving implausible negative
values four times in the time series (Table 8). The average F from the Z-M method was F =0.70.
Indices of Relative Abundance
Young-of-the-year abundance as measured by survey CPT was depressed in 2000,
2002, and 2008, with a large spike in 2006 (Figure 23). Terminal 2008 YOY abundance is
among the lowest of the 31 year survey period. Survey CPT of medium-size crabs, large crabs,
spawning stock, and female spawning stock biomass in 2008 were similar to the previous year
values, reflecting the continued presence of a strong 2006 year class.
- 44 -
A general period of high productivity (i.e. elevated YOY abundance) appears to have
occurred for about 15 years from 1985 to 1999. As a result, indices of medium, large crabs, and
spawning stock were at or above the median in 13 of 17 years between 1986 and 2002 (Figures
24, 25, 26). A particularly weak YOY class in 2002 precipitated a four year period of low
abundance of mediums, large crabs, and spawning stock from 2003 to 2006. Since bottoming in
2003, medium crabs and spawning stock indices increased steadily until surpassing median
CPT values in 2007. The large crab index remains below the time series median in 2008
(Figure 25). The ISSB fell below the reduced recruitment threshold in 2003 and 2005 and has
increased to robust levels in 2006, 2007, 2008 (Figure 27).
Typically, high YOY abundance is a good forecast for improved medium abundance in
ensuing years (Figure 28). The relationship with future large crabs and SSB is not as strong due
to effects of harvest and other mortality factors after the recruit stage (Figures 29, 30).
Index-Based Stock Recruitment Model
The compensatory relationship between the indices of spawning biomass (t) and recruits
(t+1) produced a fit to a Ricker stock-recruitment model (Figure 31), with the resulting model
from nonlinear least squares being
R = 270.366 * SSB * exp(-45.904 * SSB),
where R = the index of recruits and SSB = the index of SSB. The index-based reference point
SSB50 was 0.005 kg/tow. Observed SSB in 2008 of 0.022 kg/tow should produce the maximum
predicted recruitment in 2009 based on the S-R model (Figure 31). The Ricker model is
- 45 -
consistent with the documented presence of cannibalism among blue crabs, which could provide
a mechanism for the depensatory recruitment pattern at large stock sizes.
DISCUSSION
Results from this assessment support the documented view of density dependent
mortality occurring on the Delaware Bay blue crab stock (Kahn et al. 1998; Helser and Kahn
1999; Kahn and Helser 2005). The most prominent error residuals followed a predictable
pattern reflective of high compensatory mortality following large recruitment events. This
explains why heavy recruitment into the fishery-sized adult population is not observed in the full
recruit index after especially large year-classes appear, while high survival to full recruitment is
observed following low pre-recruit levels. The inability to quantify a priori, year-specific natural
mortality rates to account for density dependent compensation in the model equation is
problematic in simulating stock dynamics based closely on the observed indices. Given
constant annual input M, the model cannot account for the disappearance of large numbers of
recruits necessary to fit the following year‟s full-recruit (adult) survey. This is increasingly evident
in residuals from models with higher weighting of process error and in the OE model, since
greater weight is given to the model-calculated full recruit index that is derived from a constant
M. The updated stock-recruit model also supports the view of density dependent mortality, as
the best fit to empirical data results in a Ricker S-R curve. Previous analyses of survey data also
indicated that recruits exhibited density-dependent mortality (Kahn et al. 1998 and updated in
Kahn 2003).
Model derived total mortality Z is an increasing function of recruit abundance. Given the
estimation of Fµ from a calculated exploitation rate (using known yearly catch, estimated stock
- 46 -
size, Z, and annual mortality rate), a secondary estimate of M can be calculated derived from Z -
Fµ. This year-specific M is strongly related to recruit abundance and explains much of the yearly
variation in Z (Figure 32). Although this post-hoc method of calculating M is partially conditional
on the original constant M input, it provides an ostensibly realistic estimate of time-varying M that
accounts for density dependent effects of recruit abundance. Cannibalism is likely the primary
mechanism that incurs greater natural mortality with increasing recruit densities. Predation
experiments show increased cannibalism by large blue crabs on small juveniles as juvenile
densities increased, demonstrating a strong propensity for density dependent regulation of
recruits (Peery 1989).
Stock status is assessed based on comparisons of F to an overfishing threshold, Frep
=1.3, and to yield-based reference points, Fmax =1.0 and F0.1 =0.6. The post-hoc calculations of
annual exploitable stock size from the model outputs directly affect the F rates used to assess
the stock. The estimation of exploitable stock size is uncertain due to the difficulty in discerning
the proportion of pre-recruits that grow into the full-recruit stage within the one year time step.
Kahn et al. (1998) documented rapid growth of juveniles, with recruitment into the harvestable
size range occurring by June, and peak recruitment into the legal size fishery in August-
September. Previous assessments assumed a partial recruitment =0.4 to account for fast
growing recruits (Helser and Kahn 1999; Coakley 2004). However, within-year recruitment is
difficult to quantify given the density dependent mortality and variable growth from year to year.
Instead, the use of upper and lower bounds of exploitable stock size in this assessment are
used to account for partial, within-year recruitment as in Kahn and Helser (2005). The upper
and lower range of F rates result from the lower and upper estimates of exploitable stock size.
The range of F rates used for management purposes was taken from a preferred model
- 47 -
choice (PE0.1) after an analysis of four error-weighting model configurations. These four
configurations differed in part by how well the observed survey indices were fit, the greater fit to
indices occurring with greater downweighting of process error residuals. Thus the mixed error
PE0.1 model was preferred because of its best fit to the observed data. A consequence to the
increasing fit to indices was the decline in the estimated q parameter. This resulted in
increasing estimates of abundance in those models, which consequently had a reciprocal,
diminishing effect on F calculations – in turn resulting in the lowest F rates produced by the
various error-weighted models.
Stock Status
Terminal estimates of F increased from the previous year. In 2005, high estimates of F
(e.g. FC-K=1.05) were observed, raising concern for a rising trend in F rates. A sharp reduction in
F occurred in 2006 to FC-K=0.44, while terminal FC-K rose to 0.64. The three-year mean FC-
K=0.71 is considerably higher than the 31 year median FC-K=0.48, yet below Fmax.
Viewing the UB F as a precautionary F indicator, the 30 year mean and median UB F lies
roughly between F0.1 and Fmax across all four error-weighting model configurations (Figure 33).
Mean UB F from the preferred model was 0.78, below the common F = M paradigm. F = M is
sometimes recommended as a surrogate for FMSY (Quinn & Deriso 1999). Deriso (1982) found
that M could be viewed as an upper bound for FMSY. Thompson (1993) found that a fishing
mortality under 80% of M should keep spawning biomass per recruit above 30% SPR. The 30
year mean FC-K=0.51 was equal to 64% of M (Figure 33). Over the most-recent 3 years, C-K F
averaged 0.71, above F0.1 and 0.8*M, and UB F averaged above Fmax at 1.23 (Figure 34).
- 48 -
Since bottoming in 2003, medium crab and spawning stock CPTs have gradually
improved until finally surpassing time series norms in 2007 and 2008. Depressed indices of
mediums, large crabs, and spawning stock were below-median for four years from 2003-2006.
This stock decline began with the very low 2002 YOY index, despite an extremely high 2002
spawning stock index. An unusually warm spring could have artificially spurred this high 2002
spawning stock CPT value. Regardless, this early warming period likely accelerated the timing
of spawning, as indicated by an early presence of sponge crabs in the survey in April and May,
and a shortened May sook run in the fishery (since females were gravid and unharvestable).
Earlier than usual spawning may have had negative implications on larval transport back into
estuarine nursery areas in Delaware Bay by interrupting the coordinated timing of larval
development and fall weather events (Epifanio 1995; Garvine et al. 1997; Nantunewicz et al.
2001). Thus weak larval recruitment in 2002 could be responsible for the very low YOY
abundance in the survey. Following the depressed YOY recruitment in August-October 2002,
severe mortality associated with very low winter temperatures likely occurred in January-March
2003, leading to a further decline in abundance (personal communication, D. Kahn). Low
dredge harvest is often an indicator of abnormally high winter mortality caused by unusually low
winter temperatures. Delaware dredge harvest was approximately 50% below-average in
January-March 2003. The combination of low YOY recruitment in 2002 followed by elevated
winter mortality in 2003 would reduce population size considerably, as seen in the zero CPT in
the 2003 ISSB. Continued low YOY recruitment in 2003 would be expected following the zero
2003 ISSB. This low population abundance was seen in the depressed fishery landings in 2003
and 2004. Landings in 2003 and 2004 in Delaware were 72% of the 1973-2006 average. A
healthy rebound in harvest in 2005 and 2006 during persistently low levels of recruitment and
abundance explains the abnormally high 2005-2006 F rate from the population model. The
- 49 -
elevated landings since 2005 probably prolonged the recovery period. The only index the
remains below the median is the large crab index. Large crabs may be the last to respond as
the stock initially recovers due to the heavy harvest of jimmies (largest males) in the fishery.
The index of spawning stock biomass has shown small incremental increases since
2003, persisting at or above the SSB50 threshold since 2004. Kahn (2003) refers to the SSB50
as the reduced recruitment threshold, indicating that as the ISSB falls below SSB50, the
likelihood of low observed recruitment increases. Median recruitment is 0.77 CPT when the
ISSB is below the SSB50 threshold compared to 1.45 CPT at ISSB values above SSB50. Based
on the S-R curve, the 2008 ISSB should result in the maximum theoretical recruitment event in
2009.
This work portrays a highly resilient stock under substantial exploitation pressure.
Terminal year young-of-the-year abundance in 2008 is among the worst in 31 years, yet standing
spawning stock biomass should yield high juvenile recruitment in 2009. Fishing mortality rates
across the most-recent three years are well above time series norms, yet below Fmax. Stock
status in the terminal year in terms of abundance and F is below-average, yet these metrics
should rebound in the near future given expected recovery in recruitment.
ACKNOWLEDGMENTS
Much gratitude is given to Lindy Barry, Tom Baum, Jeffrey Brust, Brandon Muffley, and
Paul Scarlett of NJ Bureau of Marine Fisheries, and Bill Whitmore and Rick Cole of DE Division
of Fish and Wildlife for historical NJ and DE landings statistics. Further acknowledgment is
given to Dr. Desmond Kahn of DE DFW for both his quantitative and anecdotal contributions to
- 50 -
this report. Funding for this research was provided by NOAA under the Atlantic Coastal
Fisheries Cooperative Management Act (ACFMA).
- 51 -
REFERENCES CITED
Agresti, A. 1990. Categorical Data Analysis. John Wiley & Sons, New York, NY.
Basson, M., Rosenberg, A. A. and Beddington, J. R. (1988) The accuracy and reliability of two
new methods for estimating growth parameters from length-frequency data. J. Cons. int.
Explor. Mer 44:277-285.
Baum, T., Scarlett, P., Muffley, B. and L. Barry. Personal communications. New Jersey Bureau
of Marine Fisheries, Division of Fish and Wildlife.
Benefield, r.L. 1968. Survey of the blue crab (Callinectes sapidus) sport fishery of the Galveston
Bay system 1968. TX Parks and Wildlife Department, Coastal Fisheries Project Report
1968:35-41.
Booth, K.J. and L.G. Martin. 1993. Striped bass feeding behavior and the potential effect on the
blue crab population in the Chesapeake Bay. Maryland Department of Natural
Resources, Tidewater Administration Fisheries Technical Memo No. 2 (Series), 7 pages.
Blundon, J.A. and V.S. Kennedy. 1982. Mechanical and behavioral aspects of blue crab,
Callinectes sapidus, predation on Chesapeake Bay bivalves. J. Exper. Mar. Biol. and
Ecol. 65:47-65.
Churchill, E.P. 1921. Life history of the blue crab. Bull. U.S Bureau of Fisheries for 1917-1918.
36:91-128.
- 52 -
Coakley, J. 2004. Stock assessment of Delaware Bay blue crab (Callinectes sapidus) for 2004.
Department of Natural Resources and Environmental Control, Delaware Division of Fish
and Wildlife, 89 Kings Highway, Dover, DE 19901.
Cole, R., and R. Beck. 1975. Technical Assistance to Commercial Fisheries. Federal Aid Report.
Cole, R.V., W.H. Whitmore, and D.M. Kahn. 1997. Recreational blue crab effort and harvest in
the Delaware estuary. Delaware Division of Fish and Wildlife, Dover DE.
Cole, R.W. 1998. Changes in harvest patterns and assessment of possible long term impacts
on yield in the Delaware commercial blue crab fishery. Journal of Shellfish Research
17(2):469-474.
Collie, J.S. and G. H. Kruse. 1998. Estimating king crab (Paralithodes camtschaticus)
abundance from commercial catch and research survey data pp. 73-83 in Jamieson, G.
S. and A. Campbell, eds. Proceedings of the North Pacific Symposium on Invertebrate
Stock Assessment and Management. Can. Spe. Pub. Fish. Aq. Sci 125.
Collie, J.S., and M.P. Sissenwine. 1983. Estimating population size from relative abundance
data measured with error. Canadian Journal of Fisheries and Aquatic Sciences 40:1871-
1879.
Conser, R.J. 1995. A modified DeLury modelling framework for data-limited assessments:
Bridging the gap between surplus production models and age-structured models. A
- 53 -
working paper prepared for the ICES Working Group on Methods of Fish Stock
Assessment, Copenhagen, Denmark, February 1995.
Conser, R.J., and J. Idoine. 1992. A modified DeLury model for estimating mortality rates and
stock sizes of American lobster populations. NEFSC Research Document SAW 14/7.
Darnell, R.M. 1958. Food habits of fishes and larger invertebrates of Lake Pontchartrain,
Louisiana, an estuarine community. Publication of the Institute of Marine Science, U.
Texas 5:353-416.
DDFW: Delaware Division of Fish and Wildlife in Cooperation with New Jersey Division of Fish,
Game and Wildlife. 1999. 1999 Delaware Bay Blue Crab Fishery Management Plan.
Dittel, A. and C.E. Epifanio. 1982. Seasonal abundance and vertical distribution of crab larvae in
Delaware Bay. Estuaries 5:197-202.
Eggleston, D.B. 1990. Foraging behavior of the blue crab, Callinectes sapidus, on juvenile
oysters, Crassostrea virginica: effects of prey density and size. Bulletin of Marine Science
46(1):62-82.
Eggleston, D.B., R.N. Lipcius and A.H. Hines. 1992. Density-dependent predation by blue crabs
upon infaunal clam species with contrasting distribution and abundance patterns. Mar.
Ecol. Prog. Ser. 85:55-68.
Epifanio, C.B. 1995. Transport of blue crab (Callinectes sapidus) larvae in the waters off Mid-
- 54 -
Atlantic states. Bull. Mar. Sci. 57:713-725.
Fischler, K. J. 1965. The use of catch-effort, catch-sampling and tagging data to estimate a
population of blue crabs. Trans. Am. Fish. Soc. 94:287-310.
Fogarty, M.J., A.A. Rosenberg, and M.P. Sissenwine. 1992. Fisheries risk assessments:
Sources of uncertainty. Environ. Sci. Tech. 26:440-447.
Fournier, D.A., J.R. Sibert, and M. Terciero. 1991. Analysis of length frequency samples with
relative abundance data for the Gulf of Maine northern shrimp by the MULTIFAN method.
Can. J. Fish. Aquat. Sci. 48:591-598.
Garvine R.W., Epifanio C.C., Epifanio C.E. and K.C. Wong.1997. Transport and recruitment of
blue crab larvae: a model with advection and mortality. Estuar Coast Shelf Sci 45:99–
111.
Gosner, K.L. 1978. A field guide to the Atlantic seashore. The Peterson field guide series; 24.
Houghton Mifflin Co. Boston, USA.
Guillory, V. 1998. A survey of the recreational blue crab fishery in Terrebonne Parish, LA. J.
Shellfish Res. 17(2):4543-4550.
Guillory, V., (11 other authors). 2001. The blue crab fishery of the Gulf of Mexico, United States:
A regional management plan. Gulf States Marine Fisheries Commission, P.O. Box 726,
Ocean Springs, MS 39566.
- 55 -
Gulland, J.A. 1983. Fish stock assessment: A manual of basic methods. John Wiley & Sons,
New York, NY. 223 p.
Helser, T. E. 2000. Stock assessment of Delaware Bay blue crab (Callinectes sapidus) for
2000. Department of Natural Resources and Environmental Control, Delaware Division
of Fish and Wildlife, 89 Kings Highway, Dover, DE 19901.
Helser, T.E., and D.M. Kahn. 1999. Stock assessment of Delaware Bay blue crab (Callinectes
sapidus) for 1999. Department of Natural Resources and Environmental Control,
Delaware Division of Fish and Wildlife, 89 Kings Highway, Dover, DE 19901.
------------------------------------2001. Stock assessment of Delaware Bay blue crab (Callinectes
sapidus) for 2000. Department of Natural Resources and Environmental Control,
Delaware Division of Fish and Wildlife, 89 Kings Highway, Dover, DE 19901.
Helser, T.E., A. Sharov, and D.M. Kahn. 2001. A stochastic decision-based approach to
assessing the status of the Delaware Bay blue crab (Callinectes sapidus) stock, Pages
9-24 In Uncertainty in Fisheries Models (J. Berkson and L. Kline, eds.). American
Fisheries Society Symposium 24.
Herring, R. and J.Y. Christmas, Jr. 1974. Blue crabs for fun…and food. Mississippi Game and
Fish 1974:12-14.
Hoenig and Choudary Hanumara (1982)
- 56 -
Kahn, D.M. 1996. Use of indices of relative abundance as predictors of later abundance and
yield for the Delaware Bay blue crab stock. Delaware Division of Fish and Wildlife, Dover
DE.
Kahn, D. M. 2003. Estimation of fishing mortality from a catch-survey model of the Delaware bay
blue crab stock. Delaware Div. Fish. And Wild., Dover DE.
Kahn, D.M, R.W. Cole, S.M. Michels, and W. Whitmore. 1998. Development of life-stage
specific indices of relative abundance and stock-recruitment relationships for the
Delaware Bay blue crab stock. Journal of Shellfish Research 17(2): 529-542.
Kahn, D. M. and T.E. Helser. 2005. Abundance, dynamics and mortality rates of the Delaware
Bay stock of blue crabs, Callinectes sapidus. J. Shellfish Res. 24:269-284.
Kvalseth, T. O. Cautionary note about R2. Amer. Statistician 39:279-285.
Leffler, C.W. 1972. Some effects of temperature on the growth and metabolic rate of juvenile
blue crabs, Callinectes sapidus, in the laboratory. Marine Biology 14:104-110.
Mace, P.M. 1994. Relationships between common biological reference points used as
thresholds and targets of fisheries management strategies. Can. J. Fish. Aquat. Sci.
51:110-122.
Mansour, R.A. 1992. Foraging ecology of the blue crab, Callinectes sapidus, in lower
- 57 -
Chesapeake Bay, Ph.D. Dissertation. College of William and Mary, Williamsburg, VA.
McMillen-Jackson, A.L., T.M. Bert, and P. Steele. 1994. Population genetics of the blue crab
Callinectes sapidus: modest population structuring in a background of high gene flow.
Marine Biology 118:53-64.
Miller, R.E., Sulkin, S.D., and R.L. Lippson. 1975. Composition and seasonal abundance of the
blue crab, Callinectes sapidus. Chesapeake Science 16(1):27-31.
Miller, T.J. and E.D. Houde. 1998. Blue crab target setting. Reference No. UMCES[CBL] 98-129.
Final report for Living Resources Subcommittee, Chesapeake Bay Program, 158 pp.
Natunewicz, C., Epifanio, C.E., and R.W. Garvine. 2001. Transport of crab larvae patches in the
open ocean. Mar. Ecol. Prog. Ser. 222:143-154.
