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North American Journal of Fisheries Management

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Visualizing Trade-Offs between Yield andSpawners per Recruit as an Aid to Decision Making

Patrick J. Schmalz, Mark Luehring, Joe Dan Rose, John M. Hoenig & Melissa K.Treml

To cite this article: Patrick J. Schmalz, Mark Luehring, Joe Dan Rose, John M. Hoenig & MelissaK. Treml (2016) Visualizing Trade-Offs between Yield and Spawners per Recruit as an Aidto Decision Making, North American Journal of Fisheries Management, 36:1, 1-10, DOI:10.1080/02755947.2015.1088489

To link to this article: http://dx.doi.org/10.1080/02755947.2015.1088489

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ARTICLE

Visualizing Trade-Offs between Yield and Spawnersper Recruit as an Aid to Decision Making

Patrick J. Schmalz*Minnesota Department of Natural Resources, Division of Fish and Wildlife, 5351 North Shore Drive,

Duluth, Minnesota 55804, USA

Mark Luehring and Joe Dan RoseGreat Lakes Indian Fish and Wildlife Commission, Post Office Box 9, Odanah, Wisconsin 54861, USA

John M. HoenigVirginia Institute of Marine Science, College of William and Mary, Post Office Box 1346,

Gloucester Point, Virginia 23062, USA

Melissa K. TremlMinnesota Department of Natural Resources, Division of Fish and Wildlife, 500 Lafayette Road,

St. Paul, Minnesota 55155, USA

AbstractThere is a fundamental conflict between harvesting fish and conserving their biomass. Managers mediate this

conflict with regulations that control fishery methods and amounts of harvest. In most recreational fisheries, aside fromclosed seasons, the precise control of fishing effort is difficult to achieve because fisher entry into a managed area isoften unlimited and because effort can be influenced by both direct and indirect factors. Choosing the best fishingregulations is also complicated by a need to jointly regulate and accommodate the desires of different user groups whoshare the fishery. Regulations may need to account for (1) low-consumptive uses of fish populations that occur fromcatch-and-release fishing by recreational anglers and/or (2) both tribal subsistence and commercial fishers. We applieda suite of graphical techniques to data on a shared fishery, that for Walleye Sander vitreus in Mille Lacs Lake,Minnesota, to examine the trade-offs between fishery yield and spawner biomass on a per-recruit basis across a rangeof harvest tactics, so that fisheries managers could simultaneously evaluate a variety of regulations. We also usedBluegill Lepomis macrochirus data from several Minnesota lakes to further evaluate the utility of our approach. Someregulations were uniformly better than others because they provided higher yield for a given spawning biomass, andhigher spawning biomass for a given yield at equilibrium, under a range of plausible levels of fishing effort. For a givenlevel of fishing effort, we were able to identify a frontier in the yield–biomass space whereby an increase in either theyield or the biomass could only be achieved by a reduction in the other. In the absence of density-dependent changes togrowth, maturity, or mortality, regulations that included a minimum length produced more optimal yield and spawnerbiomass than those that did not include a minimum length. We reduced the daunting task of choosing from dozens ofregulations by considering just a few graphs that best demonstrated the trade-offs offered by a suite of regulations.

There is a fundamental trade-off between fishery yield and

spawner biomass (Quinn and Deriso 1999). In exploited popu-

lations, maximizing (or optimizing) yield (Punt and Smith

2001) competes with the management goal of maintaining

fish populations via the protection of spawners (Hilborn and

Walters 1992; Kell et al. 2005). Evaluations of the trade-offs

among conflicting management strategies are common for

marine species (e.g., Hake Merluccius spp., Orange Roughy

*Corresponding author: patrick.schmalz@state.mn.usReceived December 24, 2014; accepted August 21, 2015

1

North American Journal of Fisheries Management 36:1–10, 2016

� American Fisheries Society 2016

ISSN: 0275-5947 print / 1548-8675 online

DOI: 10.1080/02755947.2015.1088489

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Hoplostethus atlanticus, Northeast Atlantic flatfish stocks,

Minke Whale Balaenoptera acutorostrata, and Sea Lion Pho-

carctos hookeri; Butterworth and Punt 1999; Smith et al.

1999; Kell et al. 2005) but less common for freshwater fisher-

ies (e.g., Great Lakes Yellow Perch Perca flavescens; Irwin

et al. 2008) despite their usefulness to decision makers. Evalu-

ations of management strategies have focused primarily on

alternative harvest policies that set harvest levels (e.g., control

rule evaluations; Deroba and Bence 2008) but do not specifi-

cally address harvest tactics (e.g., harvest methods, size limits,

and harvest limits). However, fisheries management actions

will regulate the harvest of fish by specifying an appropriate

harvest tactic. Regulations commonly specify the types and/or

sizes of the fishing gear, restrict the size of fish harvested, and/

or restrict the number of fish harvested.

Some fishing gears and methods are more selective than

others, which can increase fishery yield and/or protect future

fishery production at a given level of stock biomass (Arm-

strong et al. 1990; Valdemarsen 2005; Garcia et al. 2011).

