Explaining and Predicting Recruitment of Y ellow Perch in North American Inland Lakes
Abstract: Managing sustainable fisheries populations relies on an understanding of the interplay
between recruitment, growth, and mortality. Recruitment is frequently noted as the most
influential parameter of these three dynamic rate functions. The erratic recruitment dynamics of
yellow perch (Perca flavescens) often confound fisheries scientists, managers, and regulators of
inland lakes. Y ellow perch populations provide many recreationally important fisheries directly
or supports fisheries for other species. Additionally, recruitment patterns of yellow perch are
expected to become more erratic under changing environmental conditions such as climate
change. Traditional fisheries modeling approaches often fail to capture the dynamics and
complexities of recruitment. In this paper, we describe the initial stages of building an SD model
of yellow perch recruitment for inland lakes. We compare this approach to traditional fisheries
recruitment modeling approaches and describe the next steps in model development and use.
Initial model sensitivity testing shows promise in our model to date and is congruent with
ecological information. We believe that our final SD model will benefit fisheries scientists,
managers, and regulators in anticipating and potentially mitigating recruitment variation to
provide sustainable recreational fisheries in inland lakes across the geographic range of yellow
perch.
Introduction:
Populations of wild animals are affected by three dynamic rate functions:
e recruitment — the number of individuals that are hatched in a year or the number
of individuals that survive to a specific size or life stage on an annual basis;
e growth — the amount of weight or length gained by an individual annually; and
e mortality — the percentage of a population that dies, either naturally or by harvest,
in a given year.
These three functions interact to determine the nature (e.g., abundance, size structure) of a
population (Figure 1). For example, recruitment add individuals to a population; growth in body
length or weight adds biomass to a population; and mortality reduces both the number of
individuals in a population and the population’s biomass (Willis et al., 2008).
Managing sustainable fisheries populations relies on an understanding of the interplay between
recruitment, growth, and mortality. But recruitment is frequently noted as the most influential
parameter of the three (Ricker, 1975). Seemingly minor fluctuations in recruitment may
contribute to substantial changes in other parameters (e.g., Carline et al., 1984). For example, a
higher number of recruits may lead to reduced growth rates via intraspecific competition (i.e.,
competition for food, habitat, or other resources within a population). Conversely, years of
lower or failed recruitment may reduce competition for such resources and lead to higher growth
rates within the population (Anderson, 1988).
Most research of recreational fisheries indicates that recruitment from egg to adult in fishes is
established early in life after a point at which natural mortality stabilizes and before a cohort is
large enough to be harvested (e.g., Ludsin and Devries, 1997; Isermann and Willis, 2008). Both
biotic (i.e., density dependent) and abiotic (i.e., density independent) factors influence
recruitment from one successive life stage (e.g., egg, larvae, juvenile, adult) to the next. Biotic
factors may include prey availability, competition, and predation, to name a few. Abiotic factors
may include climate, habitat, environmental stochasticity, etc. The relative influence of these
biotic and abiotic factors may depend on the species of interest and the life stage being studied.
Recruitment dynamics have been studied for many recreationally important fishes, including
yellow perch (Perca flavescens). Y ellow perch support many recreationally important fisheries
across North A merican from the A tlantic to the Pacific Coasts (e.g., Mayer et al., 2000, Wilberg
et al., 2005; Isermann and Willis, 2008) but are also an important prey species for other
recreational fisheries such as walleye (Sander vitreus), northem pike (Esox lucius), and
smallmouth bass (Micropterus dolomieu; Hansen et al., 1998; Blackwell et al., 1999). Erratic
recruitment patters (i.e., strong year classes followed by weak or missing year classes) have been
noted in many yellow perch populations (Forney, 1971; Kallemeyn, 1987; Sanderson et al.,
1999; Isermann and Willis, 2008), and recruitment patterns are expected to become more erratic
under changing environmental conditions such as climate change (Farmer et al., 2015).
Managing such varying yellow perch populations as prey and for human consumption will be
challenging.