Newcombe, C.L., Sandoz, M.D., and R. Rogers-Talbert. 1949. Differential growth and molting
characteristics of the blue crab, Callinectes sapidus. Journal of Experimental Zoology
110(1):113-152.
Olmi, E.J., III. 1995. Ingress of blue crab megalopae in the York River, Virginia, 1987-1989.
Bulletin of Marine Science 57(3):753-780.
ORC-Macro 2006. New Jersey Blue Crab Recreational Fishery Survey 2005 Final Report.
Submitted to NJ Department of Environmental Protection. ORC-Macro, 126 College St.
Burlington, VT 05401.
- 58 -
Pauly, D. 1987. A review of the ELEFAN system for analysis of length-frequency data in fish
and aquatic vertebrates. Pages 7-34 in Pauly, D. and Morgan, G. R. (Eds) Length-based
methods in fisheries research. ICLARM, Manila, Philippines and KISR, Safat, Kuwait.
468p.
Peery, C.A. 1989. Cannibalism experiments with the blue crab (Callinectes sapidus Rathbun):
potential effects of size and abundance. Thesis (M.A.)--College of William and Mary.
(Series) viii, 29 leaves, [2] leaves of plates. Virginia Institute of Marine Science.
Prager, M.H., J.R. McConaugha, C.M. Jones, and P.J. Geer. 1990. Fecundity of blue crab,
Callinectes sapidus, in Chesapeake Bay: biological, statistical, and management
considerations. Bull. Mar. Sci. 46:170-179.
Quinn, T.J.,III and R.B. Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, Inc.
NY.
Ricker, W.E. 1975. Computation and Interpretation of Biological Statistics of Fish Populations.
Bulletin of the Fisheries Research Board of Canada, Bulletin No. 191.
Rothschild, B.J., and eight co-authors. 1992. Assessment of the Chesapeake Bay blue crab
stock. Ref. No. UMCEES[CBL] 92-082. Final Report for NO/NMFS Grant NA16FU0520-
01. 201 p.
Rugolo, R., K. Knotts, A. Lange, V. Crecco, M. Terceiro, C. Bonzek, C. Stagg., R. O‟Reilly, and
- 59 -
D. Vaughan. 1997. Stock assessment of Chesapeake Bay blue crab. Report of the
Technical Subcommittee (TSC) of the Chesapeake Bay Stock Assessment Committee of
the National Marine Fisheries Service, NOAA.
Rugolo, L. J., K. S. Knotts, A. M. Lange and V. A. Crecco. 1998. Stock assessmnet of
Chesapeake Bay blue crab (Callinectes sapidus Rathbun). J. of Shellfish Research
17(3):906-930.
Shepherd, J. G. 1987. A weakly parametric method for the analysis of length composition data.
Pages 113-120 in Pauly, D. and Morgan, G. R. (Eds) Length-based methods in fisheries
research. ICLARM, Manila, Philippines and KISR, Safat, Kuwait. 468p.
Smith, L.D. and A.H. Hines. 1991. The effect of cheliped loss on blue crab Callinectes sapidus
foraging rate on soft-shell clams Mya arenareia. J. Exp. Mar. Biol. and Ecol. 15(2):245-
256.
Speir, Harley J. 2001. A review of predation on blue crabs in Chesapeake Bay. Maryland DNR.
Fisheries Tech. Memo Series no.24.
Sponaugle, S. and P. Lawton. 1990. Portunid crab predation on juvenile hard clams: effects of
substrate type and prey density. Mar. Ecol. Prog. Ser. 67:43-53.
Tatum, W. 1982. The blue crab fishery of Alabama. Pages 23-28 In: H.M. Perry and W.A. Van
Engel (eds.), Symposium on the Natural Resources of the Mobile Estuary, Alabama.
Mississippi/Alabama Sea Grant Consortium, Publication MASGP-80-022.
- 60 -
Thompson, W.F, and F. H. Bell. 1934. Biological statistics of the Pacific halibut fishery. 2. Effect
of changes in intensity upon total yield and yield per unit of gear. Rep. Int. Fish. (Pacific
Halibut). Comm. 6: 108 p.
Van Engle, W.A. 1958. The blue crab and its fishery in Chesapeake Bay. Part 1-Reproduction,
early development, growth, and migration. Commercial Fisheries Review 20:6-17.
Vetter, E.F. 1985. Estimation of natural mortality in fish stocks: A Review: Fish. Bull. U.S. 86(1):
25-43.
Williams, A. B. 1974. The swimming crabs of the genus Callinectes (Decapoda:Portunidae).
Fish Bull. 72(3):3685-798.
Virnstein, R.W. 1977. The importance of predation by crabs and fishes on bethic infauna in
Chesapeake Bay. Ecology 58:1199-1217.
- 61 -
TABLES
Table 1. Annual (Jan-Dec) combined commercial and recreational landings (kg) by state (1973-2008).
Year Delaware New Jersey Total Landings
DE% NJ%
1973 659,911 820,173 1,480,085
44.6% 55.4%
1974 833,411 987,466 1,820,877
45.8% 54.2%
1975 1,423,009 956,288 2,379,297
59.8% 40.2%
1976 1,404,644 877,861 2,282,506
61.5% 38.5%
1977 317,301 118,850 436,151
72.8% 27.2%
1978 135,747 335,654 471,402
28.8% 71.2%
1979 225,815 315,225 541,041
41.7% 58.3%
1980 786,461 610,516 1,396,977
56.3% 43.7%
1981 373,715 572,024 945,739
39.5% 60.5%
1982 384,735 291,567 676,303
56.9% 43.1%
1983 468,405 495,956 964,361
48.6% 51.4%
1984 449,456 664,928 1,114,384
40.3% 59.7%
1985 1,132,213 1,019,033 2,151,246
52.6% 47.4%
1986 1,272,152 1,088,662 2,360,813
53.9% 46.1%
1987 1,594,431 1,108,155 2,702,585
59.0% 41.0%
1988 1,631,292 1,538,426 3,169,719
51.5% 48.5%
1989 2,156,766 1,577,485 3,734,251
57.8% 42.2%
1990 3,042,722 1,609,572 4,652,295
65.4% 34.6%
1991 2,323,051 1,498,659 3,821,710
60.8% 39.2%
1992 2,102,506 2,008,828 4,111,334
51.1% 48.9%
1993 2,769,425 2,386,022 5,155,447
53.7% 46.3%
1994 2,578,601 1,747,332 4,325,933
59.6% 40.4%
1995 2,953,825 2,794,578 5,748,403
51.4% 48.6%
1996 2,025,045 1,066,922 3,091,967
65.5% 34.5%
1997 2,123,682 1,327,959 3,451,641
61.5% 38.5%
1998 2,152,935 2,089,433 4,242,368
50.7% 49.3%
1999 2,320,158 2,064,485 4,384,643
52.9% 47.1%
2000 1,942,930 1,790,908 3,733,838
52.0% 48.0%
2001 1,765,894 1,925,687 3,691,581
47.8% 52.2%
2002 1,468,479 2,087,797 3,556,275
41.3% 58.7%
2003 712,223 973,332 1,685,555
42.3% 57.7%
2004 1,141,669 1,148,463 2,290,132
49.9% 50.1%
2005 1,460,426 2,070,484 3,530,910
41.4% 58.6%
2006 1,495,913 1,808,890 3,304,803
45.3% 54.7%
2007 1,785,263 1,720,550 3,505,813
50.9% 49.1%
2008 1,885,928 2,212,242 4,098,170
46.0% 54.0%
Average 1,480,559 1,325,289 2,805,849
51.7% 48.3%
- 62 -
Table 2. Historic, annual, Delaware Bay blue crab landings in Delaware by fishery and market grade based on a calendar year (Jan-Dec). Landings are shown in thousands of kilograms.
Commercial Dredge Commercial Pot Recreational
Total Year 1 2 3 1 2 3 Peeler Hard Crabs
1973 0 0.0 0 245 169 222 8 16 660
1974 5 0.0 26 298 317 126 44 19 833
1975 20 0.3 148 447 282 475 20 30 1,423
1976 53 0.2 203 336 320 415 50 27 1,405
1977 123 0.0 12 90 32 50 6 4 317
1978 0 0.0 0 49 41 35 7 3 136
1979 2 0.0 17 71 52 71 9 5 226
1980 7 0.0 60 190 105 394 13 17 786
1981 1 0.0 7 148 101 82 25 8 374
1982 5 0.0 27 167 58 113 6 8 385
1983 1 0.0 11 170 54 216 5 11 468
1984 4 0.0 38 170 100 111 17 10 449
1985 8 0.0 70 485 248 279 17 25 1,132
1986 19 0.0 197 266 372 348 47 25 1,272
1987 17 0.0 302 347 419 451 28 30 1,594
1988 30 0.2 361 239 474 429 71 29 1,631
1989 20 0.0 367 491 399 785 53 42 2,157
1990 46 0.0 481 991 753 624 88 59 3,043
1991 29 0.0 207 733 249 1,043 11 51 2,323
1992 9 0.0 144 420 798 488 200 43 2,103
1993 38 0.0 547 706 473 869 86 51 2,769
1994 22 0.0 502 670 591 608 138 47 2,579
1995 5 0.0 256 1,017 636 745 235 60 2,954
1996 47 0.0 623 427 405 392 100 31 2,025
1997 35 0.0 336 554 329 780 49 42 2,124
1998 24 0.0 254 661 537 543 91 44 2,153
1999 22 0.0 308 835 552 512 43 47 2,320
2000 23 0.0 283 841 283 438 35 39 1,943
2001 17 0.0 379 828 191 292 26 33 1,766
2002 27 0.0 221 613 175 386 16 29 1,468
2003 15 0.0 137 313 82 135 8 23 712
2004 22 2.1 91 615 114 220 38 41 1,142
2005 17 0.3 97 686 331 236 40 54 1,460
2006 21 0.0 179 588 247 389 20 53 1,496
2007 34 0.1 226 648 340 441 35 62 1,785
2008 33 0.0 247 556 344 618 22 66 1,886
Average 22 0 204 470 305 399 47 33 1,481
- 63 -
Table 3. Historical, annual, Delaware Bay blue crab landings in New Jersey by fishery and market grade
based on a calendar year. Landings are shown in thousands of kilograms.
Commercial Dredge Commercial Pot
Recreational Total
Harvest Year Female Male Mixed Female Male Mixed Peeler Mixed
1950 - - 110 - - 392 5 76 583
1951 - - 70 - - 161 4 31 266
1952 - - 48 - - 217 3 42 310
1953 - - 8 - - 162 2 31 203
1954 - - 3 - - 252 3 49 306
1955 - - 24 - - 140 4 27 195
1956 - - 35 - - 138 3 27 202
1957 - - 29 - - 309 2 60 400
1958 - - 48 - - 165 2 32 246
1959 - - 51 - - 197 0 38 286
1960 - - 63 - - 341 6 66 477
1961 - - 24 - - 148 21 29 221
1962 - - 40 - - 382 56 74 552
1963 - - 20 - - 225 12 44 300
1964 - - 11 - - 153 3 30 197
1965 - - 26 - - 227 12 44 308
1966 - - 17 - - 177 1 34 229
1967 - - 7 - - 129 2 25 163
1968 - - 3 - - 35 0 7 45
1969 - - 2 - - 188 3 36 230
1970 - - 0 - - 232 12 45 289
1971 - - 7 - - 326 5 63 401
1972 - - 27 - - 387 5 75 494
1973 - - 94 - - 601 8 116 820
1974 - - 47 - - 750 45 145 987
1975 - - 80 - - 722 14 140 956
1976 - - 102 - - 623 33 121 878
1977 - - 18 - - 83 2 16 119
1978 - - 2 - - 274 7 53 336
1979 - - 8 - - 250 10 48 315
1980 - - 62 - - 455 6 88 611
1981 - - 9 - - 457 17 88 572
1982 - - 0 - - 242 4 45 292
1983 - - 0 - - 409 8 79 496
1984 - - 2 - - 555 13 95 665
1985 - - 31 - - 838 45 104 1,019
1986 - - 104 - - 793 40 154 1,093
1987 - - 245 - - 696 33 134 1,109
1988 - - 223 - - 1,006 106 204 1,539
1989 - - 221 - - 1,068 75 213 1,577
- 64 -
1990 - - 131 - - 1,126 133 219 1,610
1991 - - 86 - - 1,166 17 229 1,499
1992 - - 57 - - 1,505 148 299 2,009
1993 - - 333 - - 1,649 69 335 2,387
1994 - - 100 - - 1,246 155 251 1,752
1995 - - 187 - - 1,887 346 374 2,795
1996 - - 133 - - 721 65 147 1,067
1997 - - 58 - - 979 92 199 1,328
1998 - - 102 - - 1,525 173 290 2,089
1999 - - 14 - - 1,614 121 315 2,064
2000 - - 44 - - 1,401 70 276 1,791
2001 133 11 0 417 973 24 88 280 1,926
2002 100 4 0 503 1,070 24 94 292 2,087
2003 57 11 0 136 570 12 45 143 973
2004 72 11 0 129 690 5 76 165 1,148
2005 67 15 2 293 1,249 11 129 304 2,070
2006 52 5 0 445 968 9 66 263 1,808
2007 32 3 0 415 884 12 116 259 1,720
2008 23 2 0 541 1,206 7 85 347 2,212
Average 67 8 54 360 951 506 46 132 926
- 65 -
Table 4. Annual commercial fishing licenses sold by state. New Jersey dredge fishery licenses from 1990-
1996 included all state waterbodies. From 1997 on, totals indicate Delaware Bay dredge licenses only.
Delaware Commercial Licenses New Jersey Commercial Licenses
Season Crab Pot Dredge Total %
Change Crab Pot Dredge Total
%
Change
1975 91 12 103 - - - - -
1976 106 22 128 24% - - - -
1977 66 26 92 -28% - - - -
1978 40 0 40 -57% - - - -
1979 45 0 45 13% - - - -
1980 67 10 77 71% - - - -
1981 56 0 56 -27% - - - -
1982 53 5 58 4% - - - -
1983 60 5 65 12% - - - -
1984 70 5 75 15% - - - -
1985 77 6 83 11% - - - -
1986 102 12 114 37% - - - -
1987 111 15 126 11% - - - -
1988 126 5 131 4% - - - -
1989 132 22 154 18% - - - -
1990 172 31 203 32% 311 166 477 -
1991 169 16 185 -9% 312 133 445 -7%
1992 164 30 194 5% 365 209 574 29%
1993 184 23 207 7% 420 289 709 24%
1994 219 42 261 26% 506 222 728 3%
1995 219 42 261 0% 458 280 738 1%
1996 219 40 259 -1% 430 301 731 -1%
1997 214 40 254 -2% 408 93 501 -
1998 214 17 231 -9% 394 82 476 -5%
1999 214 37 251 9% 377 81 458 -4%
2000 212 35 247 -2% 364 90 454 -1%
2001 212 34 246 0% 352 91 443 -2%
2002 209 34 243 -1% 346 80 426 -4%
2003 204 33 237 -2% 333 94 427 0%
2004 204 38 242 2% 325 92 417 -2%
2005 204 36 240 -1% 319 93 412 -1%
2006 202 35 237 -1% 314 86 400 -3%
2007 218 36 254 7% 309 87 396 -1%
2008 206 39 245 -4% 302 86 388 -2%
- 66 -
Market GradeLandings
Unit
Common Unit
Equivalent
Numbers per
Landings Unit
#1 Male Hard Crab; pot bushel 40 lb 93.8
#1 Male Hard Crab; dredge bushel 40 lb 114.0
#2 Male Hard Crab; (both gears) bushel 40 lb 134.7
#3 Female Hard Crab; (both gears) bushel 40 lb 123.0
Hard Crab (unspecified male); dredge bushel 40 lb 114.492
Hard Crab (unspecified male); pot bushel 40 lb 110.477
Hard Crab (unspecified); dredge bushel 40 lb 122.322
Hard Crab (unspecified); pot bushel 40 lb 114.844
Hard Crab (unspecified); pot; Apr bushel 40 lb 118.277
Hard Crab (unspecified); pot; May bushel 40 lb 117.673
Hard Crab (unspecified); pot; Jun bushel 40 lb 114.479
Hard Crab (unspecified); pot; Jul bushel 40 lb 114.990
Hard Crab (unspecified); pot; Aug bushel 40 lb 113.391
Hard Crab (unspecified); pot; Sep bushel 40 lb 114.076
Hard Crab (unspecified); pot; Oct bushel 40 lb 114.504
Hard Crab (unspecified); pot; Nov bushel 40 lb 114.097
Peeler bushel 62.49 lb 300
Peeler pound - 4.801*
Peeler numbers 0.2083 lb* -
Table 5. Bushels to numbers conversions used in the assessment.
- 67 -
Table 6. Inputs used in the CSA model for the baseline combined-sex model.
Survey Indices (#/tow) Survey Avg. Wt. (kg) Harvest
Survey
Year Recruits
Full
Recruits Recruits Full Recruits Numbers x 10
6 kg / individual
1978 2.179413968 0.350253368 0.015 0.157 3.26 0.1545
1979 1.32930109 0.774146407 0.022 0.144 7.27 0.1545
1980 5.767955596 0.468614581 0.010 0.171 6.58 0.1526
1981 2.030260442 1.513766476 0.015 0.144 4.48 0.1597
1982 0.544536843 0.46892669 0.028 0.154 5.87 0.1570
1983 0.883959568 0.546902374 0.011 0.176 5.72 0.1562
1984 3.361388811 0.964780884 0.008 0.168 11.00 0.1556
1985 7.966658785 0.608828139 0.003 0.169 17.14 0.1523
1986 1.56224118 0.862671413 0.013 0.137 18.03 0.1514
1987 2.935679713 0.743670955 0.003 0.139 18.31 0.1481
1988 3.861174428 1.508443138 0.007 0.140 25.73 0.1494
1989 24.96839025 2.898483119 0.006 0.138 28.29 0.1504
1990 0.738158815 1.064904509 0.009 0.167 24.71 0.1584
1991 4.7393749 1.317453373 0.005 0.200 26.76 0.1458
1992 3.737739177 2.492882919 0.012 0.139 33.85 0.1525
1993 8.174420139 1.453676758 0.003 0.157 30.09 0.1496
1994 11.21657274 1.392456331 0.001 0.144 36.44 0.1455
1995 2.640472671 1.458674286 0.002 0.132 24.81 0.1528
1996 4.199889055 1.227599426 0.004 0.132 23.34 0.1512
1997 14.50449176 1.506677451 0.005 0.131 25.85 0.1497
1998 5.31589812 1.590245527 0.010 0.133 29.74 0.1544
1999 9.411201926 1.545717644 0.005 0.136 25.10 0.1567
2000 8.346600638 1.415226221 0.005 0.126 23.48 0.1578
2001 3.543692105 1.016729103 0.009 0.145 24.94 0.1570
2002 2.555592295 0.717219467 0.007 0.143 11.63 0.1576
2003 3.774410082 0.645217539 0.006 0.150 14.10 0.1588
2004 4.337943308 0.83509377 0.006 0.162 18.69 0.1574
2005 3.305993672 1.209721485 0.006 0.147 23.91 0.1580
2006 5.944976484 0.367942464 0.004 0.135 20.32 0.1552
2007 5.767057689 1.423435108 0.005 0.133 26.42 0.1560
2008 1.363581233 0.831014775 0.013 0.134
Mean 5.19 1.14 0.008 0.148 19.86 0.1539
2 y Mean 3.57 1.13 0.009 0.134 23.37 0.1556
- 68 -
Index of Abundance Units Survey Period Size Subset
YOY Index GM CPT (numbers) Sep-Oct < 60 mm
Recruit Index GM CPT (numbers) Apr-Aug 60 - 119 mm
Index of Large Crabs GM CPT (numbers) Apr-Oct >= 120 mm
Index of Spawning Stock AM CPT (numbers) Apr-May >= 120 mm
Index of Spawning Stock Biomass AM CPT (kg) Apr-May females >= 120 mm
Table 7. Supplementary fishery independent indices of population abundance from the DDFW trawl survey.