Ideally, fisheries management biologists seek a combination

of gears and methods that maximize the yield from a given

stock, while ensuring its long term reproductive capacity.

Comparing different gears and methods has been common in

fisheries for decades (Pope et al. 1975; MacLennan 1992).

Evaluating the trade-offs between fishery status indicators

(e.g., yield per recruit [YPR], spawner biomass per recruit

[SBPR], spawning stock biomass ratio as the ratio of fished

SBPR to unfished SBPR [SSBR]) among alternative harvest

tactics is an important step in decision making (Rademeyer

et al. 2007; Irwin et al. 2008). SSBR provides a measure of

the effect of fishing on the potential reproductive capacity of

a stock. Critical recruitment overfishing threshold levels

range from 0.3 for more resilient species to 0.6 for less resil-

ient species (Gabriel and Mace 1999) provide thresholds to

fishing effort.

When potential harvest tactics are numerous, comparing

alternative tactics can be burdensome. The number of possible

harvest tactics increases when fishery resources are shared

among multiple users (e.g., anglers, tribal subsistence fishers,

and commercial fishers; Schmalz et al. 2011). The types of

gear used, the seasons fished, and the preferred sizes of har-

vested fish all may differ among such groups. Comparing

alternative harvest tactics that seek optimal harvest while

maintaining adequate long term productive capacity becomes

complex. Therefore, clear presentation of alternatives can pro-

mote better informed management decisions.

Our objective was to demonstrate a relatively simple

method for visually assessing the trade-offs between fishery

yield and spawner biomass, while accommodating numerous

possible harvest tactics. We used real data from Walleyes

in Mille Lacs Lake, Minnesota. We also used Bluegill data

from numerous Minnesota lakes to create a hypothetical

population that was used to demonstrate the utility of our

approach.

METHODS

Mille Lacs Lake example.—Mille Lacs Lake, a 53,620-ha

lake in north-central Minnesota, has an important Walleye

fishery that is shared by state-licensed anglers and Ojibwa

(Chippewa) tribal fishers (rights retained in the Treaty of

1837). Annual total allowable harvest (TAH) of Walleyes at

Mille Lacs Lake is determined by a fixed exploitation policy

and by its population biomass, as estimated from an age-struc-

tured stock assessment model. Tribal fishers declare a fixed

quota each year that, on average, approximates 25–30% of

Walleye TAH, with the remaining TAH allocated to the recre-

ational fishery (Schmalz et al. 2011). Tribal gill-net and spear

harvests are directly monitored: if tribal harvest reaches its

TAH, harvest ceases. For the state recreational angling fishery,

fish size and daily bag limits have been used to control the

TAH, along with accountability for post-release mortality

(Reeves and Bruesewitz 2007). From 1997 to 2014, this indi-

rect approach to recreational harvest management resulted in

11 different starting angling regulations for the open water

season, two midseason changes to more strict regulations, and

five midseason changes to less strict regulations (Table 1;

Schmalz et al. 2011). Despite the direct management of the

TABLE 1. Walleye angling length restrictions at the start of the open-water

season, 1983–2014, for state-licensed anglers on Mille Lacs Lake. NoMin Dno minimum length limit; Min D minimum length limit; HS D harvest slot

limit, with lower and upper limits for fish that can be harvested; PS D pro-

tected slot limit, with lower and upper limits for fish that cannot be harvested.

All of the slot-type regulations include a provision that allows for the harvest

of one large fish (e.g.,>711 mm).

Fishing year Angling regulation Daily limit

1983–1984 NoMin 6

1985–1996 NoMin (one fish >508 mm) 6

1997–1998 381-mm Min 6

1999 356–508 mm HS

(one fish >660 mm)

6

2000 356–457 mm HS

(one fish >711 mm)

6

2001 406–508 mm HS

(one fish >711 mm)

6

2002 356–406 mm HS

(one fish >711 mm)

4

2003 432–711 mm PS

(one fish >711 mm)

4

2004–2007 508–711 mm PS

(one fish >711 mm)

4

2008–2011 457–711 mm PS

(one fish >711 mm)

4

2012 432–711 mm PS

(one fish >711 mm)

4

2013–2014 457–508 mm HS

(one fish >711 mm)

2

2 SCHMALZ ET AL.

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tribal fishery and the numerous angling regulation changes to

date, there has been a decline in this Walleye population

(Figure 1). Estimates of SSBR, 2002–2011, have varied, aver-

aging 0.27 for males and 0.35 for females (Bence et al. 2014).

It is hypothesized that ecosystem changes on Mille Lacs

Lake have caused decreased subadult Walleye survival,

leading to intense research on the possible causes. For

example, increased water clarity from a combination of

improved water quality and zebra mussel Dreissena poly-

morpha invasion may make subadult Walleyes more vul-

nerable to predation due to increased predator efficiency

and altered subadult Walleye behavior. In addition,

declines in Cisco Coregonus artedi, a key prey item of

adult Walleyes and Northern Pike Esox lucius, the primary

predators in Mille Lacs Lake, may have led to recently

observed increases in Walleye and Northern Pike predation

on subadult Walleyes. Aquatic invasive species such as

Spiny Waterflea Bythotrephes sp. may also be causing sub-

stantial changes to the zooplankton community, altering

food web dynamics (Minnesota Department of Natural

Resources, unpublished). From a management perspective,

the Walleye decline has led managers to evaluate a broader

range of harvest management options that include alterna-

tive angling regulations that have not been previously

applied.