Indeed, much research has been focused on identifying the particular life stage or stages where
yellow perch year class strength is established and the abiotic and biotic factors that influence
recruitment from one life stage to the next. Most work focused on early life stages (i.e., egg,
larvae, and juvenile). Density-independent factors that have been identified as important
influences on yellow perch recruitment at this stage include lake morphology characteristics
(Isermann, 2003), climatological variables (Ward et al., 2004; Jensen, 2008; Redman et al.,
2011; Weber et al., 2011), fluctuations in water levels (Kallemeyn, 1987; Dembkowski et al.,
2014), and environmental variability (Clady and Hutchinson, 1975). Potentially important
density-dependent factors include prey density (Jolley et al., 2010; Redman et al., 2011), prey
size (Fisher and Willis, 1997), prey community composition (Whiteside et al., 1985), spawning
stock characteristics (Sanderson et al., 1999; Tyson and Knight, 2001; Wilberg et al., 2005),
competition (Shroyer and McComish, 2000), and predation (Fomey, 1974). Abiotic factors
appear to be more influential on recruitment between the earliest life stages (e.g., egg to larvae;
e.g., Kallemeyen, 1987; Ward et al., 2004; Weber et al., 2011), whereas biotic factor appear to
more important in determining recruitment between later life stages (e.g., juvenile to adult;
Dembkowski, 2014).
Most studies of yellow perch recruitment focus on one or two particular life stages and tend to
follow traditional statistical approaches (see Discussion below). To our knowledge, only one
study has examined yellow perch recruitment between successive life stages (Wilberg et al.,
2005), but this work focused solely on the Lake Michigan population. Overfishing has occurred
in many Great Lakes, but there have been no such documented cases in inland lakes to our
knowledge. Recruitment of yellow perch populations in inland lakes is likely regulated by
different factors than those in the Great Lakes, and most recreational perch fisheries in the
United States now occur on inland lakes.
To date, no study has employed a System Dynamics (SD) simulation approach to model
recruitment of yellow perch populations in inland lakes. Using SD has distinct advantages
compared to other traditional approaches to studying fish recruitment. First, SD allows for
modeling recruitment to successive life stages that reflects natural processes (e.g., adults deposit
eggs; eggs hatch; larvae grow to become juveniles; juveniles grow to adults; and the cycle
repeats). Second, SD models can handle complex feedback processes endogenously while also
incorporating exogenous factors that promote or inhibit recruitment at each life stage
simultaneously. Finally, SD models can be used to test various scenarios that may support or
reduce recruitment so that fisheries managers may take proactive steps as needed. The goal of
this paper is to describe the initial stages of building an SD model of yellow perch recruitment
for inland lakes. We will compare and contrast this approach to traditional fisheries recruitment
modeling approaches and describe the next steps in model development and use.
Natural
mortality
Recruitment
POPULATION
Harvest
mortality :
Growth
Figure 1. The three dynamic rate functions (recruitment, growth, and mortality) that interact to
determine the nature of wild animal populations (adapted from Willis et al., 2008)
Model Overview:
The model is based on a typical aging chain dynamic of disaggregated stocks and flows
representing specific stages relevant to the population of interest (Sterman 2000; Ford, 2010), in
this case yellow perch (Figure 2). The model was created in Vensim™ (Ventana Systems,
Harvard, MA) modeling environment. The time unit used for simulation was 1 month, with a
time-step of 0.0625 and simulation horizon of 240 months (or 20 years). Currently, climatic
forcing functions are not well parameterized or non-existent in the model. However, these are
actively being refined since they are the key exogenous components for this model. The key
endogenous components are the stock-and-flow linkages between various life stages of a typical
perch population. The main strength of using the SD platform was the ease of use handling the
core feedback mechanisms for the population and a rapid simulation time. The main
contributions of the model were the inclusion of all relevant life stages that typically are not
included in traditional fish population models (see Discussion section below). In the sections that
follow, we describe the scientific foundations that inform each of the stock-and-flow components
of the model and the basic equations used for the early (immature) versus mature life stages. For
a full list of variable names and equations used, see Tables A and B Supplementary Material.
Description of Endog Model Dy
This model begins at the egg deposition phase (initial stock) and progress through successive life
stages until yellow perch reach sexual maturity and, thus, can produce eggs (final stock; Figure
2). Each life stage in the model is considered important to understanding recruitment of yellow
perch as demonstrated or hypothesized in scientific literature (Table 1). As each life stage
progresses to the next, some individuals are removed from the population through mortality,
which may occur due to natural phenomena (e.g., starvation, predation, weather events) or
anthropogenic effects (namely, harvest of adults of a legally defined body length). Mortality
may be density-dependent (i.e., the rate of mortality is based on the density of the population; for
example, starvation; endogenous factors) or density-independent (i.e., the rate of mortality is
unrelated to population density; for example, harvest; weather events; exogenous forces).
Mortality at the earliest life stages of yellow perch is hypothesized to be driven by both density-
dependent and -independent factors (Table 1). Those individuals that survive move on to the
next life stage.