- 69 -
Table 8. Baseline combined-sex model outputs and calculated quantities from the preferred model PE0.1.
Model Results q = 0.03868
Upper B C-K Lower B Lower B C-K Upper B Lower B C-K Upper B Z-M upper B C-K Lower B
Survey Year RecruitsPost-Recruits Total Harvest Z A stock size stock size stock size U U U F F F F M M M
1978 54.98 9.02 64.00 3.26 1.16 0.68 64.0 35.1 23.4 0.05 0.09 0.14 0.086 0.16 0.23 0.36 1.07 1.00 0.92
1979 33.33 20.16 53.49 7.27 1.45 0.77 53.5 29.4 19.8 0.14 0.25 0.37 0.258 0.47 0.70 0.65 1.20 0.98 0.76
1980 142.00 12.51 154.51 6.58 1.37 0.75 154.5 84.8 45.8 0.04 0.08 0.14 0.078 0.14 0.26 0.57 1.29 1.23 1.11
1981 49.49 39.23 88.71 4.48 1.85 0.84 88.7 48.7 18.4 0.05 0.09 0.24 0.111 0.20 0.54 1.05 1.74 1.65 1.32
1982 14.71 13.91 28.62 5.87 0.73 0.52 28.6 15.7 19.7 0.21 0.37 0.30 0.289 0.53 0.42 -0.07 0.44 0.20 0.31
1983 24.12 13.82 37.94 5.72 0.50 0.40 37.9 20.8 28.7 0.15 0.27 0.20 0.192 0.35 0.25 -0.30 0.31 0.15 0.25
1984 80.45 22.94 103.39 11.00 1.81 0.84 103.4 56.7 27.9 0.11 0.19 0.39 0.231 0.42 0.86 1.01 1.58 1.39 0.96
1985 182.84 16.86 199.70 17.14 2.07 0.87 199.7 109.6 42.4 0.09 0.16 0.40 0.203 0.37 0.96 1.27 1.86 1.70 1.11
1986 41.48 25.29 66.77 18.03 1.26 0.72 66.8 36.6 37.0 0.27 0.49 0.49 0.475 0.86 0.86 0.46 0.78 0.39 0.40
1987 78.64 18.97 97.61 18.31 0.93 0.60 97.6 53.6 56.9 0.19 0.34 0.32 0.288 0.52 0.49 0.13 0.64 0.40 0.43
1988 105.09 38.60 143.69 25.73 0.72 0.51 143.7 78.9 95.6 0.18 0.33 0.27 0.251 0.46 0.38 -0.08 0.47 0.26 0.34
1989 543.74 69.90 613.64 28.29 2.66 0.93 613.6 336.8 71.2 0.05 0.08 0.40 0.132 0.24 1.14 1.86 2.53 2.42 1.52
1990 21.86 42.92 64.78 24.71 0.76 0.53 64.8 35.6 55.0 0.38 0.69 0.45 0.544 0.99 0.64 -0.04 0.21 -0.23 0.12
1991 126.18 30.33 156.51 26.76 0.92 0.60 156.5 85.9 89.0 0.17 0.31 0.30 0.262 0.48 0.46 0.12 0.66 0.44 0.46
1992 95.30 62.28 157.58 33.85 1.44 0.76 157.6 86.5 71.4 0.21 0.39 0.47 0.405 0.74 0.89 0.64 1.03 0.70 0.54
1993 194.88 37.51 232.39 30.09 1.81 0.84 232.4 127.5 68.3 0.13 0.24 0.44 0.280 0.51 0.95 1.01 1.53 1.30 0.85
1994 261.39 38.17 299.56 36.44 1.98 0.86 299.6 164.4 78.0 0.12 0.22 0.47 0.279 0.51 1.07 1.18 1.70 1.47 0.90
1995 68.77 41.55 110.32 24.81 1.26 0.72 110.3 60.5 56.2 0.22 0.41 0.44 0.395 0.72 0.78 0.46 0.86 0.54 0.48
1996 107.28 31.40 138.68 23.34 1.27 0.72 138.7 76.1 62.2 0.17 0.31 0.38 0.298 0.54 0.66 0.47 0.98 0.73 0.61
1997 332.83 38.82 371.65 25.85 2.10 0.88 371.7 204.0 71.5 0.07 0.13 0.36 0.166 0.30 0.86 1.30 1.93 1.79 1.23
1998 132.80 45.63 178.44 29.74 1.48 0.77 178.4 97.9 70.3 0.17 0.30 0.42 0.320 0.58 0.81 0.68 1.16 0.90 0.67
1999 221.65 40.56 262.21 25.10 1.90 0.85 262.2 143.9 64.3 0.10 0.17 0.39 0.214 0.39 0.87 1.10 1.69 1.51 1.03
2000 193.13 39.18 232.31 23.48 2.09 0.88 232.3 127.5 52.2 0.10 0.18 0.45 0.241 0.44 1.07 1.29 1.85 1.65 1.02
2001 86.23 28.72 114.95 24.94 1.79 0.83 114.9 63.1 44.1 0.22 0.40 0.57 0.466 0.85 1.21 0.99 1.32 0.94 0.58
2002 62.99 19.19 82.18 11.63 1.56 0.79 82.2 45.1 28.9 0.14 0.26 0.40 0.279 0.51 0.79 0.76 1.28 1.05 0.77
2003 92.21 17.28 109.50 14.10 1.58 0.79 109.5 60.1 36.6 0.13 0.23 0.38 0.256 0.47 0.77 0.78 1.32 1.11 0.81
2004 107.94 22.54 130.48 18.69 1.44 0.76 130.5 71.6 49.5 0.14 0.26 0.38 0.271 0.49 0.71 0.64 1.17 0.95 0.73
2005 75.82 30.82 106.64 23.91 2.32 0.90 106.6 58.5 34.4 0.22 0.41 0.70 0.577 1.05 1.79 1.52 1.74 1.27 0.53
2006 146.83 10.47 157.31 20.32 1.44 0.76 157.3 86.3 57.5 0.13 0.24 0.35 0.244 0.44 0.67 0.64 1.20 1.00 0.77
2007 135.60 37.21 172.81 26.42 2.00 0.86 172.8 94.8 49.9 0.15 0.28 0.53 0.353 0.64 1.22 1.20 1.64 1.35 0.77
2008 35.25 23.44 58.69 58.7 32.2
mean 124.19 30.53 154.48 19.86 1.52 0.75 157.68 86.54 50.87 0.15 0.27 0.38 0.28 0.51 0.78 0.72 1.24 1.01 0.74
median 95.30 30.58 134.58 23.41 1.47 0.77 134.58 73.86 51.03 0.14 0.26 0.39 0.27 0.48 0.78 0.67 1.24 1.00 0.76
3 y mean 105.89 23.71 129.60 23.55 1.92 0.84 145.59 79.90 47.26 0.17 0.31 0.53 0.39 0.71 1.23 1.12 1.53 1.21 0.69
2 y mean 85.42 30.33 115.75 23.37 1.72 0.81 165.06 90.59 53.70 0.14 0.26 0.44 0.30 0.54 0.95 0.92 1.42 1.18 0.77
Min 14.71 9.02 28.62 3.26 0.50 0.40 28.62 15.71 18.39 0.04 0.08 0.14 0.08 0.14 0.23 -0.30 0.21 -0.23 0.12
Max 543.74 69.90 613.64 36.44 2.66 0.93 613.64 336.77 95.63 0.38 0.69 0.70 0.58 1.05 1.79 1.86 2.53 2.42 1.52
Stock Size (Millions) Sep 1
- 70 -
Figure 1. Delaware Bay blue crab size frequency distributions from research trawl survey.
0 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
0 20 40 60 80 100 120 140 160 180 200
1
10
100
10000 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
0 20 40 60 80 100 120 140 160 180 200
1
10
100
10000 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
0 20 40 60 80 100 120 140 160 180 200
1
10
100
10000 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
0 20 40 60 80 100 120 140 160 180 200
1
10
100
1000 Year=1979 Month=7
Year=1980 Month=5
Year=1980 Month=4
Year=1979 Month=8
Year=1979 Month=9
Year=1979 Month=10 Year=1980 Month=7
Year=1980 Month=6
Carapace Width (mm)
Log
10 F
requency
FIGURES
- 71 -
0 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
0 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
0 20 40 60 80 100 120 140 160 180 200
1
10
100
1000 0 20 40 60 80 100 120 140 160 180 200
1
10
100
1000 0 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
0 20 40 60 80 100 120 140 160 180 200
1
10
100
10000 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
0 20 40 60 80 100 120 140 160 180 200
1
10
100
1000
Year=1980 Month=8
Year=1980 Month=9
Year=1980 Month=10
Year=1981 Month=4
Year=1981 Month=5
Year=1981 Month=8
Year=1981 Month=7
Year=1981 Month=6
Carapace Width (mm)
Log
10 F
requency
Figure 1 (Continued).
- 72 -
Age (years)
0 1 2 3 4 5 6 7 8
Pred
icted
Car
apac
e W
idth
(mm
)
0
50
100
150
200
250
K=0.75 Lmax=234.7
K=0.62 Lmax=200.6
K=0.93 Lmax=200.3
Figure 2. Predicted growth trajectories derived from von Bertalanffy growth parameters estimatedby MULTIFAN applied to Delaware research trawl survey size frequency distributions.
0
50
100
150
200
250
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Age (yr)
Ca
rap
ace
Wid
th (
mm
)
Female 1
Female 2
Male 1
Male 2
Figure 3. Male and female seasonal growth curves estimated using a modified ELEFAN method in the
LFDA analysis.
- 73 -
BLUE CRAB MATURATION BY WIDTH
Width (mm)
60 70 80 90 100 110 120 130 140 150 160 170 180 190
Pro
port
ion F
em
ale
s M
atu
re
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
ObservedPredicted
n = 3869
0
1
2
3
4
5
6
19
73
19
75
19
77
19
79
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
20
03
20
05
20
07
Har
vest
kg
Mil
lio
ns
Delaware
New Jersey
Figure 4. Observed and predicted proportion of maturity by carapace width for Delaware Bay female blue
crabs. Predicted maturity was estimated using logistic regression applied to data from unculled at-sea
samples from the Delaware commercial fishery, 1995-1997.
Figure 5. Annual combined commercial and recreational landings weight of Delaware Bay blue crabs by
state.
R2 = 0.97
- 74 -
0%
5%
10%
15%
20%
25%
1 2 3 4 5 6 7 8 9 10 11 12
Lan
din
gs
Month
sook run
0
5
10
15
20
25
19
73
19
75
19
77
19
79
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
20
03
20
05
20
07
Mil
lio
ns
Males Females
Figure 6. Monthly commercial blue crab landings in Delaware from 1973 to 2008 based on fishermen
submitted logbook records.
Figure 7. Annual male and female Delaware and New Jersey total landings in numbers.
- 75 -
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
3,500,000
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Kilo
gra
ms
Logbooks Survey
_̂_̂_̂
_̂
_̂_̂
_̂_̂_̂
_̂̂_
_̂ _̂_̂_̂_̂̂_̂_
_̂_̂_̂_̂
_̂_̂_̂
_̂Maurice River
Mispillion River
Leipsic River
Delaware
New Jersey
_̂_̂̂_̂_̂_
_̂_̂
_̂
_̂_̂
_̂_̂_̂
_̂
_̂
_̂
26 Core Sites Used in Assessment
Supplemental Survey Sites
Figure 8. Annual DE landings calculated from the DDFW dockside intercept survey versus fishermen
submitted logbook reports.
Figure 9. Delaware
Division of Fish and
Wildlife Trawl Survey
stations.
- 76 -
0
10
20
30
40
50
60
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
Nu
mb
ers
(m
illi
on
s)
2004 Assessment
2004 (unexpanded NJ landings)
2005 Assessment
2006 Assessment
0
5
10
15
20
25
0 5 10 15 20 25
Model E
stim
ate
d R
ecru
its
Observed Recruits
Figure 10. Annual harvests calculated in 2004, 2005, and 2006 illustrating the effects of
methodological progressions in quantifying harvest.
Figure 11. Residual pattern of under-prediction of recruits in the assessment model as the
observed recruit index CPT increases.
- 77 -
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
-0.20 -0.10 0.00 0.10 0.20
Fu
ll-R
ec
ruit
Re
sid
ua
ls y
+1
Recruit Residuals y
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 5 10 15 20 25
Fu
ll R
ecru
it R
esid
uals
y+
1
Observed Recruits y
Figure 12. Residual pattern of over-prediction of full recruits in the year following high observed recruit
CPT.
Figure 13. Negative relationship between recruit residuals and full recruit residuals in the following year.
- 78 -
0
100
200
300
400
500
600
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Mil
lio
ns
Recruits
Full Recruits
Harvest
0
100
200
300
400
500
600
Mil
lio
ns
Recruits
median
Figure 14. Preferred-model estimates of recruit and full recruit abundance in relation to observed harvest
in numbers.
Figure 15. Preferred-model estimates of annual recruit abundance in numbers.
- 79 -
0
10
20
30
40
50
60
70
80M
illio
ns
Post-Recruits
median
0
2
4
6
8
10
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Mil
lio
ns
(k
g)
Full Recruit Biomass
Harvest
Median Harvest
Figure 16. Preferred-model estimates of annual full recruit abundance in numbers.
Figure 17. Preferred-model estimates of annual full recruit biomass (Sep 1) in relation to observed harvest
weight.
- 80 -
0.0
0.5
1.0
1.5
2.0
2.5
3.0
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
Ins
tan
tan
eo
us
To
tal M
ort
ali
ty R
ate
Z
Median
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 100 200 300 400 500 600
Ins
tan
tan
eo
us
To
tal M
ort
ali
ty R
ate
Z
Recruits x million
Figure 18. Estimates of annual instantaneous total mortality rate Z from the preferred-model PE0.1.
Figure 19. Estimates of Z shown as a function of annual recruit abundance from the preferred-model
PE0.1.
- 81 -
0
100
200
300
400
500
600
700
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Exp
loit
ab
le S
tock (
nu
mb
ers
x m
illi
on
)
Upper B
C-K
Lower B
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Exp
loit
ati
on
Rate
Upper Bound
Collie-Kruse
Lower Bound
Figure 20. Range of exploitable stock size estimates.
Figure 21. Range of annual exploitation rates.
- 82 -
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Fis
hin
g M
ort
ali
ty F
Upper Bound F Collie-Kruse F Lower Bound F
Frep
F0.1
Fmax
Figure 22. Range of annual fishing mortality rates generated from the catch equation derived from three
estimates of exploitable stock size.
- 83 -
0.0
1.0
2.0
3.0
4.0
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Geo
metr
ic M
ean
CP
T
Median
0
5
10
15
20
25
30
35
40
45
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
Geo
metr
ic M
ean
CP
T
Median
Figure 23. YOY index.
Figure 24. Index of Recruits (medium crabs).
- 84 -
0.0
0.4
0.8
1.2
1.6
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Geo
metr
ic M
ean
CP
T Median
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Ari
thm
eti
c M
ean
CP
T
Median
Figure 25. Index of Large Crabs.
Figure 26. Index of Spawners. Spawning stock is composed of males and females and expressed in
numbers.
- 85 -
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
Ari
thm
eti
c M
ean
CP
T (kg
)Index of SSB
SSB50 Threshold
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
0 10 20 30 40 50
Recru
its (
y+
1)
YOY Index (y)
Figure 27. Index of Spawning Stock Biomass. Spawning stock biomass is composed of females only.
Figure 28. Relationship between YOY abundance and recruit abundance in the following year.
- 86 -
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 10 20 30 40 50
Larg
e C
rab
s (
y+
2)
YOY Index (y)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
Sp
aw
ners
(y+
2)
YOY Index (y)
Figure 29. Relationship between YOY abundance and large crab abundance lagged 2 years.
Figure 30. Relationship between YOY abundance and spawning stock biomass lagged 2 years.
- 87 -
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 100 200 300 400 500 600
Natu
ral
Mo
rtali
ty R
ate
M
Recruits (millions)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14
Ind
ex o
f R
ecru
its, Y
+1
Index of Spawning Stock Biomass, Y
Low Recruitment SSB Threshold
2009 Predicted Recruitment
Figure 31. Stock Recruitment Model.
Figure 32. Post-hoc estimates of annual M (M = Z - F) as a function of model estimated recruit
abundance.
- 88 -
0.0
0.2
0.4
0.6
0.8
1.0
1.2
LB C-K UB
F
PE0.1 PE0.5 EW OE
Fmax
F0.1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Fis
hin
g M
ort
ali
ty F
Upper Bound F Collie-Kruse F Lower Bound F
Frep
F0.1
Fmax
Figure 33. Average annual F from 1978 to 2006 estimated from three different calculations of exploitation
rates (LB, C-K, UB), across four different error-weighting configurations of the combined-sex CSA model.
Figure 34. Annual upper bound, lower bound, Collie-Kruse F rates in relation to existing F-based
benchmarks (Frep, Fmax, F0.1).
