Estimating natural chinook salmon production using tagged and marked hatchery releases as surrogates

8/6/2019 Estimating natural chinook salmon production using tagged and marked hatchery releases as surrogates

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Natural salmon production estimation. DRAFTNOT FOR CITATION, May 9, 2003 1

Estimating natural chinook salmon production using tagged and markedhatchery releases as surrogates

K.B. Newmana, A.C. Hicksa, and D.G. Hankinb

aDivision of Statistics, University of Idaho, Moscow, Idaho 83844, USA

bDepartment of Fisheries, Humboldt State University, Arcata, California, USA

May 9, 2003

The authors thank California Department of Fish and Game for financial support. We alsothank Lyman McDonald and Randy Bailey for helpful suggestions and Bailey Environmental andCH2M-Hill for financial support during earlier stages of this work.


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Abstract

Information about the abundance of naturally produced salmon is necessary for harvest man-

agement and for monitoring the status of endangered and threatened species. Tagging, marking,and recovering naturally produced stocks would be the most direct means of estimating abundanceof natural stocks. It is generally quite difficult, however, to capture large enough numbers of natu-rally produced fish, in particular of juveniles, to provide sufficiently precise information. Hatcheryproduced juvenile salmon, in contrast, are easily and relatively inexpensively marked and taggedin very large numbers. Assuming that some hatchery releases can serve as surrogates for natu-rally produced salmon, we develop tagging and marking schemes for hatchery releases along withstatistical procedures such that release and recovery data in combination with adult escapementdata can be used to estimate natural salmon abundances. Estimation procedures are developedfor the case of selective fisheries where adipose-clipped fish are harvested and unmarked fish arereturned to the water. Estimates of the delayed mortality of caught fish returned to the water are

also proposed. An interactive computer program, CFM Sim, was developed to simulate the lifehistory and sampling processes and to estimate life history parameters and measures of incidentalmortality. The program can be used to compare the effects on estimate quality for alternativemarking, tagging, and sampling rates.


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1 Introduction

Throughout California and the Pacific Northwest, stocks of naturally produced salmon are believed

to be in serious decline (Nehlsen et al. 1991). A wide variety of state and federal regulationsand recovery planning efforts are hoped to rebuild abundances of these natural stocks. For ex-ample, the Central Valley Project Improvement Act (CVPIA) mandates that natural productionof chinook salmon (Oncorhychus tshawytscha) doubles from each of the Sacramento-San Joaquinriver system watersheds relative to a 1967-1991 baseline abundance period (Public Law 102-575,Section 3406(b)(1)). Measures to increase natural production include those designed to improvehabitat conditions (restoration projects and changes in water management) and those intendedto improve harvest management for natural stocks. To reduce harvest impacts on natural stocksto levels more consistent with their underlying productivities, but still allow substantial harvestof abundant hatchery stocks, fishery managers have recently introduced mark-selective fisheries.In these fisheries, only marked hatchery fish may be retained whereas captured unmarked fish,

consisting of both hatchery and natural stocks, must be released. As Lawson and Sampson (1996)showed, a large number of factors determine whether or not the non-catch (hook and release) mor-tality suffered by unmarked fish in such selective fisheries will be substantially less than the fishingmortality rates on targeted marked hatchery fish. Non-catch mortality in intense selective fisheriesmay in some cases be large and will be very difficult to estimate.

The external mark relied upon in these mark selective fisheries has been an adipose fin clip.Since the mid-70s, it has been permissible to release hatchery fish with adipose fin clips only ifsuch fish also received coded-wire tags (CWT). Heightened interest in mark-selective fisheries hasresulted in the mass marking of large number of hatchery fish that have been released with adiposefin clips but without coded-wire tags, in conflict with the earlier rule that adipose fin clips shouldbe used only for hatchery fish receiving coded wire tags. Such desequestering of the adipose

fin clip results in substantial analytical complications with respect to how one might estimateimportant life history and fishery parameters based on returns of marked fish. Groups of codedwire-tagged hatchery salmon have been used routinely as surrogates, also known as indicator stocks(e.g., Shaul, et al. (2003)), for natural stocks by fishery management agencies. The suitability ofusing a hatchery stock as a surrogate for a natural stock has always been problematic in that itmay or may not be true that a hatchery surrogate group and the intended natural stock shareocean survival rates, migration paths, and maturation rates. With the advent of mass marking andselective fisheries, however, the fishing mortality rates on marked fish from surrogate groups thatare subject to selective fisheries are no longer equivalent those of natural stocks. Also, althoughthe adipose fin clip unambiguously identified a fish as of hatchery origin, the watershed of originremains unknown if the fish do not receive CWT.

In most river systems with significant production of hatchery chinook salmon, absence of orvariability in hatchery marking practices has made it extremely difficult or impossible to estimatethe separate contribution to production by natural and hatchery stocks (Hankin 1982). In thispaper, we propose several alternative general tagging and marking procedures for hatchery releasesand associated statistical procedures for estimating natural stock abundances, and we present ex-ample applications of these procedures to the Sacramento-San Joaquin river system where hatcheryfish and natural production originate from a large number of sources. For all alternatives, we as-sume that suitable releases of hatchery stocks have been identified as good surrogates for associatednatural stocks. We formulate marking (ad-clip), tagging (CWT), and estimation procedures forthree general situations: (a) no selective fisheries; (b) selective harvest in all marine and freshwa-


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ter fisheries; and (c) selective harvest in freshwater fisheries only. For selective fisheries cases, weexamine the use of recoveries of stealth hatchery fish - fish receiving CWT but not ad-clipped- as a device for estimating non-catch mortalities of natural stocks that may result from selective

fisheries; elsewhere, stealth fish have been called double-index tagged (SFEC 2002; Zhou 2002).

The structure of the remainder of our paper is as follows. In the next section, we introducenotation and a simplified sketch of chinook salmon life history. In section 3, we introduce someadditional definitions and notation along with four different marking and tagging schemes. Insection 4, we present statistical procedures for estimating natural stock abundances for the threegeneral harvest scenarios. In section 5, we discuss a computer program, CFM Sim, that allows usersto examine the effects of different marking, tagging, and recovery levels on the quality of abundanceestimates. We conclude with a discussion of how our procedures compare with other procedures,we consider the costs of implementing tagging and marking programs suitable for selective fisheries,and mention a more general state-space modeling framework for the interaction between salmonpopulation dynamics, harvest, and observations made on the stocks.

2 Chinook salmon life history sequence and notation

The following oversimplification of chinook salmon life history was assumed. Juvenile chinooksalmon leave freshwater and enter the ocean sometime during their first year (age 1). Next followsa sequence of binary events experienced by fish still alive at each point in time: overwinter survivalor not, harvest or not by the ocean fishery, maturation or not. If a fish matures, the next sequenceis harvest or not by a freshwater mainstem fishery, movement to a particular watershed, thenterminal harvest or not, then escapement to a hatchery (if one is present) or in-river escapement.For maturing fish, between the end of the ocean fishing period and the time the fish escape inland,

100% survival is assumed. If maturation is less than 100%, those fish not maturing repeat theabove cycle of overwinter survival, ocean harvest, and maturation. One oversimplification of thissequence is the omission of sex distinctions; for example, maturation probabilities are age-specificbut not sex-specific.

Our notation follows somewhat from Hankin and Healey (1986) and is summarized in Table1. The term stock is used to designate a particular hatchery release group or fish that are theprogeny of naturally spawning returns to a particular watershed. In this section the suffix i denotesa particular stock, but in later sections n and h will be used to distinguish natural and hatcherystocks.

Production of a stock is defined as the total catch and escapement of the stock in a given year,

which may or may not match with a single calendar year. Escapement includes all fish that returnto spawn, whether they stray from their natal stream or in the case of hatchery fish spawn in thewild. For estimation purposes we will later distinguish between in-river escapement (spawning inthe wild) and in-hatchery escapement (returning to a hatchery).

We use the term natural production to define the catch plus escapement of fish that derivesfrom wild fish and/or stray hatchery fish spawning naturally in streams and successfully generatingsurviving progeny. We use the term wild fish to refer to these surviving progeny, regardless ofparental origin, and we distinguish them from hatchery fish which are fish that were spawnedand reared at fish hatcheries rather than on natural spawning grounds.

Given the assumed sequence of events, the expected abundance at age a (Na) is a function of


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survival (S), harvest (), and maturation () rates; for example, assuming harvest begins at age 2,

E[Ni4] = RiSi0(1 O2)(1 2)S3(1 O3)(1 3)S4.