Mille Lacs Lake data.—We used the data from an annual

fall survey conducted on Mille Lacs Lake to estimate Walleye

yield per recruit (YPR) and spawner biomass per recruit

(SBPR). This survey is conducted in September and early

October by the Minnesota Department of Natural Resources

(MNDNR). The survey uses 76.2-m, multifilament, nylon gill

nets that measure 1.83 m in depth and have five 15.2-m panels

of 19.1-, 25.4-, 31.7-, 38.1-, and 50.8-mm bar mesh (MNDNR

1993). In our analysis, we used data collected 2002–2011

because, in 2002, the number of set gill nets was expanded to

52 in order to cover the entire lake (i.e., both near- and off-

shore). Walleyes collected in the surveys were enumerated,

measured (total length in mm), weighed (g), and examined

internally to determine their sex and maturity. Otoliths were

removed from all of the captured Walleyes, and used to esti-

mate ages. Estimated ages ranged from 0 to 25 years, but fish

aged 16 years and older were combined into a single age-

group (16C). For our analysis, we added one year to each fall-

estimated age to correspond with the following year’s spawn-

ing age, resulting in ages 1–16 and 17C rather than 0–15 and

16C. Mean weight-at-age estimates were calculated for all

Walleyes (for YPR calculations) and for mature Walleyes

only (for SBPR calculations). The proportion of Walleyes

mature at age were calculated from the sex and maturity data

(Table 2). We did not need to make adjustments to the mean

weights at age from the fall survey, to account for the spring

spawning weights, because we used spawner biomass metrics

that were based on ratios. Instantaneous natural mortality (M)

was assumed to be related to body size and decline with age

(modified from Lorenzen 1996; Hansen et al. 2011: Table 2).

Specifically, we estimated M for the males and females sepa-

rately, using the lower 90% confidence interval of a mortality-

weight model for juvenile and adult fish in lakes (Lorenzen

1996), and then we took the average of the mortalities. Aver-

age sex- and age-specific instantaneous tribal fishing mortality

(Tribal F), 2002–2011, was estimated with a statistical catch-

at-age (SCAA) model and treated as constant for this analysis

(Table 2).

Bluegill data.—Data collected during MNDNR long-term

monitoring were used to estimate Bluegill YPR and SBPR.

Bluegills were sampled during the summer, 2008–2011, from

four lakes, using trap nets that each consisted of two 0.9-m £1.8-m frames; a single 12.2-m lead; a cod end with five 0.8-m

diameter hoops and two throats; and 19-mm, bar-mesh, nylon

webbing (MNDNR 1993; McInerny and Cross 2005). Fish

were measured to total length (mm), weighed (g), and sub-

sampled for internal determinations of sex and maturity. Oto-

liths were also removed from a subsample of Bluegills and

used to estimate their age. Estimated ages ranged from 1 to

12 years, but fish ages 10 years and older were combined into

a single age-group (10C). Mean weight-at-age estimates were

calculated for all Bluegills with data from all the lakes in all

years. The mean weight at age of mature Bluegills and the pro-

portion of Bluegills that were mature at age were calculated

from sex and maturity data of Elk Lake because this was the

only lake sampled during Bluegill spawning (Table 3). Blue-

gill M was assumed to be a constant 0.3 for all ages (Beard

et al. 1997).

Computation of YPR and SBPR.—A YPR analysis was con-

ducted to estimate the yield to anglers per fish (for fish that had

FIGURE 1. Walleye population trends at Mille Lacs Lake, Minnesota, 1986–

2013, as estimated from (1) fall gill-net assessment catches, in kg per net, of

mature Walleyes (primary y-axis), and (2) stock assessment model spawner

biomass (secondary y-axis). Open triangles represent fall gill-net catches from

32-net annual assessments, 1986–2013 (maturity determined beginning in

1986), at locations primarily located near shore. The solid circles represent

catches from fall surveys that used either eight (1998–2001) or twenty (2002–

2013) gill-net sets, primarily located off shore. The solid squares are the esti-

mated spawner biomasses from the SCAAmodel. The Loess method smoothed

curves by applying a stiffness parameter, f D 2/3, to all three time series.