- 89 -
APPENDIX I
MODEL ID: Delaware Bay Blue Crab 2009 combined-sex PE0.1
CSA Version 3.04
Input File: C:\NFT\CSA\2009\RW2009A.DAT
Date of Run: 10-NOV-2009 Time of Run: 11:41
Model Type: Both Process & Observed Error
Process Equation Uses Pope Approximation
Estimated Relative Abundance
Recruits
Year Observed Estimated Residual
1978 0.217941E+01 0.212683E+01 0.244197E-01
1979 0.132930E+01 0.128938E+01 0.304928E-01
1980 0.576796E+01 0.549307E+01 0.488314E-01
1981 0.203026E+01 0.191441E+01 0.587558E-01
1982 0.544537E+00 0.569207E+00 -0.443088E-01
1983 0.883960E+00 0.933150E+00 -0.541546E-01
1984 0.336139E+01 0.311217E+01 0.770345E-01
1985 0.796666E+01 0.707304E+01 0.118975E+00
1986 0.156224E+01 0.160461E+01 -0.267596E-01
1987 0.293568E+01 0.304204E+01 -0.355877E-01
1988 0.386117E+01 0.406525E+01 -0.515048E-01
1989 0.249684E+02 0.210345E+02 0.171448E+00
1990 0.738159E+00 0.845653E+00 -0.135950E+00
1991 0.473937E+01 0.488112E+01 -0.294714E-01
1992 0.373774E+01 0.368663E+01 0.137697E-01
1993 0.817442E+01 0.753893E+01 0.809294E-01
1994 0.112166E+02 0.101118E+02 0.103689E+00
1995 0.264047E+01 0.266025E+01 -0.746446E-02
1996 0.419989E+01 0.415006E+01 0.119364E-01
1997 0.145045E+02 0.128754E+02 0.119144E+00
1998 0.531590E+01 0.513741E+01 0.341539E-01
1999 0.941120E+01 0.857444E+01 0.931152E-01
2000 0.834660E+01 0.747137E+01 0.110776E+00
2001 0.354369E+01 0.333581E+01 0.604535E-01
2002 0.255559E+01 0.243676E+01 0.476150E-01
2003 0.377441E+01 0.356724E+01 0.564509E-01
2004 0.433794E+01 0.417564E+01 0.381331E-01
2005 0.330599E+01 0.293310E+01 0.119677E+00
2006 0.594498E+01 0.568027E+01 0.455483E-01
2007 0.576706E+01 0.524559E+01 0.947739E-01
2008 0.136358E+01 NA NA
Post-Recruits
Year Observed Estimated Residual
1978 0.350253E+00 0.348853E+00 0.400542E-02
1979 0.774146E+00 0.779855E+00 -0.734752E-02
1980 0.468615E+00 0.484104E+00 -0.325173E-01
1981 0.151377E+01 0.151746E+01 -0.243674E-02
1982 0.468927E+00 0.538061E+00 -0.137525E+00
1983 0.546902E+00 0.534491E+00 0.229544E-01
1984 0.964781E+00 0.887277E+00 0.837435E-01
1985 0.608828E+00 0.652211E+00 -0.688317E-01
1986 0.862671E+00 0.978448E+00 -0.125935E+00
1987 0.743671E+00 0.733848E+00 0.132973E-01
1988 0.150844E+01 0.149321E+01 0.101509E-01
1989 0.289848E+01 0.270393E+01 0.694795E-01
1990 0.106490E+01 0.166036E+01 -0.444153E+00
1991 0.131745E+01 0.117342E+01 0.115776E+00
1992 0.249288E+01 0.240914E+01 0.341668E-01
1993 0.145368E+01 0.145118E+01 0.172319E-02
1994 0.139246E+01 0.147650E+01 -0.586004E-01
1995 0.145867E+01 0.160725E+01 -0.970020E-01
1996 0.122760E+01 0.121470E+01 0.105612E-01
1997 0.150668E+01 0.150187E+01 0.319886E-02
1998 0.159025E+01 0.176532E+01 -0.104443E+00
1999 0.154572E+01 0.156894E+01 -0.149133E-01
2000 0.141523E+01 0.151553E+01 -0.684711E-01
2001 0.101673E+01 0.111090E+01 -0.885776E-01
2002 0.717219E+00 0.742191E+00 -0.342250E-01
- 90 -
2003 0.645218E+00 0.668548E+00 -0.355201E-01
2004 0.835094E+00 0.872078E+00 -0.433350E-01
2005 0.120972E+01 0.119221E+01 0.145805E-01
2006 0.367942E+00 0.405134E+00 -0.962932E-01
2007 0.142344E+01 0.143961E+01 -0.112983E-01
2008 0.831015E+00 0.906673E+00 -0.871335E-01
Process Error
Year Calculated Estimated Residual
1978 NA NA NA
1979 0.100930E+01 0.779855E+00 0.815567E-01
1980 0.699598E+00 0.484104E+00 0.116437E+00
1981 0.247722E+01 0.151746E+01 0.154982E+00
1982 0.140022E+01 0.538061E+00 0.302444E+00
1983 0.311558E+00 0.534491E+00 -0.170678E+00
1984 0.478352E+00 0.887277E+00 -0.195369E+00
1985 0.144866E+01 0.652211E+00 0.252357E+00
1986 0.292819E+01 0.978448E+00 0.346640E+00
1987 0.589620E+00 0.733848E+00 -0.691980E-01
1988 0.111654E+01 0.149321E+01 -0.919244E-01
1989 0.168254E+01 0.270393E+01 -0.150019E+00
1990 0.977021E+01 0.166036E+01 0.560452E+00
1991 0.343460E+00 0.117342E+01 -0.388519E+00
1992 0.187308E+01 0.240914E+01 -0.795901E-01
1993 0.166683E+01 0.145118E+01 0.438128E-01
1994 0.308663E+01 0.147650E+01 0.233189E+00
1995 0.405296E+01 0.160725E+01 0.292486E+00
1996 0.113182E+01 0.121470E+01 -0.223497E-01
1997 0.167146E+01 0.150187E+01 0.338326E-01
1998 0.564135E+01 0.176532E+01 0.367390E+00
1999 0.215959E+01 0.156894E+01 0.101039E+00
2000 0.376285E+01 0.151553E+01 0.287582E+00
2001 0.329454E+01 0.111090E+01 0.343771E+00
2002 0.120819E+01 0.742191E+00 0.154090E+00
2003 0.106009E+01 0.668548E+00 0.145780E+00
2004 0.145661E+01 0.872078E+00 0.162222E+00
2005 0.167606E+01 0.119221E+01 0.107720E+00
2006 0.109623E+01 0.405134E+00 0.314779E+00
2007 0.209061E+01 0.143961E+01 0.117979E+00
2008 0.216704E+01 0.906673E+00 0.275540E+00
Input Time of Survey = 0.0000
Input Time of Catch = 0.7500
Input Catchability Ratio
Year SRINIT
1978 1.0000
1979 1.0000
1980 1.0000
1981 1.0000
1982 1.0000
1983 1.0000
1984 1.0000
1985 1.0000
1986 1.0000
1987 1.0000
1988 1.0000
1989 1.0000
1990 1.0000
1991 1.0000
1992 1.0000
1993 1.0000
1994 1.0000
1995 1.0000
1996 1.0000
1997 1.0000
1998 1.0000
1999 1.0000
2000 1.0000
2001 1.0000
2002 1.0000
2003 1.0000
2004 1.0000
2005 1.0000
- 91 -
2006 1.0000
2007 1.0000
2008 1.0000
Catchability Coefficient
Initial Guess: 0.100000E-01
First Pass: 0.386849E-01
Minimum Bound 0.100000E-04
Maximum Bound 0.100000E+02
Post-Bootstrap: 0.047177
Normalized Sum of Squares = 0.336612E-01
Residual Sum of Squares = 0.215432E+01
Variance = 0.742869E-01
Standard Deviation = 0.272556E+00
Weighting Factors for Residuals
Recruits = 1.0000
Post-Recruits = 1.0000
Process Error = 0.1000
Population Estimates
Year Recruits Post-Recruits Total
1978 0.549785E+02 0.901781E+01 0.639963E+02
1979 0.333303E+02 0.201592E+02 0.534895E+02
1980 0.141995E+03 0.125140E+02 0.154509E+03
1981 0.494872E+02 0.392263E+02 0.887135E+02
1982 0.147140E+02 0.139088E+02 0.286228E+02
1983 0.241218E+02 0.138165E+02 0.379384E+02
1984 0.804493E+02 0.229360E+02 0.103385E+03
1985 0.182837E+03 0.168596E+02 0.199697E+03
1986 0.414790E+02 0.252928E+02 0.667718E+02
1987 0.786363E+02 0.189699E+02 0.976062E+02
1988 0.105086E+03 0.385992E+02 0.143686E+03
1989 0.543739E+03 0.698964E+02 0.613636E+03
1990 0.218601E+02 0.429201E+02 0.647802E+02
1991 0.126177E+03 0.303328E+02 0.156509E+03
1992 0.952989E+02 0.622762E+02 0.157575E+03
1993 0.194881E+03 0.375128E+02 0.232393E+03
1994 0.261390E+03 0.381673E+02 0.299557E+03
1995 0.687673E+02 0.415474E+02 0.110315E+03
1996 0.107279E+03 0.314000E+02 0.138679E+03
1997 0.332827E+03 0.388231E+02 0.371650E+03
1998 0.132801E+03 0.456335E+02 0.178435E+03
1999 0.221648E+03 0.405571E+02 0.262205E+03
2000 0.193134E+03 0.391762E+02 0.232310E+03
2001 0.862303E+02 0.287166E+02 0.114947E+03
2002 0.629899E+02 0.191856E+02 0.821755E+02
2003 0.922129E+02 0.172819E+02 0.109495E+03
2004 0.107940E+03 0.225431E+02 0.130483E+03
2005 0.758203E+02 0.308185E+02 0.106639E+03
2006 0.146834E+03 0.104727E+02 0.157307E+03
2007 0.135598E+03 0.372139E+02 0.172812E+03
2008 0.352484E+02 0.234374E+02 0.586858E+02
Biomass Estimates
Year Recruits Post-Recruits Total
1978 0.828674E+00 0.141963E+01 0.224830E+01
1979 0.723964E+00 0.289871E+01 0.362267E+01
1980 0.135524E+01 0.213768E+01 0.349293E+01
1981 0.743086E+00 0.566651E+01 0.640960E+01
1982 0.414076E+00 0.214428E+01 0.255836E+01
1983 0.269870E+00 0.243262E+01 0.270249E+01
1984 0.680936E+00 0.385339E+01 0.453433E+01
1985 0.579028E+00 0.284711E+01 0.342614E+01
1986 0.521963E+00 0.347002E+01 0.399198E+01
1987 0.209306E+00 0.262780E+01 0.283711E+01
1988 0.735140E+00 0.538671E+01 0.612185E+01
1989 0.305169E+01 0.965220E+01 0.127039E+02
1990 0.192042E+00 0.714834E+01 0.734039E+01
1991 0.648630E+00 0.607909E+01 0.672771E+01
1992 0.111848E+01 0.866971E+01 0.978819E+01
1993 0.515635E+00 0.588703E+01 0.640267E+01
- 92 -
1994 0.303633E+00 0.548541E+01 0.578904E+01
1995 0.122076E+00 0.550195E+01 0.562403E+01
1996 0.405133E+00 0.413368E+01 0.453881E+01
1997 0.176616E+01 0.506790E+01 0.683406E+01
1998 0.137653E+01 0.604999E+01 0.742652E+01
1999 0.101213E+01 0.549763E+01 0.650976E+01
2000 0.896546E+00 0.494702E+01 0.584356E+01
2001 0.815819E+00 0.417319E+01 0.498900E+01
2002 0.410776E+00 0.274421E+01 0.315498E+01
2003 0.541857E+00 0.258959E+01 0.313145E+01
2004 0.661260E+00 0.364719E+01 0.430845E+01
2005 0.475921E+00 0.451667E+01 0.499259E+01
2006 0.660338E+00 0.140995E+01 0.207029E+01
2007 0.692150E+00 0.495972E+01 0.565187E+01
2008 0.469262E+00 0.314799E+01 0.361726E+01
Catch Estimate
Year Landings Discards Total
Numbers Numbers Numbers
1978 0.325510E+01 0.000000E+00 0.325510E+01
1979 0.726712E+01 0.000000E+00 0.726712E+01
1980 0.658287E+01 0.000000E+00 0.658287E+01
1981 0.447772E+01 0.000000E+00 0.447772E+01
1982 0.587166E+01 0.000000E+00 0.587166E+01
1983 0.571796E+01 0.000000E+00 0.571796E+01
1984 0.110004E+02 0.000000E+00 0.110004E+02
1985 0.171438E+02 0.000000E+00 0.171438E+02
1986 0.180290E+02 0.000000E+00 0.180290E+02
1987 0.183147E+02 0.000000E+00 0.183147E+02
1988 0.257332E+02 0.000000E+00 0.257332E+02
1989 0.282940E+02 0.000000E+00 0.282940E+02
1990 0.247080E+02 0.000000E+00 0.247080E+02
1991 0.267550E+02 0.000000E+00 0.267550E+02
1992 0.338520E+02 0.000000E+00 0.338520E+02
1993 0.300856E+02 0.000000E+00 0.300856E+02
1994 0.364355E+02 0.000000E+00 0.364355E+02
1995 0.248069E+02 0.000000E+00 0.248069E+02
1996 0.233351E+02 0.000000E+00 0.233351E+02
1997 0.258505E+02 0.000000E+00 0.258505E+02
1998 0.297422E+02 0.000000E+00 0.297422E+02
1999 0.250964E+02 0.000000E+00 0.250964E+02
2000 0.234756E+02 0.000000E+00 0.234756E+02
2001 0.249377E+02 0.000000E+00 0.249377E+02
2002 0.116286E+02 0.000000E+00 0.116286E+02
2003 0.141022E+02 0.000000E+00 0.141022E+02
2004 0.186919E+02 0.000000E+00 0.186919E+02
2005 0.239130E+02 0.000000E+00 0.239130E+02
2006 0.203248E+02 0.000000E+00 0.203248E+02
2007 0.264210E+02 0.000000E+00 0.264210E+02
Catch Estimate
Year Landings Discards Total
Weight Weight Weight
1978 0.502986E+00 0.000000E+00 0.502986E+00
1979 0.112289E+01 0.000000E+00 0.112289E+01
1980 0.100474E+01 0.000000E+00 0.100474E+01
1981 0.715234E+00 0.000000E+00 0.715234E+00
1982 0.921771E+00 0.000000E+00 0.921771E+00
1983 0.893418E+00 0.000000E+00 0.893418E+00
1984 0.171114E+01 0.000000E+00 0.171114E+01
1985 0.261106E+01 0.000000E+00 0.261106E+01
1986 0.272870E+01 0.000000E+00 0.272870E+01
1987 0.271297E+01 0.000000E+00 0.271297E+01
1988 0.384398E+01 0.000000E+00 0.384398E+01
1989 0.425474E+01 0.000000E+00 0.425474E+01
1990 0.391463E+01 0.000000E+00 0.391463E+01
1991 0.389989E+01 0.000000E+00 0.389989E+01
1992 0.516320E+01 0.000000E+00 0.516320E+01
1993 0.450065E+01 0.000000E+00 0.450065E+01
1994 0.530062E+01 0.000000E+00 0.530062E+01
1995 0.379063E+01 0.000000E+00 0.379063E+01
1996 0.352826E+01 0.000000E+00 0.352826E+01
1997 0.386961E+01 0.000000E+00 0.386961E+01
1998 0.459136E+01 0.000000E+00 0.459136E+01
1999 0.393158E+01 0.000000E+00 0.393158E+01
2000 0.370390E+01 0.000000E+00 0.370390E+01
2001 0.391420E+01 0.000000E+00 0.391420E+01
- 93 -
2002 0.183239E+01 0.000000E+00 0.183239E+01
2003 0.223933E+01 0.000000E+00 0.223933E+01
2004 0.294258E+01 0.000000E+00 0.294258E+01
2005 0.377889E+01 0.000000E+00 0.377889E+01
2006 0.315360E+01 0.000000E+00 0.315360E+01
2007 0.412282E+01 0.000000E+00 0.412282E+01
Mortality Estimates
Year Total Natural Fishing
Mortality Mortality Mortality
1978 1.155165 0.800000 0.355165
1979 1.452634 0.800000 0.652634
1980 1.370908 0.800000 0.570908
1981 1.852888 0.800000 1.052888
1982 0.728336 0.800000 -0.071664
1983 0.503254 0.800000 -0.296746
1984 1.813544 0.800000 1.013544
1985 2.066282 0.800000 1.266282
1986 1.258428 0.800000 0.458428
1987 0.927709 0.800000 0.127709
1988 0.720613 0.800000 -0.079387
1989 2.660061 0.800000 1.860061
1990 0.758770 0.800000 -0.041230
1991 0.921537 0.800000 0.121537
1992 1.435220 0.800000 0.635220
1993 1.806452 0.800000 1.006452
1994 1.975471 0.800000 1.175471
1995 1.256530 0.800000 0.456530
1996 1.273142 0.800000 0.473142
1997 2.097311 0.800000 1.297311
1998 1.481514 0.800000 0.681514
1999 1.901058 0.800000 1.101058
2000 2.090599 0.800000 1.290599
2001 1.790313 0.800000 0.990313
2002 1.559197 0.800000 0.759197
2003 1.580446 0.800000 0.780446
2004 1.443127 0.800000 0.643127
2005 2.320677 0.800000 1.520677
2006 1.441518 0.800000 0.641518
2007 1.997871 0.800000 1.197871
Average Mortality (1978 - 2007)
Z F
1.521353 0.721353
Harvest Rate Estimates
Year Combined Landings Derived F
1978 0.926801E-01 0.926801E-01 0.143157
1979 0.247555E+00 0.247555E+00 0.430304
1980 0.776314E-01 0.776314E-01 0.118675
1981 0.919696E-01 0.919696E-01 0.141989
1982 0.373788E+00 0.373788E+00 0.729942
1983 0.274624E+00 0.274624E+00 0.488543
1984 0.193878E+00 0.193878E+00 0.322654
1985 0.156427E+00 0.156427E+00 0.252977
1986 0.491988E+00 0.491988E+00 1.098667
1987 0.341901E+00 0.341901E+00 0.646918
1988 0.326331E+00 0.326331E+00 0.608363
1989 0.840158E-01 0.840158E-01 0.128998
1990 0.694979E+00 0.694979E+00 2.184839
1991 0.311488E+00 0.311488E+00 0.572725
1992 0.391447E+00 0.391447E+00 0.778485
1993 0.235891E+00 0.235891E+00 0.406065
1994 0.221627E+00 0.221627E+00 0.377080
1995 0.409748E+00 0.409748E+00 0.830916
1996 0.306604E+00 0.306604E+00 0.561225
1997 0.126740E+00 0.126740E+00 0.200545
1998 0.303718E+00 0.303718E+00 0.554481
1999 0.174400E+00 0.174400E+00 0.285901
2000 0.184130E+00 0.184130E+00 0.304117
2001 0.395308E+00 0.395308E+00 0.789362
2002 0.257847E+00 0.257847E+00 0.452112
2003 0.234676E+00 0.234676E+00 0.403568
2004 0.261022E+00 0.261022E+00 0.458921