Individual yellow perch survive and grow until they reach sexual maturity. The timing of sexual
maturity in yellow perch differs by sex and population. In most populations, male yellow perch
reach sexual maturity during their second year of life (age-2) while females may be at least 3
years old before becoming sexually mature (age-3; see Jansen, 1996). However, yellow perch
populations that grow slower may mature earlier (age-1 in males and age-2 in females; Jansen,
1996). Interestingly, sexual maturity is often reached before yellow perch reach harvestable
sizes (Jansen, 1996).
Growth in body length and weight is also intimately related to mortality and survival. High
density fish populations tend to grow slower than low density- populations as relative influence
of density-dependent factors on mortality decreases (Ware, 1975; Anderson, 1988). Fish that
4
Figure 2. Basic structure of the SD model proposed to explain and predict yellow perch recruitment in inland North A merican lakes.
egg
success-failure yolk larvae
rate
mort risk
exo feeders
mort rate
mort exo
mortality feeders
ageO
Yolk sac Exo feed Summer money
eggs deposited larvae growth |_larvae_| reach Liarvae_| age 0s -P
feeding oe
<Time> start of months to A months to (maturation! t—Age0 mort rate
ring? | months to
Ne spring? larvae etal ageO
month® months to [Spring] age! morality
counter age1 age 1s
year turation2 «Age 1 mort rate
duration eggs deposited : = ration:
per Age3+ clr = months to age mortality
produce:
or
eggs deposity
per Age2 imaturation3 <#— Age 2 mort rate
percentage of 2s female months to
reproducing fraction age3
age3+
grow faster may also survive at higher rates, either by avoiding predation or by having enough
energy reserves to survive starvation and harsh winters. Thus, many of the factors that influence
mortality and survival may also influence growth and vice versa (e.g., Weber et al., 2011).
Fecundity, or the number of eggs produced by a female yellow perch, may be related to age
where younger perch tend to produce more eggs than older individuals (Jansen, 1996).
Fecundity may also be related to environmental conditions whereby female yellow perch can
reduce or increase the number of eggs produced annually based on whether environmental
conditions are favorable or not (see Jansen, 1996).
Overall, survival, mortality, growth, and fecundity are influenced by environmental conditions
that vary intra- and interannually, and tradeoffs may occur to increase survival at the expense of
other dynamics. For example, if water temperatures are too warm and create a metabolic
demand on fish, then fecundity and growth may be reduced to conserve energy that will be used
to enhance survival and reduce mortality (Jansen, 1996). Other factors that reduce survival such
as harvest, may vary by year, season, and sex. For example, female yellow perch may be
harvested at higher rates than males by anglers, especially during the winter (Clady, 1977; Weber
and Les, 1982; Purchase et al., 2005; Isermann et al., 2007). The SD model for this study will
include the influences of these factors on survival, mortality, growth, and fecundity.
Description of Quantitative Model and Preliminary Testing:
The quantitative model is represented by seven stocks representing distinct ages and seasons
between the egg stage through Spring age 3+ (i.e., yellow perch that are at least 3 years old;
Figure 2). These ages and seasons were hypothesized to be either significant stages after
potentially catastrophic mortality periods (e.g., after switching to exogenous feeding; the first
overwinter period) or of sexual maturity. Two different formulations were used to represent the
flows from one age class stock to another due to the differing time delays associated with
younger versus mature fish in the model. The first half of the aging chain (eggs to Summer age
Os) happens within about a three-month period (A pril through June). Eggs are produced and
hatched in the spring, and larvae survive and grow rapidly and in a batched-like process (i.e.,
individual eggs and larvae are less likely to be accounted for over time until they reach maturity).
Therefore, the flows were characterized with a smoothed delay such that the maturation outflows
were equal to:
stock level * percentage of fish aging onward
average time in stock
and the mortality outflows were equal to the remaining fish not aging forward. The second half
of the aging chain (Summer age 0s to Spring age 3+) represent aggregated stocks by age in years,
where it would be less realistic to formulate the maturation flow based on an average maturation
time (i.e., climatic factors between each year age class will impact the maturation flow rates, and
2-year-old fish should not rapidly become 3-year-old fish until the correct duration of time has
passed). Therefore, a fixed delay was applied to the mature fish age progression, where
maturation = fixed delay (stock level*(1-mortality rate), 12 months, stock level*(1-mortality rate)),
6
and mortality was equal to the remaining stock level. The final stock, Spring age 3+, represents
the mature individuals of the population that no longer exhibit the maturation indicators seen in
the younger age classes. Therefore, the mortality outflow was constructed similar to a batched
process, with the outflow being smoothed over the average residence time in the stock. In this
case, the average residence time, shown as life expectancy, was set equal to 48 months. Initial
values for the immature stocks (eggs to Spring age 0s) were set to 0 to avoid fish maturation
during months that eggs and larvae are not able to survive. The remaining initial values were set
to arrive at an equilibrium population of Spring age 3+ fish.