TRADE-OFFS BETWEEN YIELD AND SPAWNERS PER RECRUIT 3

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reached age 1), under different fishing regulation scenarios,

using a modified Thompson-Bell model (Ricker 1975; Nelson

2014). An SBPR analysis was conducted to estimate spawning

potential (Gabriel et al. 1989; Nelson 2014) under the same

fishing regulation scenarios used in the YPR analysis. The esti-

mates of YPR and SBPR were generated separately for the

male and female recruits, and then they were summed to obtain

the population YPR and SBPR. Model inputs included the

sex- and age-specific mean weights and the proportions mature

for both Mille Lacs Lake Walleyes (Table 2) and Minnesota

Bluegills (Table 3). Because tribal fishing for Walleyes on

Mille Lacs Lake used a quota that is a relatively constant frac-

tion of Walleye biomass, and because fishing methods were

also relatively stable, sex- and age-specific Tribal F was set

TABLE 2. Sex-specific mean weight at age for all Walleyes and mature Walleyes, and proportion of mature Walleyes by sex. Walleyes were sampled during

fall gill-net assessments in Mille Lacs Lake during 2002–2011. Instantaneous natural mortality by age was estimated as a function of body weight; sex-specific

tribal fishing mortality was the 2002–2011 average of rates, as estimated by the walleye SCAA model. Mean angling catch-and-release mortality by age during

2004–2013 was estimated using relationships derived by Reeves and Bruesewitz (2007).

Mean weight,

all fish (kg)

Mean weight,

mature fish (kg)

Proportion

mature

Tribal fishing

mortality

Age Females Males Females Males Females Males Natural mortality Females Males Angling release mortality

1 0.05 0.05 0 0 0 0 0.73 0 0 0.066

2 0.13 0.13 0 0 0 0 0.52 0 0 0.047

3 0.33 0.32 0.45 0.39 0 0.26 0.38 0 0.01 0.036

4 0.62 0.57 0.77 0.58 0.08 0.95 0.31 0 0.13 0.037

5 0.94 0.76 0.96 0.76 0.75 1.00 0.27 0.02 0.16 0.038

6 1.24 0.92 1.24 0.91 0.97 1.00 0.25 0.02 0.11 0.040

7 1.46 1.09 1.46 1.09 0.99 1.00 0.23 0.02 0.09 0.042

8 1.68 1.17 1.68 1.17 0.98 1.00 0.23 0.02 0.08 0.046

9 1.87 1.29 1.87 1.29 1.00 1.00 0.22 0.02 0.07 0.048

10 2.00 1.32 2.00 1.32 1.00 1.00 0.22 0.01 0.07 0.063

11 2.18 1.35 2.18 1.35 1.00 1.00 0.21 0.01 0.08 0.063

12 2.33 1.46 2.33 1.46 1.00 1.00 0.20 0.02 0.09 0.063

13 2.52 1.56 2.52 1.56 1.00 1.00 0.20 0.02 0.09 0.063

14 2.57 1.65 2.57 1.65 1.00 1.00 0.20 0.02 0.09 0.063

15 2.56 1.68 2.56 1.68 1.00 1.00 0.20 0.02 0.09 0.063

16 2.71 1.64 2.71 1.64 1.00 1.00 0.19 0.02 0.09 0.063

17 2.83 1.69 2.83 1.69 1.00 1.00 0.19 0.02 0.09 0.063

TABLE 3. Sex-specific mean weight at age for all Bluegills and mature Bluegills, and proportion of mature Bluegills by sex. Bluegills were sampled during

summer trap-net assessments on four Minnesota lakes in 2008–2011.

Mean weight,

all fish (kg)

Mean weight,

mature fish (kg) Proportion mature

Lake (location) Age Females Males Females Males Females Males Natural mortality Release mortality

Elk

(47�110N, 95�130W)

1 0.008 0.008 0.008 0.009 0.00 0.00 0.30 0.10

2 0.013 0.014 0.014 0.014 0.01 0.00 0.30 0.10

Hill

(47�110N, 93�350W)

3 0.023 0.025 0.031 0.018 0.03 0.00 0.30 0.10

4 0.033 0.044 0.036 0.044 0.08 0.31 0.30 0.10

Pearl

(45�230N, 94�180W)

5 0.076 0.097 0.076 0.097 0.35 0.82 0.30 0.10

6 0.075 0.100 0.075 0.092 0.70 0.96 0.30 0.10

Portage

(46�570N, 95�070W)

7 0.097 0.129 0.097 0.129 1.00 1.00 0.30 0.10

8 0.128 0.154 0.128 0.154 1.00 1.00 0.30 0.10

9 0.150 0.179 0.150 0.179 1.00 1.00 0.30 0.10

10 0.165 0.200 0.165 0.200 1.00 1.00 0.30 0.10

4 SCHMALZ ET AL.

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equal to its own source of mortality and held constant across all

regulation evaluations (Table 2). This allowed us to consider

the effect of constant tribal fishing on spawner biomass, calcu-

late angler-specific yield, and then compare fishery benchmarks

to unfished spawner biomass (e.g., SSBR).

Partial recruitment vectors.—Instantaneous fishing mortal-

ity (F) by angling was calculated by multiplying the fully

recruited F with a partial recruitment vector. For both species,

partial recruitment vectors were specified two ways. In the first

scenario, and for both Walleyes and Bluegills, a recruitment

vector was set, according to a logistic fishing selectivity func-

tion that had a slope of 0.3 and a location parameter equal to

the age at which 50% selectivity occurred, to evaluate the

effects of increasing age at 50% selectivity to the fishery on

the trade-offs between yield and spawner biomass. This

method was used to compare YPR and SSBR isopleths that we

also developed in this study.