2005 0.408597E+00 0.408597E+00 0.827553
- 94 -
2006 0.235426E+00 0.235426E+00 0.405109
2007 0.278582E+00 0.278582E+00 0.497301
Surplus Production
Average Adjustment Factor (Delta) = 1.0000
Year Biomass Delta Biomass Catch Biomass Surplus Production
1978 2.248 1.374 0.503 1.877
1979 3.623 -0.130 1.123 0.993
1980 3.493 2.917 1.005 3.921
1981 6.410 -3.851 0.715 -3.136
1982 2.558 0.144 0.922 1.066
1983 2.702 1.832 0.893 2.725
1984 4.534 -1.108 1.711 0.603
1985 3.426 0.566 2.611 3.177
1986 3.992 -1.155 2.729 1.574
1987 2.837 3.285 2.713 5.998
1988 6.122 6.582 3.844 10.426
1989 12.704 -5.364 4.255 -1.109
1990 7.340 -0.613 3.915 3.302
1991 6.728 3.060 3.900 6.960
1992 9.788 -3.386 5.163 1.778
1993 6.403 -0.614 4.501 3.887
1994 5.789 -0.165 5.301 5.136
1995 5.624 -1.085 3.791 2.705
1996 4.539 2.295 3.528 5.824
1997 6.834 0.592 3.870 4.462
1998 7.427 -0.917 4.591 3.675
1999 6.510 -0.666 3.932 3.265
2000 5.844 -0.855 3.704 2.849
2001 4.989 -1.834 3.914 2.080
2002 3.155 -0.024 1.832 1.809
2003 3.131 1.177 2.239 3.416
2004 4.308 0.684 2.943 3.627
2005 4.993 -2.922 3.779 0.857
2006 2.070 3.582 3.154 6.735
2007 5.652 -2.035 4.123 2.088
2008 3.617
Levenburg-Marquadt NLLS Parameter Statistical Summary
Parameter Parameter Est. Std. Error CV
1 R 1978 0.212683E+01 0.557451E+00 0.262104E+00
2 R 1979 0.128938E+01 0.341290E+00 0.264693E+00
3 R 1980 0.549307E+01 0.143385E+01 0.261029E+00
4 R 1981 0.191441E+01 0.513205E+00 0.268075E+00
5 R 1982 0.569207E+00 0.150975E+00 0.265237E+00
6 R 1983 0.933150E+00 0.246206E+00 0.263843E+00
7 R 1984 0.311217E+01 0.814876E+00 0.261836E+00
8 R 1985 0.707304E+01 0.183254E+01 0.259088E+00
9 R 1986 0.160461E+01 0.414020E+00 0.258019E+00
10 R 1987 0.304204E+01 0.779789E+00 0.256338E+00
11 R 1988 0.406525E+01 0.105518E+01 0.259561E+00
12 R 1989 0.210345E+02 0.550246E+01 0.261593E+00
13 R 1990 0.845653E+00 0.225432E+00 0.266578E+00
14 R 1991 0.488112E+01 0.125698E+01 0.257518E+00
15 R 1992 0.368663E+01 0.965844E+00 0.261986E+00
16 R 1993 0.753893E+01 0.195227E+01 0.258959E+00
17 R 1994 0.101118E+02 0.261248E+01 0.258359E+00
18 R 1995 0.266025E+01 0.693727E+00 0.260775E+00
19 R 1996 0.415006E+01 0.107391E+01 0.258770E+00
20 R 1997 0.128754E+02 0.335313E+01 0.260430E+00
21 R 1998 0.513741E+01 0.133482E+01 0.259825E+00
22 R 1999 0.857444E+01 0.223384E+01 0.260523E+00
23 R 2000 0.747137E+01 0.194738E+01 0.260645E+00
24 R 2001 0.333581E+01 0.854945E+00 0.256293E+00
25 R 2002 0.243676E+01 0.634778E+00 0.260501E+00
26 R 2003 0.356724E+01 0.923496E+00 0.258882E+00
27 R 2004 0.417564E+01 0.107944E+01 0.258509E+00
28 R 2005 0.293310E+01 0.754890E+00 0.257370E+00
29 R 2006 0.568027E+01 0.145394E+01 0.255963E+00
30 R 2007 0.524559E+01 0.136020E+01 0.259303E+00
31 N 1978 0.348853E+00 0.949858E-01 0.272280E+00
32 N 1979 0.779855E+00 0.201475E+00 0.258349E+00
- 95 -
33 N 1980 0.484104E+00 0.126317E+00 0.260929E+00
34 N 1981 0.151746E+01 0.392241E+00 0.258485E+00
35 N 1982 0.538061E+00 0.137062E+00 0.254733E+00
36 N 1983 0.534491E+00 0.138352E+00 0.258847E+00
37 N 1984 0.887277E+00 0.230997E+00 0.260344E+00
38 N 1985 0.652211E+00 0.170176E+00 0.260921E+00
39 N 1986 0.978448E+00 0.250689E+00 0.256211E+00
40 N 1987 0.733848E+00 0.192091E+00 0.261759E+00
41 N 1988 0.149321E+01 0.388360E+00 0.260085E+00
42 N 1989 0.270393E+01 0.706685E+00 0.261355E+00
43 N 1990 0.166036E+01 0.397151E+00 0.239196E+00
44 N 1991 0.117342E+01 0.312519E+00 0.266332E+00
45 N 1992 0.240914E+01 0.619767E+00 0.257256E+00
46 N 1993 0.145118E+01 0.379209E+00 0.261312E+00
47 N 1994 0.147650E+01 0.385392E+00 0.261018E+00
48 N 1995 0.160725E+01 0.413547E+00 0.257300E+00
49 N 1996 0.121470E+01 0.316741E+00 0.260756E+00
50 N 1997 0.150187E+01 0.392549E+00 0.261374E+00
51 N 1998 0.176532E+01 0.458448E+00 0.259696E+00
52 N 1999 0.156894E+01 0.409585E+00 0.261058E+00
53 N 2000 0.151553E+01 0.395013E+00 0.260644E+00
54 N 2001 0.111090E+01 0.288182E+00 0.259414E+00
55 N 2002 0.742191E+00 0.193684E+00 0.260962E+00
56 N 2003 0.668548E+00 0.174360E+00 0.260805E+00
57 N 2004 0.872078E+00 0.227373E+00 0.260725E+00
58 N 2005 0.119221E+01 0.308753E+00 0.258975E+00
59 N 2006 0.405134E+00 0.106156E+00 0.262026E+00
60 N 2007 0.143961E+01 0.375160E+00 0.260598E+00
61 N 2008 0.906673E+00 0.237002E+00 0.261397E+00
62 Q 0.386849E-01 0.119542E-01 0.309015E+00
Model Type: Both Process & Observed Error
Error Type: Parametric Log-Normal Error With Bias
Number of Bootstraps: 2000
-- Non-Linear Least Squares Fit --
Maximum Monte-Carlo Iterations = 200
Scaled Gradient Tolerance = 0.3450E-03
Scaled Step Tolerance = 0.2420E-04
Relative Function Tolerance = 0.2420E-07
Absolute Function Tolerance = 0.1420E-13
Bootstrap Summary Report
Number of Bootstrap Repitions Requested = 2000
Number of Bootstrap Repititions Completed = 2000
Number of Bootstrap Repititions Not Converged = 0
Number of Bootstrap Repititions Infeasible F = 0
Bootstrap Output Variable: Recruit Abundance
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.549785E+02 0.478866E+02 0.146707E+02 0.306363E+00
1979 0.333303E+02 0.292157E+02 0.866799E+01 0.296690E+00
1980 0.141995E+03 0.121675E+03 0.366025E+02 0.300822E+00
1981 0.494872E+02 0.428053E+02 0.132450E+02 0.309423E+00
1982 0.147140E+02 0.137037E+02 0.401864E+01 0.293252E+00
1983 0.241218E+02 0.229276E+02 0.659457E+01 0.287625E+00
1984 0.804493E+02 0.677793E+02 0.203275E+02 0.299907E+00
1985 0.182837E+03 0.147534E+03 0.426079E+02 0.288800E+00
1986 0.414790E+02 0.380916E+02 0.100412E+02 0.263607E+00
1987 0.786363E+02 0.727584E+02 0.189899E+02 0.260999E+00
1988 0.105086E+03 0.100293E+03 0.276969E+02 0.276161E+00
1989 0.543739E+03 0.426339E+03 0.123478E+03 0.289623E+00
1990 0.218601E+02 0.211005E+02 0.602523E+01 0.285549E+00
1991 0.126177E+03 0.116941E+03 0.314751E+02 0.269154E+00
1992 0.952989E+02 0.854089E+02 0.231935E+02 0.271558E+00
1993 0.194881E+03 0.164358E+03 0.475953E+02 0.289583E+00
1994 0.261390E+03 0.216732E+03 0.638615E+02 0.294656E+00
1995 0.687673E+02 0.623417E+02 0.170113E+02 0.272872E+00
1996 0.107279E+03 0.952008E+02 0.275347E+02 0.289228E+00
1997 0.332827E+03 0.268220E+03 0.813312E+02 0.303225E+00
1998 0.132801E+03 0.117180E+03 0.332993E+02 0.284171E+00
- 96 -
1999 0.221648E+03 0.183104E+03 0.555609E+02 0.303439E+00
2000 0.193134E+03 0.158132E+03 0.477829E+02 0.302170E+00
2001 0.862303E+02 0.740453E+02 0.203571E+02 0.274927E+00
2002 0.629899E+02 0.540673E+02 0.155985E+02 0.288502E+00
2003 0.922129E+02 0.786274E+02 0.229186E+02 0.291484E+00
2004 0.107940E+03 0.938062E+02 0.276837E+02 0.295116E+00
2005 0.758203E+02 0.619646E+02 0.173248E+02 0.279593E+00
2006 0.146834E+03 0.128389E+03 0.359298E+02 0.279851E+00
2007 0.135598E+03 0.113158E+03 0.329183E+02 0.290906E+00
2008 0.352484E+02 0.295522E+02 0.462638E+01 0.156549E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 -0.7092E+01 0.3644E+00 -12.899373 0.6207E+02 0.2364E+00
1979 -0.4115E+01 0.2146E+00 -12.345013 0.3744E+02 0.2315E+00
1980 -0.2032E+02 0.9362E+00 -14.310564 0.1623E+03 0.2255E+00
1981 -0.6682E+01 0.3317E+00 -13.502405 0.5617E+02 0.2358E+00
1982 -0.1010E+01 0.9266E-01 -6.865993 0.1572E+02 0.2556E+00
1983 -0.1194E+01 0.1499E+00 -4.950862 0.2532E+02 0.2605E+00
1984 -0.1267E+02 0.5356E+00 -15.748978 0.9312E+02 0.2183E+00
1985 -0.3530E+02 0.1237E+01 -19.308393 0.2181E+03 0.1953E+00
1986 -0.3387E+01 0.2370E+00 -8.166450 0.4487E+02 0.2238E+00
1987 -0.5878E+01 0.4445E+00 -7.474824 0.8451E+02 0.2247E+00
1988 -0.4794E+01 0.6285E+00 -4.561720 0.1099E+03 0.2521E+00
1989 -0.1174E+03 0.3810E+01 -21.591297 0.6611E+03 0.1868E+00
1990 -0.7596E+00 0.1358E+00 -3.474616 0.2262E+02 0.2664E+00
1991 -0.9236E+01 0.7335E+00 -7.319665 0.1354E+03 0.2324E+00
1992 -0.9890E+01 0.5638E+00 -10.377910 0.1052E+03 0.2205E+00
1993 -0.3052E+02 0.1264E+01 -15.662242 0.2254E+03 0.2112E+00
1994 -0.4466E+02 0.1743E+01 -17.084537 0.3060E+03 0.2087E+00
1995 -0.6426E+01 0.4066E+00 -9.343971 0.7519E+02 0.2262E+00
1996 -0.1208E+02 0.6723E+00 -11.258345 0.1194E+03 0.2307E+00
1997 -0.6461E+02 0.2323E+01 -19.411372 0.3974E+03 0.2046E+00
1998 -0.1562E+02 0.8225E+00 -11.762704 0.1484E+03 0.2244E+00
1999 -0.3854E+02 0.1512E+01 -17.389845 0.2602E+03 0.2135E+00
2000 -0.3500E+02 0.1325E+01 -18.123011 0.2281E+03 0.2094E+00
2001 -0.1218E+02 0.5305E+00 -14.130742 0.9842E+02 0.2068E+00
2002 -0.8923E+01 0.4019E+00 -14.165215 0.7191E+02 0.2169E+00
2003 -0.1359E+02 0.5958E+00 -14.732791 0.1058E+03 0.2166E+00
2004 -0.1413E+02 0.6951E+00 -13.093947 0.1221E+03 0.2268E+00
2005 -0.1386E+02 0.4961E+00 -18.274366 0.8968E+02 0.1932E+00
2006 -0.1845E+02 0.9031E+00 -12.561966 0.1653E+03 0.2174E+00
2007 -0.2244E+02 0.8909E+00 -16.549045 0.1580E+03 0.2083E+00
2008 -0.5696E+01 0.1641E+00 -16.160064 0.4094E+02 0.1130E+00
Year 5. % Percentile 95. % Percentile
1978 0.286267E+02 0.750380E+02
1979 0.174700E+02 0.451571E+02
1980 0.724467E+02 0.187907E+03
1981 0.251921E+02 0.668098E+02
1982 0.840608E+01 0.213467E+02
1983 0.140707E+02 0.351199E+02
1984 0.407872E+02 0.104829E+03
1985 0.886915E+02 0.224939E+03
1986 0.246616E+02 0.567517E+02
1987 0.472130E+02 0.109296E+03
1988 0.646600E+02 0.152796E+03
1989 0.263140E+03 0.651616E+03
1990 0.125110E+02 0.320236E+02
1991 0.758971E+02 0.175376E+03
1992 0.544853E+02 0.126651E+03
1993 0.100279E+03 0.249133E+03
1994 0.131809E+03 0.333292E+03
1995 0.395424E+02 0.936470E+02
1996 0.601292E+02 0.147562E+03
1997 0.161742E+03 0.419784E+03
1998 0.731563E+02 0.178577E+03
1999 0.110335E+03 0.284314E+03
2000 0.932286E+02 0.244585E+03
2001 0.484813E+02 0.112123E+03
2002 0.333964E+02 0.826499E+02
2003 0.492243E+02 0.119556E+03
2004 0.575816E+02 0.146444E+03
- 97 -
2005 0.402105E+02 0.938528E+02
2006 0.800361E+02 0.194776E+03
2007 0.691867E+02 0.172502E+03
2008 0.234750E+02 0.380624E+02
Bootstrap Output Variable: Post-Recruit Abundance
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.901781E+01 0.813393E+01 0.253182E+01 0.311266E+00
1979 0.201592E+02 0.180822E+02 0.535190E+01 0.295975E+00
1980 0.125140E+02 0.114457E+02 0.358191E+01 0.312949E+00
1981 0.392263E+02 0.349955E+02 0.101525E+02 0.290108E+00
1982 0.139088E+02 0.139484E+02 0.378285E+01 0.271204E+00
1983 0.138165E+02 0.122001E+02 0.380176E+01 0.311618E+00
1984 0.229360E+02 0.191832E+02 0.601343E+01 0.313473E+00
1985 0.168596E+02 0.160452E+02 0.494374E+01 0.308113E+00
1986 0.252928E+02 0.254152E+02 0.706137E+01 0.277841E+00
1987 0.189699E+02 0.169218E+02 0.538372E+01 0.318154E+00
1988 0.385992E+02 0.342251E+02 0.106349E+02 0.310733E+00
1989 0.698964E+02 0.591359E+02 0.179328E+02 0.303246E+00
1990 0.429201E+02 0.500054E+02 0.853776E+01 0.170737E+00
1991 0.303328E+02 0.256234E+02 0.840874E+01 0.328167E+00
1992 0.622762E+02 0.546699E+02 0.161318E+02 0.295076E+00
1993 0.375128E+02 0.336555E+02 0.107759E+02 0.320183E+00
1994 0.381673E+02 0.361394E+02 0.112547E+02 0.311424E+00
1995 0.415474E+02 0.402078E+02 0.118233E+02 0.294054E+00
1996 0.314000E+02 0.279907E+02 0.866827E+01 0.309684E+00
1997 0.388231E+02 0.347859E+02 0.106540E+02 0.306275E+00
1998 0.456335E+02 0.443281E+02 0.131215E+02 0.296008E+00
1999 0.405571E+02 0.370269E+02 0.116677E+02 0.315114E+00
2000 0.391762E+02 0.370920E+02 0.112344E+02 0.302880E+00
2001 0.287166E+02 0.277724E+02 0.826480E+01 0.297591E+00
2002 0.191856E+02 0.177919E+02 0.577611E+01 0.324648E+00
2003 0.172819E+02 0.159274E+02 0.501933E+01 0.315138E+00
2004 0.225431E+02 0.211203E+02 0.662957E+01 0.313896E+00
2005 0.308185E+02 0.276112E+02 0.841529E+01 0.304778E+00
2006 0.104727E+02 0.101442E+02 0.343256E+01 0.338375E+00
2007 0.372139E+02 0.335104E+02 0.995321E+01 0.297019E+00
2008 0.234374E+02 0.228318E+02 0.741163E+01 0.324618E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 -0.8839E+00 0.5997E-01 -9.801518 0.9902E+01 0.2557E+00
1979 -0.2077E+01 0.1284E+00 -10.302679 0.2224E+02 0.2407E+00
1980 -0.1068E+01 0.8358E-01 -8.537149 0.1358E+02 0.2637E+00
1981 -0.4231E+01 0.2459E+00 -10.785586 0.4346E+02 0.2336E+00
1982 0.3952E-01 0.8459E-01 0.284166 0.1387E+02 0.2727E+00
1983 -0.1616E+01 0.9238E-01 -11.699591 0.1543E+02 0.2463E+00
1984 -0.3753E+01 0.1585E+00 -16.361980 0.2669E+02 0.2253E+00
1985 -0.8143E+00 0.1120E+00 -4.830113 0.1767E+02 0.2797E+00
1986 0.1224E+00 0.1579E+00 0.483830 0.2517E+02 0.2805E+00
1987 -0.2048E+01 0.1288E+00 -10.796641 0.2102E+02 0.2561E+00
1988 -0.4374E+01 0.2571E+00 -11.332043 0.4297E+02 0.2475E+00
1989 -0.1076E+02 0.4677E+00 -15.394839 0.8066E+02 0.2223E+00
1990 0.7085E+01 0.2481E+00 16.508185 0.3583E+02 0.2383E+00
1991 -0.4709E+01 0.2155E+00 -15.525870 0.3504E+02 0.2400E+00
1992 -0.7606E+01 0.3988E+00 -12.213786 0.6988E+02 0.2308E+00
1993 -0.3857E+01 0.2559E+00 -10.282524 0.4137E+02 0.2605E+00
1994 -0.2028E+01 0.2557E+00 -5.313214 0.4020E+02 0.2800E+00
1995 -0.1340E+01 0.2661E+00 -3.224133 0.4289E+02 0.2757E+00
1996 -0.3409E+01 0.2083E+00 -10.857615 0.3481E+02 0.2490E+00
1997 -0.4037E+01 0.2548E+00 -10.399041 0.4286E+02 0.2486E+00
1998 -0.1305E+01 0.2949E+00 -2.860478 0.4694E+02 0.2795E+00
1999 -0.3530E+01 0.2726E+00 -8.704106 0.4409E+02 0.2647E+00
2000 -0.2084E+01 0.2555E+00 -5.320094 0.4126E+02 0.2723E+00
2001 -0.9442E+00 0.1860E+00 -3.288141 0.2966E+02 0.2786E+00
2002 -0.1394E+01 0.1329E+00 -7.264053 0.2058E+02 0.2807E+00
2003 -0.1354E+01 0.1163E+00 -7.837539 0.1864E+02 0.2693E+00
2004 -0.1423E+01 0.1516E+00 -6.311781 0.2397E+02 0.2766E+00