After arriving at an equilibrium population of Spring 3+ aged fish, three preliminary tests were
conducted on several of the more uncertain parameter values, including: mortality rates for
Summer age-0 fish (shown as A ge0 mort rate in Figure 2), mortality rates for Spring age-1 fish
(shown as Age 1 mort rate in Figure 2), number of Spring age-2 fish capable of reproducing
(shown as percentage of 2s reproducing in Figure 2), the eggs produced per Spring age-2 fish
that is reproducing (shown as eggs deposited per A ge2), and the eggs produced per Spring age-
3+ fish (shown as eggs deposited per Age3+). The values used for model development (based on
information in Table 1) along with the adjusted values used for sensitivity testing are provided in
Table C in the Supplementary Material.
Results:
Dynamic equilibrium was reached between month one and fifty (i.e., delay). Both Spring age 3+
and Spring age 2 stocks remained stable with low oscillation. However, Summer age 0s and eggs
oscillate widely throughout the simulation (Figure 3)
140000
120000
100000
80000
60000
40000
20000
---SummerAge0s ——SpringAge2s ——SpringAge3+ —FEggs
Figure 3 Egg, Summer age 0, Spring age 2, and Spring age 3+ stocks at dynamic equilibrium.
E
Reproductive scenarios displayed minimal variation after in initial delay for the Spring age 3+
stock in both the high and low scenarios, although a slight positive trend was observed for our
high reproduction scenario (Figures 4 and 5). Spring age 1s appear to be relatively sensitive to
mortality factors that act on the Summer age 0 stock. Results show a short delay in the beginning
and then an exponential decrease for our high mortality scenarios (Figures 6 and 7). Similar
sensitivity responses were observed for low and high mortality scenarios of Spring age 1s in
relation to Spring age 2s (Figures 8 and 9). Low and high egg production by Spring age 2s
appeared to have minimal impact on Exogenous feeding larvae stock, either in delays or
oscillations (Figure 10 and 11). However, stocks of Exogenous feeding larvae and Y olk sac
larvae appeared to be sensitive to both high and low variations in eggs produced by Spring
Age3+ stocks (Figures 12 and 13). Overall, expected corresponding increases or decreases in
stocks were noted for all scenarios, except Spring age 2s. We also observed the greatest
oscillation in Y olk sac larvae and Summer age 0s across all simulations (Figures 14 and 15).
160000
140000
120000
100000
80000
60000
40000
20000
Eggs
— —SpringAge2s ——SpringAge3+ + Eggs
Figure 4. High reproduction scenario illustrating Spring A ge 2s and A ge 3+ relative to egg
production.
140000
120000
100000
80000 8
60000 4
40000
20000
Months
— —SpringAge2s —SpringAge3+ + Eggs
Figure 5. Low reproduction scenario illustrating Spring A ge 2s and Age 3+ relative to egg
production.
500
0 50 100 150 200 250
Months
—Summerage0s ---Spring Age ls
Figure 6. The impact of high mortality of Summer age 0s on Spring age 1s.
1000
Months
Spring Age 1s
<---> Summer Age 0s
Figure 7. The impact of low mortality of Summer age 0s on Spring age 1s.
35
S
ire)
N
(USED 8,7 ay Burs
now So
aang ag
ns
Ss mH Ss
a a 4
(USED ST aby Burd
nm oO
Ss oOo
irs)
250
200
150
100
50
Months
— Spring Age 2s
— Spring Age 1s
Figure 8. The impact of high mortality of Spring age 1s on Spring age 2s.
10
0 50 100 150 200 250 300
Months
- - -Spring Age 1s Spring Age 2s
Figure 9. The impact of low mortality of Spring age 1s on Spring age 2s.
140000
120000
100000
80000
60000 : | | |
40000 : | : | q | | | | |
eC Ci CO CC i
20000 fe fe ARR TR PR TR FR AR PRR PRP TR FR RR
1 ' ' iv '
, Ue
0 50 100 150 200 250
Months
Exogenous Feeding Larvae
Figure 10. The influence of high egg production by Spring age 2’s on Exogenous feeding larvae.