Conditional on the abundance at age a, Nia, the expected catches and escapements for age a fishare

E[COia] = NiaOa

E[CFia] = Nia(1 Oa)aFa

E[CTia] = Nia(1 Oa)a(1 Fa)k

j=1

ijTiaj

E[Eia] = Nia(1 Oa)a(1 Fa)k

j=1

ij(1 Tiaj)

where ij is the probability a stock i fish returns to watershed j.

Figure 1 contains schematic diagrams of the life history sequence for a single cohort, distin-guishing the marine phase and freshwater phase. The freshwater phase is oversimplified in thatonce a fish enters a terminal area or watershed, it is first vulnerable to a fishery (if one takesplace) and then escapes either to a hatchery or to the river.

3 Marking and tagging schemes and data collection needs

Each of the marking and tagging schemes is developed with current hatchery practices in mindalong with the need to generate particular kinds of data for estimating catch and escapement inthe presence or absence of selective fisheries. Hatchery practices will need to be modified to someextent, however, in that uniquely identifiable tag codes are needed for releases that are specifiedsurrogates for a particular natural stock. In general, releases from a hatchery will fall into one offive categories which are denoted by the subscripts a, b, c, d, and e. The five release categories are:

Ad hoc releases, a: these fish are not assumed to represent natural fish, e.g., experimentalreleases, and are internally tagged with CWT and adipose-clipped. There are no restrictionson the numbers in this group and multiple CWT codes can be used.

Surrogate releases, b: these fish are assumed to have the same natural survival rates, migrationpaths, fisheries vulnerability (in non-selective fisheries), and maturation probabilities as a

designated natural stock. These fish are marked and tagged and the CWT code must beunique for later identification.

CFM releases, c: fish that are CWTd and adipose-clipped and are a constant fraction, f,of a larger group of releases (Hankin 1982). This larger group (CFM and Remainder) maybe a mixture of types of releases, fingerlings or yearlings, for example, and include so-calledproduction releases. The CWT codes need to be unique, however, for each of the subgroupsin the mixture if inferences about the subgroups are desired.

Remainder releases, d: fish that are not CWTd and may or may not receive an adipose-clip.They are the complement of the CFM releases, i.e., the remainder is a constant fraction, 1- f,of a larger group of releases.


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Stealth releases, e: fish that are CWTd but not marked and assumed to be biologicallyequivalent to the Surrogate release (thus represent the same natural stock as the Surrogates).These fish are assumed to have the same straying rates (if any) as the natural stock. The

CWT code needs to be unique.

The combination ofSurrogate and Stealthreleases have been called Double Index Tag (DIT) releaseselsewhere (SFEC 2002; Zhou 2002), and we discuss this related work in Section 6 .

In the next section we discuss procedures for estimating production under different marking andtagging schemes and fisheries combinations. The different fisheries situations, referred to previously,are no selective fisheries (NS), all fisheries are selective (AS), and only freshwater mainstem andterminal area fisheries are selective (FS). With each fisheries situation, two different marking andtagging schemes are considered. For the no selective fisheries case, the two schemes, labelled NS1and NS2, differ in that in the former case all Remainder fish receive an adipose-clip and in thelatter case none of the Remainder fish are marked (and none are tagged). Also, under NS1 andNS2 there are no Stealth releases. For both selective fisheries cases, the schemes are labelled AS1,AS2, FS1, and FS2, where, like the NS case, all Remainder fish are adipose-clipped under AS1 andFS1, while all Remainder fish are unmarked under AS2 and FS2.

For estimation purposes, some fish recovered in catch and escapement samples will have tobe scanned or wanded to detect CWTs. Under all tagging and marking schemes and all fisheriesscenarios, the estimation procedures assume that adipose-clipped fish will be scanned for tags. Weassume that when a CWT is detected, the fish head will be removed and the CWT will be extractedand read, recognizing the possibility of false positives and false negatives (see Vander Haegen, et al.(2002) for scanning difficulties, especially with large chinook salmon). Whether or not fish withoutadipose-clips are scanned varies with the marking and tagging scheme, the fisheries situation, and

whether the sample is from a catch or from escapement.For reference purposes the different marking and tagging schemes are summarized in Table 2.

Table 3 summarizes the CWT scanning protocol and whether or not aging is of unmarked fish insamples is necessary.

4 Production estimates

Different estimation procedures are described for the six different marking, tagging, and harvestcombinations (Table 2). The underlying basis for the estimation procedures is a combinationof simple random sample mean expansions (Cochran 1977) and a method of moments approach

(Mood, Graybill, and Boes 1974).

The estimation procedures are oversimplified in that we ignore the details of how total ocean,freshwater mainstem, and terminal area catches and watershed-specific escapement are estimated.To some degree the particulars of estimating these values are not important in that the pointestimates of stock specific production will be calculated the same way given such estimates of totals.Simple random samples (SRS) are assumed for the sampling of both harvest and escapement. Thusall temporal (and spatial) stratification is ignored. In the case of harvest, SRSs of sizes nO, nF,and nTj are taken from the total ocean, freshwater, and terminal area j catches, CO, CF, and CTj .Likewise for escapement, a SRS of size nEj is taken from the total escapement to watershed j,denoted Ej. Or in the case of a hatchery being present in a watershed, SRSs of size nEj, and


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nEj, are taken from the in-river and in-hatchery escapements.

This oversimplification is disadvantageous in that the precision of catch data may be underes-timated compared to the stratified samples typically taken from ocean fisheries. For escapementestimation, it is difficult to say what the actual precision is, or will be, but some degree of stratifi-cation would likely be done. Conversely, the oversimplification is advantageous in that the essentialdifferences in estimation procedures for different marking and tagging alternatives are more appar-ent.

While hatchery fish may stray to other watersheds, for estimation purposes we assume thatnatural fish do not. Thus the natural fish sampled from the terminal catch and escapement areassumed native to that watershed. This assumption can be relaxed but the estimation becomesmore complicated.

Finally, while we assume that the Surrogate and Stealthreleases are biologically identical, naturalfish can differ from both groups in one important regard. The initial survival rates from time of

release to age 2 can differ between the natural fish and the Surrogate and Stealth fish. Ourestimation procedures lead to a convenient cancellation of the Surrogate or Stealth initial survivalrates.

Table 4 contains some of the notation used in the estimation equations.

4.1 NS1

For this situation there is no selective fishery, there are no Stealth releases, and all Remainder fishare adipose-clipped. Thus all hatchery releases are receiving at least an adipose clip.

NS1: Hatchery specific production

For hatchery i releases, the estimates of total catches in the ocean, freshwater, and terminal areafisheries are simple mean expansion estimates assuming simple random samples are taken from eachfishery. Letting CO, CF, and CTj be estimates of the total non-stock specific catches, and letting x,y, and t refer to sample recoveries in ocean, freshwater mainstem, and terminal area catches withadditional subscripting for the hatchery release group categories (a, b, and c),

COhi =

COnO

xai + xbi +

xcif

(1)

CFhi = CFnF

yai + ybi + ycif (2)

CThi = kj=1

CTjnTj

taij + tbij +

tcijf

. (3)

Recall that f is the constant fraction marking fraction; this fraction could in practice vary betweenhatcheries and would then be denoted fi.

For escapement estimation it is assumed that hatchery fish can return to any watershed (inaddition to the one the natal hatchery is located in). The escapement to any watershed is estimatedin a similar manner as harvest. The escapement of hatchery stock i is the sum ofk watershed specific


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escapement estimates. The subscripts and refer to fish that escaped either in-river or in-hatchery, respectively. Letting z denote escapement sample recoveries with additional subscripting and and hatchery release group categories,

Ehi, = kj=1

Ej,nEj,

zaij, + zbij, +

zcij,f

(4)

Ehi, = kj=1

Ej,nEj,

zaij, + zbij, +

zcij,f

. (5)

The total escapement is simply the sum of the in-river and in-hatchery escapements.

Ehi = Ehi, + Ehi, (6)NS1: Watershed specific natural production

The natural escapement and terminal area catch are estimated first, and then the catches of naturalstocks in the ocean and freshwater are estimated with a method of moments style estimator basedon the escapement estimates. Recall the assumption that natural fish from watershed j do notstray to other watersheds, and the same holds for other natural stocks. Because all hatchery fishhave at least an ad-clip, any fish in the in-river escapement without an ad-clip is a natural fish. Lettnj , znj,, and znj, be the number of unclipped fish, thus natural fish, observed in the samplestaken from the terminal area j catch, watershed j in-river escapement sample, and watershed jin-hatchery escapement sample (equalling zero in the absence of a hatchery), respectively. Thenthe estimates of terminal catch and natural escapement to watershed j are

CTnj = CTjnTj

tnj (7)

Enj = Ej,nEj,

znj, +Ej,nEj,

znj, (8)

The ocean and freshwater mainstem catches of natural stock j are estimated using the recoveriesof the Surrogate group and the estimated escapement for both the natural and the Surrogate group.The ages of recoveries of natural and hatchery Surrogate fish need to be known because of variationbetween cohorts in the number of Surrogate fish released, in natural stock outmigration numbers,and in survival, maturation, and harvest rates. Let the Surrogate group come from hatchery iand denote the age specific recoveries with an additional subscript a for age a. The ocean andfreshwater catches of natural stock j are estimated as follows.

