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INTERACTIONS BETWEEN DEMOGRAPHIC
STOCHASTICITY AND GENETIC INTEGRITY OF LAKE

STURGEON POPULATIONS

presented by

AMY M. SCHUELLER

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INTERACTIONS BETWEEN DEMOGRAPHIC STOCHASTICITY AND GENETIC
INTEGRITY OF LAKE STURGEON POPULATIONS

By

Amy M. Schueller

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILSOPHY
Fisheries and Wildlife and
Ecology, Evolutionary Biology and Behavior

2009

ABSTRACT

INTERACTIONS BETWEEN DEMOGRAPHIC STOCHASTICITY AND GENETIC
INTEGRITY OF LAKE STURGEON POPULATIONS

By

Amy MI Schueller
Rehabilitation of lake sturgeon populations has become important because lake sturgeon
were once abundant throughout the Great Lakes basin, but have been reduced to <1% of
historic levels due to habitat degradation and overexploitation. Objectives of this study
were to 1) determine which lake sturgeon population parameters have the greatest
influence upon demographic and genetic characteristics, 2) determine the minimum
viable population size (MVP) for lake sturgeon and how inbreeding depression may
affect MVP, and 3) determine strategies for supplementation stocking in order to
maintain long-term persistence of populations while maintaining the smallest genetic
impact. An individual based modeling approach that represented demographic processes
in a stochastic manner and genetic processes was used to address these objectives for this
long-lived species. Sensitivity analyses were performed by holding all parameters at a
nominal value and changing one parameter at a time across a range of plausible values.
All responses were hypersensitive to YOY mortality, post YOY mortality, and age at first
maturation and probability of mating for females, and were relatively insensitive to age at
first maturation and probability of mating for males. The effects of inbreeding depression
on MVP were incorporated under two scenarios: 1) individuals with inbreeding
coefficients above a threshold experienced reduced fitness and 2) individuals experienced

reduced fitness at a rate related to their inbreeding coefficient. Three mechanisms for

inbreeding depression were explored: YOY viability, post YOY viability, and progeny
number. Minimum viable population size was defined as a population size with ~5%
chance of extinction over 250 years and was estimated at 80 individuals without
inbreeding. With inbreeding depression, MVP estimates ranged from 80-1 ,800,
depending upon the scenario. Thus, both demographic stochasticity and inbreeding
contributed to extinction risk. The model was used to explore supplementation scenarios
which included three initial population sizes, two time frames, varying sex ratios,
variance in family size, and different percentages of the adult population contributing
progeny. All supplementation scenarios that I considered resulted in reduced extinction
risk, increased population sizes, increased gene retention, and reduced inbreeding over
time. Within the range of conditions that I explored, supplementing larger populations
over longer time frames and capturing the greatest number of adults from the population
for producing progeny were the most important considerations for maintaining genetic

integrity in lake sturgeon.

ACKNOWLEDGMENTS

I would like to start off by acknowledging those that have provided mentoring and
guidance during my time here at MSU. First, Dr. Daniel Hayes has not only been a
wonderful advisor, but also a great friend. Thank you for helping me to become a peer
in the fisheries field. I have learned skills from you that go beyond academic to life
skills, which are so crucial to success. Also, thank you for being a great friend and
accepting my personal choices. I would also like to thank my graduate committee, Drs.
Kim Scribner, Michael Jones, and Dana Infante, for their guidance. Finally, I would like
to thank the F enske Fellowship selection committee Kelley Smith, William Taylor,
Jessica Mistak, Dana Infante, and Gary Whelan. I would especially like to thank my
F enske Fellowship mentor, Gary Whelan, who provided me with management agency
experience.

During my time here, the friends that I have made have been supportive of me
both academically and personally. I will never forget the support they provided during
some of the most trying times that I have ever had in my life experiences thus far. There
are so many of you that I can’t possibly begin to list you all for fear that I will leave
someone out accidentally. But, thank you all, you have made my time here some of the
best years of my life.

Finally, I would like to thank my family. To my parents and siblings, thank you
for always being supportive. Whatever decisions I have made, you have always stood by
me but have been excited for me, and for that I really appreciate all of you. My biggest

thanks of all go to Ray and Nora, my wonderful family. Nora, thanks for enduring as I

iv

studied at home or worked on the computer. Whenever I get home, you always make me
smile as you come to give me a hug. Finally, Ray, there is no way I can ever express my
gratitude to you. Thank you for your never ending patience and support. Thank you for

being so laid back and flexible as we have made our journey together. I can’t tell you

how much I appreciate you and Nora. I love you both.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................. vii
LIST OF FIGURES ................................................................................. x
INTRODUCTION ................................................................................... 1
CHAPTER 1: SENSTIVITY OF LAKE STURGEON POPULATION DYNAMICS
AND GENETICS TO DEMOGRAPHIC PARAMETERS .................................... 8
Introduction ................................................................................. l 0
Methods ..................................................................................... 14
Results ....................................................................................... 21
Discussion ................................................................................... 25

CHAPTER 2: MINIMUM VIABLE POPULATION SIZE FOR LAKE STURGEON
USING AN INDIVIDUAL BASED MODEL OF DEMOGRAPHICS AND

GENETICS .......................................................................................... 42
Introduction ................................................................................. 44
Methods ..................................................................................... 49
Results ....................................................................................... 58
Discussion ................................................................................... 60
Recommendations .......................................................................... 69

CHAPTER 3: EVALUATION OF STOCKING STRATEGIES FOR LAKE
STURGEON: TRADEOFFS BETWEEN DEMOGRAPHIC STOCHASTICITY AND

GENETIC INTEGRITY ........................................................................... 78
Introduction ................................................................................. 79
Methods ..................................................................................... 83
Results ....................................................................................... 92
Discussion ................................................................................... 95
Management Implications ............................................................... 102

CONCLUSIONS .................................................................................. 11 1

APPENDIX A ...................................................................................... 121

APPENDIX B ...................................................................................... 142

LITERATURE CITED ........................................................................... 148

vi

LIST OF TABLES

Table 1.1. Baseline parameter values as determined from the literature and from lake
sturgeon biologists (Baker 1980; Hay- Chmielewski and Whelan 1997; Auer 1999; Bruch
1999; Billard and Lecointre 2001) ................................................................ 32

Table 1.2. Percent of populations extinct (i2 SE), percent of populations increasing (i2
SE), average percent genes retained (i2 SE), and final mean inbreeding for the baseline
simulations for the initial populations sizes of 50 and 200 ..................................... 33

Table 1.3. Local sensitivity (the average outcome for i10% deviations), S, for each
model parameter, each initial populations size, and each model output .................... 34

Table 1.4. Broad sensitivity (the average outcome for i30% deviations), S, for each
model parameter, each initial populations size, and each model output ..................... 35

Table 2.1. Baseline parameter values as determined from the literature and from lake
sturgeon biologists .................................................................................. 72

Table 2.2. Minimum viable population size for no inbreeding depression, threshold
inbreeding depression, and gradual inbreeding depression for several fitness components,
and the final mean inbreeding coefficient and percent of genes retained at MVP for each
of the scenarios. For the percent of genes retained, simulations which went extinct were
assigned a zero. Means (i2 SE) are provided for percent of genes retained ............... 73

Table 3.1. The percent of extinct populations (:1: 2 SE), mean final population size,
percent of genes retained (i 2 SE), and mean final inbreeding coefficient for baseline
conditions with no stocking at the end of 250 years ........................................... 104

Table 3.2. The number stocked per year under the trickle scenario, the total stocked under
the trickle scenario, the number stocked per year under the pulse scenario, and the total
stocked under the pulse scenario for each of the population types in order to achieve the
desired mean final population size. Numbers stocked per year were obtained using
interpolation using a linear equation, and total stocked was estimated as the number
stocked per year before rounding times the number of years stocked. The first line under
each scenario is the baseline with no stocking .................................................. 105

Table 3.3. The number stocked per year under the trickle scenario, the total stocked
under the trickle scenario, the number stocked per year under the pulse scenario, and the
total stocked under the pulse scenario for each of the population types in order to achieve
the desired percent of genes retained. Numbers stocked per year were obtained using
interpolation using a power function, and total stocked was estimated as the number

vii

stocked per year before rounding times the number of years stocked. The first line under
each scenario is the baseline with no stocking ................................................ 106

Table 3.4. The number stocked per year under the trickle scenario, the total stocked

under the trickle scenario, the number stocked per year under the pulse scenario, and the

total stocked under the pulse scenario for each of the population types in order to achieve

the desired mean final inbreeding coefficient. Numbers stocked per year were obtained
using interpolation using a Weibull firnction, and total stocked was estimated as the

' number stocked per year before rounding times the number of years stocked. The first

line under each scenario is the baseline with no stocking .................................... 107

Table 3.5. The percent of genes retained (i=2 SE) and mean final inbreeding coefficient
for skewed sex ratios for each population size and stocking strategy. For each initial
population size or scenario, baseline outputs are included for no stocking ............... 108

Table 3.6. The percent of genes retained (i2 SE) and mean final inbreeding coefficient
for unequal family sizes for each population size and stocking strategy. None indicates
equal family size, and up to 5x indicates that family size could vary up to five times
higher than the baseline family size. For each initial population size or scenario, baseline
outputs are included for no stocking ......... " ................................................... 1 09

Table 3.7. The percent of genes retained (i2 SE) and mean final inbreeding coefficient
for reduced numbers of adults used for mating purposes for each population size and
stocking strategy. One hundred percent indicates all adults contributing progeny for
stocking purposes, and 20% indicates only 20% of mature adults contributing progeny for
stocking purposes. For each initial population size or scenario, baseline outputs are
included for no stocking .......................................................................... 110

Table A. 1. Sensitivity, S, of percent of extinct populations for each of the parameters for
an initial population size of 50 where Ra is the model response for the altered parameter,

R, is the model response for the nominal parameter, Pa is the altered parameter, and P" is
the nominal parameter ............................................................................ 121

Table A2. Sensitivity, S, of average percent of genes retained for each of the parameters
for an initial population size of 200 where Ra is the model response for the altered
parameter, R, is the model response for the nominal parameter, Pa is the altered
parameter, and P” is the nominal parameter. NR represents no response because of
computing limitations ............................................................................. 123

Table A3. Sensitivity, S, of the percent of increasing populations for each of the
parameters for an initial population size of 200 where R0 is the model response for the
altered parameter, Rn is the model response for the nominal parameter, P0 is the altered
parameter, and P" is the nominal parameter. NR represents no response because of
computing limitations ............................................................................. 125

viii

Table A.4. Sensitivity, S, of the final mean inbreeding for each of the parameters for an

initial population size of 200 where Ra is the model response for the altered parameter, R,
is the model response for the nominal parameter, P0 is the altered parameter, and P” is the
nominal parameter. NR represents no response because of computing limitations. .....127

Table A5. Sensitivity, S, of average percent of genes retained for each of the parameters
for an initial population size of 50 where Ra is the model response for the altered
parameter, Rn is the model response for the nominal parameter, Pa is the altered
parameter, and P" is the nominal parameter .................................................... 129

Table A6. Sensitivity, S, of the percent of increasing populations for each of the
parameters for an initial population size of 50 where Ra is the model response for the
altered parameter, Rn is the model response for the nominal parameter, Pa is the altered
parameter, and P" is the nominal parameter ................................................... 131