140000
120000
100000
80000
60000
om FEEEEERRELEEEEEEELL |
20000
—-Eggs ----- Exogenous Feeding Larvae
Figure 11. The influence of low egg production by Spring age 2’s on Exogenous feeding larvae.
900000
800000
700000
600000
500000
400000
300000
200000
100000
Months
—Eggs ----- Exogenous Feeding Larvae
Figure 12. The influence of high egg production by Spring age 3’s on Exogenous feeding larvae.
Months
—Eggs ----- Exogenous Feeding Larvae
Figure 13. The influence of low egg production by Spring age 3’s on Exogenous feeding larvae.
250000
200000
150000
100000
50000
0 ice a pe
150 200 250
Months
----- Eggs - Exogenous Feeding Larvae —------ Yolk Sac Larvae
Figure 14. Influence of high mortality of eggs, Exogenous feeding larvae and Y olk sac larvae on
Spring age 1s.
Spring A ge 2s (Fish)
Months
~ Summer A ge 0s Spring Age 1s - - - Spring Age 3+ Spring Age 2s
Figure 15. Influence of high mortality of Spring age 1s on Summer age 0s, Spring age 1s, Spring
age 2s, and Spring age 3+.
Overall, the model was most sensitive to mortality and reproductive characteristics of Spring age
3+ but not very sensitive to Spring age 2s. These results are expected given the some of the life
history characteristics of yellow perch. As previously noted, male yellow perch may reach
sexual mature by the spring of their second year (Spring age 2s) but maturation of females may
be delayed at least one year (Spring age 3+; Jansen 1996). Given that fecundity is a measure of
reproduction by females, we would expect that the model would be more sensitive to Spring age
3+ yellow perch rather than Spring age 2s. Thus, sensitivity analyses are congruent with
ecological knowledge of the species.
Discussion:
Several traditional statistical modeling approaches have been previously developed and used to
explain and predict recruitment of harvestable or sexually mature fish in general and yellow
perch specifically. These approaches are generally categorized as “stock assessments,” whereby
“stock” refers to the number or biomass of harvestable or sexually mature fish or their
reproductive capability and “recruit” refers to the population still alive at any time after the egg
stage. Three stock assessment types include stock-recruitment models, surplus production
models, and statistical catch-at-age models. Each model type varies in complexity.
Stock-recruitment models are the simplest type and examine only a relationship between the
stock and recruit life stage. “Stock” in this stage is a measure of the reproductive capacity of
female fish such as fecundity and recruits are often defined as fish that reach the minimum size
14
allowed for harvest (though not always). Depending on the specific stock-recruitment equation
used (e.g., Beverton and Holt, 1957; Ricker, 1975), the model may account for density-
dependent survival rates. Further, density-independent environmental factors may be included
within the equation in order to account for unexplained variability in the relationship between
stock and recruits (Haddon, 2001). However, the equation does not account for feedback
between the recruit back to the stock.
To our knowledge, only one published study has modeled yellow perch recruitment using a
stock-recruitment recruitment approach. Henderson (1985) tested three hypotheses of
recruitment variation in South Bay, Lake Huron, U.S.A. Results showed that recruitment was
not a function of parental stock abundance or water temperature but was positively related to
lake water levels. Stock-recruitment models for yellow perch populations in natural lakes in
South Dakota, U.S.A. are currently under development (Dembkowski, unpublished data) but
have not been created for other inland lakes across the geographic range of perch to our
knowledge.
Surplus-production models are also simple in nature and are advantageous for modeling
recruitment when limited information on the population of interest is available (Haddon, 2001).
The “stock” used in this model pools recruitment, growth, and mortality into a single production
function (e.g., all fish of a harvestable size) rather using a measure reproductive capacity. The
only data required for this model type is an index of relative abundance of the stock and the
associated catch data (e.g., fishing effort; Haddon, 2001). Surplus-production models are often
used to predict how much biomass of a commercially or recreationally important fishery may be
harvested or lost due to other human factors over the long term. In fact, economic data,
including the cost to fish and the revenue gained may be included in models (Christy and Scott,
1965; Grafton et al., 2006). However, much like stock-recruitment models, surplus production
models also do not account for feedback between the recruit back to the stock.
To date, only one study has used a surplus production model to predict biomass loss of yellow
perch due to the impacts of water intakes for industrial and municipal purposes and subsequent
impingement of eggs, larvae, and standing stock biomass in Lake Michigan, U.S.A. (Spigarelli et
al., 1981). Results showed minimal impact on all three life stages of yellow perch due to
impingement. However, no surplus production models for yellow perch have been developed for
inland lakes in North America.