2005 -0.3207E+01 0.2014E+00 -10.407095 0.3403E+02 0.2473E+00
2006 -0.3285E+00 0.7711E-01 -3.136281 0.1080E+02 0.3178E+00
2007 -0.3703E+01 0.2375E+00 -9.951867 0.4092E+02 0.2433E+00
- 98 -
2008 -0.6056E+00 0.1663E+00 -2.583756 0.2404E+02 0.3083E+00
Year 5. % Percentile 95. % Percentile
1978 0.483456E+01 0.126141E+02
1979 0.109687E+02 0.278404E+02
1980 0.653905E+01 0.177353E+02
1981 0.213309E+02 0.536100E+02
1982 0.872924E+01 0.207743E+02
1983 0.717332E+01 0.193676E+02
1984 0.113084E+02 0.304909E+02
1985 0.925141E+01 0.252718E+02
1986 0.157587E+02 0.387294E+02
1987 0.986766E+01 0.272322E+02
1988 0.200072E+02 0.534406E+02
1989 0.352182E+02 0.903981E+02
1990 0.371543E+02 0.645311E+02
1991 0.148879E+02 0.409789E+02
1992 0.326723E+02 0.844813E+02
1993 0.193712E+02 0.531146E+02
1994 0.211016E+02 0.571310E+02
1995 0.245169E+02 0.621994E+02
1996 0.165077E+02 0.439186E+02
1997 0.207304E+02 0.547576E+02
1998 0.270469E+02 0.688407E+02
1999 0.214809E+02 0.579127E+02
2000 0.223071E+02 0.579945E+02
2001 0.166131E+02 0.427418E+02
2002 0.101170E+02 0.284465E+02
2003 0.932091E+01 0.250219E+02
2004 0.124376E+02 0.333230E+02
2005 0.163719E+02 0.436430E+02
2006 0.563598E+01 0.159735E+02
2007 0.197358E+02 0.515705E+02
2008 0.133848E+02 0.369728E+02
Bootstrap Output Variable: Total Abundance
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.639963E+02 0.560205E+02 0.154840E+02 0.276399E+00
1979 0.534895E+02 0.472979E+02 0.112534E+02 0.237927E+00
1980 0.154509E+03 0.133121E+03 0.377478E+02 0.283561E+00
1981 0.887135E+02 0.778008E+02 0.186640E+02 0.239895E+00
1982 0.286228E+02 0.276521E+02 0.578458E+01 0.209192E+00
1983 0.379384E+02 0.351277E+02 0.830703E+01 0.236481E+00
1984 0.103385E+03 0.869626E+02 0.228880E+02 0.263194E+00
1985 0.199697E+03 0.163580E+03 0.442210E+02 0.270333E+00
1986 0.667718E+02 0.635068E+02 0.121047E+02 0.190604E+00
1987 0.976062E+02 0.896802E+02 0.205632E+02 0.229294E+00
1988 0.143686E+03 0.134518E+03 0.313848E+02 0.233314E+00
1989 0.613636E+03 0.485475E+03 0.128899E+03 0.265512E+00
1990 0.647802E+02 0.711059E+02 0.762403E+01 0.107221E+00
1991 0.156509E+03 0.142564E+03 0.342924E+02 0.240540E+00
1992 0.157575E+03 0.140079E+03 0.304377E+02 0.217290E+00
1993 0.232393E+03 0.198013E+03 0.520178E+02 0.262698E+00
1994 0.299557E+03 0.252872E+03 0.677153E+02 0.267785E+00
1995 0.110315E+03 0.102550E+03 0.215807E+02 0.210442E+00
1996 0.138679E+03 0.123191E+03 0.308210E+02 0.250188E+00
1997 0.371650E+03 0.303006E+03 0.850661E+02 0.280740E+00
1998 0.178435E+03 0.161509E+03 0.383947E+02 0.237726E+00
1999 0.262205E+03 0.220131E+03 0.600346E+02 0.272722E+00
2000 0.232310E+03 0.195224E+03 0.519709E+02 0.266211E+00
2001 0.114947E+03 0.101818E+03 0.235132E+02 0.230934E+00
2002 0.821755E+02 0.718592E+02 0.181634E+02 0.252763E+00
2003 0.109495E+03 0.945548E+02 0.249309E+02 0.263667E+00
2004 0.130483E+03 0.114926E+03 0.299107E+02 0.260259E+00
2005 0.106639E+03 0.895758E+02 0.215048E+02 0.240074E+00
2006 0.157307E+03 0.138533E+03 0.371620E+02 0.268253E+00
2007 0.172812E+03 0.146668E+03 0.366185E+02 0.249669E+00
2008 0.586858E+02 0.523841E+02 0.107651E+02 0.205502E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
- 99 -
1978 -0.7976E+01 0.3895E+00 -0.3547E+03 0.7197E+02 0.2151E+00
1979 -0.6192E+01 0.2872E+00 -0.1709E+03 0.5968E+02 0.1886E+00
1980 -0.2139E+02 0.9702E+00 -0.6123E+03 0.1759E+03 0.2146E+00
1981 -0.1091E+02 0.4835E+00 -0.1703E+03 0.9963E+02 0.1873E+00
1982 -0.9707E+00 0.1312E+00 -0.3794E+02 0.2959E+02 0.1955E+00
1983 -0.2811E+01 0.1961E+00 -0.1040E+03 0.4075E+02 0.2039E+00
1984 -0.1642E+02 0.6300E+00 -0.3622E+03 0.1198E+03 0.1910E+00
1985 -0.3612E+02 0.1277E+01 -0.1054E+04 0.2358E+03 0.1875E+00
1986 -0.3265E+01 0.2803E+00 -0.8179E+02 0.7004E+02 0.1728E+00
1987 -0.7926E+01 0.4928E+00 -0.2794E+03 0.1055E+03 0.1949E+00
1988 -0.9168E+01 0.7311E+00 -0.1498E+03 0.1529E+03 0.2053E+00
1989 -0.1282E+03 0.4065E+01 -0.1009E+04 0.7418E+03 0.1738E+00
1990 0.6326E+01 0.2215E+00 0.8618E+02 0.5845E+02 0.1304E+00
1991 -0.1395E+02 0.8278E+00 -0.2073E+03 0.1705E+03 0.2012E+00
1992 -0.1750E+02 0.7851E+00 -0.1787E+03 0.1751E+03 0.1739E+00
1993 -0.3438E+02 0.1394E+01 -0.5370E+03 0.2668E+03 0.1950E+00
1994 -0.4669E+02 0.1839E+01 -0.8064E+03 0.3462E+03 0.1956E+00
1995 -0.7765E+01 0.5129E+00 -0.1381E+03 0.1181E+03 0.1828E+00
1996 -0.1549E+02 0.7713E+00 -0.3412E+03 0.1542E+03 0.1999E+00
1997 -0.6864E+02 0.2444E+01 -0.1004E+04 0.4403E+03 0.1932E+00
1998 -0.1693E+02 0.9383E+00 -0.2279E+03 0.1954E+03 0.1965E+00
1999 -0.4207E+02 0.1639E+01 -0.6463E+03 0.3043E+03 0.1973E+00
2000 -0.3709E+02 0.1428E+01 -0.6346E+03 0.2694E+03 0.1929E+00
2001 -0.1313E+02 0.6022E+00 -0.2632E+03 0.1281E+03 0.1836E+00
2002 -0.1032E+02 0.4671E+00 -0.3270E+03 0.9249E+02 0.1964E+00
2003 -0.1494E+02 0.6499E+00 -0.4771E+03 0.1244E+03 0.2004E+00
2004 -0.1556E+02 0.7539E+00 -0.3611E+03 0.1460E+03 0.2048E+00
2005 -0.1706E+02 0.6139E+00 -0.3418E+03 0.1237E+03 0.1738E+00
2006 -0.1877E+02 0.9310E+00 -0.9068E+03 0.1761E+03 0.2111E+00
2007 -0.2614E+02 0.1006E+01 -0.4626E+03 0.1990E+03 0.1841E+00
2008 -0.6302E+01 0.2789E+00 -0.1742E+03 0.6499E+02 0.1656E+00
Year 5. % Percentile 95. % Percentile
1978 0.356443E+02 0.847245E+02
1979 0.317679E+02 0.675371E+02
1980 0.823243E+02 0.200361E+03
1981 0.521271E+02 0.111351E+03
1982 0.202894E+02 0.382856E+02
1983 0.241183E+02 0.503037E+02
1984 0.564350E+02 0.128179E+03
1985 0.102578E+03 0.244231E+03
1986 0.486778E+02 0.875123E+02
1987 0.627852E+02 0.129122E+03
1988 0.940558E+02 0.194387E+03
1989 0.313984E+03 0.715771E+03
1990 0.613487E+02 0.849577E+02
1991 0.974726E+02 0.208304E+03
1992 0.101472E+03 0.198913E+03
1993 0.128817E+03 0.291500E+03
1994 0.163010E+03 0.377174E+03
1995 0.749135E+02 0.142961E+03
1996 0.844129E+02 0.179707E+03
1997 0.191441E+03 0.463839E+03
1998 0.109801E+03 0.231440E+03
1999 0.142629E+03 0.330049E+03
2000 0.125338E+03 0.289022E+03
2001 0.722128E+02 0.145844E+03
2002 0.471062E+02 0.105902E+03
2003 0.628230E+02 0.139287E+03
2004 0.753817E+02 0.170456E+03
2005 0.627421E+02 0.129156E+03
2006 0.890124E+02 0.207331E+03
2007 0.985730E+02 0.214013E+03
2008 0.382215E+02 0.721383E+02
Bootstrap Output Variable: Recruit Biomass
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.828674E+00 0.721780E+00 0.221127E+00 0.306363E+00
1979 0.723964E+00 0.634590E+00 0.188276E+00 0.296690E+00
1980 0.135524E+01 0.116130E+01 0.349345E+00 0.300822E+00
1981 0.743086E+00 0.642751E+00 0.198882E+00 0.309423E+00
1982 0.414076E+00 0.385645E+00 0.113091E+00 0.293252E+00
- 100 -
1983 0.269870E+00 0.256510E+00 0.737787E-01 0.287625E+00
1984 0.680936E+00 0.573695E+00 0.172055E+00 0.299907E+00
1985 0.579028E+00 0.467227E+00 0.134935E+00 0.288800E+00
1986 0.521963E+00 0.479338E+00 0.126357E+00 0.263607E+00
1987 0.209306E+00 0.193660E+00 0.505452E-01 0.260999E+00
1988 0.735140E+00 0.701605E+00 0.193756E+00 0.276161E+00
1989 0.305169E+01 0.239279E+01 0.693008E+00 0.289623E+00
1990 0.192042E+00 0.185369E+00 0.529320E-01 0.285549E+00
1991 0.648630E+00 0.601152E+00 0.161803E+00 0.269154E+00
1992 0.111848E+01 0.100240E+01 0.272210E+00 0.271558E+00
1993 0.515635E+00 0.434875E+00 0.125933E+00 0.289583E+00
1994 0.303633E+00 0.251759E+00 0.741822E-01 0.294656E+00
1995 0.122076E+00 0.110670E+00 0.301987E-01 0.272872E+00
1996 0.405133E+00 0.359522E+00 0.103984E+00 0.289228E+00
1997 0.176616E+01 0.142333E+01 0.431589E+00 0.303225E+00
1998 0.137653E+01 0.121461E+01 0.345157E+00 0.284171E+00
1999 0.101213E+01 0.836123E+00 0.253712E+00 0.303439E+00
2000 0.896546E+00 0.734065E+00 0.221813E+00 0.302170E+00
2001 0.815819E+00 0.700538E+00 0.192597E+00 0.274927E+00
2002 0.410776E+00 0.352589E+00 0.101723E+00 0.288502E+00
2003 0.541857E+00 0.462026E+00 0.134673E+00 0.291484E+00
2004 0.661260E+00 0.574675E+00 0.169596E+00 0.295116E+00
2005 0.475921E+00 0.388949E+00 0.108747E+00 0.279593E+00
2006 0.660338E+00 0.577387E+00 0.161582E+00 0.279851E+00
2007 0.692150E+00 0.577606E+00 0.168029E+00 0.290906E+00
2008 0.469262E+00 0.393429E+00 0.615910E-01 0.156549E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 -0.1069E+00 0.5492E-02 -0.1290E+02 0.9356E+00 0.2364E+00
1979 -0.8937E-01 0.4660E-02 -0.1235E+02 0.8133E+00 0.2315E+00
1980 -0.1939E+00 0.8935E-02 -0.1431E+02 0.1549E+01 0.2255E+00
1981 -0.1003E+00 0.4981E-02 -0.1350E+02 0.8434E+00 0.2358E+00
1982 -0.2843E-01 0.2608E-02 -0.6866E+01 0.4425E+00 0.2556E+00
1983 -0.1336E-01 0.1677E-02 -0.4951E+01 0.2832E+00 0.2605E+00
1984 -0.1072E+00 0.4534E-02 -0.1575E+02 0.7882E+00 0.2183E+00
1985 -0.1118E+00 0.3919E-02 -0.1931E+02 0.6908E+00 0.1953E+00
1986 -0.4263E-01 0.2982E-02 -0.8166E+01 0.5646E+00 0.2238E+00
1987 -0.1565E-01 0.1183E-02 -0.7475E+01 0.2250E+00 0.2247E+00
1988 -0.3354E-01 0.4397E-02 -0.4562E+01 0.7687E+00 0.2521E+00
1989 -0.6589E+00 0.2138E-01 -0.2159E+02 0.3711E+01 0.1868E+00
1990 -0.6673E-02 0.1193E-02 -0.3475E+01 0.1987E+00 0.2664E+00
1991 -0.4748E-01 0.3771E-02 -0.7320E+01 0.6961E+00 0.2324E+00
1992 -0.1161E+00 0.6617E-02 -0.1038E+02 0.1235E+01 0.2205E+00
1993 -0.8076E-01 0.3345E-02 -0.1566E+02 0.5964E+00 0.2112E+00
1994 -0.5187E-01 0.2024E-02 -0.1708E+02 0.3555E+00 0.2087E+00
1995 -0.1141E-01 0.7219E-03 -0.9344E+01 0.1335E+00 0.2262E+00
1996 -0.4561E-01 0.2539E-02 -0.1126E+02 0.4507E+00 0.2307E+00
1997 -0.3428E+00 0.1233E-01 -0.1941E+02 0.2109E+01 0.2046E+00
1998 -0.1619E+00 0.8525E-02 -0.1176E+02 0.1538E+01 0.2244E+00
1999 -0.1760E+00 0.6905E-02 -0.1739E+02 0.1188E+01 0.2135E+00
2000 -0.1625E+00 0.6149E-02 -0.1812E+02 0.1059E+01 0.2094E+00
2001 -0.1153E+00 0.5019E-02 -0.1413E+02 0.9311E+00 0.2068E+00
2002 -0.5819E-01 0.2621E-02 -0.1417E+02 0.4690E+00 0.2169E+00
2003 -0.7983E-01 0.3501E-02 -0.1473E+02 0.6217E+00 0.2166E+00
2004 -0.8658E-01 0.4258E-02 -0.1309E+02 0.7478E+00 0.2268E+00
2005 -0.8697E-01 0.3114E-02 -0.1827E+02 0.5629E+00 0.1932E+00
2006 -0.8295E-01 0.4062E-02 -0.1256E+02 0.7433E+00 0.2174E+00
2007 -0.1145E+00 0.4548E-02 -0.1655E+02 0.8067E+00 0.2083E+00
2008 -0.7583E-01 0.2185E-02 -0.1616E+02 0.5451E+00 0.1130E+00
Year 5. % Percentile 95. % Percentile
1978 0.431482E+00 0.113102E+01
1979 0.379464E+00 0.980853E+00
1980 0.691453E+00 0.179344E+01
1981 0.378278E+00 0.100320E+01
1982 0.236561E+00 0.600732E+00
1983 0.157420E+00 0.392914E+00
1984 0.345229E+00 0.887291E+00
1985 0.280877E+00 0.712360E+00
1986 0.310336E+00 0.714152E+00
1987 0.125666E+00 0.290912E+00
1988 0.452334E+00 0.106890E+01
- 101 -
1989 0.147685E+01 0.365714E+01
1990 0.109910E+00 0.281329E+00
1991 0.390160E+00 0.901544E+00
1992 0.639466E+00 0.148644E+01
1993 0.265327E+00 0.659181E+00
1994 0.153110E+00 0.387155E+00
1995 0.701961E-01 0.166243E+00
1996 0.227076E+00 0.557264E+00
1997 0.858295E+00 0.222761E+01
1998 0.758287E+00 0.185100E+01
1999 0.503832E+00 0.129828E+01
2000 0.432775E+00 0.113538E+01
2001 0.458678E+00 0.106079E+01
2002 0.217788E+00 0.538985E+00
2003 0.289249E+00 0.702530E+00
2004 0.352756E+00 0.897144E+00
2005 0.252400E+00 0.589110E+00
2006 0.359935E+00 0.875940E+00
2007 0.353158E+00 0.880522E+00
2008 0.312522E+00 0.506724E+00
Bootstrap Output Variable: Post-Recruit Biomass
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.141963E+01 0.128048E+01 0.398571E+00 0.311266E+00
1979 0.289871E+01 0.260006E+01 0.769555E+00 0.295975E+00
1980 0.213768E+01 0.195519E+01 0.611873E+00 0.312949E+00
1981 0.566651E+01 0.505534E+01 0.146660E+01 0.290108E+00
1982 0.214428E+01 0.215038E+01 0.583191E+00 0.271204E+00
1983 0.243262E+01 0.214802E+01 0.669361E+00 0.311618E+00
1984 0.385339E+01 0.322290E+01 0.101029E+01 0.313473E+00
1985 0.284711E+01 0.270959E+01 0.834860E+00 0.308113E+00
1986 0.347002E+01 0.348681E+01 0.968778E+00 0.277841E+00
1987 0.262780E+01 0.234409E+01 0.745780E+00 0.318154E+00
1988 0.538671E+01 0.477629E+01 0.148415E+01 0.310733E+00
1989 0.965220E+01 0.816626E+01 0.247639E+01 0.303246E+00
1990 0.714834E+01 0.832841E+01 0.142196E+01 0.170737E+00
1991 0.607909E+01 0.513525E+01 0.168522E+01 0.328167E+00
1992 0.866971E+01 0.761081E+01 0.224577E+01 0.295076E+00
1993 0.588703E+01 0.528170E+01 0.169111E+01 0.320183E+00
1994 0.548541E+01 0.519395E+01 0.161752E+01 0.311424E+00
1995 0.550195E+01 0.532456E+01 0.156571E+01 0.294054E+00
1996 0.413368E+01 0.368486E+01 0.114114E+01 0.309684E+00
1997 0.506790E+01 0.454088E+01 0.139076E+01 0.306275E+00
1998 0.604999E+01 0.587693E+01 0.173962E+01 0.296008E+00
1999 0.549763E+01 0.501911E+01 0.158159E+01 0.315114E+00
2000 0.494702E+01 0.468383E+01 0.141864E+01 0.302880E+00
2001 0.417319E+01 0.403597E+01 0.120107E+01 0.297591E+00
2002 0.274421E+01 0.254487E+01 0.826187E+00 0.324648E+00
2003 0.258959E+01 0.238663E+01 0.752117E+00 0.315138E+00
2004 0.364719E+01 0.341698E+01 0.107258E+01 0.313896E+00
2005 0.451667E+01 0.404661E+01 0.123332E+01 0.304778E+00
2006 0.140995E+01 0.136573E+01 0.462129E+00 0.338375E+00
2007 0.495972E+01 0.446613E+01 0.132652E+01 0.297019E+00
2008 0.314799E+01 0.306666E+01 0.995493E+00 0.324618E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 -0.1391E+00 0.9440E-02 -0.9802E+01 0.1559E+01 0.2557E+00
1979 -0.2986E+00 0.1846E-01 -0.1030E+02 0.3197E+01 0.2407E+00
1980 -0.1825E+00 0.1428E-01 -0.8537E+01 0.2320E+01 0.2637E+00
1981 -0.6112E+00 0.3553E-01 -0.1079E+02 0.6278E+01 0.2336E+00
1982 0.6093E-02 0.1304E-01 0.2842E+00 0.2138E+01 0.2727E+00
1983 -0.2846E+00 0.1626E-01 -0.1170E+02 0.2717E+01 0.2463E+00
1984 -0.6305E+00 0.2663E-01 -0.1636E+02 0.4484E+01 0.2253E+00