In the second vector scenario, partial recruitment to the

angling fishery at age (partial F at age) was specified according

to numerous length-specific regulations. For Walleyes, partial F

at age was estimated for each fishing regulation by adjusting

sex-specific capture selectivity (estimated using methods devel-

oped by Myers et al. 2014) and by using harvest rates (propor-

tion of harvested Walleyes from total catch), and estimated

release mortality. Harvest rates were estimated from annual creel

survey data that were collected at Mille Lacs Lake under several

length-based regulations (Table 1). When we evaluated angling

length regulations that were not previously used for Walleyes at

Mille Lacs Lake, and wished to combine them with observed

length regulation data, we assumed the harvest rates in those

new length bins to be the same as the harvest rates for the bins

from the observed regulation data (e.g., the harvest rates for a

381-mm minimum length from the measured data could be used

for length limits less than 381 mm). Harvest rate estimates were

standardized for each 25.4-mm length bin based on both the creel

data and whether a given regulation allowed for harvest in a

given length bin. An exception was made for those bins that

were nearest to a regulation limit (i.e., the bin either immediately

before a minimum or immediately after a maximum). In those

length bins, we used professional judgment to set noncompliance

harvest rates D 0.2, for lengths shorter than the limits, and 0.15

for lengths longer than the limits. Average, age-specific, postre-

lease angling mortality rates were based on a function of fish

length and water temperature (Reeves and Bruesewitz 2007;

Table 2). For Bluegills, partial F at age was estimated for each

fishing regulation from their age-specific harvest rates under the

various length-based angler restrictions (Table 4). Postrelease

angling mortality was held constant across all ages, at 0.1

(Table 3; Beard et al. 1997). The length-based partial F at age

vectors were converted to sex-specific, age-based F at age vec-

tors with sex-specific, age-length keys. For Walleyes, we consid-

ered 21 different angling regulations: four minimum length

limits (Min), ten harvest slot limits (HS), and seven protected

slot limits (PS) (Table 4). For Bluegills, we considered eight

different regulations: three minimum length limits, three pro-

tected slot limits, and two harvest slot limits (Table 4). A harvest

slot specifies a range of lengths from which harvest is allowed,

and a protected slot specifies a range of lengths from which har-

vest is prohibited (Isermann and Paukert 2010). Calculations of

YPR and SBPR were made using (1) a simplified formulation

that was written in R Statistical Software by M. H. Prager (Con-

sulting in Marine Resource Population Dynamics, personal com-

munication), and (2) the ypr and sbpr functions in the R

package, “fishmethods” (Nelson 2014).

Visualization of trade-offs.—When fishing regulation

options are numerous, choosing the appropriate graphical

display to visualize the trade-offs among various population

and fishery metrics can be challenging. We chose to evalu-

ate the trade-offs between fishery yield and spawner bio-

mass using three types of visual display. First, we added the

SSBR isopleths to the traditional YPR isopleths (Beverton

and Holt 1957) to create graphs that compared the changes

in the YPR and SSBR as functions of the fully recruited

angling mortality (Full Angling F) and the age at which

50% fishery selectivity occurs (Goodyear 1993; M. H.

Prager, Consulting in Marine Resource Population Dynam-

ics, personal communication). Since we were interested in

the trade-off comparisons among specific length-based fish-

ing regulations (i.e., selectivity patterns), we plotted the

YPRs as functions of the SSBRs, specifying the points

where equal fishing effort would occur along the YPR-

SSBR functions, under different selectivity patterns, to help

identify the better regulations. We compared three length-

specific angling regulations for each species: the Walleye

regulations consisted of a 457-mm minimum length limit

(Min457), a 457-mm to 711-mm protected slot limit

(PS457–711), and a 457-mm to 508-mm harvest slot limit

(HS457–508); and the Bluegill regulations consisted of a no

minimum length limit (NoMin), a 178 mm minimum length

limit (Min178), and a 127-mm to 178-mm harvest slot limit

(HS127–178). Each Walleye regulation was compared at

three levels of Walleye F, as estimated from Walleye

SCAA models, 1987–2013: (1) Low F D 0.2, which was the

10th percentile F estimate; (2) average F D 0.4, which was

the median F estimate; and (3) high F D 0.75, which was

the 90th percentile estimate. For consistency, we used the

same three levels of F for Bluegills. Finally, we plotted

SSBR as a function of YPR, with an average F D 0.4, with

a high F D 0.75 (Walleyes only), and under numerous

selectivity patterns (Table 4), to identify the trade-offs

between fishery yield and spawner biomass across a range

of alternative regulations.

RESULTS

The SSBR and YPR isopleths were the first graphical

approach we used to compare fishery management trade-offs.

These graphs successfully demonstrated that a combination of

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delayed age at 50% selection and high F maximized the YPR

of both Mille Lacs Lake Walleyes (Figure 2) and Minnesota

Bluegills (Figure 3). In both cases, the resulting estimated

SSBRs were quite low (0.2 < SSBR< 0.3). At a given level

of F, an increased age at 50% fishery selectivity (analogous

to minimum length restrictions) resulted in increased YPR

and SSBR, up to an ideal age and depending on F; and then

the YPR declined as the SSBR continued to increase. For

example, at an average F D 0.4 for Mille Lacs Lake Wal-

leyes, an age of 3.9 years at 50% selection was needed to

obtain an SSBR of at least 0.3 (Figure 2). At a constant age

and at 50% fishery selectivity, increasing the F resulted in a

higher YPR and a lower SSBR, particularly for younger ages.