The third type of commonly used stock assessment are age-structured models. These models
offer an advantage over surplus-production models by differentiating “stock” into sex, size, age,
or some combination of the three (Haddon, 2001). This distinction helps to account for time
delays in production (e.g., the time it takes for a juvenile recruit to reach sexual maturity;
Haddon, 2001). The data required for this model type thus includes not only stock and recruit
information but also the sex, size, or age of the recruits. Cohorts of fish can be followed over
time, typically on an annual basis.
Age-structured models have also been developed for yellow perch populations in southwestern
Lake Michigan, U.S.A. (Wilberg et al., 2005). The model partitioned stock by age, size, and sex
15
to examine whether reproductive failure or recreational and commercial fishing led to a
population collapse. Further, various management actions were evaluated in predicting potential
recovery responses of the population. However, the model did not include environmental
factors, provided no feedback between recruits and stocks, and was for a Great Lakes fishery
rather than an inland lake fishery.
Overall, traditional fisheries stock assessments, including those for yellow perch, are useful to
fisheries scientists, managers, and regulators but appear to be limited in their ability to fully
capture feedbacks in the system and the complexity of factors that may influence recruitment of
fishes, including both density-dependent and -independent effects. Modeling the process of
recruitment with only stocks and recruits often fails because the models do not capture
catastrophic mortality events that occur at different life stages and at different rates between
stock and recruit. Differentiation of stock by sex, age, or length may help to a certain extent, but
even these more structured models do not account for feedbacks from recruits back to the stock.
An SD modeling approach could overcome these limitations of traditional fisheries stock
assessments. Critical life stages can be represented as several different stocks and flows can
represent both survival and mortality. Growth rates of fish may influence those flows as the
ability of fish to reach the next life stage may depend on their body size and the rate at which
sizes are achieved. In this way, SD models can integrate the three dynamic rate functions
(recruitment, growth, and mortality) that interact to determine the nature of fish populations (see
Figure 1).
Further, SD models can integrate the various density-dependent and -independent environmental
and anthropogenic factors that influence fish growth, survival, and mortality at various life
stages. The inclusion of these relationships into the model can allow for the stimulation of
various scenarios (see Next Steps in Model Development below) to examine the effects of
environmental and anthropogenic changes on various life stages over the long term. We believe
this model will be useful for fisheries scientists, managers, and regulators to identify limits to
recruitment and develop management strategies to help provide more consistent and sustainable
yellow perch populations for recreation and to serve as prey for other recreationally important
fish in the same waterbodies.
Next Steps in Model Development:
Initial model testing shows promise in developing a yellow perch recruitment model with stocks
and flows between important life stages but does not yet capture the complexity of factors that
may influence recruitment. First, growth of fish in terms of body length and weight has yet to be
included as a subcomponent. Both length and weight influence survival and mortality at several
life stages in different ways. For example, age-0 yellow perch that grow large enough in body
length and at a relatively rapid rate may avoid predation and be more likely to survive, but adult
perch of a certain length may become vulnerable to harvest mortality. Additionally, inclusion of
growth, particularly in body weight, may also provide linkages to other factors such as food
supply and fecundity.
The model must also incorporate exogenous environmental and anthropogenic factors in order
the capture the complexity of recruitment. Climate, fish community characteristics, angling, and
management decisions can influence survival, mortality, and growth at each life stage. Inclusion
of these factors also allows for the development of various scenarios to predict yellow perch
recruitment over the long term. At a minimum, we plan to test at least three scenario types that
have been hypothesized to impact recruitment of yellow perch in inland lakes:
e Scenario Type #1(Climate): How might recruitment of yellow perch respond to increased
water temperatures and precipitation and decreased duration in ice cover as predicted
under climate change?
e Scenario Type #2 (Fish Community): How might recruitment of yellow perch respond if
smallmouth bass (Micropterus dolomieu; a predator) and bluegill (Lepomis microchirus;
acompetitor) increased in abundance?
e Scenario Type #3 (Angling and Management): How might recruitment of yellow perch
respond if bag limits (i.e., the number of allowable fish harvested by anglers) increased?
How might recruitment respond if female yellow perch were harvested at a greater rate
than males in the winter months?