COnj = 5a=2

COnO

xbia

CTnja + Enjakj=1

CTjnTj

tbija +Ej,nEj,

zbija, +Ej,nEj,

zbija,

(9)CFnj = 5

a=2

CFnF

ybia

CTnja + Enjakj=1

CTjnTj

tbija +Ej,nEj,

zbija, +Ej,nEj,

zbija,

(10)


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where

CTnja =

CTnj pTnja (11)

Enja = Enj,pnja, + Enj,pnja,. (12)The estimated percentage of age a natural fish in the terminal catch, the in-river escapement, andthe in-hatchery escapement is denoted pTnja, pnja, and pnja,. These estimates are assumed basedupon scale samples taken from subsamples of recoveries of unclipped fish, namely subsamples oftnj , znj,, and znj,. Letting nT(age)j, nE(age)j,, and nE(age)j, be the size of samples taken fromtnj , znj,, and znj,, and vnja, wnja,, and wnja, are the respective number of natural fish in theaging subsamples identified as age a,

pTnja =vnja

nT(age)jpnja, =

wnja,nE(age)j,

pnja, =wnja,

nE(age)j,(13)

nT(age)j

=5

a=2 vnja nE(age)j, = 5a=2 wnja, nE(age)j, =5

a=2 wnja, (14)The intuition behind the estimates of COnj and CFnj can be seen by substituting expected

values for the estimated values on the right hand sides of equations (9) and (10). For example,with ocean catch,

COnj = 5a=2

COnO

xbia

CTnja + Enjakj=1

CTjnTj

tbija +Ej,nEj,

zbija, +Ej,nEj,

zbija,

5a=2

NbiaOaNnja(1 Oa)a(1 Fa)(Tja + (1 Tja))k

j=1 Nbia(1 Oa)a(1 Fa)ij(Tja + (1 Tja))

=5

a=2

NbiaOaNnja(1 Oa)a(1 Fa)

Nbia(1 Oa)a(1 Fa)kj=1 ij

=5

a=2

NbiaOaNnjaNbia

=5

a=2

NnjaOa

where Nbia and Nnja is the abundance of age a fish from the hatchery i Surrogate group and thenatural stock j prior to ocean harvest.

The estimated production for the natural stock from watershed j is the sum of equations (7)-(10).

Pnj = COnj + CFnj + CTnj + Enj (15)4.2 NS2

With NS2 there is no selective fishery, no Stealth releases, and, in contrast to NS1, the entireRemainder group is unmarked. Subsequently, some of the estimation procedures differ from NS1due to the need to separate natural production and the Remainderfish in the terminal area catchand escapement.


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NS2: Hatchery specific production

Estimation of hatchery production, with its catch and escapement components, is identical with

NS1, using equations (1)-(6).

NS2: Watershed specific natural production

To estimate natural terminal catch and escapement to a given watershed, estimates of hatcheryterminal catch or escapement to the watershed are subtracted from the estimate of total terminalcatch or escapement. Assuming that there are r hatchery stocks that contribute to the escapementin watershed j,

CTnj =

CTj

r

i=1CThij (16)

Enj = Ej, ri=1

Ehij, + Ej, ri=1

Ehij,, (17)where

CThij = CTjnCTj

taij + tbij +

tcijf

,

Ehij, = Ej,nEj,

zaij, + zbij, +

zcij,f

, and

Ehij, = Ej,

nEj, zaij, + zbij, +zcij,

f .The catches of the natural stock in the ocean and freshwater mainstem fisheries, COnj and CFnj

are estimated as for NS1, using equations (9) and (10). However, estimation of the age-specificnatural stock numbers in the terminal catch and the escapement is more difficult because unmarkedfish are not solely natural fish, i.e., unmarked Remainder fish are present. For both the terminalcatch and the in-river and in-hatchery escapements, unmarked fish in the samples (nTj, nEj,,and nEj,) need to be aged, or at least subsamples of the unmarked fish need to be aged. Weassume that random subsamples of the unmarked fish in the samples of the terminal catch andescapement are taken to age the unmarked fish. Let tuj , zuj,, and zuj, be the unmarked fish inthe terminal catch, in-river escapement, and in-hatchery escapement samples, respectively. Then

nT(age)j, nE(age)j,, and nE(age)j, are the corresponding subsample sizes, where nT(age)j tuj ,nE(age)j, zuj,, and nE(age)j, zuj,. Let vuja, wuja,, and wuja, be the age a fish in theterminal catch, in-river escapement, and in-hatchery escapement subsamples. The catch, in-riverescapement, and in-hatchery escapement of age a unmarked fish is estimated by multiplying theestimated proportion of unmarked fish (denoted pTuj , pEuj,, and pEuj,) and the (conditional)proportion of age a unmarked fish (denoted pa|Tuj , pa|Euj,, and pa|Euj,) against the estimatedcatch and escapements.

CTuja = CTj pTuj pa|TujEuja, = Ej, pEuj, pa|Euj,

Euja, =

Ej, pEuj, pa|Euj,


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where,

pTuj =tujnTj

, pa|Tuj =vuja

nT(age)j

pEuj, =zuj,nEj,

, pa|Euj, =wuja,

nE(age)j,

pEuj, =zuj,nEj,

, pa|Euj, =wuja,

nE(age)j,

The unmarked hatchery components of the terminal catch and the escapement, namely the Re-mainder groups, are estimated using the sample recoveries of CFM fish and the constant markingfraction f. For hatchery i,

CTdija =

CTjnTj

tcija

1 f

f

Edija, = Ej,

nEj,

zcija,

1 f

f

Edija, = Ej,

nEj,

zcija,

1 f

f

Estimates of the age-specific natural components of the terminal catch and escapement are thencalculated by subtraction.

CTnja = CTuja ri=1

CTdija (18)Enja, = Euja, r

i=1Edija, (19)

Enja, = Euja, ri=1

Edija, (20)Finally, the total natural terminal catch and escapement are estimated by summing over ages.

CTnj = 5a=2

CTnja (21)

Enj =

5

a=2(

Enja, +

Enja,) (22)

4.3 AS1

With AS1, selective fisheries occur in all locations, ocean, freshwater mainstem, and terminal areas,Remainder fish are marked, and Stealth releases are made. All unmarked fish in escapement samplesare scanned for CWTs, thus recoveries from the Stealth group are identified. It is further assumedthat the selective fisheries do not retain any unmarked fish, but some unmarked fish will die afterbeing caught and released.


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where Oat, Fat, and

Tajt are the incidental fishing mortality probabilities for age a fish during

year t in the ocean, freshwater mainstem, and watershed j terminal fisheries (the presumed natalwatershed of the natural fish).

at = 0 means that no fishery intercepted the chosen stock of age a that would return in yeart, or that no fish died upon release from any fishery. Therefore, snt is an indication of how manymore fish would have escaped if there was no fishery or all unmarked fish survived all fisheries.

Each age-specific component of snt can be rewritten in terms of at. Let Rn,ta denote thenumber of outmigrating natural fish a years prior to the year t return and S0,ta be the initialsurvival rate for that cohort.

E(En2t|2t = 0) E(En2t|2t = 0) = Rn,t2S0,t22t Rn,t2S0,t2(1 O2t)2t(1

F2t)(1

T2jt)

= Rn,t2S0,t22t 1 (1 O2t)(1

F2t)(1

T2jt)= Rn,t2S0,t22t2t

E(En3t|3t = 0) E(En3t|3t = 0) = Rn,t3S0,t3(1 2,t1)S3t3t3t

E(En4t|4t = 0) E(En4t|4t = 0) = Rn,t4S0,t4(1 2,t2)S3,t1(1 3,t1)S4t4t4t

E(En5t|5t = 0) E(En5t|5t = 0) = Rn,t5S0,t5(1 2,t3)S3,t2(1 3,t2)S4,t1(1 4,t1)S5t5t

To estimate snt, the E(Enat|at = 0) are calculated using the Surrogate and Stealth groups. Weassume either that the maturation rates for all ages are known and constant or that natural survivalrates for ages 3, 4, and 5 are known and constant. There may be ways to avoid assuming knownmaturation or survival rates, but some other parameters will likely have to be assumed known. Weshow how to calculate snt assuming known and constant natural survival rates, but due to the

length of the calculations and cumbersome notation the details of the estimating equation are givenin Appendix A. We also note that aging of escapement samples is an additional data requirement.