For example, from a low F D 0.2 to a high F D 0.75, 50%

selection for age-4 Walleyes led to estimated SSBR declines

from > 0.4 to »0.2, while YPR increased from > 0.12 kg to

> 0.18 kg (Figure 2).

In our more detailed graphical approach, we compared spe-

cific length-based regulations by plotting points of equal F

along the SSBR-YPR functions. For both fishery examples,

we found that the Min regulations resulted in higher SSBRs,

for any given YPR across its entire range, relative to all other

types of regulations. For Mille Lacs Lake Walleyes, a Min457

was better than both HS457–508 and PS457–711 (Figure 4).

The Min457 also resulted in a higher YPR than what was

observed for both the HS457–508 and PS457–711, for any

given SSBR. For Minnesota Bluegills, a Min178 was better

than both a NoMin and an HS127–178 (Figure 5). Of greater

interest, however, was our ability to plot and compare the

YPR and SSBR at common levels of F and effort, across the

TABLE 4. Complete list of the angling harvest length restrictions used in the yield per recruit and spawner biomass per recruit analysis for Mille Lacs Lake

Walleyes and Minnesota Bluegills. See Table 1 for definitions of angling regulation abbreviations. Regulation numbers are used in Figure 6 (Walleyes) and Fig-

ure 7 (Bluegills).

Angling regulation Abbreviation Regulation number

Mille Lacs Lake Walleyes

NoMin (One fish >508 mm) NoMin 1

381-mm Min Min381 2

432-mm Min Min432 3

457-mm Min Min457 4

482-mm Min Min482 5

356–406-mm HS (one fish >711 mm) HS356-406 6

381–432-mm HS (one fish >711 mm) HS381-432 7

406–457-mm HS (one fish >711 mm) HS406-457 8

406–508-mm HS (one fish >711 mm) HS406-508 9

432–482-mm HS (one fish >711 mm) HS432-482 10

457–508-mm HS (one fish >711 mm) HS457-508 11

457–559-mm HS (one fish >711 mm) HS457-559 12

508–559-mm HS (one fish >711 mm) HS508-559 13

508–609-mm HS (one fish >711 mm) HS508-609 14

533–584-mm HS (one fish >711 mm) HS533-584 15

508–711-mm PS (one fish >711 mm) PS508-711 16

457–711-mm PS (one fish >711 mm) PS457-711 17

432–711-mm PS (one fish >711 mm) PS432-711 18

406–508-mm PS (one fish >711 mm) PS406-508 19

381–482-mm PS (one fish >711 mm) PS381-482 20

356–457-mm PS (one fish >711 mm) PS356-457 21

Minnesota Bluegills

NoMin NoMin 1

152-mm Min Min152 2

178-mm Min Min178 3

203-mm Min Min203 4

152–203-mm PS PS152-203 5

203–254-mm PS PS203-254 6

127–178-mm HS HS127-178 7

152–203-mm HS HS152-203 8

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different fishing regulations, in order to identify those regula-

tions that were superior to others. A regulation that is superior

to another regulation (i.e., “win-win”) is one that results in

both a higher YPR and a greater SSBR, at common F. In the

FIGURE 2. Mille Lacs Lake Walleye YPR and SSBR as a function of the age

at which 50% selection to the angling fishery occurs, at Full Angling F. The hor-

izontal dashed line represents the age (3.9 years) where 50% selection results in

an SSBR D 0.3 at a median F D 0.4, as estimated from the SCAA model. The

vertical dashed lines represent low F D 0.2 (10th percentile of SCAA-estimated

F) and high F D 0.75 (90th percentile of SCAA-estimated F).

FIGURE 3. Minnesota Bluegill YPR and SSBR as a function of the age at

which 50% selection to the angling fishery occurs, at Full Fishing F. The verti-

cal dashed lines represent low F D 0.2, median F D 0.4, and high F D 0.75.

FIGURE 4. SSBR versus YPR for three length-based angling regulations for

the Mille Lacs Lake Walleye fishery. The levels (symbols) of full fishing mor-

tality rate, under each fishing regulation (lines), are the10th percentile (F D0.2), median (F D 0.4), and 90th percentile (F D 0.75) of SCAA-estimated F.

The horizontal line at SSBR D 0.3 is a reference point. This example shows a

regulation (HS457-508) that is uniformly superior [higher YPR and SSBR

(“win-win”) at all levels of F] to another regulation (PS457-711). Moving

from a PS457-711 regulation to a min457 regulation results in gains to both

the yield and spawner biomass, at high F, but most values of full F result in

“win-neutral” outcomes where the yield can be increased with either little or

no change in spawner biomass. Min457 D minimum length 457 mm, HS457–

508 D harvest slot limit from 457 to 508 mm, and PS457-711 D protected slot

limit from 457 to 711 mm.