Conclusion:
This paper presented the first version of a yellow perch population dynamics model to be used
for fisheries management and research relevant to North American inland lakes. The model was
constructed in Vensim modeling environment. A fter initial model development to reach a
generalized population in equilibrium state, several sensitivity tests were run on the most
uncertain parameters, including: Spring age-0 mortality rate, Spring age-1 mortality rates;
percentage of Spring age-2 fish that are reproducing, and the number of eggs produced per
reproducing Spring age-2 and age-3+ fish. Results showed that the model behaved fairly well to
the altered conditions, with corresponding and logical increases or decreases in fish population
responding to the altered parameter value. Although intemally consistent, the model needs
improvement in auxiliary variables representing mortality (whether natural or anthropogenic)
and reproduction that better represent the climate, lake, or management forces known to
influence yellow perch inland lake populations across their geographic range. A dditional testing
and validation of the model are also needed to ensure that the boundary and structure of the
model are appropriate once the auxiliary variables described above are improved. Compared to
other types of the fisheries recruitment models, the SD approach is likely to improve our
understanding of yellow perch population dynamics through the integration of and feedbacks
between critical life stages with important environmental and anthropogenic factors hypothesized
to influence populations of perch in inland lakes where these fish provide recreational fisheries
as well as serve as prey to other recreationally important species in the same waterbody.
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21
Supplementary Material:
Table A. Description and rates survival and mortality at each life stage of yellow perch (both sexes) and fecundity of sexually mature
female perch as described in scientific literature. Each of these factors will be used in the model identified in Figure 2.
Life stage Variable name Description Rate or Justification or Citation
Relationship
Egg Viability Fertilized eggs with potential 95.0% Clady (1975; in Dahlberg, 1979)
to hatch
Survival Percent of cohort surviving 1.6-— 18.4% Clady (1976; Carlander, 1997)
from fertilized egg to
hatch/swim-up larvae
Yolk-sac larvae | Survival Percentage of cohort 100.0% No published data available. Assumed to
surviving between egg hatch be high given relatively short time frame.
to T 25 days post-emergence
Exogenous Survival Percentage of larvae 2.0% Noble (1975; in Dahlberg 1979).
feeding larvae surviving from T25 days post
emergence to time Ts days post
emergence
Summer age-0 Survival Percentage of larvae 100.0% No published data available. Assumed to
surviving between T55 days post be high when predator abundance is low
emergence and the first juvenile and available cover is high.
stage (August)
Fall age-0 Survival Percentage of juveniles 100.0% No published data available. Assumed to
surviving between the first be high when prey resources are abundant
juvenile stage (August) to the and predator abundance is low.
end of the growing period
(October)
Spring age-1 Annual mortality | Percentage of the cohort that 5.0— 60.0% | No published data available but several
leaves the population due to studies have hypothesized that the first
death during the first winter overwinter period may be a point of
period catastrophic mortality depending on
winter severity and lake characteristics
(see Jansen 2008 for a review).
22
Life stage Variable name Description Rate or Justification or Citation
Relationship
Spring age-2 Annual mortality | Percentage of the cohort that | 45.0 — 92.0% Isermann (2003)
leaves the population due to
death
Fecundity Number of eggs produced by | 3,630-—14,696 | Clady (1976); Jackson et al. (2008)
individual females of this eggs/female
cohort
Spring age-3 Annual mortality | Percentage of the cohort that | 45.0 — 92.0% Isermann (2003)
leaves the population due to
death
Fecundity Number of eggs produced by | 5,390-—31,419 | Clady (1976); Jackson et al. (2008)
individual females of this eggs/female
cohort
23
Table B. Equations used in the yellow perch recruitment model as described in Figure 2.