It is worth highlighting some critical aspects of the estimation procedure. First, the procedurecan yield negative estimates of set for the Stealth fish (see equation (51)), in particular whenestimated escapements exceed the expected escapements in the absence of fishing mortality. Theprobability of negative estimates increases as errors in catch and escapement estimates increase.Second, the data requirements in terms of which years of catch and escapement data are needed isa limiting factor of this approach. When assuming known survival rates for ages 3, 4, and 5, datafor the preceding three years, the current year, and the next three years are required. Assumingknown maturation may be less restrictive on the data requirements, but this assumption may be

considered less believable than fixed age 3 and higher survival rates. Differences in the time ofrelease for hatchery fish are known to have an effect on maturation probabilities (Hankin 1990).Third, neither assuming known maturation rates nor assuming known survival rates (age 3, 4, or5) is a desirable assumption. Both maturation rates and survival rates are likely to vary naturallywithin cohorts of the same stock and between different stocks. One possibility is to specify aprobability distribution for the known set of survival rates and then randomly sample from thatdistribution and compute different estimates of the above parameters, which will then partiallyreflect the uncertainty in the estimates. Finally, the assumption that Stealth fish behave exactly asthe natural stock, particularly with regard to not straying from the natal watershed, is crucial tothe estimate of snt. In Appendix E we show how straying of the Stealth group affects the estimateand give a procedure for adjusting the estimate when the Stealth group does stray.


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4.4 AS2

As with AS1, selective fisheries occur in the ocean, mainstem, and terminal areas, but catches of

the unmarked Remainder fish would be released along with Stealth fish.

AS2: Hatchery specific production

The estimates are similar to those for NS1, except that expansions for the Remainder fish basedon the CFM fish are not made in the catch estimates.

COhi = COnO

(xai + xbi + xci) (27)

CFhi =

CFnF

(yai + ybi + yci) (28)

CThi = kj=1

CTjnTj

(taij + tbij + tcij) . (29)

However, as for NS2, estimates of the Remainder fish in the escapement sample are needed.

Ehi = kj=1

Ej,nEj,

(zaij, + zbij, + zcij, + zeij,) +5

a=2

Edija,

+k

j=1

Ej,nEj,

(zaij, + zbij, + zcij, + zeij,) +5

a=2

Edija,

(30)

Edija, and Edija, are estimates of unmarked Remainder fish from hatchery i age a fish in thein-river and in-hatchery escapement to watershed j. How these are estimated in shown in the nextsection.

AS2: Watershed specific natural production

Let Euj, and Euj, denote the in-river and in-hatchery escapement of unmarked fish to watershedj and zuj, and zuj, be the number of unmarked fish observed in the escapement samples. Notethat zuj, and zuj, include Remainderfish and natural fish, but not the unmarked Stealth fish.

Euj, = Ej,nEj, zuj, (31)Euj, = Ej,

nEj,zuj, (32)

The escapements of age a Stealthfish from hatchery i fish, denoted Eeija, and Eeija,, are estimatedas follows.

Eeija, = Ej,nEj,

zeija, (33)

Eeija, =

Ej,nEj,

zeija, (34)


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The escapements of age a Remainderfish from hatchery i, Edija, and Edija,, are estimated usingthe ratio of release numbers for this group and a stealth group assumed to have the same lifehistory parameters. Note that this stealth group may or may not be the same as that used for

the natural fish. If not, yet another subcategory of hatchery releases is required. In particular asubset of the Remainder group may require that a CWT is implanted. To reduce the notation, andcomplexity, we suppose that a single Stealth group suffices. Then

Edija, = Rdi,taRei,ta

Eeija, (35)Edija, = Rdi,ta

Rei,taEeija, (36)

where Rdi,ta and Rei,ta are the number of type d and e fish released from hatchery i that are nowage a. The escapement of natural fish to watershed j is estimated by subtracting these estimatesof Remainder fish from the estimated escapement of unmarked fish.

Enj = Euj, ri=1

5a=2

Edija, + Euj, ri=1

5a=2

Edija, (37)AS2: Incidental fishing mortality

The procedure for estimating snt is similar to that for AS1. Details are given in Appendix B.

4.5 FS1

Selective fisheries occur in freshwater fisheries (mainstem and terminal areas) but not in the oceanfisheries. The estimation procedures are a mixture of the non-selective and all-selective alternatives,with some minor differences.

FS1: Hatchery specific production

Estimation of ocean catch is similar to that in alternative NS1, except that the catch of the Stealthfish must be accounted for. It is highly unlikely that some or all of the unclipped fish caught inthe ocean fisheries will be scanned for a CWT tag in the head, thus the Surrogate group will beused to represent the Stealth group. Release numbers for Surrogate groups will likely vary betweenyears and that needs to be accounted for in the estimation. Further, aging of some fish from the

ocean catch sample will have to be done. Ocean catch can then be estimated as follows.COhi = COnO

xai + xbi +

xcif

+5

a=2

xeia

(38)

where

xeia = xbiaRei,taRbi,ta

. (39)

The freshwater and terminal catches are estimated the same as in alternatives NS1 and AS1(equations (2) and (3)). Hatchery escapement is estimated as in alternative AS1, using equations(23) and (24).


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FS1: Watershed specific natural production

The natural production is ocean catches and escapement. The escapement of natural stock j, Enj ,

would be estimated as in NS1, using equation (8). The ocean catches for the natural stock fromwatershed j can be estimated using the Stealth recoveries.

COnj = 5a=2

COnOxeia

Enjakj=1

Ej,nEj,

zeija, +Ej,nEj,

zeija,

(40)where Enja = Enj,pnja, + Enj,pnja, (41)The proportions at age in the escapement sample, pnja , would be estimated as for NS1 (see equation(13)).

FS1: Incidental fishing mortality

As for AS1, the expected incidental mortality suffered in the selective fisheries, sn, can again beestimated, but with FS1 the mortality arises only from the mainstem and terminal area fisheries.Details of the estimation procedure are given in Appendix C.

The incidental mortality rates, at, suffered in all freshwater fisheries (mainstem and terminalfisheries combined) can be estimated for each age. The ocean fishery is not a selective fisheryand the ocean exploitation rate can be estimated, assuming known survival parameters (equations(58)-(61) in Appendix C). Similar to AS1, age a freshwater incidental mortality for a stock thatreturns to watershed j with certainty is defined by

at = 1 (1 Fat)(1

Tjat). (42)

Estimates of at for natural stocks use estimates of expected escapement for Stealth fish in theabsence of selective fisheries (equations (63)-(66) in Appendix C).

at = 1 EeatE(Eeat|at = 0) (43)The intuition behind this can be shown with the method of moments. For example, the incidentalmortality on age 3 fish would be (substituting parameters for estimates),

e3t 1 Re,t3S0,t3(1 O2,t1)(1 2,t1)S3(1 O3t)3t(1 F3jt)(1 Tj3t)Re,t3S0,t3(1 O2,t1)(1 2,t1)S3(1 O3t)3t= 1 (1 F3t)(1

Tj3t)

Note that under AS1 and AS2, at can also be estimated, but its interpretation is more compli-cated than for the FS cases, in that at can include incidental mortality rates from more than oneyear.

The expected incidental mortality for natural fish, snt, can, as for AS1 and AS2, be defined interms of at using equation (25). snt can be estimated using estimates ofE(Enat|at = 0) (shownin equation (56)) and using the estimated escapement in place ofE(Enat|at = 0).


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4.6 FS2

Selective fisheries occur in the freshwater fisheries, as in FS1, but the Remainder group is completely

unmarked and indistinguishable from natural fish.

FS2: Hatchery production

Estimation of hatchery specific ocean catches is identical to the procedure for FS1 (equation (38)).Estimating hatchery specific freshwater catch is similar to FS1, except that the Remainder groupis not kept in these fisheries, thus is not accounted for in the equations.

CFhi = CFnF

(yai + ybi + yci) (44)

CThi =k

j=1CTjnTj (taij + tbij + tcij) . (45)

Escapement of hatchery fish is estimated the same as for AS2 (equation (30)).

One piece of the hatchery production left out of the calculations is the incidental mortality ofthe Remainder fish. In general this will be estimable only if surrogates for the Remainder groupare identified (see related remarks for AS2 and estimation of hatchery and natural escapement).

