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Population Model Suggests New Threshold for Managing Alaska«s
Togiak Fishery for Pacific Herring in Bristol Bay
Fritz Funk and Katherine A. Rowell
Reprinted from the
Alaska Fishery Research Bulletin
Vol. 2 No. 2, Winter 1995
Alaska Fishery Research Bulletin 2(2):125¬136. 1995.
Copyright © 1995 by the Alaska Department of Fish and Game
Population Model Suggests New Threshold for Managing Alaska«s
Togiak Fishery for Pacific Herring in Bristol Bay
Fritz Funk and Katherine A. Rowell
ABSTRACT: The threshold biomass for fisheries on Pacific herring Clupea pallasi that spawn near Togiak, in Bristol
Bay, Alaska, was reviewed based on the data collected in the decade following threshold harvest policy initiation in
1987. The current threshold of 31,752 mt (35,000 tons), below which fishing is precluded, was found to be too low.
This threshold had been set at 25% of the spawning biomass during a period that included substantial harvests. A
threshold set at 25% of the average unfished biomass (AUB) is widely used in other herring fisheries along the
Pacific coast. A 1,000-year simulation of abundance was used to determine AUB under several possible spawner-
recruit relationships and sets of stock-assessment data. Four alternative age-structured assessment (ASA) models fit
to the available data for Togiak herring under different sets of assumptions were used to represent the uncertainty in
the stock-assessment data. A large discrepancy between abundance trends from aerial surveys and trends apparent
in age-composition data resulted in a large amount of uncertainty about past biomass levels in the ASA model,
which was reflected in the AUB estimates. Ricker and empirical spawner-recruit models fit to the information from
the ASA analysis were used to simulate density-dependent effects on recruitment. The uncertainty in the basic
population dynamics data provoked a wide range of AUB estimates under different sets of assumptions. AUB
estimates ranged from approximately 159,000 to 433,000 mt, and the resulting thresholds ranged from approxi-
mately 40,000 to 108,000 mt. Based on this information, we recommend that the Togiak threshold be raised to at
least 45,000 to 50,000 mt, pending further resolution of the discrepancies between abundance trends from aerial
surveys and abundance trends from age compositions. Setting thresholds at 25% of AUB only rarely triggered
fishery closures and these fishery closures produced very little reduction in long-term average yield.
INTRODUCTION
Harvest policies for Pacific herring Clupea pallasi
fisheries in Alaska include 2 types of management
control: thresholds and exploitation rates. When the
spawning biomass is below the threshold, no commer-
cial fishing is allowed. When the spawning biomass is
above the threshold, exploitation rates are generally
20%. Some fisheries gradually increase the exploita-
tion rate up to a 20% maximum as the biomass in-
creases above the threshold. Two types of thresholds
can be defined depending on the rationale used in
establishing the threshold. A conservation threshold,
below which a population may experience complete
reproductive failure, might be defined based on fea-
tures of a well-understood spawner-recruit relation-
ship. This type of threshold is designed to prevent the
extinction of the species or stock. Alternatively, for
Pacific herring and many other exploited species,
a productivity threshold is defined in terms of quickly
rebuilding a population to commercially productive
levels. Thresholds defined in terms of productivity are
always higher than conservation thresholds designed
to merely prevent extinction.
Similar to many harvest policies, the threshold/
exploitation rate harvest policy reflects a tradeoff
between maximizing the yield from a resource and
maintaining stable yields over the long term. For ex-
ample, a herring exploitation rate > 20% will increase
the average yield considerably, but stock size and har-
vests will be much more variable from year to year. At
very high exploitation rates stock size fluctuations can
be so pronounced that reproductive failures occur dur-
ing periods of low abundance. At very low exploita-
tion rates, yields can be more constant from year to
year, and stock size will fluctuate less. The 20% ex-
ploitation rate for herring is a compromise between
the extremes.
A threshold is included in the harvest policy for
Pacific herring to combine some advantages of constant
Authors: FRITZ FUNK is statewide herring biometrician for the Alaska Department of Fish and Game, Commercial Fisheries
Management and Development Division, P.O. Box 25526, Juneau, AK 99802-5526. KATHERINE A. ROWELL is the Togiak Herring
Research Biologist for the Alaska Department of Fish and Game, Commercial Fisheries Management and Development Division,
333 Raspberry Road, Anchorage, AK 99518-1599.
125
126 Articles
exploitation rate policies with some advantages of fixed
escapement policies. When the biomass is high, a con-
stant exploitation rate is used to provide a balance
between average yield and variation of yield. When
the biomass drops to low levels, the fixed escapement
strategy is adopted to protect the population and more
quickly return it to productive levels.