Table A7 Sensitivity, S, of the final mean inbreeding for each of the parameters for an
initial population size of 50 where Ra is the model response for the altered parameter, Rn
is the model response for the nominal parameter, Pa is the altered parameter, and P" is the
nominal parameter. NR indicates no response because none of the populations persisted
long enough to determine a final mean inbreeding ........................................... 133

Table B. 1. Baseline population parameter values for each of the three plausible scenarios

explored. All under scenario means that the parameter value was used for all three
scenarios ............................................................................................ 142

ix

LIST OF FIGURES

Figure 1.1. Basic model structure for simultaneous simulation of lake sturgeon
demographics and genetics ......................................................................... 36

Figure 1.2. Percent change in parameter versus sensitivity, S, for average percent of
genes retained for lake sturgeon with an initial population size of 50 ....................... 37

Figure 1.3. Percent change in parameter versus sensitivity, S, for the percent of
populations increasing for lake sturgeon with an initial population size of 200 ............ 38

Figure 1.4. The average percent of genes retained versus final mean inbreeding for the
initial population sizes of 200 and 50 ............................................................. 39

Figure 1.5. The percent of populations increasing versus the final mean inbreeding for
the initial population sizes of 200 and 50 ........................................................ 40

Figure 1.6. The percent of populations increasing versus percent of genes retained for the
initial population sizes of 200 and 50 ............................................................ 41

Figure 2.1. Model structure for simulations of lake sturgeon demographic and genetic
parameters ............................................................................................ 74

Figure 2.2. Percent of extant populations across a range of initial population sizes
(persistence curves) under the scenarios of no inbreeding, threshold inbreeding
depression as reduced progeny number at the threshold 0.125, and threshold inbreeding
depression as decreased YOY viability at the threshold 0.125 ............................... 75

Figure 2.3. Percent of genes retained across a range of initial population sizes under the
scenarios of no inbreeding, threshold inbreeding depression as reduced progeny number
at the threshold 0.125, and threshold inbreeding depression as decreased YOY viability at
the threshold 0.125. Percent of genes retained represent all simulations, including
populations with no survivors. Error bars (i2 SE) for each scenario are represented in the
same line type for each scenario. Simulations with no survivors were considered to have
no genes retained .................................................................................... 76

Figure 2.4. Final mean inbreeding across a range of initial population sizes under the
scenarios of no inbreeding, threshold inbreeding depression as reduced progeny number
at the threshold 0.125, and threshold inbreeding depression as decreased YOY viability at
the threshold 0.125. Final inbreeding coefficients only represent extant populations at the
end of the 250 year simulation duration; populations with no survivors were not assigned
an inbreeding coefficient ........................................................................... 77

Figure A.1. Percent change in parameter versus sensitivity, S, for average percent of
genes retained for lake sturgeon with an initial population size of 200 .................... 135

Figure A.2. Percent change in parameter versus sensitivity, S, for percent of increasing
populations for lake sturgeon with an initial population size of 200 ....................... 136

Figure A.3. Percent change in parameter versus sensitivity, S, for final mean inbreeding
for lake sturgeon with an initial population size of 200 ...................................... 137

Figure A.4. Percent change in parameter versus sensitivity, S, for percent of extinct
populations for lake sturgeon with an initial population size of 50 .......................... 138

Figure A.5. Percent change in parameter versus sensitivity, S, for average percent of
genes retained for lake sturgeon with an initial population size of 50 ..................... 139

Figure A.6. Percent change in parameter versus sensitivity, S, for percent of increasing
populations for lake sturgeon with an initial population size of 50 ......................... 140

Figure A.7. Percent change in parameter versus sensitivity, S, for final mean inbreeding
for lake sturgeon with an initial population size of 50 ....................................... 141

Figure B]. The frequency of the number of batches, B, randomly assigned to males and
females in the model using a random uniform distribution and the

equation B = 1 + integer(-2 *ln(1- U(O,l)). The frequency of number of mates per
individual from empirical data from DeHaan (2003) ........................................ 143

Figure B2. The frequency of the number of progeny for an individual male or female
from the model and from empirical data (DeHaan 2003) .................................... 144

Figure B3. The number of individuals that need to be stocked using the trickle strategy
in order to attain a mean final population size for each scenario as determined by
interpolation using a linear function where a) less than MVP, b) brink of MVP, and c)
large, declining ..................................................................................... 145

Figure B4. The number of individuals that need to be stocked using the trickle strategy
in order to attain a mean percent of genes retained for each scenario as determined by
interpolation using a power function where a) less than MVP, b) brink of MVP, and c)
large, declining ..................................................................................... 146

Figure B5. The number of individuals that need to be stocked using the trickle strategy
in order to attain a mean final inbreeding level for each scenario as determined by
interpolation using a Weibull function where a) less than MVP, b) brink of MVP, and c)
large, declining .................................................................................... 147

xi

INTRODUCTION

The lake sturgeon Acipenserfulvescens is one of nine sturgeon species found on
the North American continent and is one of 27 sturgeon species worldwide (Birstein
1993; Auer 1996a; Billard and Lecointre 2001). Lake sturgeons, a long-lived and late
maturing species, spawn from late April to mid-May (Hay-Chmielewski and Whelan
1997). Afier reaching maturity at 12 to 22 years, male sturgeon spawn every other year,
and after reaching maturity at 14 to 33 years, female sturgeon spawn once every 3 to 7
years (Roussow 1957; Harkness and Dymond 1961). Lake sturgeons are a
potarnodromous fish which spawn in freshwater river systems and spend their entire lives
solely in freshwater systems (Rochard et a1. 1990; Auer 1996a; Hay-Chmielewski and
Whelan 1997). Lake sturgeon populations are ofien delineated by the river of spawning
for management purposes (Hay-Chmielewski and Whelan 1997), whereby they spawn in
natal streams, but mixing of populations commonly occurs in the Great Lakes during the
non-spawning season.

Lake sturgeons were once found throughout Great Lakes drainage basin in the
United States and Canada (Birstein et a1. 1997; Hay-Chmielewski and Whelan 1997;
Smith and Baker 2005). Lake sturgeons were initially an unwanted by-catch in the early
commercial fisheries of the Great Lakes; however, by the year 1885, lake sturgeon
became a highly sought after, commercially fished species (Kelso et a1. 1996; Hay-
Chmielewski and Whelan 1997). In 1885, commercial catch was near peak in the United
States waters of the Great Lakes and ranged widely from 82,000 kg harvested in Lake
Superior waters to 2.1 million kg harvested in Lake Erie waters (Auer 1996a). Catches of

lake sturgeon diminished rapidly in all of the Great Lakes in the early 1900’s (Auer

1996a). In 1977, all commercial fishing of the lake sturgeon ceased in waters of the
United States, however, a small tribal harvest still occurs (Hay-Chmielewski and Whelan
1997). Currently, only a few water bodies in Michigan are open to sport fishing catch-
and-release and limited harvest of lake sturgeon.

Because lake sturgeon have been reduced to less than 1% of their historic levels
due to habitat degradation, overharvest, and fragmentation of spawning populations, lake
sturgeon restoration and protection have become a high priority throughout the Great
Lakes basin (Johnson et al. 1998; Auer 1999; Holey et al. 2000; McQuown et al. 2003).
Factors that have contributed to the decline of lake sturgeon in the past continue to
contribute to declines in abundance, and impede restoration where populations have been
extirpated. Therefore, actions aimed at restoration and protection of the imperiled lake
sturgeon have been developed and implement in many areas of the Great Lakes. For
example, stocking and habitat restoration have been suggested, and stocking has been
implemented for some populations in the state of Michigan (Hay-Chmielewski and
Whelan 1997). Lake sturgeon restoration plans have been completed by Michigan (Hay-
Chmielewski and Whelan 1997), Wisconsin (WDNR 2008), and Ontario (OMNR 2006),
although considerable uncertainty exists as to the best course of action for lake sturgeon
restoration.

Although lake sturgeon populations are greatly reduced, genetic diversity of these
populations hasn’t been depressed yet (DeHaan et al. 2006). Hope remains that genetic
integrity of the lake sturgeon populations in the Great Lakes basin can be maintained, but
actions need to be taken to minimize the risk of extinction and the effects of inbreeding

due to current low levels of abundance. Conserving the genetic integrity (defined here as

both the retention of genes and reduced inbreeding accrual) is believed to be important
for conserving this species (Hay-Chmielewski and Whelan 1997; McQuown et al. 2003;
Keller and Waller 2002). Inbreeding occurs when individuals who are closely related
mate, and most readily occurs in small populations where random mating can more
readily result in breeding among related individuals (Hedrick and Kalinowski 2000;
Brook et al. 2002; Keller and Waller 2002). Inbreeding is often thought to result in a
decrease in an individual’s fitness relative to non-inbred offspring, resulting in what is
called inbreeding depression. Inbreeding depression can be manifested in any traits
related to reduced fitness (e.g., poor survival (viability), lower fecundity; Crnokrak and
Roff 1999; Hedrick and Kalinowski 2000; Amos and Balmford 2001), but has been
difficult to demonstrate empirically (Newman and Pilson 1997).

Much debate has occurred over the past decades as to which process is most
important for the risk of extinction for small population sizes: demographic stochasticity
or genetic stochasticity, specifically inbreeding and inbreeding depression. Some have
argued that demographic stochasticity is more important than genetic composition for
small population sizes (Lande 1988; Young 1991; Harcourt 1991). Arguably, if you have
no animals, you have no genes to conserve. However, others have demonstrated that
inbreeding depression can lead to reduced population viability at small population sizes.
Frankham (1995a) concluded that the risk of extinction increased with inbreeding. Keller
and Waller (2002) found that many studies are now available whereby inbreeding
depression has been found in the wild and can be detrimental to long-term persistence.
Many argue that while inbreeding depression may not be the driving force towards

extinction, it still has an impact and increases the risk of extinction (Mills and Smouse

1994). Therefore, a need exists to explore the relationship between demographics and
genetics in regards to the long-term persistence of populations (Boyce 1992), specifically
for long-lived species such as the lake sturgeon

Demographic stochasticity is a factor in the extinction process but has rarely been
considered for a long-lived species such as the lake sturgeon (Higgins 1999). Small
populations suffer from demographic stochasticity and inbreeding and for some of the
population sizes, rehabilitation may be unlikely to be successful (Pimm et al. 1988; Tracy
and George 1992; Lande 1993; Lynch and Walch 1998; Amos and Balmford 2001;
Keller and Waller 2002). Therefore, identifying those situations where rehabilitation
efforts will be most successful will be beneficial to the restoration and protection of lake
sturgeon populations in the Great Lakes basin. Because of the longevity of this species,
empirical tests of restoration strategies are impractical. Modeling is a useful tool because
of the flexibility available, and it can also be used to integrate both population dynamics
and genetics information in order to inform management decisions and determine the
relative contributions of demographics and genetics to extinction risk (Brook et al. 2002).

An individual based model, which tracks individuals through time, was developed
that incorporated both demographic stochasticity and inbreeding. This model was then
used to address three main topics: 1) what population parameters are important for lake
sturgeon persistence and genetic integrity and how sensitive the parameters are to
perturbation, 2) the likely fate of lake sturgeon populations with no management actions
with and without inbreeding depression, and 3) the impact of management intervention

(supplementation) on the demographics and genetics of this species.