FS2: Watershed specific natural production

The natural production is ocean catch and escapement. The escapement for natural stock j isestimated as in NS2, using equation (17). The ocean catch is estimated as for FS1, using equation(40), except that Enja is estimated differently, using equations (19) and (20).FS2: Incidental fishing mortality

Details of the estimation of snt for FS2 are given in Appendix D. As for alternative FS1, theincidental mortality of natural fish in the freshwater fisheries (mainstem and terminal) can beestimated using the Stealth and Surrogate groups (see equation (57)).

5 Simulation and estimation program, CFM Sim

CFM Sim, short for Constant Fractional Marking Simulation, is an IBM PC compatible computerprogram that simulates the following processes for multiple stocks of chinook salmon over multipleyears:

1. the initial marking and tagging of fish, followed by natural mortality, fishing mortality, andmaturation processes, each repeated for ages 2, 3, 4, and 5;

2. the sampling of marine and freshwater catches and escapements, where the catches and es-capements generally include a mixture of stocks;


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3. the statistical estimation of catches and escapements for each stock separately, based on thecatch and escapement sample data.

The program was designed to simulate these processes for hatchery-raised and naturally-spawnedchinook salmon from Californias Central Valley using any of the six alternatives described above.The user can model hatchery and natural stocks in 14 different watersheds in the Central Valleysimultaneously, with a limit of one hatchery and one natural stock per watershed. Multiple yearscan be simulated to determine trends over time, and any number of simulations can be performedto determine the natural and sampling variability.

5.1 User input

The primary reason for developing CFM Sim was to provide a tool for fisheries biologists andbiometricians that could be used to study the effects of different constant fractional marking (cfm)rates on the quality of estimates of production. CFM Sim can be used to compare the accuracyof production estimates when a cfm rate of f=20% or a cfm rate of f=40% is applied to releasesfrom a Central Valley artificial production facility.

Many other factors besides the CFM rate affect the quality of production estimates. Some ofthe factors that the user of CFM Sim can manipulate include the following:

marine survival rates (S0, S3, S4, and S5);

age-specific ocean, freshwater, and terminal fishing harvest rates (Oa, Fa, Taj);

sampling rate of catches in the marine fisheries (nO/CO);

sampling rate of catches in the freshwater fisheries (nF/CF and nTj/CTj );

sampling rate of spawning escapement (nEj,/Ej,);

sampling rate of the hatchery return (nEj,/Ej,);

maturation rates (2, 3, and 4).

For example, the user can evaluate changes in the accuracy of production estimates for the water-sheds in the Central Valley due to changes in age 4 marine harvest rates while holding the cfm ratef and other rates constant.

CFM Simcan also be used to analyze the effect of selective fisheries on the spawning escapementof natural and hatchery bound Central Valley chinook salmon stocks. A user can vary any shakermortality rate (Lawson and Sampson 1996), which is defined as a fraction of the harvest rate, tostudy the effects on both escapement and total shaker mortality.

A simple spreadsheet format is used to input stock specific parameters, which include age specificsurvival, harvest and maturation rates, hatchery release numbers, stock-recruitment parameters forthe natural stocks, straying rates, sampling rates, sub-sampling rates for aging as well as aging errorprobabilities, and latent hooking mortality parameters in the case of selective fisheries. Parametersare also watershed specific where applicable (i.e., escapement sampling rates).


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5.2 Program output

The primary interest of CFM Simis to determine the error and variability of estimated production.

Therefore, estimated production is compared to true production in order to provide a measureof the quality of the estimates. CFM Sim uses the mean relative absolute error, labeled M AE, asthis measure. To calculate the M AE for a given stock, the relative absolute error is calculated foreach simulated year and then averaged across all the years of a single simulation.

M AEi =1

recY rs

recY rsj=1

|Pi,j Pi,j|

Pi,j, (46)

where recY rs is the total number of recovery years, Pi,j is the true production, and Pi,j is theestimated production, for simulation i and recovery year j. For example, suppose just two yearswere simulated. The true production was 10,000 and 11,000 for both years and the corresponding

estimates were 9,500 and 11,200. Then

M AE =1

2

|9, 500 10, 000|

10, 000+|11, 200 11, 000|

11, 000

=

1

2(0.05 + 0.018) = 0.034

or a 3.4% relative absolute error for that single simulation. The two years would then be simulatedagain and another M AE would be calculated.

The average, median, standard deviation, minimum, and maximum of the M AEs are calculatedover all simulations and output by stock into new spreadsheets. These statistics give an idea as tothe quality of the estimates of production and can be used to compare different marking, tagging,

and sampling scenarios, for example. A relatively large average or median MAE indicates thatproduction is not being estimated accurately, while a relatively large standard deviation shows thatthe estimates of production are not precise.

Also output to a spreadsheet are the summary statistics for the ratio of the last years simulatedproduction to the first years simulated production for each natural stock. Ratios of true productionand estimated production are reported and can be used to gauge the increase in natural productionover the time period entered and if it will be detected using the estimation procedures describedhere.

Some estimates may be negative in alternatives NS2, AS2, and FS2. When any of these al-ternatives are run, numbers of negative estimates that occurred are reported. This will help to

determine how frequently absurd estimates may occur given the parameters entered.

When selective fishery alternatives are run, an additional worksheet outputs summary statisticsfor the mean relative absolute prediction error between the true s, and the estimated s for eachnatural and hatchery stock.

A number of different external files are also created. The true and estimated production isreported for all stocks from the last simulation to give an insight into a simulation. The M AEs foreach stock and simulation are reported in case the summary statistics do not define the accuracyand precision well enough, and the total natural production for all recovery years and simulationsis also reported. When requested, more detailed files for each stock are created that contain valuessuch as true catches and escapement for each simulation.


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6 Discussion

6.1 Related work

The Pacific Salmon Commission established an Ad-hoc Selective Fishery Evaluation Committee(ASFEC) in 1993 which later developed into a standing Selective Fishery Evaluation Committee(SFEC). Several reports by this committee (ASFEC 1995; SFEC 1998, 1999) have focused onmarking, tagging, and estimation techniques for coho salmon fisheries in particular. The SFECrefers to the combination of Surrogate and Stealth groups as Double Index Tagging (DIT) whereSurrogate fish are referred to as marked fish and Stealth fish are labelled unmarked.

Zhou (2002) summarized the SFEC procedures for estimating the incidental fishing mortalityof unmarked hatchery fish and we restate his summary here using our notation. Zhou considersthe situation where selective fishing occurs in a terminal fishery and fisheries prior to the terminal

fishery are implicitly non-selective. In our framework this would mean non-selective ocean andfreshwater mainstem fisheries followed by a selective terminal fishery. Zhou shows how the numberof unmarked fish that die as a result of the selective fishery is estimated (which he labels Cms ) and,more directly, how the harvest rate on the unmarked fish (labelled Hus ) is estimated. The expectedvalue of Cms is what we would label se (dropping the time subscript), while the expectation ofHus would be

T. The SFEC describes two procedures for estimating se.

The SFECs first method assumes that initial marine survival, S0, is the same for both theSurrogate and Stealth groups, exactly as we assume, and label the procedure the equal marinesurvival method. Implicitly the SFEC methods assume that harvest rates experienced by Surrogateand Stealth groups are the same prior to the terminal area fishery. Using our notation, we re-formulate this procedure for coho salmon (thus S0 corresponds to survival to year 2, not maturing,

and then surviving to the start of fishing in year 3, and 3=1). We assume just one fishery priorto the terminal area, say an ocean fishery; also time subscripts are dropped.

se,1 =ReRb

(CTb + Eb) Ee

ReRb

(RbS0(1 O)T + RbS0(1 O)(1 T)) ReS0(1 O)(1 T)

= ReS0(1 O)T

Then incidental terminal area fishing mortality or harvest rate is estimated by

T =se,1

Re

Rb(CTb + Eb)

ReS0(1 O)

T

ReS0(1 O)= T.

We also note that in the case of coho salmon, 1-T, is equivalent to (with no age subscriptneeded).

The SFECs second method implicitly allows for different initial survival rates for the Surrogateand Stealth groups but assumes equal harvest rates in the preceding non-selective fishery. Thisprocedure is labelled the equal exploitation rate method. The ratio of (estimated) catches forthe two groups is substituted for the ratio of release numbers in this case. Here we denote differentinitial survival rates by Sb0 and Se0 for the Surrogate and Stealth groups.

se,2 =

Ce

Cb(

CTb +

Eb)

Ee


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ReSe0ORbSb0O

(RbSb0(1 O)T + RbSb0(1 O)(1 T)) ReSe0(1 O)(1 T)

= ReSe0(1 O)T

And incidental terminal area fishing mortality or harvest rate is estimated by

T =se,2CeCb (CTb + Eb)

ReSe0(1 O)

T

ReSe0(1 O)= T.

