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Age-structured assessment of
three Aleutian fish stocks with
predator-prey interactions
Doug Kinzey
School of Aquatic and Fishery Sciences
University of Washington
Introduction
 Fisheries are embedded in a naturally interacting
system of predators and prey.
 Predator-prey relationships are not explicitly
considered in the formal, statistical procedures
(single-species assessments) used to evaluate the
status of most commercially-harvested populations,
however.
 Nevertheless, management decisions about harvest
levels and risks are often based on single-species
assessments.
Single-species assessments
 Formal assessments are based on statistically
complex models that may include age-structure and
other details but consider interactions among species
only indirectly.
 For instance, natural (non-fishing) mortality may enter
these models as a single, constant value across all
age classes, ie, an assumed 20 or 30% mortality per
age class per year.
Objective
The aim of this study is to:
 select a core group of populations for which individual
assessments have been conducted that also interact
as predators and prey, and for whom diet data are
available as a time series;
 incorporate the predator-prey interactions into an
age-based, statistical assessment of the populations
simultaneously, and
 compare the outcomes between the single-species
and multispecies versions of the models representing
these populations.
Aleutian model
 The interaction among walleye pollock, Atka
mackerel, Pacific cod and fisheries in the Aleutian
Islands, Alaska, from 1979 - 2003 was chosen for
modeling.
 These are the basis of the three principle fisheries in
the region.
 Single-species assessments are available for all
three stocks from the NOAA Alaska Fisheries
Science Center.
 An archived database of stomach samples collected
since the 1970s from these and other Aleutian
species is also maintained by the AFSC.
Aleutian chain
Ecosystem significance
 These three populations of fish comprise a central
role in the food web of the Aleutian region.
 They are the main prey items of Steller sea lions and
are important in the diets of many other mammal and
seabird species.
 Competition with fisheries has been postulated as
one component in the decline of Steller sea lions and
several other fish-dependent predators in the region.
Existing models (single-species)
Stock assessments:
 The pollock (Barbeaux et al 2003) and mackerel
(Lowe et al 2003) assessments were age-based and
produced using the “Amak” toolbox modeling
software developed by Jim Ianelli at the Alaska
Fisheries Science Center.
 The cod assessment (Thompson and Dorn 2003)
was length-based and produced using the program
“Synthesis”, developed by Rick Methot at the
Northwest Fisheries Science Center.
Data for single-species models
Used in likelihood components (the differences between
model outputs and these data are minimized):
 Total fishery catches, 1979-2003
 Proportions at age from the fishery, some years
 Proportions at age from surveys, some years
 Biomass index from surveys, some years
Considered known (used but not estimated by model):
 weight-at-age from the fishery, some years
 weight-at-age from surveys, some years
 maturity at age, some years
Data example:
pollock proportions at age
Pollock Age Composition (Fishery)
Pollock Age Composition (Survey)
0.35
0.25
0.3
0.2
0.25
0.15
0.2
0.1
0.15
0.1
0.05
0.05
1990
1992
0
1
2
3
4
5
1994
6
7
Age
8
9
10 11
12
1996
13 14
Year
0
1
2
3
4
5
6
7
Age
8
1991
9
10
11
12
13
2002
14
15
15
The pollock fishery shows a high proportion of older
fish in the early 1990s that isn’t reflected in surveys.
Year
Single-species calculations
 About 2,000 lines of Amak code (AD Model Builder)
 27 main equations with interactions
 84 estimated parameters for pollock and 351 for
mackerel
 penalties on recruitment deviations and selectivity
parameter estimates
 Pacific cod was assessed using a different model
structure (Synthesis)
 This is already pretty complicated!
Single-species model output:
numbers at age
Pollock Numbers at Age
Mackerel Numbers at Age
140
1200
120
1000
100
800
80
600
200
S21
0
S26
Age
S25
11
1
13
15
9
11
5
Age
7
S21
3
1
0
Year
9
S16
5
S11
20
S1
S5
S9
S13
Year
S17
400
7
S1
S6
40
3
60
The assessments combine the various sources of
information with the model structure to estimate such
population features as numbers-at-age.
Multispecies model: diet data
Prey proportions have been identified in over 8,000
individual stomachs from these three species caught
in the Aleutians since the 1980s.
 2,700+ Pacific cod stomachs
 3,600+ walleye pollock stomachs
 1,600+ Atka mackerel stomachs
Multispecies interactions
 Pollock and mackerel are the main prey of cod,
comprising about 19% and 27% of total cod stomach
contents, respectively, in Aleutian diet studies.
 Although probably of lesser importance than
fisheries, cod are the main predators of adult pollock
and mackerel, and are also among the major
predators of juveniles of both species.
 To some extent, all three species can be predators of
one another (including cannibalism) at various life
stages.
Diet Reflects Prey Abundance
Proportion of Prey in Cod Diet by Longitude
0.7
0.6
0.5
0.4
0.3
Pollock
Mackerel
0.2
0.1
0
E
E
E
E
0
2 74 76 78 18 8 W 6 W 4 W 2 W 0 W 8 W 6 W
7
1
1
1
1
17 17 17 17 17 16 16
The proportion of prey species in cod diets is partly a
result of prey abundance.
-Data provided by Ivonne Ortiz, University of Washington
Multispecies modeling approach
 Separate the parameter representing natural
mortality in Amak into two sources (explicitly modeled
and additional mortality).
 Add two likelihood components representing stomach
proportions and total ration.
 Use the fit to diet data to select among alternative
functional forms representing predation.
 Re-estimate original single-species parameters as
well as new multispecies parameters in the expanded
model.
Model comparisons
 Use the Markov Chain Monte Carlo algorithim to
sample the posterior distributions of the model
outputs in order to characterize the uncertainty
around parameters of interest.
 Parameters of interest include numbers-at-age,
productivity and natural mortality not accounted for by
fishing or the three species included explicitly (the
mortality potentially available to other predators).
Possible outcomes
 Single- and multispecies models could have similar
estimates of central tendencies and variances for the
parameters of interest.
 The two approaches could have similar estimates of
central tendencies but different estimates of
variances (differing uncertainty).
 The two approaches could produce different
estimates of both central tendencies and variances.
Potential significance:
fisheries
Depending on the final outcomes, this study could
suggest either:
 Conventional single-species assessments adequately
represent population features of interest without
requiring the addition of predator-prey interactions, or
 including predator-prey modeling and data on diets
into the assessments changes the estimates of
features of interest enough to warrant including these
factors in future assessments.
Potential significance:
other species
 If the combined mortality due to fisheries and the
species included in the multispecies model is greater
than the mortality estimated in the single-species
assessments, this could imply a smaller source of
prey for the predator species not included in the
model.
 This modeling could also suggest changes in fishing
mortality on particular ages/species of predatory fish
that might increase the potential prey for other
species in the ecosystem.
Acknowledgements
 Project funding is from the Washington Cooperative
Fish and Wildlife Research Unit and the North Pacific
Universities Marine Mammal Research Consortium.
 Alaska Fisheries Science Center Scientists Kerim
Aydin, Jim Ianelli, Sandra Lowe, Steve Barbeaux and
Grant Thompson are providing access to data and
computer code.
 My advisor Dr André Punt and the Punt lab members
at the University of Washington are furnishing
discussion and ideas concerning statistical theory
and practical aspects of natural resource modeling.