The largest herring fishery in Alaska occurs on
herring that spawn along the north shore of Bristol
Bay, near the village of Togiak (Figure 1). Catches in
this fishery have ranged from 10,000 to 27,000 mt since
1980. The current threshold for the Togiak fishery of
31,752 mt (35,000 tons) was established by regula-
tion in 1987. When this regulation was adopted, only
a limited time series of stock assessment information
was available for the Togiak herring population. Ini-
tial thresholds for Togiak and other Alaskan herring
fisheries were established rather arbitrarily, usually
based on some proportion of past catches or abun-
dances. At Togiak the threshold level was set at 25%
of the average annual aerial survey biomass estimates
from 1978 through 1985, excluding 3 years when abun-
dance estimates were unreliable. The purpose of our
analysis is to update threshold recommendations for
the Togiak herring fishery based on recent stock-
assessment information and the contemporary concept
of productivity thresholds.
Most threshold analyses express threshold levels
as a percentage of a long-term average of annual
spawning biomass in the absence of fishing, or aver-
age unfished biomass (AUB), which is also referred to
as ƒpristine biomass.≈ Although AUB is an estimate of
the long-term average biomass absent fishing, AUB is
of necessity based on observed historical data that al-
most always has been collected under the influence of
fishing. Simulation models (e.g., Zheng et al. 1993;
Haist 1990; Schwiegert 1993) are usually used to try
to remove the effects of fishing on the recruitment level
and observed measures of abundance when calculat-
ing AUB.
Threshold levels have been set at 25% of AUB for
the major British Columbia herring fisheries since 1985
(Haist 1990). The British Columbia threshold criteria
was originally based on the simulation model described
in Hall et al. (1988), and was subsequently reviewed
by Haist (1990) and Schwiegert (1993).
Recently, Zheng et al. (1993) and Zheng (1994)
analyzed harvest policies for Pacific herring in Alaska
using a much more comprehensive model than earlier
studies. This model incorporated stock assessment
measurement error, harvest policy implementation
error, autocorrelation of environmental effects on re-
cruitment, and alternative forms of spawner-recruit
relationships. Thresholds set at 25% of AUB with ex-
ploitation rates of 20% were on the conservative side
of the recommendations by Zheng et al. (1993) and
Zheng (1994). Although setting exploitation rates at
20% was more conservative than their optimal policy,
they noted the effect of having such a conservative
harvest policy caused little loss in their measure of
long-term yield and stability of yield. At a 20% ex-
ploitation rate, average yields were maximized when
ALASKA
Figure 1. Location of herring spawning and sac roe fishery near Togiak in Bristol Bay.
127 Model Suggests New Threshold for Togiak Herring • Funk and Rowell
thresholds were approximately 25% of the AUB (Fig-
ure 2). Our analysis applies the methods of Zheng et
al. (1993) using a recent time series of abundance data
for Togiak herring from an age-structured assessment
(ASA) model (Rowell and Funk 1994). The objective
of our work was to recommend a revised threshold for
management of the Togiak herring fishery that reflects
the uncertainty in the stock-assessment information
for Togiak herring.
METHODS
Following Zheng et al. (1993) and Zheng (1994),
we determined AUB for the Togiak herring popula-
tion using a population-simulation model based on
historical data. The model simulated a herring popu-
lation undergoing the processes of recruitment, growth,
maturation, and natural mortality for a long period.
Because all of the pertinent data for Togiak herring
were collected after substantial fisheries began, we
assumed throughout this analysis that fishing effects
were confined to removals from the population. There-
fore, we assumed that fishing did not affect growth,
natural mortality, maturity, or the relationship between
spawning biomass and recruits. Two primary areas of
uncertainty about AUB were investigated: (1) uncer-
tainty about the relationship between spawners and
recruits, and (2) uncertainty in stock assessment in-
formation. A great deal of the uncertainty about the
spawner-recruit relationship was due to the relatively
100%
short time series of available data. Consequently, there
is a wide range of possible functional forms for the
spawner-recruit relationship, as well as a large amount
of variability in the relationship. The uncertainty in
stock assessment for Togiak herring results primarily
from poor correlation between aerial survey abundance
trends and long-term abundance trends evident in the
time series of age-composition data. Stock-assessment
uncertainty also results from a relatively wide range
of possible maturity schedules and natural survival and
from the effects of aging error on stock-assessment
estimates.
Population Dynamics Data Sources
The basic set of population dynamics data came
the ASA model used for the 1995 Togiak herring fore-
cast (Rowell and Funk 1994). This ASA model syn-
thesizes the multitude of observed data for 1978 to
1994 (purse seine age compositions, age compositions
of the total run, and selected aerial survey biomass
estimates) into a single set of estimates of cohort abun-
dance, maturity, purse seine availability, and survival.
The central problem in interpreting Togiak stock as-
sessment information is that abundance trends from
aerial surveys conflict strongly with abundance trends
determined from the time series of age compositions.
Biomass estimates from aerial surveys describe very
little change in abundance between 1978 to 1994
(Figure 3). However, the time series of age-composi-
tion data collected over this period clearly and consis-
tently show the recruitment and senescence of the very
large 1977 and 1978 year classes. In contrast to the
Percent of Maximum Yield
Maximum at 25% AUB
aerial survey data, age-composition data depict greatly
increased abundance during the mid to late 1980s.