1985 -0.1375E+00 0.1892E-01 -0.4830E+01 0.2985E+01 0.2797E+00
1986 0.1679E-01 0.2167E-01 0.4838E+00 0.3453E+01 0.2805E+00
1987 -0.2837E+00 0.1784E-01 -0.1080E+02 0.2912E+01 0.2561E+00
1988 -0.6104E+00 0.3589E-01 -0.1133E+02 0.5997E+01 0.2475E+00
1989 -0.1486E+01 0.6458E-01 -0.1539E+02 0.1114E+02 0.2223E+00
1990 0.1180E+01 0.4132E-01 0.1651E+02 0.5968E+01 0.2383E+00
1991 -0.9438E+00 0.4319E-01 -0.1553E+02 0.7023E+01 0.2400E+00
- 102 -
1992 -0.1059E+01 0.5552E-01 -0.1221E+02 0.9729E+01 0.2308E+00
1993 -0.6053E+00 0.4017E-01 -0.1028E+02 0.6492E+01 0.2605E+00
1994 -0.2915E+00 0.3675E-01 -0.5313E+01 0.5777E+01 0.2800E+00
1995 -0.1774E+00 0.3523E-01 -0.3224E+01 0.5679E+01 0.2757E+00
1996 -0.4488E+00 0.2742E-01 -0.1086E+02 0.4582E+01 0.2490E+00
1997 -0.5270E+00 0.3326E-01 -0.1040E+02 0.5595E+01 0.2486E+00
1998 -0.1731E+00 0.3909E-01 -0.2860E+01 0.6223E+01 0.2795E+00
1999 -0.4785E+00 0.3695E-01 -0.8704E+01 0.5976E+01 0.2647E+00
2000 -0.2632E+00 0.3226E-01 -0.5320E+01 0.5210E+01 0.2723E+00
2001 -0.1372E+00 0.2703E-01 -0.3288E+01 0.4310E+01 0.2786E+00
2002 -0.1993E+00 0.1900E-01 -0.7264E+01 0.2944E+01 0.2807E+00
2003 -0.2030E+00 0.1742E-01 -0.7838E+01 0.2793E+01 0.2693E+00
2004 -0.2302E+00 0.2453E-01 -0.6312E+01 0.3877E+01 0.2766E+00
2005 -0.4701E+00 0.2951E-01 -0.1041E+02 0.4987E+01 0.2473E+00
2006 -0.4422E-01 0.1038E-01 -0.3136E+01 0.1454E+01 0.3178E+00
2007 -0.4936E+00 0.3165E-01 -0.9952E+01 0.5453E+01 0.2433E+00
2008 -0.8134E-01 0.2233E-01 -0.2584E+01 0.3229E+01 0.3083E+00
Year 5. % Percentile 95. % Percentile
1978 0.761081E+00 0.198577E+01
1979 0.157721E+01 0.400320E+01
1980 0.111702E+01 0.302959E+01
1981 0.308139E+01 0.774435E+01
1982 0.134576E+01 0.320271E+01
1983 0.126298E+01 0.340998E+01
1984 0.189987E+01 0.512266E+01
1985 0.156230E+01 0.426770E+01
1986 0.216200E+01 0.531345E+01
1987 0.136692E+01 0.377233E+01
1988 0.279210E+01 0.745790E+01
1989 0.486339E+01 0.124833E+02
1990 0.618804E+01 0.107477E+02
1991 0.298373E+01 0.821271E+01
1992 0.454844E+01 0.117610E+02
1993 0.304000E+01 0.833548E+01
1994 0.303272E+01 0.821086E+01
1995 0.324668E+01 0.823682E+01
1996 0.217317E+01 0.578170E+01
1997 0.270611E+01 0.714794E+01
1998 0.358582E+01 0.912676E+01
1999 0.291180E+01 0.785025E+01
2000 0.281685E+01 0.732331E+01
2001 0.241426E+01 0.621137E+01
2002 0.144708E+01 0.406884E+01
2003 0.139668E+01 0.374937E+01
2004 0.201225E+01 0.539123E+01
2005 0.239942E+01 0.639619E+01
2006 0.758778E+00 0.215053E+01
2007 0.263031E+01 0.687311E+01
2008 0.179778E+01 0.496600E+01
Bootstrap Output Variable: Total Biomass
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.224830E+01 0.200226E+01 0.500742E+00 0.250088E+00
1979 0.362267E+01 0.323465E+01 0.836104E+00 0.258483E+00
1980 0.349293E+01 0.311649E+01 0.783805E+00 0.251503E+00
1981 0.640960E+01 0.569810E+01 0.153035E+01 0.268572E+00
1982 0.255836E+01 0.253602E+01 0.604917E+00 0.238530E+00
1983 0.270249E+01 0.240453E+01 0.689408E+00 0.286712E+00
1984 0.453433E+01 0.379660E+01 0.107528E+01 0.283222E+00
1985 0.342614E+01 0.317682E+01 0.881494E+00 0.277477E+00
1986 0.399198E+01 0.396615E+01 0.973295E+00 0.245401E+00
1987 0.283711E+01 0.253775E+01 0.755646E+00 0.297762E+00
1988 0.612185E+01 0.547789E+01 0.153054E+01 0.279403E+00
1989 0.127039E+02 0.105591E+02 0.272470E+01 0.258044E+00
1990 0.734039E+01 0.851378E+01 0.139644E+01 0.164022E+00
1991 0.672771E+01 0.573641E+01 0.172748E+01 0.301144E+00
1992 0.978819E+01 0.861322E+01 0.230806E+01 0.267968E+00
1993 0.640267E+01 0.571657E+01 0.173506E+01 0.303514E+00
1994 0.578904E+01 0.544571E+01 0.163871E+01 0.300918E+00
1995 0.562403E+01 0.543523E+01 0.156874E+01 0.288624E+00
1996 0.453881E+01 0.404438E+01 0.117090E+01 0.289513E+00
1997 0.683406E+01 0.596421E+01 0.157237E+01 0.263634E+00
- 103 -
1998 0.742652E+01 0.709154E+01 0.184684E+01 0.260429E+00
1999 0.650976E+01 0.585523E+01 0.167381E+01 0.285866E+00
2000 0.584356E+01 0.541790E+01 0.149420E+01 0.275791E+00
2001 0.498900E+01 0.473650E+01 0.125543E+01 0.265054E+00
2002 0.315498E+01 0.289745E+01 0.861733E+00 0.297410E+00
2003 0.313145E+01 0.284866E+01 0.803999E+00 0.282238E+00
2004 0.430845E+01 0.399166E+01 0.112372E+01 0.281517E+00
2005 0.499259E+01 0.443556E+01 0.127164E+01 0.286692E+00
2006 0.207029E+01 0.194311E+01 0.535787E+00 0.275736E+00
2007 0.565187E+01 0.504374E+01 0.137679E+01 0.272970E+00
2008 0.361726E+01 0.346009E+01 0.103224E+01 0.298328E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 -0.2460E+00 0.1248E-01 -0.1094E+02 0.2494E+01 0.2008E+00
1979 -0.3880E+00 0.2061E-01 -0.1071E+02 0.4011E+01 0.2085E+00
1980 -0.3764E+00 0.1944E-01 -0.1078E+02 0.3869E+01 0.2026E+00
1981 -0.7115E+00 0.3774E-01 -0.1110E+02 0.7121E+01 0.2149E+00
1982 -0.2234E-01 0.1354E-01 -0.8731E+00 0.2581E+01 0.2344E+00
1983 -0.2980E+00 0.1679E-01 -0.1103E+02 0.3000E+01 0.2298E+00
1984 -0.7377E+00 0.2916E-01 -0.1627E+02 0.5272E+01 0.2040E+00
1985 -0.2493E+00 0.2048E-01 -0.7277E+01 0.3675E+01 0.2398E+00
1986 -0.2584E-01 0.2177E-01 -0.6472E+00 0.4018E+01 0.2422E+00
1987 -0.2994E+00 0.1818E-01 -0.1055E+02 0.3136E+01 0.2409E+00
1988 -0.6440E+00 0.3713E-01 -0.1052E+02 0.6766E+01 0.2262E+00
1989 -0.2145E+01 0.7755E-01 -0.1688E+02 0.1485E+02 0.1835E+00
1990 0.1173E+01 0.4079E-01 0.1599E+02 0.6167E+01 0.2264E+00
1991 -0.9913E+00 0.4454E-01 -0.1473E+02 0.7719E+01 0.2238E+00
1992 -0.1175E+01 0.5792E-01 -0.1200E+02 0.1096E+02 0.2105E+00
1993 -0.6861E+00 0.4172E-01 -0.1072E+02 0.7089E+01 0.2448E+00
1994 -0.3433E+00 0.3744E-01 -0.5931E+01 0.6132E+01 0.2672E+00
1995 -0.1888E+00 0.3533E-01 -0.3357E+01 0.5813E+01 0.2699E+00
1996 -0.4944E+00 0.2842E-01 -0.1089E+02 0.5033E+01 0.2326E+00
1997 -0.8698E+00 0.4018E-01 -0.1273E+02 0.7704E+01 0.2041E+00
1998 -0.3350E+00 0.4197E-01 -0.4511E+01 0.7761E+01 0.2379E+00
1999 -0.6545E+00 0.4019E-01 -0.1005E+02 0.7164E+01 0.2336E+00
2000 -0.4257E+00 0.3474E-01 -0.7284E+01 0.6269E+01 0.2383E+00
2001 -0.2525E+00 0.2863E-01 -0.5061E+01 0.5242E+01 0.2395E+00
2002 -0.2575E+00 0.2011E-01 -0.8163E+01 0.3413E+01 0.2525E+00
2003 -0.2828E+00 0.1906E-01 -0.9031E+01 0.3414E+01 0.2355E+00
2004 -0.3168E+00 0.2611E-01 -0.7353E+01 0.4625E+01 0.2430E+00
2005 -0.5570E+00 0.3104E-01 -0.1116E+02 0.5550E+01 0.2291E+00
2006 -0.1272E+00 0.1231E-01 -0.6143E+01 0.2197E+01 0.2438E+00
2007 -0.6081E+00 0.3366E-01 -0.1076E+02 0.6260E+01 0.2199E+00
2008 -0.1572E+00 0.2335E-01 -0.4345E+01 0.3774E+01 0.2735E+00
Year 5. % Percentile 95. % Percentile
1978 0.130188E+01 0.287566E+01
1979 0.213595E+01 0.476247E+01
1980 0.205148E+01 0.455346E+01
1981 0.358273E+01 0.852908E+01
1982 0.173494E+01 0.361526E+01
1983 0.150953E+01 0.368021E+01
1984 0.238761E+01 0.580404E+01
1985 0.195964E+01 0.486552E+01
1986 0.267015E+01 0.578232E+01
1987 0.154226E+01 0.398710E+01
1988 0.342752E+01 0.827152E+01
1989 0.682151E+01 0.153060E+02
1990 0.643630E+01 0.109146E+02
1991 0.355517E+01 0.884973E+01
1992 0.550155E+01 0.128571E+02
1993 0.341647E+01 0.882654E+01
1994 0.325245E+01 0.851810E+01
1995 0.335680E+01 0.835624E+01
1996 0.249227E+01 0.618651E+01
1997 0.384446E+01 0.891979E+01
1998 0.465559E+01 0.105476E+02
1999 0.361676E+01 0.888379E+01
2000 0.342663E+01 0.816127E+01
2001 0.304246E+01 0.705550E+01
2002 0.173489E+01 0.449580E+01
2003 0.180971E+01 0.435973E+01
- 104 -
2004 0.251138E+01 0.607586E+01
2005 0.274122E+01 0.687970E+01
2006 0.124034E+01 0.289421E+01
2007 0.317954E+01 0.763694E+01
2008 0.214143E+01 0.543957E+01
Bootstrap Output Variable: Fishing Mortality
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.355165E+00 0.336667E+00 0.297424E+00 0.883436E+00
1979 0.652634E+00 0.638419E+00 0.277163E+00 0.434139E+00
1980 0.570908E+00 0.537802E+00 0.308995E+00 0.574551E+00
1981 0.105289E+01 0.926240E+00 0.275362E+00 0.297291E+00
1982 -0.716637E-01 0.427499E-01 0.268424E+00 0.627895E+01
1983 -0.296746E+00 -0.174996E+00 0.280108E+00 -0.160065E+01
1984 0.101354E+01 0.903018E+00 0.285394E+00 0.316045E+00
1985 0.126628E+01 0.106345E+01 0.298239E+00 0.280446E+00
1986 0.458428E+00 0.553440E+00 0.270513E+00 0.488785E+00
1987 0.127709E+00 0.184519E+00 0.276388E+00 0.149788E+01
1988 -0.793868E-01 0.407559E-01 0.276455E+00 0.678320E+01
1989 0.186006E+01 0.145384E+01 0.286048E+00 0.196753E+00
1990 -0.412298E-01 0.265054E+00 0.278429E+00 0.105046E+01
1991 0.121537E+00 0.172750E+00 0.280944E+00 0.162631E+01
1992 0.635220E+00 0.652455E+00 0.266240E+00 0.408059E+00
1993 0.100645E+01 0.914041E+00 0.283142E+00 0.309770E+00
1994 0.117547E+01 0.104626E+01 0.287703E+00 0.274982E+00
1995 0.456530E+00 0.522745E+00 0.258942E+00 0.495351E+00
1996 0.473142E+00 0.479958E+00 0.274593E+00 0.572118E+00
1997 0.129731E+01 0.112676E+01 0.303735E+00 0.269565E+00
1998 0.681514E+00 0.693093E+00 0.279392E+00 0.403109E+00
1999 0.110106E+01 0.989901E+00 0.288907E+00 0.291855E+00
2000 0.129060E+01 0.115872E+01 0.290618E+00 0.250810E+00
2001 0.990313E+00 0.969764E+00 0.277673E+00 0.286330E+00
2002 0.759197E+00 0.723431E+00 0.284935E+00 0.393866E+00
2003 0.780446E+00 0.713455E+00 0.287596E+00 0.403104E+00
2004 0.643127E+00 0.638036E+00 0.281301E+00 0.440886E+00
2005 0.152068E+01 0.140502E+01 0.272823E+00 0.194177E+00
2006 0.641518E+00 0.628049E+00 0.289490E+00 0.460935E+00
2007 0.119787E+01 0.107984E+01 0.294307E+00 0.272546E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 -0.1850E-01 0.6663E-02 -0.5208E+01 0.3737E+00 0.7960E+00
1979 -0.1422E-01 0.6206E-02 -0.2178E+01 0.6668E+00 0.4156E+00
1980 -0.3311E-01 0.6949E-02 -0.5799E+01 0.6040E+00 0.5116E+00
1981 -0.1266E+00 0.6778E-02 -0.1203E+02 0.1180E+01 0.2334E+00
1982 0.1144E+00 0.6525E-02 -0.1597E+03 -0.1861E+00 -0.1443E+01
1983 0.1217E+00 0.6830E-02 -0.4103E+02 -0.4185E+00 -0.6693E+00
1984 -0.1105E+00 0.6844E-02 -0.1090E+02 0.1124E+01 0.2539E+00
1985 -0.2028E+00 0.8066E-02 -0.1602E+02 0.1469E+01 0.2030E+00
1986 0.9501E-01 0.6411E-02 0.2073E+02 0.3634E+00 0.7444E+00
1987 0.5681E-01 0.6309E-02 0.4448E+02 0.7090E-01 0.3898E+01
1988 0.1201E+00 0.6741E-02 -0.1513E+03 -0.1995E+00 -0.1386E+01
1989 -0.4062E+00 0.1111E-01 -0.2184E+02 0.2266E+01 0.1262E+00
1990 0.3063E+00 0.9257E-02 -0.7429E+03 -0.3475E+00 -0.8012E+00
1991 0.5121E-01 0.6386E-02 0.4214E+02 0.7032E-01 0.3995E+01
1992 0.1723E-01 0.5966E-02 0.2713E+01 0.6180E+00 0.4308E+00
1993 -0.9241E-01 0.6660E-02 -0.9182E+01 0.1099E+01 0.2577E+00
1994 -0.1292E+00 0.7053E-02 -0.1099E+02 0.1305E+01 0.2205E+00
1995 0.6621E-01 0.5977E-02 0.1450E+02 0.3903E+00 0.6634E+00
1996 0.6816E-02 0.6142E-02 0.1441E+01 0.4663E+00 0.5888E+00
1997 -0.1706E+00 0.7790E-02 -0.1315E+02 0.1468E+01 0.2069E+00
1998 0.1158E-01 0.6253E-02 0.1699E+01 0.6699E+00 0.4170E+00
1999 -0.1112E+00 0.6922E-02 -0.1010E+02 0.1212E+01 0.2383E+00
2000 -0.1319E+00 0.7137E-02 -0.1022E+02 0.1422E+01 0.2043E+00
2001 -0.2055E-01 0.6226E-02 -0.2075E+01 0.1011E+01 0.2747E+00
2002 -0.3577E-01 0.6421E-02 -0.4711E+01 0.7950E+00 0.3584E+00
2003 -0.6699E-01 0.6603E-02 -0.8584E+01 0.8474E+00 0.3394E+00
2004 -0.5091E-02 0.6291E-02 -0.7916E+00 0.6482E+00 0.4340E+00
2005 -0.1157E+00 0.6626E-02 -0.7606E+01 0.1636E+01 0.1667E+00
2006 -0.1347E-01 0.6480E-02 -0.2100E+01 0.6550E+00 0.4420E+00
2007 -0.1180E+00 0.7091E-02 -0.9853E+01 0.1316E+01 0.2237E+00
- 105 -
Year 5. % Percentile 95. % Percentile
1978 -0.153434E+00 0.830322E+00
1979 0.181412E+00 0.109207E+01
1980 0.222595E-01 0.104113E+01
1981 0.477901E+00 0.138479E+01
1982 -0.400999E+00 0.481566E+00
1983 -0.637354E+00 0.290312E+00
1984 0.447107E+00 0.139022E+01
1985 0.568434E+00 0.153689E+01
1986 0.102911E+00 0.988847E+00
1987 -0.260139E+00 0.635599E+00
1988 -0.398175E+00 0.497893E+00
1989 0.991081E+00 0.192117E+01
1990 -0.190538E+00 0.723091E+00
1991 -0.290517E+00 0.634181E+00
1992 0.204520E+00 0.107669E+01
1993 0.427989E+00 0.136669E+01
1994 0.579353E+00 0.153000E+01
1995 0.904320E-01 0.947435E+00
1996 0.408959E-01 0.940752E+00
1997 0.647025E+00 0.162647E+01
1998 0.217060E+00 0.115643E+01
1999 0.513157E+00 0.145935E+01
2000 0.687618E+00 0.164581E+01
2001 0.519247E+00 0.143278E+01
2002 0.241965E+00 0.120313E+01
2003 0.253139E+00 0.118173E+01
2004 0.165762E+00 0.108038E+01
2005 0.950477E+00 0.185348E+01
2006 0.168402E+00 0.111522E+01
2007 0.609026E+00 0.157176E+01
Bootstrap Output Variable: Total Mortality
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.115517E+01 0.113667E+01 0.297424E+00 0.261663E+00
1979 0.145263E+01 0.143842E+01 0.277163E+00 0.192686E+00
1980 0.137091E+01 0.133780E+01 0.308995E+00 0.230972E+00
1981 0.185289E+01 0.172624E+01 0.275362E+00 0.159516E+00
1982 0.728336E+00 0.842750E+00 0.268424E+00 0.318510E+00
1983 0.503254E+00 0.625004E+00 0.280108E+00 0.448170E+00
1984 0.181354E+01 0.170302E+01 0.285394E+00 0.167581E+00
1985 0.206628E+01 0.186345E+01 0.298239E+00 0.160047E+00
1986 0.125843E+01 0.135344E+01 0.270513E+00 0.199871E+00
1987 0.927709E+00 0.984519E+00 0.276388E+00 0.280734E+00
1988 0.720613E+00 0.840756E+00 0.276455E+00 0.328817E+00
1989 0.266006E+01 0.225384E+01 0.286048E+00 0.126916E+00
1990 0.758770E+00 0.106505E+01 0.278429E+00 0.261423E+00
1991 0.921537E+00 0.972750E+00 0.280944E+00 0.288815E+00
1992 0.143522E+01 0.145245E+01 0.266240E+00 0.183303E+00
1993 0.180645E+01 0.171404E+01 0.283142E+00 0.165190E+00
1994 0.197547E+01 0.184626E+01 0.287703E+00 0.155830E+00
1995 0.125653E+01 0.132275E+01 0.258942E+00 0.195761E+00
1996 0.127314E+01 0.127996E+01 0.274593E+00 0.214533E+00