Zhou (2002) studied the performance of both procedures for estimating T by introducingrandomness in actual survival and harvest rates (making number initially surviving and numbercaught Binomial random variables), and randomness in catch and escapement estimates. He foundthat the relative errors in estimates of T can be quite large over a range of reasonable expectedsurvival and harvest rates and catch and escapement estimation errors. For example, if the trueincidental harvest rate, T, was 6% (40% encounter rate times 15% hook-and-release mortality

rate), the average absolute relative deviation, |T 6|/6 ranged from 56.9% to 16.0% given S0

ranging from 1% to 12%. Thus in the case of S0=1%, on average T was 3% above or below 6%.

6.2 Remarks on estimation

As the number of equations indicate, estimation of life history parameters, catches, and naturalescapement for chinook salmon can be quite complex, and the complexity greatly increases withthe introduction of selective fisheries (as can be seen from the Appendices). More subtle is the factthat, in the case of selective fisheries, estimates of natural escapements and incidental mortalitycan occasionally be negative. This was also demonstrated by Zhou (2002) with the simpler cohosalmon situation. This may be seen from equations that estimate maturation rates and involve

subtracting estimates of catches and escapements from estimates of abundance prior to catch andescapement. When estimates of catches and escapements exceed estimated initial abundance,estimated maturation is negative, subsequently estimates of set can be negative. Simulationstudies we have done indicate that the chance of negative estimates increases as the imprecisionof escapement estimates, in particular, worsens. Relatively precise estimates of escapement arethen crucial for yielding sensible estimates of incidental mortality under the proposed method ofmoments style procedures we have described.

We are currently working on an alternative approach to the problem of simultaneously modelinglife history processes, harvest, and data collection uncertainty by using a state-space model (Schnute1994; Newman 1998 and 2000). The parameter estimates would be either maximum likelihood orBayesian and are theoretically more efficient than method of moments approaches (and will notyield nonsensical negative estimates of escapement, for example). The estimation procedures, incontrast to the estimators given here, would not be closed form, however, and the procedureswill be even more numerically and computationally intensive. The state-space model framework isextremely flexible, however, and allows one to readily incorporate different estimates of abundances,e.g., two estimates of a given stocks escapement.

6.3 Management implications and issues

For managing and monitoring natural stock abundances, the use of marked and tagged hatcherystocks is an economic alternative to marking and tagging natural stocks directly. Besides complex


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estimation problems, there are other basic management issues and implications worth raising.

First, a key condition for the applicability of all the estimators we have developed is that thelife history and fishery experiences of Surrogate and/or Stealth hatchery releases are representativeof those experienced by wild fish. To increase the likelihood that this is so, hatchery managers needto know the time and duration of outmigration of wild stocks, and perhaps fish size, condition,and other relevant variables. The rearing and release of the Surrogate stock should therefore mimicthe wild stock outmigration strategy as closely as possible. Also, releases of Surrogate and Stealthgroups need to be made directly from hatcheries so as to minimize straying rates and make it morelikely that the assumption of equal straying rates of wild, Surrogate, and Stealth releases are met.Ultimately, the best way to determine representativeness of a surrogate release is to mark and tag(or just tag) some outmigrating wild stock juveniles. This would be expensive and collecting largenumbers might be difficult, but the effort would yield invaluable information.

Second, the introduction of selective fisheries greatly complicates both data requirements and

data analysis methods. The complexity is considerably greater for chinook salmon, because ofthe multiple maturation ages, than for coho salmon. In particular, it is worth emphasizing thatestimates of incidental mortality losses to a wild chinook salmon stock (due to catch and release inmark-selective fisheries) for a particular year t would not be possible until a few years later becauseescapement estimates in several years past year t are needed. Tag detection is also more difficult forchinook salmon than coho salmon because of the formers larger size (Vander Haegen, et al. 2002);thus the time required to thoroughly scan an unmarked chinook salmon, a possible Stealth fish, fora CWT, increases data collection costs. A related data issue, and estimation complication, that wehave not dealt with is tag loss. Many hatcheries currently hold samples tagged juveniles for at leasttwo weeks prior to release so that such fish can be scanned to determine CWT tag retention rates.The introduction of selective fisheries and mass marking practices will certainly increase the scopeand importance of such tag retention studies. We have not yet explored how one might attempt tostatistically account for possible tag loss following release, especially if large numbers of hatcheryfish are deliberately released with adipose fin clips but without CWTs.

Third, additional complications to estimation, and data record keeping, can be lessened bymaintaining constant fractional marking across years, and ideally across hatcheries. To increasethe probability that a given CFM is biologically similar to particular Remainder fish, the fractionalmarking rate f needs to be applied within each unique breeding and rearing combination. Theremay be several release types (different months or sizes of release) among the Remainderproduction-type releases and each type will need to be marked at rate f. Ideally, the same marking and taggingrate f should be applied within each raceway from which both CFM and Remainder fish will bereleased.

Fourth, the levels of marking, tagging, sampling, aging fish, and reading tags that are requiredto effectively implement the estimation procedures presented in this paper, in non-selective orselective fisheries, greatly exceed current data generation and collection efforts. A key concern iswhether resource management agencies will have sufficient funds for generating and gathering thenecessary data, and for doing so at levels that yield sufficiently precise estimates. for example,samples of untagged and unmarked fish in spawning escapements and at hatcheries will need tobe aged. Unmarked fish in escapements will need to be scanned for tags in the case of selectivefisheries. For many systems current escapement estimation procedures are likely inadequate foryielding the desired level of precision in production estimates, and for lessening the chance ofnonsensical estimates, thus more time and money needs to be invested in improving escapement


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estimates.

Fifth, while our primary objective was to develop procedures for estimating wild chinook salmonproduction, with particular attention to Sacramento river system stocks, a recent U.S. statute,signed into law in February 2003, requires that all federal and federally funded salmon and steel-head hatcheries mark all the fish they release. This new requirement for mass marking places anincreased and critical importance on rapid development and refinement of the kinds of statisticalprocedures that we have described in this paper. Mass marking has apparently now become a re-quirement, but analytical procedures necessary for handling the mass marked fish have not yet beenfully developed. The intent behind the legislation is to maintain, or increase, harvest of hatcheryfish while protecting wild fish, and the legislation effectively increases the scope of selective fisheries.But mass marking and selective fisheries may seriously compromise the integrity of the coded wiretag data base and the nature of how CWT recovery data have been used in salmon management forthe past 25 years. For chinook salmon, the complexity of the analysis with selective fisheries andStealth fish is such that we question that the complex estimation procedures will be used correctly

in practice. Also, at best our procedures can only estimate the overall incidental fishing mortalityrates. We have been unable to develop estimation procedures that might estimate such incidentalmortality rates for individual, time, area, and gear-specific fisheries, but current management reg-ulations are often made at that fine level of resolution (see, for example, the 2003 ocean salmonfisheries plan of the Pacific Fisheries Management Council, http:www.pcouncil.org).

References

ASFEC (Ad-hoc Selective Fishery Evaluation Committee). 1995. Selective fishery evaluation.Pacific Salmon Commission, Ad-hoc Selective Fishery Evaluation Committee, Vancouver.

Cochran, W.G. 1977. Sampling Techniques, 3rd Ed. John Wiley and Sons, New York.

Hankin, D.G. 1982. Estimating escapement of Pacific salmon: marking practices to discriminatewild and hatchery fish. Transactions of the American Fisheries Society 111: 286298.

Hankin, D.G. 1990. Effects of month of release of hatchery-reared chinook salmonon size at age,maturation schedule, and fishery contribution. ODFW Information Report 904.

Hankin, D.G., and Healey, M.C. 1986. Dependence of exploitation rates for maximum yield andstock collapse on age and sex structure of chinook salmon (Oncorhynchus tshawytscha) stocks.Canadian Journal of Fisheries and Aquatic Sciences 43:17461759.

Lawson, P.W., and Sampson, D.B. 1996. Gear-related mortality in selective fisheries for oceansalmon. North American Journal of Fisheries Management 15:512520.

Mood, A.M., Graybill, F.A., and Boes, D.C. 1974. Introduction to the Theory of Statistics, 3rdEd.. McGraw-Hill, New York.