98% Rowell and Funk (1994) attempted to resolve this
96% conflict by selecting a subset of the highest quality
annual aerial survey data. In particular, fishery man-
agers had increased confidence in the recent
(1992¬1994) aerial survey biomass estimates. Rowell
and Funk«s (1994) strategy was to use only the aerial
94%
92% survey estimates from 1981 and 1992¬1994 in their
ASA model and to give these aerial survey estimates
very low weight. The low weights on aerial surveys
were sufficient to stabilize ASA estimates but allowed
90%
88% relative abundance trends to be determined almost en-
0% 10% 20% 30% 40% 50% 60% tirely from the time series of age-composition data.
This effectively constrained biomass estimates early
Threshold Percent of AUB (1981) and late (1992¬1994) in the time series but al-
lowed abundance to fluctuate during the middle to late
Figure 2. Average yield at a 20% exploitation rate as a func-
tion of threshold level where average yield is expressed as 1980s.
a percentage of the maximum yield at a 20% exploitation The conflict between aerial survey and age
rate (data from Zheng 1994). composition abundance trends also increases the
128 Articles
Table 1. Primary differences among the 4 sets of
Pacific herring stock-assessment data used for the
Togiak population simulations.
Model Survival Rate Maturity Age Range
Highest Assessment Low Late 4 to 15+
Medium Assessment Moderate-High Moderate 4 to 15+
Med.-Low Assessment Moderate Moderate 4 to 9+
Low Assessment High Early 4 to 15+
uncertainty about the processes of survival and matu-
ration. In the 1995 Togiak herring forecast analysis
described by Rowell and Funk (1994), reasonable fits
to the age composition and aerial survey data could be
obtained with survival rates as low as 60%, if matura-
tion occurred relatively late, or with survival rates as
high as 85%, if maturation occurred early. Survival
rates and maturity schedules were very closely corre-
lated. In the 1995 Togiak herring forecast analysis
(Rowell and Funk 1994) the effect of aging errors was
Aerial Surveys for tuning ASA Models
Other (poorly rated) Aerial Surveys
Highest Assessment Model
investigated by pooling herring age 9 years and older
into a single category instead of pooling herring age
15 years and older into a single category.
Four sets of population dynamics data resulting
from ASA were used to describe the uncertainty in the
stock-assessment data and the effect of aging error
(Table 1). The 4 sets of stock-assessment data encom-
passed a relatively wide range of survival and matu-
rity estimates (Figure 4). Changing these assumptions
had little effect on recent abundance estimates but
strongly affected the magnitude of the run biomass
during the high-abundance period of the mid 1980s
(Figure 3). With no constraints on maturity or survival,
the ASA model resulted in low survival rates, late
maturities, and a relatively high peak (1985) biomass
estimate of 673,000 mt (highest assessment model).
Specifying that maturation occurred at relatively young
ages resulted in a high survival rate (constrained at
85%) and produced a peak biomass estimate of only
337,000 mt (lowest assessment model). Pooling all
herring age 9 and older into a single category to re-
Assessment Model:
100% Highest
Constrained to Medium
maximum of 85%
Survival Rate
Maturity
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
Run Biomass (mt)
Medium Assessment Model
Medium-Low Assessment Model
Medium-Low
90%
50%
60%
70%
80%
Lowest
Lowest Assessment Model
Constrained to 1 at age 8
0%
20%
40%
60%
80%
100%
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
4 5 6 7 8 9 10 11 12 13 14 15
Year Age
Figure 3. Range of run biomass estimates from the age-struc- Figure 4. Survival rate (top) and maturity (bottom) estimates
tured assessment (ASA) model used for the 1995 Togiak from the 4 age-structured assessment models used for the
forecast of Pacific herring under various assumptions, and Pacific herring Togiak population simulations.
highly and poorly rated aerial survey biomass estimates.
129 Model Suggests New Threshold for Togiak Herring • Funk and Rowell
duce the influence of age determination errors pro-
duced a peak biomass estimate of 471,000 mt (me-
dium-low assessment model). Survival rates and
maturity schedules in this medium-low estimate were
not constrained, and the ASA model produced inter-
mediate values for these parameters. The medium as-
sessment model was used by Rowell and Funk (1994)
as the basis for the 1995 Togiak herring forecast. Peak
biomass (1985) in this model was 517,000 mt. The
maturity schedule was constrained so that maturity at
age 4 was at least 20%, but survival and maturity
estimates were otherwise unconstrained. The lowest
and medium assessment models incorporated age-
dependent survival where survival declined linearly
starting at age 9. The slope of the decline in survival
was estimated by the ASA model.