A sensitivity analysis was run across a broad range of parameter inputs to
determine the importance and how perturbation of parameters affects the persistence and
genetic integrity of lake sturgeon populations. Sensitivity analyses have rarely explored
uncertainty effects on genetic factors (Beissinger and Westphal 1998), even though these
may be crucial to long-term population sustainability. The objective of the first chapter
of the dissertation was to determine which lake sturgeon population parameters have the
greatest influence upon demographic characteristics including rates of extinction and
percentage of populations increasing above the initial population size, and genetic
characteristics including percentage of unique alleles retained and average inbreeding
coefficient for a 250 year or approximately a 10 generation period.

The rrrinimum viable population size (MVP) with and without inbreeding
depression was estimated in order to explore the fate of populations with no management
actions. Minimum viable population size is defined as a population of sufficient size to
persist with a given probability over a given time frame (Shaffer 1981; Boyce 1992).
Minimum viable population sizes are specific to each study or species and vary
depending upon the species’ life history parameters and the tolerance of extinction risk
for the species’ management and conservation (Shaffer 1981; Lindenmayer et al. 1993).
Modeling the influence of genetic changes on demography has proven to be difficult in
many situations because translating negative genetic impacts into demographic impacts is
not straightforward and because genetic data are often unavailable (Beissinger and
Westphal 1998; Kirchner et al. 2006). However, a need exists to explore the relationship
between demographics and genetics in regards to the long-term persistence of

populations (Boyce 1992; Shaffer 1980; Jager et al. 2000; Kirchner et al. 2006). Thus,

the objective of the second chapter of the dissertation was to determine the minimum
viable population size for lake sturgeon, incorporating both demographic and genetic
stochasticity through the potential impacts of inbreeding (Mills and Smouse 1994).

In the last chapter, I explored the fate of populations when various stocking
strategies were implemented for several population scenarios. Stocking potentially
results in trade-offs between population growth rate and maintaining genetic integrity of a
species (Hansen et al. 2001). While supplementation is often focused on increasing
population abundance, supplementation can result in the loss of genetic variability and
increased inbreeding in a population (Ryman and Laikre 1991; Lynch and O’Hely 2001)
thereby reducing genetic integrity (Tessier et al. 1997; Hansen et al. 2000). However,
supplementing over multiple generations could lead to increased genetic integrity if the
population size is larger in the long-term (Wang and Ryman 2001). Thus, while
demographic stochasticity has been argued to be a more influential driving force with
respect to probability of extinction than genetic factors, including both demographic
stochasticity and genetics in population management strategies, has been advocated
(Lande 1988). As such, the objective of this section of the dissertation was to determine
the number of individuals that should be stocked in order to achieve population
abundance goals while maintaining the smallest genetic impact.

Each of these main topics has tangible management implications for lake sturgeon
populations in the Great Lakes. Estimating population parameters of importance will
help to determine which management actions will have the largest impact on increasing
the long-term persistence of populations (e. g., reducing harvest). Determining risks for

extinction for different sized populations will help managers to rank populations for

rehabilitation purposes. Finally, after choosing populations for rehabilitation, the
analysis of stocking strategies will provide guidance on which options are best to

maintain population abundance and genetic integrity.

SENSTIVITY OF LAKE STURGEON POPULATION DYNAMICS AND GENETICS

TO DEMOGRAPHIC PARAMETERS

AB STRACT.-Uncertainty in population parameters can make managing fisheries
difficult, especially for long-lived species such as lake sturgeon. Models can be used to
explore population parameter uncertainty and how uncertainty affects demographic and
genetic population outputs through the use of sensitivity analyses. The objective of this
study was to determine which lake sturgeon population parameters have the greatest
influence upon demographic characteristics including rates of extinction and percentage
of populations increasing above initial population size, and population genetic
characteristics including percentage of unique alleles retained and average inbreeding
coefficient. An individual based modeling approach that represented demographic and
genetic processes was used to address this objective. Individual lake sturgeon were
tracked throughout the modeling process with unique identifiers, allowing for the
determination of parentage, degree of inbreeding, and number of unique alleles retained.
Sensitivity analyses were performed by holding all of the parameters at a nominal value
and changing one parameter at a time across a range of plausible values. All responses
were hypersensitive to young of the year mortality, post young of the year mortality, age
at first maturation for females, and the probability of mating for females. Post young of
the year mortality rate was the most sensitive of all of the population parameters. The
outputs were relatively insensitive to changes in age at first maturation for males and

probability of mating for males. Sensitivity was dependent upon initial population size

with population parameters having differing sensitivities with respect to other parameters
for smaller and larger population sizes. The demographic and genetic outputs were
related to one another via similar relationships for each of the population sizes. These
analyses should be used to target rehabilitation efforts on altering population parameters

with the largest influence on population persistence and genetic integrity.

INTRODUCTION

One species where the evaluation of demographic and genetic integrity is
critically needed is lake sturgeon in the Great Lakes basin. Lake sturgeon were once
found throughout the Laurentian Great Lakes, spawning in many tributary streams
throughout the basin (Birstein et al. 1997; Hay-Chmielewski and Whelan 1997; Smith
and Baker 2005). However, lake sturgeon have been reduced to less than 1% of historic
levels due to habitat degradation, overharvest, and fragmentation of spawning
populations (Johnson et al. 1998; Auer 1999; Holey et al. 2000; McQuown et a1. 2003).
Factors causing the decline of lake sturgeon in the past continue to contribute to declines
in abundance and impede restoration where populations have been extirpated. Currently,
lake sturgeon restoration is a priority throughout the Great Lakes basin (Hay-
Chmielewski and Whelan 1997). Therefore, extensive management efforts aimed at
restoration and protection of the imperiled lake sturgeon have been developed. While
lake sturgeon restoration plans have been completed by Michigan (Hay-Chmielewski and
Whelan 1997), Wisconsin (WDNR 2008), and Ontario (OMNR 2006), considerable
uncertainty exists as to the best course of action for restoration because of the unique life
history of the lake sturgeon.

Identifying those situations where rehabilitation efforts will be most successful
will be beneficial to the restoration and protection of lake sturgeon populations in the
Great Lakes basin. Uncertainty in demographic parameters and the genetic integrity of a
population are important factors in the extinction process that have rarely been
considered for a long-lived species such as the lake sturgeon (Higgins 1999). Small

populations suffer from increased risks of extinction due to demographic stochasticity

10

(random births and deaths), environmental stochasticity (random environmental'factors),
catastrophes, and inbreeding, and for some population sizes, rehabilitation may be
unlikely to be successful (Pimm et al. 1988; Tracy and George 1992; Lande 1993; Lynch
and Walch 1998; Amos and Balmford 2001; Keller and Waller 2002).

Given the logistical difficulties in empirically studying such a long-lived species,
the best tactic to integrate both population dynamics and genetics information to inform
management decisions and guide current restoration efforts is through the use of
modeling. Both demographic and genetic factors contribute to extinction risk and
population decline, and should be incorporated into the modeling process (Mills and
Smouse 1994; F rankham 1995). Therefore, modeling should be used as a tool to help
understand the uncertainty surrounding population parameters and the influence those
parameters have on extinction risk.

Modeling, in general, has been used to explore and quantify parameter uncertainty
and how that uncertainty affects population outcomes such as extinction risk through the
use of sensitivity and elasticity analyses (Bart 1995; Letcher et al. 1996; Beissinger and
Westphal 1998; Reed et al. 1998; Caswell 2000; Ellner and Fieberg 2003). Sensitivity
analysis is a method whereby baseline parameter values are altered, usually one at a time
or independently, to see how the parameter alteration influences specified population
outcomes within a simulation model (Bartell et a1. 1986; Cross and Beissinger 2001;
Ellner and Fieberg 2003). Sensitivity analyses explore responses within a limited frame
of possible parameter values, generally with changes between :t1% to 21:10% of nominal
values (McCarthy et al. 1995; Essington 2003). Exploring parameters across a broader

range of values is not typically done, but could have important management implications.

11

Often, managers are more uncertain about population parameters than 21:10%, and
sensitivities have been shown to be good predictors of population outcomes even with
large parameter changes (Caswell 2000). Also, as the range of parameter values is
expanded, the importance of each population parameter with respect to other population
parameters may change. These differences in population outcomes could have large
impacts on the ability of managers to influence population level responses if the change
in a parameter due to management actions is large.

Sensitivity analyses have rarely explored uncertainty effects on genetic factors
(Beissinger and Westphal 1998), even though these are crucial to long-term population
sustainability. For example, genetic factors such as inbreeding can contribute to
increased risks of extinction at small population sizes (Newman and Pilson 1997).
Individual based models are a type of model which allows for representation of
individual genetic characteristics and population processes, yet also allow for population
level responses to be evaluated (Chambers 1993; Van Winkle et al. 1993a). Individual
based models follow individuals through time during simulations, and outputs can be
obtained on both the individual and population level. The flexibility available with an
individual based model has led to this type of model being used to research populations
of fish, plants, birds, mammals, and invertebrates (Rose and Cowan 1993; Beissinger and
Westphal 1998; Grimm 1999). For example, dispersal in a metapopulation (Travis and
Dytharn 1998), fish responses to environmental change, pollution, and individual
characteristics (Van Winkle et al. 1993b; Madenjian and Carpenter 1993; Letcher et al.
1996), management options for invasive plant species (Buckley et a1. 2003), and effects

of environmental and demographic stochasticity on red-cockaded woodpecker Picoides

12

borealis populations (Walters et al. 2002) have all been explored using individual based
models. Individual based models have been used to explore inbreeding for the southern
bluefin tuna Thunnus maccoyii and 19 other threatened species (Brook et al. 2002). The
flexibility available and the ability to track individuals within a population make
individual based models a good choice of model for assessing the sensitivity of
population genetics to population dynamics parameters.

A key goal of conserving genetic integrity is to maintain the distribution of genes
within a population. Many processes influence a population’s genetic integrity, but a
major factor is inbreeding (Hay-Chmielewski and Whelan 1997; McQuown et al. 2003).
Inbreeding occurs when individuals who are closely related mate, and most easily occurs
in small populations where random mating can more readily result in breeding among
related individuals (Brook et al. 2002; Keller and Waller 2002). Inbreeding does not
result in the loss of alleles, but does result in an increase in homozygotes and a decrease
in heterozygotes (Conner and Hart] 2004). Thus, inbreeding does not reduce genetic
diversity, but causes a redistribution of genes within the population. Inbreeding is often
thought to result in a decrease in a species’ fitness, termed inbreeding depression
(Cmokrak and Roff 1999; Amos and Balmford 2001). Genetic integrity of a species has
been shown to be positively related to population size (Secor et al. 2002). Therefore, the
genetic integrity of small populations may be reduced through inbreeding, leading to an
increased risk of extinction (F rankharn 1995). However, inbreeding is thought to have
less of an impact when accruing at a slower rate such as in long-lived species. Selection
is better able to remove deleterious alleles in these situations, and thus extinction rates are

also thought to be lower at slower rates of inbreeding accrual (Reed et al. 2003).