Nehlsen, W., Williams, J.E., and Lichatowich, J.A. 1991. Pacific salmon at the crossroads: stocksat risk from California, Oregon, Idaho, and Washington. Fisheries 16(2): 421.

Newman, K.B. 1998. State-space modeling of animal movement and mortality with application tosalmon. Biometrics 54: 274297.

Newman, K.B. 2000. Hierarchic modeling of salmon harvest and migration. Journal of Agricultural,


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Biological, and Environmental Statistics 5:98123.

Schnute, J. 1994. A general framework for developing sequential fisheries models. Canadian Journalof Fisheries and Aquatic Sciences 51:16761688.

Shaul, L., McPherson, Jones, E., and Crabtree, K. 2003. Stock status and escapement goals forcoho salmon stocks in Southeast Alaska. Alaska Department of Fish and Game, Special PublicationNo. 03-02, Anchorage.

SFEC (Selective Fishery Evaluation Committee). 1998. Pacific Salmon Commission, SelectiveFishery Evaluation Committee progress report, December 1998. SFEC, Vancouver.

SFEC (Selective Fishery Evaluation Committee). 1999. 1998 annual report. Pacific Salmon Com-mission, Selective Fishery Evaluation Committee, SFEC(99)-1, Vancouver.

SFEC (Selective Fishery Evaluation Committee). 2002. Investigation of methods to estimatemortalities of unmarked salmon in mark-selective fisheries through the use of double index tag

groups. Pacific Salmon Commission, Selective Fishery Evaluation Committee, Analytical WorkGroup, TCSFEC(02)-1. (Available at www.psc.org/Pubs/SFEC02-1.pdf.)

Vander Haegen, G.E., Swanson, A.M., and Blankenship, H.L. 2002. Detecting coded wire tags withhandheld wands: effectiveness of two wanding techniques.

Zhou, S. 2002. Uncertainties in estimating fishing mortality in unmarked salmon in mark-selectivefisheries using double-index-tagging methods. North American Journal of Fisheries Management22: 480493.


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A AS1: Estimation of Incidental Mortality

The estimation procedure assumes that the age three through five survival rates, S3, S4, and S5, are

known and constant. The approach can be partitioned into three parts: (a) estimating life historyparameters using the Surrogate group; (b) estimating se for the Stealth group using the estimatedparameters; (c) estimating sn for the natural stock using the Stealthse and escapement estimatesfor Stealth and natural stocks.

A.1 Estimating life history parameters using the Surrogate group

The notation is complicated. The year of interest is denoted by a subscript t. Catch, C, andescapement, E, have three subscripts. The first is either b for the Surrogate group or e for theStealth group. The second is age of the fish, a= 2, 3, 4, or 5. The third subscript is the year of

catch or escapement. For example, Cb4,t3 is the catch of Surrogate age 4 fish three years prior toyear t. Release number, R, has two subscripts, the first is either b or e and the second is the broodyear. Harvest rates O, F, and T are first subscripted b or e, then by age at harvest, and thenthe year of interest. Survival rate, S, is subscripted first by I, 3, 4, or 5 and then the brood year.Similarly, maturation rates, , are subscripted by age of maturation, a, and the cohort year, t a.The symbol PF, with the same subscripts, denotes the sum of all of the freshwater observationsfor a given stock, including freshwater mainstem catch, terminal area catch, and escapement. Forexample, in year t, the age a freshwater return,

PFbat = CFbat + CTbat + EFbat.

S0,tg = COb2,tg + PFb2,tg +COb3,tg+PFb3,tg+COb4,tg+PFb4,tg+COb5,tg+PFb5,tgS5

S4

S3

Rb,tg2g = 0, 1, 2, 3 (47)

2,tg =PFb2,tg

Rb,tg2S0,tg2 COb2,tg g = 0, 1, 2, 3 (48)3,tg =

PFb3,tg[Rb,tg2S0,tg2 (COb2,tg + PFb2,tg)]S3 COb3,tg g = 1, 2, 3 (49)

4,tg =PFb4,tg

[Rb,tg2S0,tg2 (COb2,tg + PFb2,tg)]S3 (COb3,tg + PFb3,tg)S4 COb4,tg g = 2, 3(50)

A.2 Estimating se for the Stealth group

set = 5a=2

E(Eeat|at = 0) Eeat (51)E(Ee2t|2t = 0) = Re,t2S0,t22t (52)E(Ee3t|3t = 0) = Re,t3S0,t3(1 2,t1)S33t (53)E(Ee4t|4t = 0) = Re,t4S0,t4(1 2,t2)S3(1 3,t1)S44t (54)E(Ee5t|5t = 0) = Re,t5

S0,t5(1 2,t3)S3(1 3,t2)S4(1 4,t1)S5 (55)


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We emphasize here that at is assumed to have the same meaning for the Stealth fish as for naturalfish. In particular, Stealth fish cannot stray to other terminal areas, else they would be subjectedpotentially to a mixture of different terminal area harvest rates. Although see Appendix E for a

way of dealing with straying Stealth fish.

A.3 Estimating sn for the natural stock

To calculate sn for natural fish represented by the Stealth group, the expected escapement ofnatural fish in the absence of fishing mortality is first calculated. Using equations (52)-(55) andage-specific estimates of the natural stock and Stealth group escapements.

E(Enat|at = 0) = E(Eeat|at = 0)Enat

Eeat(56)

Again making a method of moments style argument, the intuition behind equation (56) can be

seen. For example, at age 2,

E(Ee2t|2t = 0)En2tEe2t Re2,t2S0,t22t Rn2,t2Sn0,t2(1 O2t)2t(1

F2t)(1

Tj2t)

Re2,t2S0,t2(1 O2t)2t(1 F2t)(1

Tj2t)

= Rn2,t2Sn0,t22t

We include an additional subscript n for the natural stocks initial survival rate to emphasize thepoint that the initial survival rate can differ between Stealth and natural fish. The age-specificnatural stock escapement estimates, Ena,ta, would be calculated as for NS1, using equation (12).Then, using the age-specific escapement estimates and estimate of the expected escapement fornatural fish,

snt =5

a=2 E(Enat|at = 0) Enat (57)

B AS2: Estimation of Incidental Mortality

Notation is the same as for AS1 in Appendix A.

B.1 Estimating life history parameters using the Surrogate group

The life history parameters are estimated exactly as for AS1, using equations (47)-(50).

B.2 Estimating se for the Stealth group

The estimate of s for Stealth fish can be found using equations (51)(55).

B.3 Estimating sn for the natural stock

To estimate the fishing induced mortality on the natural stock, E(Enat|at = 0) is first estimated,using equation (56), where the age specific natural escapement estimate, Ena, is found with aprocedure similar to that used for NS2. Then snt is estimated with equation (57).


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C FS1: Estimation of Incidental Mortality

Notation is the same as for AS1 in Appendix A. The estimation sequence is as for AS1, with life

history parameters estimated using the Surrogate fish, incidental mortality ofStealth fish estimatednext, and incidental mortality of the natural fish estimated last. As discussed previously thedefinition of at is different for the FS than the AS cases.

C.1 Estimating life history parameters using the Surrogate group

The initial survival rates, S0, and the maturation probabilities, a, are estimated as for AS1, usingequations (47)-(50). The ocean harvest rates, however, need to be estimated with FS1.

O2t = COb2tRb,t2S0,t2 (58)O3t =

COb3tRb,t3S0,t3(1O2,t1)(12,t1)S3 (59)

O4t =COb4t

Rb,t4S0,t4(1O2,t2)(12,t2)S3(1O3,t1)(13,t1)S4 (60)O5t =

COb5tRb,t5S0,t54g=2(1Og,t+g5)(1g,t+g5)Sg+1 (61)

C.2 Estimating se for the Stealth group

set = 5a=2

E(Eeat|at = 0) Eeat (62)E(Ee2t|2t = 0) = Re,t2S0,t2(1 O2t)2t (63)E(Ee3t|3t = 0) = Re,t3S0,t3(1 O2,t1)(1 2,t1)S3(1 O3t)3t (64)E(Ee4t|4t = 0) = Re,t4S0,t4(1 O2,t2)(1 2,t2)S3(1 O3,t1)(1 3,t1)S4

(1 O4t)4t (65)

E(Ee5t|5t = 0) = Re,t5

S0,t5(1 O2,t3)(1 2,t3)S3(1 O3,t2)(1 3,t2)S4

(1 O4,t1)(1 4,t1)S5(1 O5t) (66)

C.3 Estimating sn for the natural stock

To calculate sn for natural fish represented by the Stealth group, the equations used for AS1 areused, namely equations (56) and (57). The expected escapements of natural fish in the absenceof freshwater fishing mortality are calculated using equations (63)-(66) and age-specific estimatesof the natural stock and Stealth group escapements. The age-specific natural stock escapementestimates,

Ena,ta, would be calculated as in equation (41).