Much of the uncertainty in the stock-assessment
data results from tuning the ASA model only to early
(1981) and late (1992¬1994) aerial surveys. The re-
cruitment of the 1977 and 1978 year classes was the
dominant event in the period studied, visible as the
large dome shape in biomass, which reached a peak
between 1984 and 1988. After reviewing aerial survey
methods and ratings (Brannian et al. 1993), we deter-
mined that aerial survey ratings during the mid 1980s
were often poor or used different methods than in
recent years (1992¬1994). As a result, aerial survey
biomass estimates from this period may not be com-
parable to those of recent years. Because there were
no comparable or reliable aerial surveys from the mid
1980s, there is considerable uncertainty about the
magnitude of the 1984¬1988 biomass peak.
Uncertainty about some of the past aerial survey
abundance estimates increased the uncertainty about
historical biomass trends. In herring aerial surveys,
surface area measurements of herring schools were
converted to biomass based on a small set of ƒcalibra-
tion samples≈ where observers estimated herring
school sizes just before purse seine vessels captured
and weighed the entire school (Lebida and Whitmore
1985). The quality of aerial survey abundance estimates
was affected by water clarity and length of the survey,
both of which are influenced by weather conditions.
Good weather conditions in recent years (1992¬1994)
have increased the confidence in the total aerial sur-
vey estimate of abundance compared to those of ear-
lier years.
Spawner-Recruit Analysis
The recruitment process for Togiak herring was
simulated using a number of different methods that
were all based on the historical recruitment time series
generated from 1 of the 4 assessment models (Table 2).
The simplest recruitment processes fixed recruitment
at the mean or median of the historical recruitment
time series. Density-independent recruitment was
modeled by selecting 1 of the historical recruitment
estimates at random for each year of the simulation.
For density-dependent recruitment, a Ricker model was
used, where the number of recruits in year y (Ry) was
estimated from the run biomass 4 years earlier (B):
y −4
F By−4 I
a 1−
H
G b K
J (1)
R = B e
y y−4
where a and b are parameters to be estimated. The
Ricker model was used both in a deterministic form
(equation 1) and in a stochastic form with multiplica-
tive lognormal errors.
Lastly, an empirical spawner-recruit model divided
the observed spawner-recruit data into 3 quantiles
based on spawning biomass. When the spawning bio-
mass was within a particular quantile, a number of
recruits was selected at random from the recruitment
data in that quantile.
Average Unfished Biomass Simulations
The Togiak herring population was simulated us-
ing an age-structured model with age 4 as the first age
in the model. Herring age 15 and older were pooled
into a single oldest category, except that in simula-
tions based on the medium-low assessment model data,
herring age 9 and older were pooled into a single
category. The simulation model began with the selec-
tion of a starting population, by choosing 1 of the
1978¬1994 population estimates at random from 1 of
the ASA models (Table 3). The model used annual time
steps, aging cohorts using
Na+1 y+1 = Sa ⋅ Na y
, (2)
, ,
where Nay
is the population size at age a in year y,
,
and Sa is the survival rate for age a from 1 of the 4
assessment models. Run biomass (By) in each year was
computed as
B =∑
ρ
⋅W ⋅ N ,,
y aa ay
(3)
a
where
ρ
a
is the estimated proportion mature at age a,
and Wa is the weight at age a (Table 3). In each year
the number of age-4 recruits (N) was selected based
4, y
on 1 of the spawner-recruit models. The density-
130 Articles
Table 2. Pacific herring year class size at age 4 (millions of fish) estimated from 4 age-structured assessment
(ASA) models of the Togiak population and results of spawner-recruit analyses on the data from each
model.
Year Highest Medium Medium-Low Lowest
Recruited Assessment Assessment Assessment Assessment
Year Class (at Age 4) Model Model Model Model
1977 1981 8,806 1,642 2,217 822
1978 1982 8,939 1,607 1,752 733
1979 1983 3,563 675 208 277
1980 1984 1,093 213 682 76
1981 1985 1,858 381 411 161
1982 1986 379 95 55 35
1983 1987 1,227 307 255 153
1984 1988 953 244 31 135
1985 1989 95 36 22 24
1986 1990 114 39 624 35
1987 1991 2,200 584 382 317
1988 1992 1,513 308 282 177
1989 1993 247 63 60 85
1990 1994 95 30 22 43
Mean 2,220 445 500 220
Median 1,160 275 269 144
Ricker a parameter -2.479 -3.943 -3.841 -4.612
Ricker b parameter -272,040 -381,936 -310,998 -356,419
Ricker residual mean square: 2.757 1.975 2.308 1.177
Quantile 1-2 boundary
Empirical 4:5:5 frequency 86,752 80,853 92,936 97,955
Empirical 5:4:5 frequency 179,651 166,893 159,196 144,994
Empirical 5:5:4 frequency 179,651 166,893 159,196 144,994
Quantile 2-3 boundary
Empirical 4:5:5 frequency 415,215 368,403 307,933 264,813
Empirical 5:4:5 frequency 415,215 368,403 307,933 264,813
Empirical 5:5:4 frequency 487,074 408,820 344,688 285,362
dependent models used the biomass 4 years earlier
(B). For the first 3 years following the starting year
y −4
of simulations with density-dependent recruitment,
spawning biomass 4 years earlier was back-calculated
from the starting population and the appropriate sur-
vival rate schedule.