FIGURE 5. SSBR versus YPR for three length-based angling regulations for

the Minnesota Bluegill fishery. The levels (symbols) of full fishing mortality

rate under each fishing regulation (lines) are F D 0.2, FD 0.4, and F D 0.75.

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Mille Lacs Lake Walleye example, HS457–508 was superior

to PS457–711 because all levels of F provided both a higher

YPR and a greater SSBR (Figure 4, symbols). The Min457

regulation demonstrated both “win-win” and “win-neutral”

(i.e., an outcome from a regulation that results in a greater

yield with either little or no change in SSBR) outcomes. The

PS457–711 regulation demonstrated both “win-neutral” and

“win-lose” (i.e., an outcome from a regulation that results in a

greater yield with a decline in SSBR) outcomes when com-

pared to the HS457–508 regulation and depending on the level

of F (Figure 4, symbols). At low F D 0.2, the Min457 regula-

tion resulted in greater YPR with either little or no change to

SSBR when compared to the PS457–711 regulation (Figure 4,

open squares). However, at high F D 0.75 and Min457, both

YPR and SSBR were higher than with the PS457–711 regula-

tion (Figure 4, solid circles). At both low F D 0.2 and median

F D 0.4, the Min457 regulation resulted in a higher YPR at the

expense of a lower SSBR than when the HS457-508 regulation

was used (Figure 4). However, at high F D 0.75, the Min457

resulted in a higher YPR, with either little or no change to the

SSBR (Figure 4, solid circles).

The plots of SSBR versus YPR showed that there is a gen-

eral trade-off between decreased SSBR and increased yield.

They also showed that similar types of regulations (e.g., HS

limits) were generally grouped together under similar combi-

nations of SSBR and YPR, particularly for the Mille Lacs

Lake Walleyes. For example, the harvest slot limits generally

favored an SSBR to a YPR, whereas the minimum length lim-

its generally favored a YPR to a SSBR. Protected slot limits

generally had both lower SSBRs and lower YPRs (see lower

and further left sections on the graphs of Figure 6). Specifi-

cally, at an average F D 0.4, the highest YPR and lowest

SSBR occurred with the NoMin (regulation 1; Figure 6, top

panel). NoMin (1), a Min381 (2), and a PS508–711 (16) were

the only Walleye regulations that had SSBR estimates below

0.3 (Figure 6). Ten other regulations estimated SSBR less

than 0.4 at average F D 0.4: five of the protected slot limits,

two of the minimum length limits, and three of harvest slot

limits (Figure 6, top panel). At high F D 0.75, the Min381

estimated the highest YPR, and the NoMin estimated the low-

est SSBR (Figure 6, bottom panel). At high F D 0.75, all but

two regulations estimated SSBR less than 0.3; only those HS

limits with a minimum length of at least 508 mm estimated

the SSBR either at or above 0.3; and none of the regulations

estimated the SSBR above 0.4 (Figure 6, bottom panel).

Unlike the Walleye regulations, the Minnesota Bluegill reg-

ulations did not produce obvious groups (Figure 7). Increased

minimum length limits resulted in less yield and greater

spawner biomass. Restricting harvest to a specific slot limit

that had the same lower end as a Min (e.g., HS152-203 com-

pared to Min152) resulted in a substantially lower yield with

minimal increases in the spawning stock. Regulations at the

upper limits of both the YPR and SSBR helped to establish a

frontier. Below and to the left of the frontier, there were only

“win-lose” (i.e., increasing one metric results in a decrease in

the other) and “lose-lose” (i.e., decreases in both metrics)

outcomes.

DISCUSSION

We demonstrate a relatively simple approach for presenting

a large amount of information about the trade-offs between

fishery yield and spawner biomass. Each type of graph had its

own strengths and weaknesses. Plots of spawning potential

ratio isopleths, superimposed on YPR isopleths, are good start-

ing points for evaluating families of management options.

These plots can be indexed by size (or age) at entry into a

FIGURE 6. SSBR versus YPR for 21 different length-based fishing regulations

for Mille Lacs Lake Walleyes at average F D 0.4 (top panel) and high

FD 0.75 (bottom panel). The regulations (described and numbered in Table 4) are

grouped by color based on one of three general categories in which they were

placed: blackD HS regulations, redDMin regulations, blueD PS and NoMin reg-

ulations. Each vertical line represents the median YPR at the given level of Full

Angling F. The horizontal lines reference SSBRD 0.3 and SSBRD 0.4. The solid

black line around the outside (up and to the right of the data) shows the frontier

where either YPR or SSBR can increase, but only by reducing the other.

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fishery and by Full Angling F. They are useful visual tools for

evaluating the trade-offs that occur when fishing regulations

that delay the age of fishing vulnerability (e.g., minimum

length restrictions) are applied; however, they do not easily

evaluate other common, but more complex, length restrictions

(e.g., slot limits).

The SSBR-YPR function plots can be used to compare many

size-based regulations over a range of fishing mortality rates,

and thus may be of more general utility than the YPR-SSBR

isopleths. However, SSBR-YPR plots can become crowded as

the number of comparison regulations increases. Irwin et al.