13

The parameters most important to the long-term persistence and genetic integrity
of lake sturgeon populations are unknown. This study will use sensitivity analyses to
address which population parameters for lake sturgeon are most influential for population
outcomes. The objective of this study is to determine which lake sturgeon population
parameters have the greatest influence upon demographic characteristics including rates
of extinction and percentage of populations increasing above the initial population size,
and genetic characteristics including percentage of unique alleles retained and average
inbreeding coefficient for a 250 year or 10 generation period. Probability of extinction
and percentage of populations increasing above the initial population size are population
outcomes indicative of long-term population persistence. Percentage of unique alleles
retained and average inbreeding coefficient are genetic outcomes which relate to long-
tenrr persistence and genetic variability. This research will help to inform management
of lake sturgeon within the Great Lakes basin by determining which population
parameters have the greatest impact on population features related to the likelihood of
population persistence. This information could then be used to focus management efforts
on rehabilitating lake sturgeon populations by altering those population parameters.

METHODS
Model Development

An individual based model was developed that incorporated demographic and
genetic processes (Figure 1.1). Lake sturgeon exhibit a polygamous mating system
which was represented based on available data whereby female lake sturgeon mature at
approximately 20 years of age and spawn approximately once every 3 years, and male

lake sturgeon mature at approximately 15 years of age and spawn approximately every

14

other year (Auer 1999; Bruch 1999; Billard and Lecointre 2001; DeHaan 2003; Nichols
et al. 2003). Once an individual reached the minimum age for maturity then the
individual was assigned a random number distributed Uniform(0,1). If that random
number was less than the probability of mating each year, then that individual returned to
the river to mate that year. Empirical data from Black Lake, Michigan, lake sturgeon
suggest that reproductive success is not related to the length or weight of the adult
sturgeon, therefore, the size of individual fish wasn’t included in this individual-based
model (DeHaan 2003). For each fish returning to spawn, the number of potential mates
or batches of offspring, B, for each spawning male and female was based on empirical
data from Black Lake, MI (Figure B.1; DeHaan 2003). Random numbers of batches
were generated using a discrete form of the exponential distribution by:

B = 1 + integer(-2 * ln(l - U(0,1)) .
This distribution represents the number of mates from empirical data (Figure 8.1;
DeHaan 2003). The batches for the males and females were randomly shuffled, and
female batches were paired with male batches. This process allowed random mating
between individuals, and allowed individuals to mate with multiple other individuals as
has been observed in lake sturgeon. In this model, any batches produced by a male or
female without a pair, or mate, were deleted. This distribution allows for a large number
of mates as the uniform distribution approaches one; however, the number of mates is
decreased based on how the batches are paired with mates. Thus, extremely large
numbers of mates is unlikely. The number of progeny, P, created (at the end of the
summer) from each mating pair, or batch, was generated using an exponential equation of

the form:

15

P = integer(l * (-ln(l - U(O,l))))
producing a distribution of numbers of offspring similar to that seen in Black Lake, MI
(DeHaan 2003). This distribution was based on the empirical number of progeny per
adults as reported by DeHaan (2003; Figure 8.2). The empirical distribution was based
on a parentage analysis whereby progeny in a sample were assigned to parents. Only
about 25% of progeny were assigned to parents, however. Because of this, the empirical
number of progeny per parent should be treated cautiously. Because the number of
progeny was modified by varying the YOY mortality rate to match observed population
sizes and trajectories, this distribution was judged to be appropriate.

The sex of offspring was randomly determined with an equal probability.
Following birth, age-specific mortality rates were applied to each individual sturgeon.
Mortality rates were set up in the model such that a random number between 0 and 1 was
generated for each individual and if that random number was less than the specified level
of mortality, then that individual suffered mortality. As such, demographic stochasticity
was implicitly incorporated into the model because the death of each individual was
randomly determined. The mortality rate from the end of the summer through the winter
to the end of the first year is unknown. Therefore, this mortality rate was varied to
produce population growth rates that mimic observed growth rates for existing
populations. This technique has proven useful in previous studies and provides a means
to develop management advice even though parameter values are uncertain (Vaughn and
Saila 1976; Hayes and Taylor 1990; Heppell et al. 2000). All parameter values were
developed from literature review and further review by local Great Lakes sturgeon

experts. Mortality after the first year was set to 0.05 based on Baker (1980). Henceforth,

l6

young of the year mortality will be referred to as such, and mortality after the first year
will be referred to simply as “mortality.” Young of the year and post young of the year
mortality rates have been treated this way by past elasticity studies for other sturgeon
species (Gross et al. 2002).

The effects of inbreeding on mortality rates of lake sturgeon are currently
unknown. For this sensitivity analysis, inbreeding was assumed not to reduce the fitness
of individual sturgeon. Also, the inbreeding at the start of the simulations was assumed
to be zero; therefore, the model was only concerned with the net accrual of inbreeding.

Individual inbreeding coefficients were determined using path analysis of the
individual’s pedigree implemented in the INBREED procedure available in SAS® (SAS
Institute Inc., 2003). From a pedigree, the inbreeding coefficient (7;) for an individual
was determined by summing all of the unique paths (P) through a common ancestor (A)

as

22:21; (1+f,.>

where n was the number of ancestors in the path ande was the inbreeding coefficient of
ancestor A (Wright 1922). Lake sturgeon are polyploid with a ploidy level of eight
(Blacklidge and Bidwell 1993). Polyploidy is thought to mask inbreeding depression;
however this effect has not been shown for other polyploid species such as salmon
species Oncorhynchus sp. (Wang et al. 2002). Therefore, I assumed polyploidy of lake
sturgeon did not affect the accrual of inbreeding or inbreeding depression. This approach
allowed for the tracking of overall individual inbreeding levels and accrual of inbreeding

rather than specifying certain alleles as deleterious.

l7

Gene retention from the founding population was tracked based on a one locus
system whereby each individual at the start of the simulations had two unique,
hypothetical alleles at one locus (MacCluer et al. 1986). The hypothetical locus was
assumed to be inherited as a Mendelian trait. As mating occurred between individuals,
some alleles were lost from the population before they could be passed on to offspring.
Random loss of unique alleles results in genetic differentiation among populations and
determines the percentage of founders that have contributed genes to the population. The
loss of unique alleles can be described through a technique called gene drop analysis
(MacCluer et al. 1986; Hedrick and Miller 1992), which tracks all unique alleles that are
retained or lost from the population through time (Hai g et al. 1993). Thus, the percent of
remaining alleles at the end of each simulation can then be expressed as the number of
remaining alleles over the number of unique alleles at the beginning of the simulation
which is two times the initial population size.

Sensitivity Analysis

A sensitivity analysis was performed by holding all of the parameters at a nominal
value (Table 1.1), as identified from the literature and sturgeon biologists, and changing
one parameter at a time across a range of plausible values to determine which parameters
most strongly influenced model predictions and to evaluate how model predictions
changed with changes in the population parameters (McCarthy et al. 1996; Essington
2003). The sensitivity of the model (S) to a parameter change was expressed as the
difference in the output when the parameter was changed, compared to the associated

output when all of the parameters were set at their nominal value:

18

_ (Ra-Rn)/R,
‘ (P.-P.>/R.

 

where Ra was the model response for the altered parameter, Rn was the model response
for the nominal or unaltered parameter, Pa was the altered parameter, and P" was the
nominal or unaltered parameter (Haefner 2005). If the percent deviation of the parameter
caused a similar percent change (absolute value of S = 1.00) in the results of the
simulation model, then the parameter was linearly related to the output (Letcher et al.
1996). If the percent deviation of the parameter caused less of a percent change (absolute
value of S < 1.00) in the results of the simulation model, then the parameter was
classified as an insensitive parameter. If the percent deviation of the parameter caused a
greater change (absolute value of S > 1.00) in the results of the simulation model, then the
parameter was classified as a highly sensitive parameter. This type of sensitivity analysis
where proportional parameter changes are compared to proportional output changes is
often called elasticity (Caswell 2000). The model was run 500 times per sensitivity
analysis for 250 years to determine which population parameters had the greatest impact
on the population outcomes of interest. Sensitivity analysis is often conducted across
parameter space close to nominal values (e. g., Essington 2003); I term this local
sensitivity. In the local sensitivity analysis, parameters were varied 2t 10% about their
nominal values. In addition to a local sensitivity analysis, I also determined sensitivity
across a broader range of values (i.e., parameters were varied :t 30% about their nominal
values) to determine if model responses were maintained beyond a local parameter space.

Sensitivities, both local and broad, were presented as average sensitivities over the range

19

of parameter perturbation (i10% or $3 0%). Thus, the sensitivities for both the negative
and positive perturbations were averaged.
Simulations

Simulations were run with two initial population sizes, 50 and 200 individuals.
The initial population size of 200 was used because this population size allowed for the
exploration of parameter values with minimal risk of extinction due to demographic
stochasticity. The initial population size of 50 was also chosen in order to explore
population outcomes with a heightened risk of extinction in order to compare the effects
of extinction on sensitivity of model outcomes. Simulations were assumed to have
current environmental and demographic conditions, which remained constant into the
future.

Based on preliminary analyses, a simulation duration of 250 years was used as
this appeared to allow time for transient responses to dissipate. For each scenario, 500
simulations were run to provide precise estimates of the mean response and variance. A
yearly time step was used in all simulations. The percent of populations extinct,
population abundance (summarized as percentage of populations increasing above the
initial population sizes of 50 and 200), average individual inbreeding coefficient in the
final year, and percent of unique alleles retained were recorded for each simulation run of
250 years. The mean final abundance was the average abundance including zeroes for
those populations that went extinct. The average individual inbreeding coefficient was
the average inbreeding coefficient for progeny produced in the final year. No uncertainty
estimates could be provided for the inbreeding coefficients because only the mean was an

output for the model. The average percent of unique alleles retained was the average

20

percent of genes retained including zeroes for those populations that went extinct. For
the percent of populations extinct, the percent of populations increasing, and the average
percent of genes retained, confidence intervals were calculated as:

(estimate :1: 2*SE)* 100
where the SE = (pq/n) A (1/2), p = (percent of extinct populations or genes retained/100),
q = 1-p, and n=number of simulations.

Outputs from models are able to show responses for demographic and genetic
questions, but those responses are also often related to one another. The relationship
between model outputs can allow exploration of joint sensitivity of model parameters.
To explore the relationship between the outputs for this model, all outputs were graphed
against each other. Extinction was excluded in this comparison because of the low
number of extinctions for the initial population size of 200. Both initial population sizes
were included in these graphs in order to see where different initial population sizes fell
on the relationship and if the same relationship existed for both initial population sizes.

RESULTS

Baseline simulation conditions resulted in different levels of population
persistence, gene retention, and inbreeding accrual for the initial population sizes
simulated. Nominal parameters were chosen such that populations were approximately
stable for an initial population size of 200. This is evident in the percent of populations
increasing (46.2%) in baseline simulations for an initial population size of 200 (Table
1.2). With an initial population size of 200, no extinctions were observed, and
approximately 9.5% of initial genes present were retained. Mean inbreeding was 0.0413

for progeny at the end of the simulation for an initial population size of 200. Extinction

21

occurred in nearly 35% of simulations for the initial population size of 50 (Table 1.2),
and the percent of populations increasing was likewise much lower than for simulations
with an initial population of 200. The percent of genes retained for an initial population
size of 50 was about half (4.62%) of the initial population size of 200, but the mean
inbreeding coefficient was nearly three times higher (f=0. l 388).