The Togiak herring population was simulated for
1,000 years. To control the effect of starting condi-
tions, results were averaged over simulations using
each of the 17 annual (1978¬1994) historical abun-
dance-at-age estimates in the starting year. To further
control the effect of starting conditions and to remove
the effects of fishing present in the starting popula-
tions, AUB was estimated using spawning biomass
from equation (3) averaged over simulation-years
251¬1,000. Preliminary runs of the model showed that
almost all effects of starting conditions were removed
within the first 250 years of the simulation.
Exploitation Simulations
Fishery exploitation was added to the unfished
biomass simulation to evaluate the long-term conse-
quences of alternative harvest policies. With exploita-
tion, equation (1) became
N +=, =S (N −∑C , ).
(4)
ay11 a ay , ayg ,
g
In the above, Cay g
is the catch at age a in year y for
,,
gear g estimated from
Cayg V , ⋅gy , , (5)
,,
= ag
µ
, ⋅Na y
where Vag, is the vulnerability at age a to gear g and
µ
gyis the fully recruited exploitation rate for gear g
,
in year y. Exploitation rates were set to zero if the run
131 Model Suggests New Threshold for Togiak Herring • Funk and Rowell
Table 3. Total run abundance (millions of recruited and unrecruited) of Pacific herring by year and age, survival
(percent surviving by age), and maturity (percent mature) estimates from the age-structured analysis (Me-
dium Assessment Model) used for the 1995 Togiak forecast (Rowell and Funk 1994).
Age (years): 4 5 6 7 8 9 10 11 12 13 14 15+
Abundance:
1978 296.8 207.2 53.7 0.5 5.5 1.4
1979 20.7 229.1 152.7 36.5 0.3 4.1
1980 93.1 14.8 166.5 108.6 24.8 0.1 2.6
1981 1,642.1 72.0 10.8 109.1 66.7 14.7 0.0 1.4
1982 1,606.8 1,285.7 54.8 8.0 78.2 47.4 9.9 0.0 0.8
1983 675.2 1,261.0 985.2 40.8 5.9 56.7 32.5 6.4 0.0 0.3
1984 213.2 532.5 978.7 748.2 30.4 4.2 38.7 21.5 4.0 0.0 0.2
1985 381.2 168.7 418.5 759.6 573.3 22.8 2.4 26.6 14.2 2.5 0.0 0.1
1986 94.8 301.6 132.6 324.5 580.3 434.3 16.0 1.4 17.3 8.8 1.5 0.0
1987 306.7 75.1 238.0 103.8 251.4 446.8 318.9 11.1 0.9 10.9 5.2 0.8
1988 243.8 243.1 59.3 186.4 80.4 193.7 328.2 223.7 7.3 0.5 6.5 3.4
1989 35.6 193.3 192.0 46.5 144.6 62.0 141.7 228.3 148.6 4.4 0.3 5.4
1990 39.2 28.2 152.5 150.1 36.0 110.9 45.4 98.7 151.1 93.2 2.6 2.9
1991 584.3 31.0 22.2 118.8 115.4 27.4 80.1 31.3 64.5 93.5 54.5 2.8
1992 307.6 462.1 24.4 17.2 90.4 86.5 19.5 54.4 20.0 39.2 53.8 31.1
1993 63.4 242.2 358.6 18.4 12.4 63.4 57.3 12.5 33.1 11.4 21.4 42.6
1994 30.4 50.0 188.6 273.2 13.6 9.0 43.2 37.2 7.6 19.4 6.2 31.9
Weight (g): 153 200 246 294 334 375 400 416 451 450 485 487
biomass was below threshold for any simulation year.
When the run biomass was above threshold, the over-
all exploitation rate (total catch/run biomass) was set
to 20%, and the fully recruited exploitation rate for
each gear (
µ
gy
) was determined by
,
02 g ⋅ y
. ⋅ AB
µ
gy
= ,
, VW
⋅ N ) (6)
a a ,
∑( ⋅ ay
a
where Ag is the allocation for gear g (75% purse seine,
25% gillnet) in the current Bristol Bay herring
management plan. The small allocation to the Dutch
Harbor food-and-bait fishery (7% of the allowable
harvest) and the small harvest reduction (159 mt) for
spawn-on-kelp fisheries in the current Bristol Bay
herring management plan were, for simplicity, not
included in the exploitation simulations. Under thresh-
olds that varied from 10 to 50% of AUB, the exploita-
tion simulations tracked average yield ( a ⋅,, )WC and
ayg
percent of years that the fishery was below threshold
and closed.