(2008) plotted similar trade-offs between Yellow Perch harvest

and spawner biomass in Lake Michigan using estimates from a

stochastic simulation model, but also limited the display to three

harvest control rules.

Parma (2002) successfully plotted Pacific Halibut Hippo-

glossus stenolepsis yield, and the probability that Halibut

spawner biomass would fall below minimum thresholds, as

two separate functions, with constant F harvest control rules.

In our study, we sought to compare a large number of regula-

tory options for Mille Lacs Lake Walleyes; therefore, we

adopted a graphical format (Figure 6) that simultaneously con-

sidered YPR and SSBR outcomes from 21 regulations at a

given level of Full Angling F. We specified the most likely F

based on a Walleye SCAA model of current data. We also pre-

pared a similar graph to explore what would happen if F was

higher than anticipated. Thus, we could summarize the impli-

cations of 21 regulations, using two graphs: one with average

F and one with high F. By applying this same approach to

Minnesota Bluegills, we also demonstrated the general appli-

cability of the approach with a separate data set.

In both examples, there is a clear frontier of conditions

where an increase in one metric can only be achieved through

a reduction in the other (Figures 6, 7). For Mille Lacs Lake

Walleyes, our evaluations showed that the protected slot limits

were inferior to both the minimum length limits and the har-

vest slot limits, both of which were further (lower and further

left) from the frontier than the protected slot limit. Regulations

with a minimum length restriction (Min and HS) fell either on

or nearer to the frontier relative to the above regulations. For

Minnesota Bluegills, the minimum length limits fell either on

or nearer to the frontier than either the protected slot limits or

the harvest slot limits. Protected slot limit regulations for

Bluegills generally resulted in a higher SSBR than the SSBR

with harvest slot limit regulations. When there are conflicting

yet common goals of maximizing yield and maintaining ade-

quate spawner biomass, managers may want to consider regu-

lations that include a minimum length restriction, provided

release mortality is not high. For Mille Lacs Lake Walleyes,

we also showed that changes within a regulation type (e.g.,

changing from one PS limit to another) will probably have a

smaller effect on a fishery than changes between regulation

types (e.g., changing from a PS limit to a HS limit). It is

important to note that our results were based on specific rates

of mortality, average recruitment, and a range of SSB, which

were all derived from data collected during a specific time

period. Benchmarks derived from this time period may be

inappropriate if future conditions differ greatly.

The Mille Lacs Lake Walleye fishery is shared by both

angler and tribal subsistence fishers. For the purpose of this

analysis, the tribal fishery was fixed at its average. To make

decisions about the joint effects of state angler and tribal fisher

harvests, managers should do additional evaluations that include

variable scenarios for the tribal fishery. However, between 2002

and 2011, the tribal fishery was relatively constant in terms of

gear used and total harvest: approximately 95% of Walleyes

were harvested from 44.5-mm bar measure, mesh gill nets; and

the rest were harvested with spears. This stable tribal exploita-

tion rate, however, is among a wide variety of management

alternatives that could be considered. In our analysis, the effects

from the various options for the angling fishery had minimal

impact on the tribal fishery, in part because the tribal harvest is

lower than the angler harvest. A regulation’s effects relative to

a biological benchmark (e.g., 30% SSBR) is dependent on the

assumptions for the tribal fishery; therefore, we recommend that

those effects be calculated for a variety of possible tribal fishery

options. Similarly, a modest error in the specification of full

fishing F has a minimal effect on the cross comparison of regu-

lations but a larger effect on the comparison of each regulation

with its biological benchmark.

Although we presented metrics focused on conservation

(e.g., the effects of various levels of F on spawner biomass),

this same approach could be used to compare other trade-offs

that may be of interest to fishery managers. Visual presentations

similar to ours could be used to compare the trade-offs between

the total catch and the catch of fish above a certain size, perhaps

when either a quality or trophy component is important to that

FIGURE 7. SSBR versus YPR for eight different length-based fishing regu-

lations for Minnesota Bluegills at F D 0.4. See Table 4, for regulation descrip-

tions, and Figure 6 for color and line descriptions.

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fishery. One could also model the trade-offs between the catch

(and release) and the harvest, or alternatively consider a catch

rate per recruit (for a size range of interest) as the metric of

angler benefit (rather than yield in weight).

ACKNOWLEDGMENTS

We thank Michael H. Prager, the late Ransom A. Myers,

and the members of the MNDNR and Great Lakes Indian Fish

and Wildlife Commission 1837 Fisheries Committee for their

helpful suggestions. We also thank Charles Anderson, John

Hoxmeier, Neil Kmiecik, Don Pereira, Dan Daugherty (AFS

editor), the anonymous AFS associate editor, and three anony-

mous reviewers for providing insightful comments on previous

drafts. We thank Mike McInerny and Cindy Tomcko for their

assistance with the Bluegill data. The study was funded in part

by the Federal Aid in Sport Fish Restoration (Dingell–John-

son) Act. This is Virginia Institute of Marine Science Contri-

bution 3519.

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