The overall sensitivities were often asymmetrical in shape and the parameter with
the highest sensitivity varied depending upon the degree of perturbation away from
nominal values (Figure 1.2). Model outputs were fairly symmetrical and linear for the
local sensitivities with small parameter deviations (Figure 1.3). However, sensitivities
were generally asymmetrical with larger parameter deviations (Figure 1.2), and the
outputs generally trended toward an asymptote or declined towards zero (Figure 1.3).

For example, as parameter values were increasingly perturbed, the percent of populations
increasing tended to either 100% or 0%, resulting in declining sensitivities toward an
asymptote of zero (Figure 1.3). When comparing local versus broad sensitivity, the
parameter of most importance changed across the range of plausible parameter values.
For example, young of the year mortality, mortality, and age at maturation for females, in
that order, were the most sensitive parameters locally, but broadly, mortality and age at
maturation for females became more sensitive than young of the year mortality (Figure
1.3). Lastly, the impact of parameter values on the model outputs varied with the
direction from the baseline the parameter was altered. For example, when parameter
values were decreased, mortality was the most important parameter both locally and
broadly; however, when parameters were increased, mortality was of less importance and

young of the year mortality was more important locally (Figure 1.2).

22

The population and genetic response variables were hypersensitive to most of the
input parameters with the exception of age at first maturation for males and probability of
mating for males in some situations (Table 1.3; Table 1.4). When hypersensitivity was
exhibited locally, hypersensitivity was also observed broadly in all cases except age at
first maturation for males for the initial population size of 50 for the percent of
populations extinct (Table 1.3; Table 1.4). In general, mortality rate was the most
sensitive parameter both locally and broadly for all response variables. Young of the
year mortality, probability of mating for females, and age at first maturation for females
all had similar patterns of sensitivity across response variables. Parameters related to age
at first maturation for males and probability of mating for males were least sensitive.
Some response variables were hypersensitive to male reproductive parameters (e. g.,
percent of populations increasing to probability of mating for males); whereas most
response variables were relatively insensitive.

The direction of response for each hypersensitive outcome varied between
parameters but was fairly consistent for both local and broad sensitivities across both
initial population sizes. For the initial population size of 50, as young of the year
mortality rate, mortality rate, age at first maturation for females, and age at first
maturation for males were increased, the percent of populations extinct increased both
locally and broadly (Table 1.3; Table 1.4). For the initial population size of 50, as
probability of mating for females and probability of mating for males were increased, the
percent of populations extinct decreased both locally and broadly. Both locally and
broadly, as young of the year mortality rate, mortality rate, age at first maturation for

females, and age at first maturation for males increased, the percent of populations

23

increasing and average percent of genes retained decreased for both initial population
sizes. Both locally and broadly, as the probability of mating for females and probability
of mating for males increased, the percent of populations increasing and average percent
of genes retained increased for both initial population sizes. As young of the year
mortality rate, mortality rate, and age at first maturation for females increased, final mean
inbreeding increased for both initial population sizes, and as the probability of mating for
females increased, final mean inbreeding decreased for both initial population sizes both
locally and broadly.

The pattern in the relationship among outputs was similar for both initial
population sizes. Graphs of these relationships show that the outputs were not
independent and exhibited joint sensitivity. As the average percent of genes retained
decreased, the final mean inbreeding increased for both initial population sizes (Figure
1.4). Both initial population sizes exhibited an exponentially decreasing relationship
between the average percent of genes retained and the final mean inbreeding. Final mean
inbreeding increased more rapidly as the average percent of genes retained decreased for
the smaller initial population size, however. As the percent of populations increasing
decreased, the mean final inbreeding increased for both initial population sizes (Figure
1.5). Both initial population sizes exhibited a decreasing S-shaped relationship between
the percent of populations increasing and the mean final inbreeding, but for the initial
population size of 50, the final mean inbreeding increased at a quicker rate as the percent
of populations increasing decreased. As the percent of populations increasing increased,
the average percent of genes retained increased for both initial population sizes (Figure

1.6). Both initial population sizes exhibited an increasing S-shaped relationship between

24

the percent of populations increasing and the average percent of genes retained, but the
smaller initial population size required a higher percent of genes retained to asymptote at
100%.

DISCUSSION

The response of all measures of population performance and genetic integrity
were hypersensitive to young of the year mortality, mortality, age at first maturation for
females, and the probability of mating for females for both initial population sizes.
Changes in all of these parameters have a large impact upon the long-term dynamics of
the population and are driving the population outputs. Changing the parameters of young
of the year mortality, age at first maturation for females, and probability of mating for
females resulted in approximately equal sensitivity to changes for each of the outcomes
of interest. The outcomes of interest were most sensitive to changes in the mortality rate
for both initial population sizes. Gross et al. (2002) found population growth rate to be
most sensitive to young of the year and adult mortality for other sturgeon species, and
Marmontel et a1. (1997) found mortality rates of various year classes to be the most
sensitive parameters for population persistence for the Florida manatee Trichechus
manatus Iatirostris, which is also a long-lived species.

The mortality rate was the most sensitive of all of the population parameters for
the outcomes of interest. Because mortality rate was hypersensitive, changing this
population parameter will have a large impact on long-term dynamics and population
persistence. This finding is similar to Shaffer (1980) and Suchy et al. (1985) who found
that mortality rate was the most sensitive parameter with the largest effects on grizzly

bear Ursus arctos population dynamics and to findings of Cuthbert et al. (2001) for

25

Hutton’s shearwater Pufiinus huttom' conservation. Sutton et al. (2004) found that lake
sturgeon mortality at older life stages was more influential on abundance and recruitment
than mortality on younger life stages for a stage-structured model with respect to
lampricide treatments. Long-lived organisms with life histories similar to lake sturgeon
have been shown to have the largest sensitivities to adult mortality rates (Heppell et al.
2000). Reducing the mortality of lake sturgeon will thus have the largest impact on
population persistence. Reductions in mortality can be accomplished through reducing
and regulating harvest, both legal and illegal (Beamesderfer and Farr 1997). Reducing
illegal harvest could be accomplished via protection of spawning adults, which is when
adults are most vulnerable to illegal harvest.

The young of the year mortality rate was also hypersensitive for the outcomes of
interest. Because of this, reducing young of the year mortality will also have a large
impact on long-term dynamics and population persistence for lake sturgeon. Young of
the year mortality could potentially be decreased through stocking or supportive breeding
via stream-side rearing. Each of these practices have been suggested in past lake
sturgeon rehabilitation strategies (Beamesderfer and Farr 1997; Hay-Chmielewski and
Whelan 1997). Stocking and supportive breeding practices would lower mortality over
the first year, which is when lake sturgeon are subject to the highest mortality rates, thus
increasing long-term population growth rate (Ryman and Laikre 1991).

Although both the age at first maturation for females and the probability of
mating for females were hypersensitive to changes, these lake sturgeon life history
parameters would be difficult to change through current management practices. In

theory, managers could alter these two parameters by selectively stocking offspring that

26

mature earlier and spawn more frequently. However, the change in the genetic
characteristics of populations due to this direct, anthropogenic selection could be
detrimental to long-term population dynamics because populations would likely loose
adaptability and unique genes. Adaptability and unique genes allow species to survive
during environmental extremes and in unique habitats (Kawecki and Ebert 2004). Also,
the current life history strategy that lake sturgeon exhibit is likely a strategy that has
evolved over a long time, and as such, negative impacts would likely occur if female
reproductive strategy was artificially altered. Because many genes have been found to be
linked to others, the loss of the genes associated with late maturation and more infrequent
spawning could possibly result in the unexpected loss of other genes, which may be
important for survival during environmental extremes and in unique habitats (Conner and
Hartl 2004). My findings are similar to findings by Jager et al. (2002), who found the
female parameters of average age at maturation and interval between spawning to be
important for populations using an individual based model of demographics for white
sturgeon Acipenser transmontanus.

Overall, the responses of the outputs of interest were relatively insensitive to
changes in both the age at first maturation for males and the probability of mating for
males. The percent of populations increasing for the initial population size of 50 was the
only scenario that was hypersensitive to both the age at first maturation for males and the
probability of mating for males. Thus, changes in these parameters have relatively little
impact upon the long-term population dynamics of lake sturgeon and are not driving the
population outputs. The lack of sensitivity for the male population parameters could be

related to an excess of males available to mate with respect to the number of females

27

present in the spawning run each year. Male lake sturgeon mate at a younger age and
more frequently than female lake sturgeon (Hay-Chmielewski and Whelan 1997), thus
affording individual males more opportunities to contribute more progeny over a lifetime.
Also, if larger numbers of males spawn each year, some males may not be able to find a
female mate, but females will nearly always be able to find a male mate. These factors
are likely the reason the outputs of the model are relatively insensitive to male mating
characteristics.

Sensitivity was not linear for any of the output parameters across the range of
plausible values explored. Many sensitivity analyses are conducted as local sensitivity
analyses, whereby all of the parameters are held at a nominal value and one parameter at
a time is changed by i10% (or less) to determine which parameters most strongly
influence model predictions (McCarthy et al. 1996; Essington 2003). However, in my
sensitivity analyses, I varied model inputs across a broader range of values. These non-
traditional sensitivity analyses delineated the shape of the sensitivity curve, depicting a
richer picture of model sensitivity. Many of the sensitivity curves reached a maximum
and then started to asymptote toward zero. This asymptote towards zero is due, in part, to
increased extinctions or sufficiently large population sizes to overcome the effects of the
change in the model input. This asymptotic behavior could also be exhibited because the
output variables have a limited window of response (i.e., percent extinction is limited to 0
to 100%). Finally, this asymptotic behavior is also the result of a limiting parameter for
the model output eventually being replaced by another limiting parameter. This type of

non-traditional sensitivity analysis helps to determine which parameters are most

28

sensitive and in what range those parameters have the greatest influence on model
outcomes.

The outputs for the model were found to have joint sensitivity, and the type of
relationship between each set of the parameters was similar for both initial population
sizes. Each output for the model describes a different aspect of the population
(demographics or genetics), but each of the outputs was related to one another. Even
though both initial population sizes had a similar relationship type, the relationships were
not exactly the same. For example, the initial population size of 50 resulted in a quicker
increase in mean final inbreeding with decreases in the average percent of genes retained
and with decreases in the percent of populations increasing. However, the joint
sensitivity between final mean inbreeding and percent of genes retained indicated that for
a given level of inbreeding, the percent of genes retained for the initial population size of
200 was much less than for the initial population size of 50 (Figure 1.4). The initial
population size of 50 also resulted in a slower increase in the percent of populations
increasing with an increase in the average percent of genes retained. The differences in
the functions for the two initial population sizes may be because the initial population
size of 50 is more prone to extinction than the initial population size of 200. Generally,
the differences observed between the two population sizes indicate that sensitivities are
dependent upon initial population size. Thus, use of any sensitivity analysis information
for species management and conservation is dependent upon the initial population sizes
that are explored.

The relationship between percent of genes retained and inbreeding level is

expected according to current theory (Conner and Hartl 2004). Gene retention was

29

similar for both initial population sizes, but the mean inbreeding coefficient was nearly
three times higher for the smaller initial population size. Smaller populations are more
prone to inbreeding, but inbreeding doesn’t result in the direct loss of alleles (Conner and
Hartl 2004); therefore, one would expect the two initial population sizes to have similar
gene retention but differing inbreeding levels (Figure 1.4).