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D FS2: Estimation of Incidental Mortality

Assumptions and notation are as given in Appendix C.

D.1 Estimating life history parameters using the Surrogate group

As for FS1, the initial survival rates, S0, and the maturation probabilities, a, are estimated asfor AS1, using equations (47)-(50). Like FS1, the ocean harvest rates need to be estimated, usingequations (58)-(61).

D.2 Estimating se for the Stealth groups

Identical with FS1, the expected change in production in the absence of fisheries can be estimatedfor the Stealth groups, using equations (62) - (66).

D.3 Estimating sn for the natural stock

The procedure to estimate s for natural fish is identical to that for FS1 in terms of estimating theexpected escapement of Stealth fish in the absence of freshwater fisheries. First equations (63)-(66)are used to estimate the expected escapements by age class, then the ratio of estimated escapementsof natural to Stealth fish by age class is used to estimate expected escapement of the natural fish,using equation (56), and finally snt is estimated with equation (57).

E Estimating sn when Stealth fish stray

To correctly estimate the expected escapement of natural fish (equation (56)), the Stealth groupmust not stray, as is assumed for natural fish, or the straying rate ( ) must be accounted for. Theeffect of straying can be seen below, using age 2 in the AS case as an example.

E(En2t|2t = 0) = E(Ee2t|2t = 0)En2tEe2t Re,t2S0,t22t

Rn,t2Sn0,t2(1 O2t)2t(1

F2t)(1

Tj2t)

Re,t2S0,t2(1 O2t)2t(1 F2t)

kj=1 2jt(1

Tj2t)

= Rn,t2Sn0,t22t(1 Tj2t)k

j=1 2jt(1 Tj2t)

The straying rate, , is now subscripted with age and brood year, while the stock subscript isassumed. This is because age and cohort variation may exist in the straying rates.

The bias may be reduced somewhat by using the Stealth escapement to the natal watershed jonly, assuming 2j 1.

E(En2t|2t = 0) =

E(Ee2t|2t = 0)

En2t

Eej2t


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Re,t2S0,t22tRn,t2Sn0,t2(1

O2t)2t(1

F2t)(1

Tj2t)

Re,t2S0,t2(1 O2t)2t(1 F2t)2jt(1

Tj2t)

=Rn,t2Sn0,t22t

2jt

Rather than assume that the straying to non-natal watersheds is insignificant, the probabilityof returning to the natal watershed can be estimated using the Surrogate group, which are alsoused to calculate survival, maturity, and harvest parameters for stealth fish. However, as with theother estimates, the implicit assumption that Surrogate and the Stealth fish have the same lifehistory parameters must hold, or bias will occur.

jat =

Cbjat + Ebjat

kj=1

Cbjat +

Ebjat

Using the above estimate jat, the estimate of the expected natural escapement without any

incidental mortality is

E(Enat|2t = 0) = E(Eeat|2t = 0)jatEnatEejat


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Table 1: Notation for abundances and life history parameters. Summation over stocks and/or agesis denoted by dropping the associated subscripts; e.g., CO is total ocean catch for a given year.

Ri : number of juvenile fish released from hatchery stock ior naturally produced juvenile fish leaving watershed i

Nia : abundance of age a fish from stock i prior to ocean harvestCOia : ocean fisheries catch of age a fish from stock iCFia : freshwater catch of age a fish from stock i

CTiaj : terminal area j catch of age a fish from stock iEiaj, : in-river escapement in terminal area j of age a fish from stock iEiaj, : in-hatchery escapement in terminal area j of age a fish from stock i

Pi : total production of stock i, 5a=2 [COia + CFia + CTia + Eia]Sia : probability an unharvested, immature age a 1 fish from stock i

is alive at age a prior to fishing, a=3,4,5Si0 : probability of surviving from time of release

to beginning of ocean harvest, where I stands for initialuOia : ocean fishery exploitation rate on age a stock i fishuFia : freshwater mainstem fishery exploitation rate on age a stock i fish

ij : probability a stock i fish goes to watershed jconditional on surviving the freshwater mainstem fishery

uTaj : terminal area j fishery exploitation rate on age a fish from stock iia : probability an age a fish from stock i matures

given survival to age a without maturing earlier

Table 2: Different hatchery fish adipose fin clip and tagging schemes. NS, AS, and FS denote noselective fisheries, all selective fisheries, and freshwater only selective fisheries, respectively, and fis the CFM fraction.

Release Groups NS1 NS2 AS1 AS2 FS1 FS2

Ad hoc Optional Optional Optional Optional Optional OptionalSurrogate Required Required Required Required Required RequiredCFM Fixed f Fixed f Fixed f Fixed f Fixed f Fixed fRemainder Marked Unmarked Marked Unmarked Marked UnmarkedStealth None None Required Required Required Required


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Table 4: Notation for samples and sample recoveries.

nO : size of a simple random sample taken from COnF : size of a simple random sample taken from CF

nTj : size of a simple random sample taken from CTjnEj, : size of a simple random sample taken from Ej,, the watershed j in-river escapementnEj, : size of a simple random sample taken from Ej,, the watershed j in-hatchery escapement

xai : # of hatchery stock i Ad hoc recoveries in ocean catch samplexbi : # of hatchery stock i Surrogate recoveries in ocean catch sample

xci : # of hatchery stock i CFM recoveries in ocean catch samplexdi : # of hatchery stock i Remainderrecoveries in ocean catch samplexei : # of hatchery stock i Stealth recoveries in ocean catch sampleyai : # of hatchery stock i Ad hoc recoveries in freshwater catch sampleybi : # of hatchery stock i Surrogate recoveries in freshwater catch sampleyci : # of hatchery stock i CFM recoveries in freshwater catch sampleydi : # of hatchery stock i Remainderrecoveries in freshwater catch sampleyei : # of hatchery stock i Stealth recoveries in freshwater catch sample

taij : # of hatchery stock i Ad hoc recoveries in terminal area j catch sampletbij : # of hatchery stock i Surrogate recoveries in terminal area j catch sampletcij : # of hatchery stock i CFM recoveries in terminal area j catch sample

tdij : # of hatchery stock i Remainderrecoveries in terminal area j catch sampleteij : # of hatchery stock i Stealth recoveries in terminal area j catch sampletnj : # of natural stock j recoveries in terminal area j catch sample

zaij, : # of hatchery stock i Ad hoc recoveries in watershed j in-river escapement samplezbij, : # of hatchery stock i Surrogate recoveries in watershed j in-river escapement samplezcij, : # of hatchery stock i CFM recoveries in watershed j in-river escapement samplezdij, : # of hatchery stock i Remainderrecoveries in watershed j in-river escapement samplezeij, : # of hatchery stock i Stealth recoveries in watershed j in-river escapement sampleznj, : # of natural stock j recoveries in watershed j in-river escapement samplezuj, : # of unmarked fish in watershed j in-river escapement samplezaij, : # of hatchery stock i Ad hoc recoveries in watershed j in-hatchery escapement sample

zbij, : # of hatchery stock iSurrogate

recoveries in watershed j in-hatchery escapement samplezcij, : # of hatchery stock i CFM recoveries in watershed j in-hatchery escapement samplezdij, : # of hatchery stock i Remainderrecoveries in watershed j in-hatchery escapement samplezeij, : # of hatchery stock i Stealth recoveries in watershed j in-hatchery escapement sampleznj, : # of natural stock j recoveries in watershed j in-hatchery escapement samplezuj, : # of unmarked fish in watershed j in-hatchery escapement sample


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Figure 1: The top sketch is the sequence of life history processes and abundances of each categoryor fate for a single cohort up to the point of maturation and entering freshwater. The bottom sketch

shows the sequence for age a fish entering freshwater that will go to watershed j with probability j .Note that if the cohort is not vulnerable to a particular fish then the harvest rate, , is effectivelyzero.

Marine Sequence.Age

Initial 2 3 4 5CO2 CO3 CO4 CO5

O2

O3

O4

O5

RS0 N2

(1O2)(12)S3 N3

(1O3)(13)S4 N4

(1O4)(14)S5 N5

(1 O2)2

(1 O3)3

(1 O4)4

(1 O4)

F2 F3 F4 F5

Freshwater Sequence.CFa CTja EhaFa

Tja

j

Fa(1Fa)

j

(1Tja)

(1 j)Era

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Estimating natural chinook salmon production using tagged and marked hatchery releases as surrogates

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