1997 0.209731E+01 0.192676E+01 0.303735E+00 0.157640E+00
1998 0.148151E+01 0.149309E+01 0.279392E+00 0.187123E+00
1999 0.190106E+01 0.178990E+01 0.288907E+00 0.161410E+00
2000 0.209060E+01 0.195872E+01 0.290618E+00 0.148372E+00
2001 0.179031E+01 0.176976E+01 0.277673E+00 0.156898E+00
2002 0.155920E+01 0.152343E+01 0.284935E+00 0.187035E+00
2003 0.158045E+01 0.151345E+01 0.287596E+00 0.190026E+00
2004 0.144313E+01 0.143804E+01 0.281301E+00 0.195615E+00
2005 0.232068E+01 0.220502E+01 0.272823E+00 0.123728E+00
2006 0.144152E+01 0.142805E+01 0.289490E+00 0.202717E+00
2007 0.199787E+01 0.187984E+01 0.294307E+00 0.156559E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 -0.1850E-01 0.6663E-02 -0.1601E+01 0.1174E+01 0.2534E+00
1979 -0.1422E-01 0.6206E-02 -0.9786E+00 0.1467E+01 0.1890E+00
- 106 -
1980 -0.3311E-01 0.6949E-02 -0.2415E+01 0.1404E+01 0.2201E+00
1981 -0.1266E+00 0.6778E-02 -0.6835E+01 0.1980E+01 0.1391E+00
1982 0.1144E+00 0.6525E-02 0.1571E+02 0.6139E+00 0.4372E+00
1983 0.1217E+00 0.6830E-02 0.2419E+02 0.3815E+00 0.7342E+00
1984 -0.1105E+00 0.6844E-02 -0.6094E+01 0.1924E+01 0.1483E+00
1985 -0.2028E+00 0.8066E-02 -0.9816E+01 0.2269E+01 0.1314E+00
1986 0.9501E-01 0.6411E-02 0.7550E+01 0.1163E+01 0.2325E+00
1987 0.5681E-01 0.6309E-02 0.6124E+01 0.8709E+00 0.3174E+00
1988 0.1201E+00 0.6741E-02 0.1667E+02 0.6005E+00 0.4604E+00
1989 -0.4062E+00 0.1111E-01 -0.1527E+02 0.3066E+01 0.9329E-01
1990 0.3063E+00 0.9257E-02 0.4037E+02 0.4525E+00 0.6153E+00
1991 0.5121E-01 0.6386E-02 0.5557E+01 0.8703E+00 0.3228E+00
1992 0.1723E-01 0.5966E-02 0.1201E+01 0.1418E+01 0.1878E+00
1993 -0.9241E-01 0.6660E-02 -0.5116E+01 0.1899E+01 0.1491E+00
1994 -0.1292E+00 0.7053E-02 -0.6541E+01 0.2105E+01 0.1367E+00
1995 0.6621E-01 0.5977E-02 0.5270E+01 0.1190E+01 0.2175E+00
1996 0.6816E-02 0.6142E-02 0.5354E+00 0.1266E+01 0.2168E+00
1997 -0.1706E+00 0.7790E-02 -0.8132E+01 0.2268E+01 0.1339E+00
1998 0.1158E-01 0.6253E-02 0.7816E+00 0.1470E+01 0.1901E+00
1999 -0.1112E+00 0.6922E-02 -0.5847E+01 0.2012E+01 0.1436E+00
2000 -0.1319E+00 0.7137E-02 -0.6308E+01 0.2222E+01 0.1308E+00
2001 -0.2055E-01 0.6226E-02 -0.1148E+01 0.1811E+01 0.1533E+00
2002 -0.3577E-01 0.6421E-02 -0.2294E+01 0.1595E+01 0.1786E+00
2003 -0.6699E-01 0.6603E-02 -0.4239E+01 0.1647E+01 0.1746E+00
2004 -0.5091E-02 0.6291E-02 -0.3528E+00 0.1448E+01 0.1942E+00
2005 -0.1157E+00 0.6626E-02 -0.4984E+01 0.2436E+01 0.1120E+00
2006 -0.1347E-01 0.6480E-02 -0.9344E+00 0.1455E+01 0.1990E+00
2007 -0.1180E+00 0.7091E-02 -0.5908E+01 0.2116E+01 0.1391E+00
Year 5. % Percentile 95. % Percentile
1978 0.646566E+00 0.163032E+01
1979 0.981412E+00 0.189207E+01
1980 0.822260E+00 0.184113E+01
1981 0.127790E+01 0.218479E+01
1982 0.399001E+00 0.128157E+01
1983 0.162646E+00 0.109031E+01
1984 0.124711E+01 0.219022E+01
1985 0.136843E+01 0.233689E+01
1986 0.902911E+00 0.178885E+01
1987 0.539861E+00 0.143560E+01
1988 0.401825E+00 0.129789E+01
1989 0.179108E+01 0.272117E+01
1990 0.609462E+00 0.152309E+01
1991 0.509483E+00 0.143418E+01
1992 0.100452E+01 0.187669E+01
1993 0.122799E+01 0.216669E+01
1994 0.137935E+01 0.233000E+01
1995 0.890432E+00 0.174744E+01
1996 0.840896E+00 0.174075E+01
1997 0.144702E+01 0.242647E+01
1998 0.101706E+01 0.195643E+01
1999 0.131316E+01 0.225935E+01
2000 0.148762E+01 0.244581E+01
2001 0.131925E+01 0.223278E+01
2002 0.104197E+01 0.200313E+01
2003 0.105314E+01 0.198173E+01
2004 0.965762E+00 0.188038E+01
2005 0.175048E+01 0.265348E+01
2006 0.968402E+00 0.191522E+01
2007 0.140903E+01 0.237176E+01
Bootstrap Output Variable: F Derived From Harvest Rate
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.143157E+00 0.179084E+00 0.511837E-01 0.285808E+00
1979 0.430304E+00 0.544287E+00 0.160207E+00 0.294342E+00
1980 0.118675E+00 0.151480E+00 0.458264E-01 0.302525E+00
1981 0.141989E+00 0.173944E+00 0.440343E-01 0.253151E+00
1982 0.729942E+00 0.830045E+00 0.231161E+00 0.278493E+00
1983 0.488543E+00 0.585001E+00 0.168011E+00 0.287198E+00
1984 0.322654E+00 0.433785E+00 0.135277E+00 0.311852E+00
1985 0.252977E+00 0.348788E+00 0.111124E+00 0.318600E+00
1986 0.109867E+01 0.131603E+01 0.387947E+00 0.294786E+00
1987 0.646918E+00 0.797624E+00 0.243907E+00 0.305792E+00
- 107 -
1988 0.608363E+00 0.726376E+00 0.213879E+00 0.294447E+00
1989 0.128998E+00 0.179050E+00 0.510553E-01 0.285145E+00
1990 0.218484E+01 0.184813E+01 0.395763E+00 0.214142E+00
1991 0.572725E+00 0.712788E+00 0.221723E+00 0.311064E+00
1992 0.778485E+00 0.102199E+01 0.319651E+00 0.312774E+00
1993 0.406065E+00 0.547630E+00 0.182068E+00 0.332465E+00
1994 0.377080E+00 0.512068E+00 0.166387E+00 0.324931E+00
1995 0.830916E+00 0.101971E+01 0.314847E+00 0.308763E+00
1996 0.561225E+00 0.726324E+00 0.231448E+00 0.318656E+00
1997 0.200545E+00 0.275094E+00 0.835300E-01 0.303641E+00
1998 0.554481E+00 0.694422E+00 0.217452E+00 0.313142E+00
1999 0.285901E+00 0.383740E+00 0.117966E+00 0.307412E+00
2000 0.304117E+00 0.408655E+00 0.127394E+00 0.311741E+00
2001 0.789362E+00 0.105985E+01 0.362093E+00 0.341646E+00
2002 0.452112E+00 0.589677E+00 0.190271E+00 0.322669E+00
2003 0.403568E+00 0.531538E+00 0.165241E+00 0.310874E+00
2004 0.458921E+00 0.595571E+00 0.193404E+00 0.324737E+00
2005 0.827553E+00 0.125263E+01 0.487412E+00 0.389112E+00
2006 0.405109E+00 0.524920E+00 0.173662E+00 0.330834E+00
2007 0.497301E+00 0.681298E+00 0.230507E+00 0.338334E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 0.3593E-01 0.1398E-02 0.2510E+02 0.1072E+00 0.4773E+00
1979 0.1140E+00 0.4397E-02 0.2649E+02 0.3163E+00 0.5065E+00
1980 0.3280E-01 0.1260E-02 0.2764E+02 0.8587E-01 0.5337E+00
1981 0.3196E-01 0.1217E-02 0.2251E+02 0.1100E+00 0.4002E+00
1982 0.1001E+00 0.5633E-02 0.1371E+02 0.6298E+00 0.3670E+00
1983 0.9646E-01 0.4332E-02 0.1974E+02 0.3921E+00 0.4285E+00
1984 0.1111E+00 0.3915E-02 0.3444E+02 0.2115E+00 0.6395E+00
1985 0.9581E-01 0.3281E-02 0.3787E+02 0.1572E+00 0.7070E+00
1986 0.2174E+00 0.9944E-02 0.1978E+02 0.8813E+00 0.4402E+00
1987 0.1507E+00 0.6411E-02 0.2330E+02 0.4962E+00 0.4915E+00
1988 0.1180E+00 0.5463E-02 0.1940E+02 0.4904E+00 0.4362E+00
1989 0.5005E-01 0.1599E-02 0.3880E+02 0.7895E-01 0.6467E+00
1990 -0.3367E+00 0.1162E-01 -0.1541E+02 0.2522E+01 0.1570E+00
1991 0.1401E+00 0.5865E-02 0.2446E+02 0.4327E+00 0.5125E+00
1992 0.2435E+00 0.8986E-02 0.3128E+02 0.5350E+00 0.5975E+00
1993 0.1416E+00 0.5157E-02 0.3486E+02 0.2645E+00 0.6883E+00
1994 0.1350E+00 0.4791E-02 0.3580E+02 0.2421E+00 0.6873E+00
1995 0.1888E+00 0.8209E-02 0.2272E+02 0.6421E+00 0.4903E+00
1996 0.1651E+00 0.6358E-02 0.2942E+02 0.3961E+00 0.5843E+00
1997 0.7455E-01 0.2504E-02 0.3717E+02 0.1260E+00 0.6630E+00
1998 0.1399E+00 0.5783E-02 0.2524E+02 0.4145E+00 0.5246E+00
1999 0.9784E-01 0.3427E-02 0.3422E+02 0.1881E+00 0.6273E+00
2000 0.1045E+00 0.3685E-02 0.3437E+02 0.1996E+00 0.6383E+00
2001 0.2705E+00 0.1011E-01 0.3427E+02 0.5189E+00 0.6978E+00
2002 0.1376E+00 0.5251E-02 0.3043E+02 0.3145E+00 0.6049E+00
2003 0.1280E+00 0.4674E-02 0.3171E+02 0.2756E+00 0.5996E+00
2004 0.1366E+00 0.5296E-02 0.2978E+02 0.3223E+00 0.6001E+00
2005 0.4251E+00 0.1446E-01 0.5137E+02 0.4025E+00 0.1211E+01
2006 0.1198E+00 0.4718E-02 0.2957E+02 0.2853E+00 0.6087E+00
2007 0.1840E+00 0.6596E-02 0.3700E+02 0.3133E+00 0.7357E+00
Year 5. % Percentile 95. % Percentile
1978 0.106243E+00 0.270618E+00
1979 0.326766E+00 0.849181E+00
1980 0.903503E-01 0.233268E+00
1981 0.111331E+00 0.252967E+00
1982 0.498773E+00 0.123343E+01
1983 0.348216E+00 0.896870E+00
1984 0.252547E+00 0.679871E+00
1985 0.202420E+00 0.556278E+00
1986 0.733472E+00 0.202854E+01
1987 0.453193E+00 0.125089E+01
1988 0.416454E+00 0.112257E+01
1989 0.109398E+00 0.266277E+00
1990 0.124312E+01 0.254285E+01
1991 0.402175E+00 0.112826E+01
1992 0.568660E+00 0.160856E+01
1993 0.311167E+00 0.878038E+00
1994 0.288652E+00 0.820683E+00
1995 0.583809E+00 0.158299E+01
- 108 -
1996 0.406961E+00 0.114150E+01
1997 0.157782E+00 0.426730E+00
1998 0.402485E+00 0.110392E+01
1999 0.220489E+00 0.593994E+00
2000 0.237322E+00 0.644921E+00
2001 0.571195E+00 0.172952E+01
2002 0.334378E+00 0.953820E+00
2003 0.304627E+00 0.827454E+00
2004 0.334051E+00 0.956652E+00
2005 0.635166E+00 0.217952E+01
2006 0.293571E+00 0.848987E+00
2007 0.383701E+00 0.107926E+01
Bootstrap Output Variable: Harvest Estimate
Year NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error Bootstrap
1978 0.926801E-01 0.113543E+00 0.297610E-01 0.262112E+00
1979 0.247555E+00 0.294861E+00 0.662948E-01 0.224834E+00
1980 0.776314E-01 0.971877E-01 0.271442E-01 0.279296E+00
1981 0.919696E-01 0.110673E+00 0.257339E-01 0.232522E+00
1982 0.373788E+00 0.402251E+00 0.765078E-01 0.190199E+00
1983 0.274624E+00 0.311879E+00 0.680181E-01 0.218091E+00
1984 0.193878E+00 0.245674E+00 0.616241E-01 0.250837E+00
1985 0.156427E+00 0.204774E+00 0.545152E-01 0.266221E+00
1986 0.491988E+00 0.533780E+00 0.893240E-01 0.167342E+00
1987 0.341901E+00 0.390040E+00 0.819452E-01 0.210094E+00
1988 0.326331E+00 0.365686E+00 0.770019E-01 0.210568E+00
1989 0.840158E-01 0.113529E+00 0.295644E-01 0.260413E+00
1990 0.694979E+00 0.639748E+00 0.624589E-01 0.976303E-01
1991 0.311488E+00 0.360097E+00 0.795094E-01 0.220800E+00
1992 0.391447E+00 0.458872E+00 0.891680E-01 0.194320E+00
1993 0.235891E+00 0.295096E+00 0.740213E-01 0.250838E+00
1994 0.221627E+00 0.280246E+00 0.704731E-01 0.251468E+00
1995 0.409748E+00 0.458537E+00 0.878284E-01 0.191541E+00
1996 0.306604E+00 0.364594E+00 0.822914E-01 0.225707E+00
1997 0.126740E+00 0.166975E+00 0.441915E-01 0.264659E+00
1998 0.303718E+00 0.353326E+00 0.786622E-01 0.222634E+00
1999 0.174400E+00 0.222103E+00 0.564632E-01 0.254221E+00
2000 0.184130E+00 0.233928E+00 0.595039E-01 0.254369E+00
2001 0.395308E+00 0.467368E+00 0.960561E-01 0.205526E+00
2002 0.257847E+00 0.312637E+00 0.748108E-01 0.239289E+00
2003 0.234676E+00 0.288950E+00 0.695519E-01 0.240706E+00
2004 0.261022E+00 0.314903E+00 0.760055E-01 0.241362E+00
2005 0.408597E+00 0.511408E+00 0.109286E+00 0.213695E+00
2006 0.235426E+00 0.285570E+00 0.724655E-01 0.253757E+00
2007 0.278582E+00 0.347526E+00 0.819302E-01 0.235753E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Year Estimate Std. Error Bias For Bias Estimate
1978 0.2086E-01 0.8128E-03 0.2251E+02 0.7182E-01 0.4144E+00
1979 0.4731E-01 0.1821E-02 0.1911E+02 0.2002E+00 0.3311E+00
1980 0.1956E-01 0.7481E-03 0.2519E+02 0.5808E-01 0.4674E+00
1981 0.1870E-01 0.7114E-03 0.2034E+02 0.7327E-01 0.3512E+00
1982 0.2846E-01 0.1825E-02 0.7615E+01 0.3453E+00 0.2216E+00
1983 0.3726E-01 0.1734E-02 0.1357E+02 0.2374E+00 0.2865E+00
1984 0.5180E-01 0.1800E-02 0.2672E+02 0.1421E+00 0.4337E+00
1985 0.4835E-01 0.1630E-02 0.3091E+02 0.1081E+00 0.5044E+00
1986 0.4179E-01 0.2205E-02 0.8494E+01 0.4502E+00 0.1984E+00
1987 0.4814E-01 0.2125E-02 0.1408E+02 0.2938E+00 0.2790E+00
1988 0.3936E-01 0.1934E-02 0.1206E+02 0.2870E+00 0.2683E+00
1989 0.2951E-01 0.9342E-03 0.3513E+02 0.5450E-01 0.5424E+00
1990 -0.5523E-01 0.1865E-02 -0.7947E+01 0.7502E+00 0.8326E-01
1991 0.4861E-01 0.2084E-02 0.1561E+02 0.2629E+00 0.3025E+00
1992 0.6743E-01 0.2500E-02 0.1722E+02 0.3240E+00 0.2752E+00
1993 0.5920E-01 0.2120E-02 0.2510E+02 0.1767E+00 0.4189E+00
1994 0.5862E-01 0.2050E-02 0.2645E+02 0.1630E+00 0.4323E+00
1995 0.4879E-01 0.2247E-02 0.1191E+02 0.3610E+00 0.2433E+00
1996 0.5799E-01 0.2251E-02 0.1891E+02 0.2486E+00 0.3310E+00
1997 0.4024E-01 0.1337E-02 0.3175E+02 0.8650E-01 0.5109E+00
1998 0.4961E-01 0.2080E-02 0.1633E+02 0.2541E+00 0.3096E+00
1999 0.4770E-01 0.1653E-02 0.2735E+02 0.1267E+00 0.4457E+00
2000 0.4980E-01 0.1735E-02 0.2704E+02 0.1343E+00 0.4430E+00
- 109 -
2001 0.7206E-01 0.2685E-02 0.1823E+02 0.3232E+00 0.2972E+00
2002 0.5479E-01 0.2074E-02 0.2125E+02 0.2031E+00 0.3684E+00
2003 0.5427E-01 0.1973E-02 0.2313E+02 0.1804E+00 0.3855E+00
2004 0.5388E-01 0.2083E-02 0.2064E+02 0.2071E+00 0.3669E+00
2005 0.1028E+00 0.3355E-02 0.2516E+02 0.3058E+00 0.3574E+00
2006 0.5014E-01 0.1971E-02 0.2130E+02 0.1853E+00 0.3911E+00
2007 0.6894E-01 0.2395E-02 0.2475E+02 0.2096E+00 0.3908E+00
Year 5. % Percentile 95. % Percentile
1978 0.698672E-01 0.166120E+00
1979 0.196019E+00 0.415941E+00
1980 0.598196E-01 0.145424E+00
1981 0.730552E-01 0.156421E+00
1982 0.279244E+00 0.527185E+00
1983 0.207070E+00 0.431685E+00
1984 0.156189E+00 0.354819E+00
1985 0.127825E+00 0.304488E+00
1986 0.375096E+00 0.674784E+00
1987 0.258352E+00 0.531477E+00
1988 0.240920E+00 0.498507E+00
1989 0.718455E-01 0.163748E+00
1990 0.529573E+00 0.733804E+00
1991 0.233997E+00 0.500040E+00
1992 0.309767E+00 0.607782E+00
1993 0.187855E+00 0.425540E+00
1994 0.175880E+00 0.406237E+00
1995 0.316152E+00 0.602991E+00
1996 0.236327E+00 0.503584E+00
1997 0.101520E+00 0.245850E+00
1998 0.234148E+00 0.493432E+00
1999 0.138189E+00 0.320399E+00
2000 0.147702E+00 0.341106E+00
2001 0.310841E+00 0.629243E+00
2002 0.199964E+00 0.449706E+00
2003 0.184400E+00 0.408563E+00
2004 0.199795E+00 0.450581E+00
2005 0.337207E+00 0.694328E+00
2006 0.178516E+00 0.415876E+00
2007 0.224916E+00 0.486603E+00
Bootstrap Output Variable: Catchability (Q)
NLLS Bootstrap Bootstrap C.V. For
Estimate Mean Std Error NLLS Soln.
0.3868E-01 0.4718E-01 0.6800E-02 0.1441E+00
NLLS
Estimate C.V. For
Bias Bias Per Cent Corrected Corrected
Estimate Std. Error Bias For Bias Estimate
0.8492E-02 0.2433E-03 0.2195E+02 0.3019E-01 0.2252E+00
5. % Percentile 95. % Percentile
0.357231E-01 0.579396E-01