Assumptions with models and other factors could pose limitations and could
result in differences in outputs for the model. First, constant environmental and
demographic conditions were assumed into the future for these simulations, and
environmental and demographic conditions were based on current conditions. Further
degradations in habitat and exploitation could increase mortality rates for lake sturgeon.
Increases in the mortality rates would increase the extinction risks and mean final
inbreeding, and decrease the percent of populations increasing and the average percent of
genes retained. Second, an Allee effect could cause a higher risk of extinction at low
population densities because of predator-prey interactions, spawning behaviors, and other
biotic factors not included in my model (Gascoigne and Lipcius 2004). An Allee effect
could result in extinction risks being underestimated at small population sizes (Beissinger
and Westphal 1998). Even with the assumptions required to model such as system,
modeling is the most feasible option because field studies on long-lived organisms such
as the lake sturgeon would be difficult due to time and money constraints.

Lake sturgeon populations have declined considerably in the past and
rehabilitation efforts, such as reduced harvest and supplementation, have been
implemented in the Great Lakes region (Hay—Chmielewski and Whelan 1997). Helping

to foster sustainability of lake sturgeon populations has been a goal of many

30

rehabilitation strategies. The results of this study illuminate the potential value of various
management practices to increase sustainability by reducing mortality sources. Some
practices that could be valuable for lake sturgeon rehabilitation include stocking, stream-
side rearing, reduced harvest, and protection from poaching. All of these practices lead
to reduced mortality rates and thus increased probabilities of population persistence as

well as lower levels of inbreeding and higher retention of unique alleles over time.

31

Table 1.1. Baseline parameter values as determined from the literature and from lake
sturgeon biologists (Baker 1980; Hay— Chmielewski and Whelan 1997; Auer 1999; Bruch
1999; Billard and Lecointre 2001).

 

Young of the year mortality rate 0.47
Mortality rate 0.05
Age at first maturation for females 20
Probability of mating for females 0.33
Age at first maturation for males 15
Probability of mating for males 0.5

 

32

Table 1.2. Percent of populations extinct (i2 SE), percent of populations increasing (2E2
SE), average percent genes retained (:t2 SE), and final mean inbreeding for the baseline

simulations for the initial populations sizes of 50 and 200.

Percent of populations extinct
Percent of populations increasing
Average percent genes retained
Final mean inbreeding

N=50

34.4 (30.2, 38.6)
9.2 (6.61, 11.79)
4.64 (2.76, 6.52)
0.1388

33

N=200

0 (0, 0)

46.2 (41.74, 50.66)
9.5 (6.87, 12.11)
0.0413

 

 

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35

 

Initialize population 1

 

 

 

TL

Random breeding l

 

_l_

Offspring produced I

 

 

 

_L

 

* Mortality of individuals I
I Loop over years I * ,

Update age of each individual I
ll

 

a—L

 

 

 

I Calculate individual inbreeding coefficients

 

l

 

End of simulation, calculate population level outputs:
oPercent of extinct populations

-Percent of increasing populations

~Percent of genes retained

-Final mean inbreeding

 

 

 

Figure 1.1. Basic model structure for simultaneous simulation of lake sturgeon
demographics and genetics.

36

— YOY mortality

 

 

 

 

 

 

Mortality 30 -
—Age of female maturation ‘
— " Female mating probability
— e of male maturation '
- ' - ale mating probability ‘
20 - I
I
\
g» .
>
:9: 1" ‘ ‘.
g ’ ‘I. —— ‘/
U) F f..- - - -- . - / ‘ -
U A ‘ ’ - - -
I I I I / T: I -— I I
-0 4 -0.3 -0.2 -0.1 Y} = 0.2 :5: 0 3 0 4
-10
I
_—// -20
.30 .

Percent parameterochange

Figure 1.2. Percent change in parameter versus sensitivity, S, for average percent of
genes retained for lake sturgeon with an initial population size of 50.

37

30"

 

 

 

Sensitivity

 

 

Young of the year mortality
—-l\rbrtality -20
Age of female maturation

— " Female mating prohall'lity
—Age of male maturation

' ' ' Male mating probatility

 

 

-30 '-
Pereent parameter change

Figure 1.3. Percent change in parameter versus sensitivity, S, for the percent of
populations increasing for lake sturgeon with an initial population size of 200.

38

45 .
40 j o ON200
0N50

 

Average percent of genes retained
a "c’
.0”. .

0 0.2 0.4 0.6 0.8
Mean final inbreeding

Figure 1.4. The average percent of genes retained versus final mean inbreeding for the
initial population sizes of 200 and 50.

39

 

 

100-000
g 90. . 0 ON200
'43 80_ 0N50
7:. 7 8
8 0 t o
.8 ’0’ ‘9
g 50. 3
h d o
4" z
95 30- z %
E 201
9 (9
r 13- g g, ,.
0 0.2 0.4 0.6 0.8

Mean final inbreeding

Figure 1.5. The percent of populations increasing versus the final mean inbreeding for
the initial population sizes of 200 and 50.

40

100 i 0.006000 6 Q. C1

O
.90 - ,1-)
70 'l . “J

6‘.
6
T»

ul-
9

t
30 g
' ON200
I
1%

Percent of increasing populations

 

 

,.
10 - ’9’
0 W i I I I I
0 10 20 30 40 50

Percent of genes retained

Figure 1.6. The percent of populations increasing versus percent of genes retained for the
initial population sizes of 200 and 50.

41

MINIMUM VIABLE POPULATION SIZE FOR LAKE STURGEON USING AN

INDIVIDUAL BASED MODEL OF DEMOGRAPHICS AND GENETICS

ABSTRACT-Lake sturgeon restoration is a priority in the Great Lakes basin, where
sturgeon have been reduced to <1% of historic levels and have been extirpated from
many areas. Population viability analysis is a useful tool to explore the relationship
between extinction risk and population size over a specified time frame, but often doesn’t
include genetic factors. My objectives were to determine the minimum viable population
size (MVP) for lake sturgeon, and to determine how inbreeding depression may affect
MVP. An individual based model was developed incorporating inbreeding depression
under two scenarios: where individuals with inbreeding coefficients above a threshold
experienced inbreeding depression (threshold), and where individuals experienced
inbreeding depression at a rate related to their inbreeding coefficient (gradual). Three
well established mechanisms previously described relating inbreeding to fitness were
explored (YOY viability, post YOY viability, and progeny number). Estimated MVP
without incorporating inbreeding with ~5% chance of extinction over 250 years was 80
individuals. MVP was 150 under a reduced progeny number inbreeding model and 80
for decreased post YOY viability for all thresholds. MVP ranged from 80-125, with
lower thresholds leading to increased MVP for YOY viability. For the gradual
inbreeding depression scenarios, MVP was 85 for decreased YOY viability, 85 for
reduced progeny number, and 1,800 for decreased post YOY viability. Results show that
MVP can be influenced by particular types of inbreeding depression, but demographic

stochasticity often dominated the process of extinction. This research will help to inform

42

lake sturgeon management within the Great Lakes basin by determining the minimum
viable population size for lake sturgeon and how inbreeding, which is expected to accrue
in remnant populations due to multiple generations of low population size, likely affects
the minimum viable population size. This can then be used to prioritize populations for

rehabilitation.

43

INTRODUCTION

Lake sturgeon Acipenserfulvescens, a long-lived species, were once found
throughout the five Great Lakes and the Great Lakes drainage basin in the United States
and Canada (Birstein et al. 1997; Hay-Chmielewski and Whelan 1997; Smith and Baker
2005). Currently, lake sturgeon restoration is a priority throughout the Great Lakes basin,
where sturgeon have been reduced to less than 1% of historic levels due to habitat
degradation, overharvest, and fragmentation of spawning populations (Johnson et al.
1998; Auer 1999; Holey et al. 2000; McQuown et al. 2003). Factors that have
contributed to the decline of lake sturgeon in the past continue to contribute to declines in
abundance and impede restoration where populations have been extirpated. Therefore,
extensive management goals, objectives, and actions aimed at restoration and protection
of the imperiled lake sturgeon have been developed. For example, stocking and habitat
restoration have been suggested and stocking has been implemented for some populations
in the state of Michigan (Hay-Chmielewski and Whelan 1997). Lake sturgeon restoration
plans have been completed by Michigan (Hay-Chmielewski and Whelan 1997),
Wisconsin (WDNR 2008), and Ontario (OMNR 2006), although considerable uncertainty
exists as to the best course of action for lake sturgeon restoration.

Lake sturgeon populations may be depressed in numbers, but the genetic diversity
of these populations hasn’t been depressed yet (DeHaan et al. 2006). Conserving the
genetic integrity (defined here as both the retention of genes and reduced inbreeding
accrual) of lake sturgeon should encompass maintaining the distribution of genes within a

population, which is affected by inbreeding (Hay-Chmielewski and Whelan 1997;

44

McQuown et al. 2003; Keller and Waller 2002). Inbreeding occurs when individuals
who are closely related mate, and most readily occurs in small populations where random
mating can more readily result in breeding among related individuals (Hedrick and
Kalinowski 2000; Brook et al. 2002; Keller and Waller 2002). Inbreeding is often
thought to result in a decrease in an individual’s fitness relative to non-inbred offspring,
resulting in what is called inbreeding depression. Inbreeding depression can be
manifested in any traits related to fitness (e. g., survival (viability), fecundity; Cmokrak
and Roff 1999; Hedrick and Kalinowski 2000; Amos and Balmford 2001), but has been
difficult to demonstrate empirically (Newman and Pilson 1997). The rate of inbreeding
accrual is hypothesized to be important because natural selection is able to remove
deleterious alleles at low rates of inbreeding, but high levels of inbreeding may result in
an excess of deleterious genes in a homozygous state. Therefore, extinction rates are also
thought to be lower at slower rates of inbreeding accrual (Reed et al. 2003a).

Small populations experience demographic and environmental stochasticity,
catastrophes, and inbreeding; for some population sizes, rehabilitation efforts may be
unlikely to be successful (Pimm et al. 1988; Tracy and George 1992; Lande 1993; Lynch
and Walch 1998; Amos and Balmford 2001; Keller and Waller 2002). Therefore,
identifying situations where rehabilitation efforts will be most successful will be
beneficial to the restoration and protection of lake sturgeon populations in the Great
Lakes basin. Because of their longevity, it is difficult if not impossible to empirically
determine the MVP for lake sturgeon and to fully document interactions between
demographic and genetic processes leading to extinction. Modeling is a useful tool,

because of the flexibility available, and can be used to integrate both population

45

dynamics and genetics information in order to inform management decisions and
determine the relative contributions of demographics and genetics to extinction risk
(Brook et al. 2002).

Population viability analysis (PVA) is a useful model-based tool for conservation
efforts for species like lake sturgeon because PVA allows for the exploration of the
relationship between extinction risk and current population size (Shaffer 1981; Shaffer
1990; Boyce 1992; Brook et al. 2000). PVA has been used to explore the effects of
environmental and demographic stochasticity on numerous species, such as the red-
cockaded woodpecker Picoides borealis (Walters et al. 2002) and the long-lived Asian
elephant Elephas maximus (Armbruster et al. 1999). PVA has also been used to explore
the risk of extinction for spring Chinook salmon Oncorhynchus tshawytscha over two
time frames and in the face of habitat degradation (Ratner et al. 1997). PVA and
simulation models provide an important means to explore assumptions about uncertain
parameter values, relationships, management actions, and feedback mechanisms within a
population in order to determine a range of possible minimum viable population sizes
(Shaffer 1981; Brook et al. 2000; Engen and Saether 2000; Leech et al. 2008).