Eq.# | Variable (type) Equation Initial value; Units
1 Age 1 mort rate =0.66 Dmnl
(flow)
2 Age 2 mort rate =0.66 Dmnl
(flow)
3 age mortality = Spring age 2's/month unit-maturation3 fish/Month
(auxillary)
4 Age0 mort rate =0.3 Dmnl
(constant)
5 age0 mortality =Summer age 0s/month unit-maturation1 Fish/Month
(auxillary)
6 agel mortality =Spring age 1s/month unit-maturation2 Fish/Month
(auxillary)
7 "age3+ mortality" =MAX ("Spring age 3+"/life expectancy, 0) fish/Month
(auxillary)
8 “egg success-failure | =0.05 Dmnol
rate" (flow)
9 Eggs (stock) =INTEG (eggs deposited-failed eggs-larvae fish
growth, inital eggs)
10 | eggs deposited =MA X (estimated eggs produced*'start of fish/Month
(auxiliary) spring?", 0)
11 | "eggs deposited per | =18000 fish/Month
Age3+" (constant)
12 | eggs deposity per =8000 fish/Month
Age2 (constant)
13 | estimated eggs =("Spring age 3+"/fish unit*female fish/Month
produced fraction* "eggs deposited per A ge3+")+(Spring
(auxiliary) age 2's/fish unit* percentage of 2s
reproducing* eggs deposity per A ge2*female
fraction)
14 | Exo feed larvae =INTEG (reach exogenous feeding- fish
(stock) maturation0-mort exo feeders, initial exo feed
larvae)
15 | exo feeders mort rate | =0.98 Dmnl
(flow)
16 | failed eggs = Eggs/month unit-larvae growth fish/Month
(auxiliary)
17 | female fraction =0.5 Dmnl
(constant)
18 FINAL TIME =240 Month
24
Eq.# | Variable (type) Equation Initial value; Units
19 fish unit (constant) = fish
20 _| inital eggs (constant) | =0 fish
21 | inital spring 1s =180 fish
(constant)
22 | inital summer 0s =0 fish
(constant)
23 | initial exo feed larvae | =0 fish
(constant)
24 | initial spring 2s =30 fish
(constant)
25 ‘| “initial spring 3+" =550 fish
(constant)
26 INITIAL TIME =0 Month
27 | initial yolk sac larvae | =0 fish
(constant)
28 | larvae growth =(Eggs*(1-"egg success-failure rate"))/months to | Fish/month
(auxiliary) larvae
29 | life expectancy =48 Month
(constant)
30 maturationO =(Exo feed larvae*(1-exo feeders mort Fish/Month
(auxiliary) rate))/months to age0
31 | maturation! = DELAY FIXED (Summer age 0s*(1-A ge0 fish/Month
(auxiliary) mort rate)/month unit, months to agel, Summer
age Os*(1-A ge0 mort rate/month unit))
32 | maturation2 = DELAY FIXED (Spring age 1s*(1-Age 1 mort | fish/Month
(auxiliary) rate)/month unit, months to age2, Spring age 1s
*(1-Age 1 mort rate)/month unit)
33 | maturation3 = DELAY FIXED (Spring age 2's*(1-Age 2 fish/Month
(auxiliary) mort rate)/month unit, months to age3, Spring
age 2's*(1-A ge 2 mort rate)/month unit)
34 month counter MODULO(Time, year duration) Month
35 _| month unit =1 Month
36 | months to age0 =2 Month
(constant)
37 | months to age =9 Month
(constant)
38 | months to age2 =12 Month
(constant)
39 | months to age3 =12 Month
(constant)
40 | months to exo feed =0.5 Month
(constant)
25
Eq.# | Variable (type) Equation Initial value; Units
41 months to larvae =0.5 Month
(constant)
41 mort exo feeders = Exo feed larvae/month unit-maturation0 Fish/Month
(auxiliary)
42 | percentage of 2s =0.125 Dmnl
reproducing
(constant)
43 Reach exogenous =(Y olk sac larvae*(1-yolk larvae mort fish/Month
feeding risk))/months to exo feed
(auxiliary)
44__| SAVEPER =TIME STEP Month [0,?]
45 | Spring age 1s (stock) | =INTEG (maturation1l-agel mortality- fish
maturation2,inital spring 1s)
46 | Spring age 2's (stock) | =INTEG (maturation2-age mortality- fish
maturation3, initial spring 2s)
47 | "Spring age 3+" =INTEG (maturation3-"age3+ mortality","initial | fish
(stock) spring 3+")
48 "start of spring?" IF THEN ELSE(month counter=4, 1, 0) 1
49 | Summer age 0s(stock) | = INTEG (maturation0-age0 mortality- fish
maturation] ,inital summer 0s)
49 __| TIME STEP = 0.0625 Month[0,?]
50 | year duration =12 Month
(constant)
51 yolk larvae mortrisk | =0.85 Dmnl
(constant)
52 | yolk mortality =Yolk sac larvae/month unit-reach exogenous _| fish/Month
(auxiliary) feeding
53 | Yolk sac larvae = larvae growth-reach exogenous feeding-yolk —_| fish
(stock)
mortality, initial yolk sac larvae)
26
Table C. Numerical values arrived at after model development and used for preliminary
sensitivity testing for three uncertain model parameters.
Model parameter Value at model equilibrium Adjusted values (low, high)
Age 0 mort rate 0.30 .01, 0.
Age 1 mort rate 0.66 0.01, 0.99
percentage of Age 2’s 0.125 0.01, 0.99
reproducing
eggs deposited per A ge 2 8,000 3,500, 14,500
eggs deposited per A ge 3+ 18,000 5,000, 32,000
27