RESULTS
Spawner-Recruit Relationships
All of the spawner-recruit relationships were
heavily influenced by the relatively large 1977 and
1978 year classes (Figure 5). Aerial surveys from the
late 1970s, while not comparable to current methods,
suggest that the ASA model underestimated the spawn-
ing biomass in 1977 and 1978. Using somewhat dif-
ferent data and assessment models, Zheng (1994)
located the 1977 and 1978 spawner-recruit data pairs
at somewhat higher spawning biomass. Results of
spawner-recruit analyses are summarized in Table 2.
The large amount of contrast among Ricker models fit
to the data from the 4 stock-assessment models reflects
the wide range of recruitment estimates in the assess-
ments. The 14 spawner-recruit observations could not
be equally partitioned into 3 spawning biomass quan-
tiles for the empirical spawner-recruit relationship.
Figure 5 depicts quantile boundaries placed at the mid-
point between the years with the 5th and 6th lowest
spawning biomass and between the years with the 9th
and 10th lowest spawning biomass. The lowest quantile
contains 5 spawner-recruit observations, the middle
quantile contains 4 observations, and the upper quantile
contains 5 observations. Quantile boundaries depicted
in Figure 5 were labeled ƒ5:4:5≈ in the AUB analyses.
The effect of moving quantile boundaries was investi-
gated by using quantile groups with 4:5:5 and 5:5:4
allocations of the 14 spawner-recruit observations to
the 3 spawning biomass groups.
Average Unfished Biomass and Thresholds
In typical AUB simulations, spawning biomass
oscillated widely because very strong year classes
132 Articles
occurred infrequently (Figure 6). Starting conditions
had a large amount of influence during the initial years
of the simulation, but the cumulative average spawn-
ing biomass became stable before the 250th simula-
tion year. AUB was calculated as an average over
simulation-years 251¬1000, well after the effect of
starting conditions disappeared. An oscillatory, sinu-
soidal biomass trajectory resulted when the determin-
istic Ricker model was used with the highest and
medium assessment models. Biomass converged to a
stable point when the Ricker model was used with the
medium-low and lowest assessment models.
Biomass occasionally exceeded 1,000,000 mt in
simulations based on the highest assessment model
(Figure 7). AUB ranged from a low of 158,853 mt for
simulations based on the lowest assessment model with
the empirical 4:5:5 spawner-recruit relationship to
a high of 433,387 mt for the highest assessment model
with the stochastic Ricker spawner-recruit relationship.
Setting thresholds at 25% of AUB corresponded to
a threshold range of 39,713¬108,347 mt. All other
combinations of stock-assessment models and
spawner-recruit models produced thresholds in excess
of 45,000 mt.
Spawner-recruit data Ricker Model Empirical 5:4:5 model boundaries
Age 4 Recruits (millions)
~
3,500
85
86
87
84
88
83
89
82
90
81
80
79 Highest Assessment Model 3,500
3,000 3,000
2,500 2,500
2,000 2,000
1,500 1,500
1,000 1,000
500 500
0 0
0 200,000 400,000 600,000
2,500
77
78
80
79
81
90
89 82
88 87
86
83
84 85
Medium-Low Assessment Model 2,500
2,000 2,000
1,500 1,500
1,000 1,000
500 500
0 0
0 200,000 400,000 600,000
Medium Assessment Model
85
86
87
84
88
83
89
90
81
82
80
79
78
77
0 200,000 400,000 600,000
84
83
87
88
81
79
80
78
77
0
Lowest Assessment Model
200,000 400,000 600,000
Spawning Biomass (mt)
Figure 5. Pacific herring spawner-recruit data from the 4 alternate stock-assessment models for Togiak, showing the Ricker model
and boundaries for the empirical spawner-recruit model with a 5:4:5 allocation of spawner-recruit data into 3 spawning
biomass intervals.
133 Model Suggests New Threshold for Togiak Herring • Funk and Rowell
When fishery exploitation was added to the simu-
lation model, highest average yields occurred with no
or very low thresholds (Figure 8). Thresholds only had
a positive effect on yield if exploitation rates were high,
i.e., > 40%; thresholds had no positive effect on long-
term yield at a 20% exploitation rate. This occurred
because the ascending limb of the spawner-recruit
relationships were shifted so far to the left that bio-
mass never dropped down to the very low levels where
recruitment would markedly decline under a 20% ex-
ploitation rate. Average yield declined for high thresh-
olds as fishery closures became excessive. With
thresholds at 25% of AUB, fishery closures occurred
in 2% of the simulation years, averaged over all as-
sessment and spawner-recruit models.
DISCUSSION
Setting thresholds at 25% of the AUB is the current
practice for herring fisheries in Canada (Schwiegert
1993) and Prince William Sound, Alaska. Our study
found that long-term average yield did not increase
under a threshold harvest policy for Togiak herring
when combined with a 20% exploitation rate. Setting
thresholds at 25% of AUB would only rarely trigger
fishery closures, and these closures would not cause
an appreciable loss of long-term yield.