Generally, minimum viable population size is defined as a population of sufficient
size to persist with a given probability over a given time frame, taking into account
stochastic population processes (Shaffer 1981; Boyce 1992). Minimum viable population
sizes are specific to each study or species and vary depending upon the species of
interest, the species’ life history, and the tolerance of extinction risk for the species’
management and conservation (Shaffer 1981; Lindenmayer et al. 1993). Two important

factors that need to be considered in a population viability analysis are demographic

46

stochasticity (random births and deaths of individuals) and genetic stochasticity (random
genetic changes due to genetic events such as inbreeding or drift; Shaffer 1981;
Lindenmayer et al. 1993; Reed and Bryant 2000; Reed 2005). Both demographic and
genetic stochasticity become increasingly important to a population’s viability as
population size decreases (Lindenmayer et al. 1993), but determining whether
demographic or genetic stochasticity is more important to long-term population
persistence is difficult (Shaffer 1981). Also, modeling the influence of genetic changes
on demography has proven to be difficult in many situations because translating negative
genetic impacts into demographic impacts is not straightforward and because genetic data
are often unavailable (Beissinger and Westphal 1998; Kirchner et al. 2006).

Much debate has occurred over the past decades as to which process is most
important for the risk of extinction for small population sizes: demographic stochasticity
or genetics, specifically inbreeding and inbreeding depression. Some have argued that
demographic stochasticity is more important than genetics at small population sizes
(Lande 1988; Young 1991; Harcourt 1991) based on the premise that if there are no
animals surviving, there are no genes left to conserve. However, others have
demonstrated that inbreeding depression can lead to reduced population viability at small
population sizes. Frankham (1995a) concluded that the risk of extinction increased with
inbreeding. Keller and Waller (2002) found that many studies are now available whereby
inbreeding depression has been found in the wild and can be detrimental to long-term
persistence. Many argue that while inbreeding depression may not be the driving force
towards extinction, that it still has an impact and increases the risk of extinction (Mills

and Smouse 1994). Therefore, a need exists to explore the relationship between

47

demographics and genetics in regards to the long-term persistence of populations (Boyce
1992; Shaffer 1980; Jager et al. 2000; Kirchner et al. 2006), specifically for long-lived
species such as the lake sturgeon.

Despite this need, very few analyses have incorporated genetic factors into
determinations of long-term population viability (Boyce 1992; Brook et al. 2002).
Genetic factors such as inbreeding and genetic drift can contribute to increased risks of
extinction at small population sizes (Boyce 1992) as was shown for the evening primrose
Clarkia pulchella in Montana (Newman and Pilson 1997). Very little work has been
completed addressing genetic stochasticity and how genetic stochasticity and the
breeding system of an animal contribute to the minimum viable population size (Shaffer
1981). Among those studies that have been conducted, inbreeding has been shown to be
a critical factor in the long-term persistence of species in the wild (Frankham 1995b).
For example, demographic and genetic factors have been explored via population
viability analysis and genetic factors were found to be important for the red-cockaded
woodpecker (Haig et al. 1993), the plant species Banksia cuneata (Burgman and Lamont
1992), generic mammal species (Mills and Smouse 1994), and for 20 threatened species
across many taxa including the southern bluefin tuna Thunnus maccoyii (Brook et al.
2002). Many of these studies are based on the concept of lethal equivalents (deleterious
genes whose effect when totaled, results in one mortality when present in the
homozygous form; Keller and Waller 2002) instead of individual inbreeding coefficients,
and results are not consistent from study to study (Swindell and Bouzat 2006).

The objective of my study was to determine the minimum viable population size

for lake sturgeon, incorporating both demographic and genetic stochasticity through the

48

potential impacts of inbreeding (Mills and Smouse 1994). This objective was addressed
using an individual based model of demographic and genetic stochasticity. Of particular
interest was modeled risk of extinction for different population sizes, but genetic
population characteristics such as percentage of unique alleles lost, and levels of
inbreeding were also critical outcomes that I evaluated. Results of this research will help
to inform lake sturgeon management within the Great Lakes basin by estimating the
minimum viable population size for lake sturgeon and how inbreeding affects the
minimum viable population size, which should help inform objectives and management
actions for rehabilitation of lake sturgeon populations.
METHODS

Model Development

An individual based model was developed that incorporated demographic and
genetic processes (Figure 2.1). Lake sturgeon exhibit a polygamous mating system
which was represented based on available data whereby female lake sturgeon mature at
approximately 20 years of age and spawn approximately once every 3 years, and male
lake sturgeon mature at approximately 15 years of age and spawn approximately every
other year (Auer 1999; Bruch 1999; Billard and Lecointre 2001; DeHaan 2003; Nichols
et al. 2003; Table 2.1). Once an individual reached the minimum age for maturity, then
the individual was assigned a random number distributed Uniform(0,1). If that random
number was less than the probability of mating, then that individual returned to the river
to mate that year. Empirical data from Black Lake, Michigan, lake sturgeon showed that
reproductive success was not related to adult length or weight (DeHaan 2003).

Therefore, the size of individual fish wasn’t included in this individual-based model. For

49

each fish returning to spawn, the number of potential mates or batches of offspring, B, for
each spawning male and female was based on empirical data from Black Lake, MI
(Figure B. l; DeHaan 2003). Random numbers of batches were generated using a discrete
form of the exponential distribution by:
B = l + integer(-2 * ln(l - U(0,1)) .

This distribution represents the number of mates from empirical data (Figure B.1;
DeHaan 2003). The batches for the males and females were randomly shuffled, and
female batches were paired with male batches. This process allowed random matings
between individuals, and allowed individuals to mate with multiple other individuals as
has been observed in lake sturgeon. In this model, any batches produced by a male or
female without a pair, or mate, were deleted. This distribution allows for a large number
of mates as the uniform distribution approaches one; however, the number of mates is
decreased based on how the batches are paired with mates. Thus, extremely large
numbers of mates is unlikely. The number of progeny, P, produced (at the end of the
summer) from each mating pair, or batch, was generated using an exponential equation of
the form:

P = integer(l * (-ln(l - U(O,l))))
producing a distribution of numbers of offspring similar to that seen in Black Lake, MI
(DeHaan 2003). This distribution was based on the empirical number of progeny per
adults as reported by DeHaan (2003; Figure 8.2). The empirical distribution was based
on a parentage analysis whereby progeny in a sample were assigned to parents. Only
about 25% of progeny were assigned to parents, however. Because of this, the empirical

number of progeny per parent should be treated cautiously. Because the number of

50

progeny was modified by varying the YOY mortality rate to match observed population
sizes and trajectories, this distribution was judged to be appropriate.

The sex of offspring was randomly determined with an equal probability.
Following birth, age-specific mortality rates were applied to each individual sturgeon.
Mortality rates were set up in the model such that a random number between 0 and l was
generated for each individual and if that random number was less than the specified level
of mortality, then that individual suffered mortality. As such, demographic stochasticity
was implicitly incorporated into the model because the death of each individual was
randomly determined. The mortality rate from the larval stage through the end of the first
year is unknown. Therefore, this mortality rate was varied to produce population growth
rates that mimic observed growth rates for existing populations. This technique has
proven useful in previous studies and provides a means to develop management advice
even though parameter values are uncertain (Vaughn and Saila 1976; Hayes and Taylor
1990; Heppell et al. 2000). All parameter values were developed from literature review
and further review by Great Lakes sturgeon experts. Mortality after age 0 was set to 0.05
based on Baker (1980; Table 2.1). Henceforth, young of the year mortality will be
referred to as YOY mortality, and mortality after the first year will be referred to as post
YOY mortality. Young of the year and post young of the year mortality rates have been
treated this way by past elasticity studies for other sturgeon species (Gross et al. 2002).

Individual inbreeding coefficients were determined using path analysis of the
individual’s pedigree implemented in the INBREED procedure available in SAS® (SAS

Institute Inc., 2003). From a pedigree, the inbreeding coefficient (fl) for an individual

51

was determined by summing all of the unique paths (P) through a common ancestor (A)

as

fxzzl'; (1+fA)

where n was the number of ancestors in the path ande was the inbreeding coefficient of
ancestor A (Wright 1922). Lake sturgeon are polyploid with a ploidy level of eight
(Blacklidge and Bidwell 1993). Polyploidy is thought to mask inbreeding depression;
however this effect has not been shown for other polyploid species such as salmon
species Oncorhynchus sp. (Wang et al. 2002). Therefore, I assumed polyploidy of lake
sturgeon did not affect the accrual of inbreeding. This approach allowed for the tracking
of overall individual inbreeding levels and accrual of inbreeding rather than specifying
certain alleles as deleterious.

Gene retention from the founding population was tracked based on a one locus
system whereby each individual at the start of the simulations had two unique,
hypothetical alleles at one locus (MacCluer et al. 1986). The hypothetical locus was
assumed to be inherited as a Mendelian trait. As mating occurred between individuals,
some alleles were lost from the population before they could be passed on to offspring.
Random loss of unique alleles results in genetic differentiation among populations and
determines the percentage of founders that have contributed genes to the population.
This loss of unique alleles can be described through a technique called gene drop analysis
(MacCluer et al. 1986; Hedrick and Miller 1992), which tracks all unique alleles that are
lost from the population through time (Haig et al. 1993). Thus, the percent of remaining

alleles at the end of each simulation can then be expressed as the number of remaining

52

alleles over the number of unique alleles at the beginning of the simulation which is two
times the initial population size.
Minimum Viable Population Size

The minimum viable population size (MVP) was considered the population size
whereby the probability of extinction was approximately 5% over a 250 year time frame
(which is approximately 10 generations for lake sturgeon). A 5% risk of extinction is a
common criterion for population viability analysis (e.g., grizzly bears Ursus arctos,
Shaffer 1980; kaka Nestor meridionalis, Leech et al. 2008; capercaillie Tetrao urogallus,
Marshall and Edwards-Jones 1998; Scott et al. 1995). MVP was determined for a
scenario with no inbreeding effects which was then used for comparison to the scenarios
which included inbreeding depression.

The impacts of inbreeding depression on individual fitness were incorporated into
the demographic model by creating demographic feedbacks for specified inbreeding
scenarios. Two types of scenarios were simulated. In the first set of scenarios, reduced
fitness was implemented by choosing an inbreeding level above which all individuals
experienced reduced fitness. I termed this a “threshold” scenario. In the next set of
scenarios, reduced fitness was implemented as a linear decline in fitness with increasing
individual inbreeding coefficient. I termed this a “gradual” scenario. Three mechanisms
for possible inbreeding depression were explored: YOY viability (i.e., survival), progeny
number, and post YOY viability. Each of these traits has been shown to be affected by
inbreeding depression in many animal species including fish (Hedrick and Miller 1992;

DeRose and Roff 1999).