Using a very different stock-assessment model and
data from the foreign herring fishery during the 1960s
and 1970s, Zheng et al. (1993) reported AUB for the
entire Bering Sea as 421,000 mt. Assuming 80% of
the herring in the eastern Bering Sea spawn at Togiak,
as estimated from aerial surveys and by Wespestad
(1991), the Togiak AUB would be 336,800 mt. The
threshold corresponding to this AUB, using the 25%
criterion, would be 84,200 mt. Because the frequency
of strong year classes drives the AUB simulations, it
is important to note that frequency of strong recruit-
ment events in the relatively short time series in this
study (1977¬1990 year classes) is similar to the fre-
quency in Zheng«s (1994) longer time series model.
The current 31,752 mt (35,000 tons) threshold for
Togiak is lower than all of the 25% AUB criteria in
our simulations for 3 reasons. First, 1978¬1985 aerial
survey biomass estimates on which the current thresh-
old is based include a history of fishing. Unfished bio-
mass based on this time series would clearly be higher
than these aerial survey estimates. Second, the
1978¬1985 period includes a number of aerial survey
estimates that are now believed to be too low. Third,
the 1978¬1985 period under-represents the influence
that strong recruitment events (e.g., 1977 and 1978
year classes) have on long-term average biomass.
Longer studies of recruitment processes in the Bering
Sea (Wespestad 1991; Zheng 1994) indicate that strong
year classes occur approximately every 8¬12 years.
The 1978¬1985 period includes data from the initial
phase of the biomass buildup resulting from a strong
recruitment event. However, because survival rates for
1,000,000 Simulated Biomass
AUB: Average for years 251 - 1,000
Cumulative Average, years 1-225
800,000 25% of AUB = threshold for this simulation
Biomass (mt)
600,000
400,000
200,000
0
0
100
200
300
400
500
600
700
800
900
1,000
Simulation Year
Figure 6. Result of a 1,000-year simulation of the Togiak population of Pacific herring using the empirical 5:4:5 spawner-recruit
model and the medium assessment model.
134 Articles
0
200,000
400,000
600,000
800,000
1,000,000
0
50,000
100,000
150,000
200,000
250,000
Highest
Assessment
Model
Average Range Middle 90%
öMiddle 50%
}
0
200,000
400,000
600,000
800,000
1,000,000
0
50,000
100,000
150,000
200,000
250,000
Medium
Assessment
Model
0
200,000
400,000
600,000
800,000
1,000,000
0
50,000
100,000
150,000
200,000
250,000
Medium-Low
Assessment
Model
Unfished Run Biomass
(
mt
)
25% of Unfished Run Biomass (mt)
0
200,000
400,000
600,000
800,000
1,000,000
0
50,000
100,000
150,000
200,000
250,000
Lowest
Assessment
Model
Historical
Median
Historical
Mean
Historical
Random
Empirical
4:5:5
Empirical
5:4:5
Empirical
5:5:4
Ricker
Stochastic
Ricker
Spawner-Recruit Model
Figure 7. Distribution of unfished Pacific herring run biomass estimates from the Togiak simulation model, under different
assumptions about stock-assessment models and spawner-recruit models. Thresholds along the right axes correspond to 25%
of average unfished unfished biomass.
135 Model Suggests New Threshold for Togiak Herring • Funk and Rowell
Bering Sea herring are relatively high, biomass pulses
from strong recruitment events last almost 10 years.
Therefore, the 1978¬1985 period under-represents the
longer-term contribution to average biomass from a
strong recruitment event. All our analyses suggest the
threshold at Togiak should be increased to be consis-
tent with the 25% AUB criterion. Because of the un-
certainty about the peak biomass levels during the mid
1980s and the uncertainty in the spawner-recruit data,
threshold recommendations from the simulation model
range from 39,713 mt to 108,347 mt. Because the ex-
tremes of all the scenarios examined are improbable
and the next lowest recommended thresholds were
from 45,000 to 50,000 mt, we recommend raising the
threshold at Togiak to at least 45,000 to 50,000 mt.
Since the beginning of the Togiak herring stock-
assessment program in 1978, the inseason aerial sur-
vey estimates were below the proposed threshold lev-
els in only 1 year: 1980 when 44,349 mt were esti-
mated. This estimate was taken when weather
conditions and visibility were poor. Currently, when
weather conditions do not permit reliable inseason bio-
mass estimates, managers base threshold and quota
decisions on the ASA model forecast of biomass. For
example, the next lowest aerial survey estimate, 47,000
mt in 1991, was not used to manage the fishery be-
cause weather and visibility had been poor; instead
the forecasted biomass of 49,689 mt was used. There-
fore, increasing the threshold to 45,000¬50,000 mt
should seldom close the Togiak herring fishery or the
Dutch Harbor food-and-bait fishery. In addition, if in
the future the Togiak population falls to dangerously
low levels, the current threshold would probably impair
the fishery for a longer period by delaying recovery;
Spawner-Recruit Model:
Density Independent Empirical 4:5:5 Empirical 5:4:5 Stochastic Ricker
35%
100%
Highest
Assessment
Model
Percent of Maximum Yield
Percent of Years Closed 15%
75%
80%
Medium
Assessment
Model
10%
70% 5%
65% 0%
10% 20% 30% 40% 50% 10% 20% 30% 40% 50%
100% 35%
95% 30%
90% 25%
85% 20%
Percent of Maximum Yield
Percent of Years Closed
85%
Medium-Low
Assessment
Model
20%
80%
Lowest
Assessment
Model
15%
75% 10%
70% 5%
65% 0%
10% 20% 30% 40% 50% 10% 20% 30% 40% 50%
Threshold as Percent of AUB
95% 30%
90% 25%
Figure 8. Relationship of average yield of Pacific herring (as a percent of the maximum yield for 20% exploitation rate) and
percent of years closed due to subthreshold biomass, expressed as a percent of average biomass (AUB), in the Togiak simula-
tions under 4 alternative stock-assessment models.
136 Articles
conversely the modestly higher threshold should help
the stock rebound to robust levels more quickly.
The moderately high current level of abundance
and the age composition predominated by the 1987
and 1988 year classes suggest that the population is
stable and will not depend on another major recruit-
ment event for sustainability for at least 5 years. Abun-
dance trends based on age compositions have been very
consistent and predictable for Togiak herring. As long
as funding levels allow representative age-composi-
tion sampling, adequate warning should be provided
if an unusual decline does occur.
This analysis attempts to include the major sources
of uncertainty that would influence the choice of
thresholds for the Togiak herring fishery. However, in-
consistencies in recording and analyzing aerial sur-
veys over the 1978¬1994 period precluded us from
properly evaluating the uncertainty resulting from
choosing a subset of the highest quality aerial survey
estimates of abundance. If further analysis of the his-
torical aerial survey data reduces uncertainty in the
stock-assessment information, threshold levels for
Togiak herring should be reexamined.
LITERATURE CITED
Brannian, L. K., K. A. Rowell, and F. Funk. 1993. Forecast of
the Pacific herring biomass in Togiak District, Bristol Bay,
1993. Alaska Department of Fish and Game, Division of
Commercial Fisheries Management and Development,
Regional Information Report 2D93-42, Anchorage.
Haist, V. 1990. An evaluation of three harvest strategies based
on forecast stock biomass for B.C. herring fisheries. Pages
90¬99 in M. F. O«Toole, editor. Proceedings of the sixth
Pacific coast herring workshop. Washington Department
of Fisheries, Progress Report 279, Olympia.
Hall, D. L., R. Hilborn, M. Stocker, and C. Walters. 1988. Al-
ternative harvest strategies for Pacific herring (Clupea
harengus pallasi). Canadian Journal of Fisheries and
Aquatic Sciences 45:888¬897.
Lebida, R. C., and D. C. Whitmore. 1985. Bering Sea herring
aerial survey manual. Alaska Department of Fish and Game,
Division of Commercial Fisheries, Bristol Bay Data Report
85-2, Anchorage.
Rowell, K. A., and F. Funk. 1994. Forecast of the 1995 Togiak
herring biomass. Alaska Department of Fish and Game,
Division of Commercial Fisheries Management and
Development, Regional Information Report 2D94-48,
Anchorage.
Schweigert, J. 1993. Evaluation of harvesting policies for the
management of Pacific herring stocks, Clupea pallasi, in
British Columbia. Pages 167¬190 in G. Kruse, D. M.
Eggers, R. J. Marasco, C. Pautzke, and T. J. Quinn II, edi-
tors. Proceedings of the international symposium on man-
agement strategies for exploited fish populations. University
of Alaska Fairbanks, Alaska Sea Grant College Program
Report 93-02.
Wespestad, V. G. 1991. Pacific herring population dynamics,
early life history, and recruitment variation relative to east-
ern Bering Sea oceanographic factors. Doctoral disserta-
tion, University of Washington, Seattle.
Zheng, J. 1994. Threshold management strategies for exploited
fish populations. Doctoral dissertation, University of Alaska
Fairbanks.
Zheng, J., F. C. Funk, G. H. Kruse, and R. Fagen. 1993. Evalu-
ation of threshold management strategies for Pacific her-
ring in Alaska. Pages 141¬166 in G. Kruse, D. M. Eggers,
R. J. Marasco, C. Pautzke, and T. J. Quinn II, editors.
Proceedings of the international symposium on manage-
ment strategies for exploited fish populations. University
of Alaska Fairbanks, Alaska Sea Grant College Program
Report 93-02.
137Model Suggests New Threshold for Togiak Herring • Funk and Rowell
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