53

Little work has been done on genetic impacts, including inbreeding and
inbreeding depression, on persistence outside of a captive environment (Caughley 1994;
Ralls et al. 1988). The fitness effects that inbreeding have on lake sturgeon are currently
unknown; therefore, I evaluated different plausible scenarios given what has been found
for other species. This is somewhat like a sensitivity analysis for inbreeding depression
in order to see what effect fitness changes have on long-term population persistence. I
choose to explore the effects of inbreeding depression with thresholds of 0.0625, 0.125,
and 0.250. These coefficients represent levels of inbreeding which have been shown to
have deleterious effects in natural populations. For example, increased levels of
inbreeding were found to decrease survival of song sparrows Melospiza melodia whereby
those individuals above an inbreeding level of approximately 0.06 all died during a
population crash (Keller et al. 1994). At an inbreeding level of approximately 0.25 the
probability of persistence was about 100% for all effective population sizes of
Drosophila melanogaster, but above 0.25, extinction risk increased (Reed et al. 2003a).
A captive wolf Canis lupus population, which demonstrated inbreeding depression, had
an average F =0.25 (Laikre and Ryman 1991). Also, a wild Mexican jay population
Aphelocoma ultramarine had reduced survival through the first year with related parents
(Brown and Brown 1998).

We also explored the population effects of a gradual reduction in fitness with
increases in inbreeding coefficient. Burgman and Lamont (1992) simulated 10%
reductions in survival and reproduction for a 10% increase in the inbreeding coefficient
for the plant species Banksia cuneata. DeRose and Roff(1999) found an 11% reduction

in fitness related to life history traits such as fecundity and survival, at the inbreeding

54

level of 0.25 using data from several animal species. Inbreeding depression of ~2-6% for
body weight and egg number was observed with a 10% increase in inbreeding coefficient
for captive reared rainbow trout Oncorhynchus mykiss (Su et al. 1996). With a 10%
increase in inbreeding coefficient, an 18.2% decrease in reproduction was found for a
wild muskox Ovibos moschatus population (Laikre et al. 1997). Captive brown bears
Ursus arctos had inbreeding coefficients ranging from 0 to 0.375 (Laikre et al. 1996),
where an increase of f by 0.1 equaled a 7% change in litter size. For captive Pacific white
shrimp Penaeus vannamei, approximately a 2-4% reduction in growth was observed with
a 10% increase in inbreeding (Moss et al. 2007). Finally, for the long-haired rat Rattus
villosissimus inbreeding depression resulted in approximately a 3% decline in litter size
with a 10% increase in the inbreeding coefficient (Lacy and Homer 1997). Given the
observed range in inbreeding depression from ~1-19%, I used slopes representative of the
observed relationships between the inbreeding coefficient and the fitness component,
which is described below. These inbreeding coefficients and scenarios (threshold and
gradual) were chosen because they represent a range of plausible values and scenarios
from past studies, and because inbreeding has been found to affect different species with
similar results (Cmokrak and Roff 1999; Reed et al. 2003a).

In total, twelve inbreeding scenarios were explored. Three scenarios were
explored for YOY viability using a threshold (0.0625, 0.125, and 0.250) whereby all
individuals above the threshold did not survive. Hence, if the individual’s inbreeding
coefficient was above the specified threshold level, then the individual had a 0% chance

of survival. Three scenarios were explored for progeny number using a threshold

(0.0625, 0.125, and 0.250) whereby all individuals above the threshold experienced a

55

10% reduction (on average per year) in the number of progeny produced. Three
scenarios were explored for post YOY viability using a threshold (0.0625, 0.125, and
0.250) whereby individuals above the cutoff threshold had a reduced survival probability
(a 10% increase in the post YOY mortality rate, which is a reduction in survival). One
scenario was explored for YOY viability using gradual inbreeding whereby individuals
were exposed to a reduced survival rate which was related to their inbreeding coefficient
by the relationship:

y = 0.47x + 0.47

where y was the individual YOY mortality rate, x was the individual’s inbreeding
coefficient, and 0.47 was the baseline YOY mortality rate (Table 2.1). For every increase
in the individual inbreeding coefficient of 0.10, the mortality rate increased by 10% from
the baseline with a maximum mortality of 100%, which was the maximum for the
threshold scenarios. A gradual change of 10% was used as it was within the range of
observed changes. One scenario was explored for progeny number using gradual
inbreeding depression whereby individuals had a reduced progeny number related to their
inbreeding coefficient. The progeny number was on average reduced 10% for each 0.10
increase in inbreeding coefficient. A gradual change of 10% was used as it was within
the range of observed changes. Finally, one scenario was explored for post YOY
viability using gradual inbreeding whereby individuals had decreased survival which was
related to their inbreeding coefficient by the relationship:

y = 0.0208x + 0.05

where y was the individual post YOY mortality rate, x was the individual’s inbreeding

coefficient, and 0.05 was the baseline post YOY mortality rate (Table 2.1). The post

56

YOY mortality rate was able to increase until y reached a maximum increase in mortality
of 10%, which was the maximum mortality increase for the post YOY viability threshold
scenarios. Because the gradual scenarios were limited by the minimum and maximum
changes of the threshold scenarios, I was able to compare the threshold versus gradual
scenarios.
Simulations

Simulations were run across a range of initial population sizes to determine MVP
based on the specified criterion. Based on preliminary analyses, a simulation duration of
250 years was used as this allowed time for transient responses to dissipate. For each
scenario, 500 simulations were run to provide precise estimates of the mean response and
the variance across the factors explored. A yearly time step was used in all simulations.
The percent of extinct populations, average individual inbreeding coefficient in the final
year, and percent of unique genes retained were recorded for each simulation run of 250
years. The average individual inbreeding coefficient is the average inbreeding coefficient
for progeny produced in the final year. No uncertainty estimates could be provided for
the inbreeding coefficients because only the mean was an output for the model. The
percent of unique genes was the average percent of genes retained where extinct
simulations were included as zero genes retained. For the average percent of genes
retained, confidence intervals were calculated as:

(estimate :t 2*SE)*100

where the SE = (pq/n) " (1/2), p = (percent of genes retained/ 100), q = l-p, and n=500.
Confidence intervals for the percent of extant populations were also calculated for each

scenario using proportions, but the error bars were not graphed because the bars fell

57

within the markers on the graphs. Simulations were assumed to have current
environmental and demographic conditions, which remained constant into the future.
RESULTS

The MVP with approximately a 5% risk of extinction over the 250 year time
frame with demographic stochasticity but no inbreeding effects was approximately 80
individuals for lake sturgeon. The risk of extinction increased rapidly for smaller
populations; initial populations of 40 had an approximately 50% extinction rate, and
populations of 15 or less went extinct in virtually all cases (Figure 2.2). The final
inbreeding coefficient averaged 0.0913 and the percent of genes retained was 7.63 (95%
CI= 5.26 to 10.01) for simulations starting at the MVP of 80, and with demographic
stochasticity but no inbreeding effects (Table 2.2).

For many of the scenarios, the MVP was not heavily influenced by inbreeding
depression (Table 2.2), as the MVPs were the same as or close to the MVP with no
inbreeding depression. MVP was 80 for decreased post YOY viability for all thresholds.
For gradual inbreeding depression, MVP was 85 for decreased YOY viability and 85 for
reduced progeny number. However, MVP increased when inbreeding depression was
incorporated as a reduction in progeny number or YOY viability based on inbreeding
thresholds, and when post YOY viability gradually decreased as a function of inbreeding.
Minimum viable population size was 150 with reduced progeny number for all
thresholds. Minimum viable population sizes ranged from 80-125, with lower thresholds
leading to increased MVP for YOY viability. The only scenario where MVP was vastly
different was with gradual inbreeding depression with a decrease in post YOY viability.

Under this scenario, MVP was approximately 1,800.

58

Mean inbreeding and the percent of genes retained after 250 years were generally
similar across all scenarios with and without inbreeding depression (Table 2.2). The final
mean inbreeding coefficient and the percent of genes retained for all of threshold
scenarios for post YOY viability were similar to the scenario with no inbreeding effects.
The final mean inbreeding coefficient for all thresholds for reduced progeny was similar
to the scenario with no inbreeding effects, but the percent of genes retained was
approximately half. The final mean inbreeding coefficient and the percent of genes
retained both increased with increasing thresholds for the inbreeding depression scenarios
for YOY viability. The final mean inbreeding coefficient and the percent of genes
retained were similar to no inbreeding effects for the gradual YOY viability scenario and
slightly less for the gradual reduced progeny number scenario. The final mean
inbreeding coefficient was similar to the no inbreeding scenario, but the percent of genes
retained was greatly reduced when compared to the no inbreeding scenario for inbreeding
depression via gradual post YOY viability.

When inbreeding depression resulted in a MVP different than 80, the persistence
curve (the curve of percent of extant populations versus initial population size) changed
when compared to the persistence curve with no inbreeding depression. Minimum viable
population size is a point on the persistence curve with a given extinction risk, and as the
initial population size increases or decreases, the risks of extinction change differently for
the different scenarios (Figure 2.2). When the MVP changed, the persistence curves
maintained high risk at small population sizes and lower risk at large populations sizes.
However, at intermediate population sizes, the risk of extinction changed at different

rates. For example, the rate at which the persistence curve reached 100% decreased as

59

the initial population size was increased with threshold inbreeding depression as reduced
progeny number (Figure 2.2). Some of the curves maintained the same shape but simply
shifted. For example, the persistence curve simply shifted causing an increase in the
MVP for threshold inbreeding depression on YOY viability (Figure 2.2). The persistence
curves were the same when compared to the persistence curve with no inbreeding
depression when the MVP was not different (e.g., gradual inbreeding depression for
progeny number). Therefore, not all persistence curves were graphed because of the
large number of lines that would be necessary and because some MVPs didn’t change,
instead a representative sample was chosen for illustrative purposes.

When inbreeding depression increased the MVP, the percent of genes retained
decreased, but the impact on the final mean inbreeding depended upon the scenario. The
percent of genes retained decreased slightly for threshold inbreeding depression on YOY
viability and decreased greatly for threshold inbreeding depression as reduced progeny
number when compared to the scenario without inbreeding (Figure 2.3). The final mean
inbreeding level increased for threshold inbreeding depression as reduced progeny
number, and the final mean inbreeding level decreased for threshold inbreeding
depression as decreased YOY viability (Figure 2.4). Finally, in scenarios where MVP
was similar to the no inbreeding depression simulation, the percent of genes retained and
the final mean inbreeding did not change when compared to the percent of genes retained
and final mean inbreeding with no inbreeding depression. Therefore, not all scenarios

were graphed.

60

DISCUSSION

Minimum viable population size is important for identifying populations for
conservation and for identifying extinction risks associated with differing population
sizes (Shaffer 1981). Populations with extremely low abundance are often difficult to
rehabilitate given the need to overcome demographic stochasticity. Traditionally,
population viability analysis models which explore minimum viable population size focus
on demographic and environmental stochasticity. Often, genetic components are not
incorporated but can have a significant impact on a population’s persistence (Boyce
1992; Shaffer 1980; Jager et al. 2000; Kirchner et al. 2006). Only one fish species
included in the large meta-analysis by Traill et al. (2007) included inbreeding effects, and
only one fish species of 102 vertebrate species were considered in another meta-analysis
of MVP by Reed et al. (2003b). Thus, incorporating both demographics and genetics to
determine the MVP may be important but has not been widely explored for fish species
(Boyce 1992; Traill et al. 2007; Reed et al. 2003b). Therefore, I aimed to explore the
MVP for different scenarios of inbreeding depression for a long-lived fish, the lake
sturgeon.

The probability of extinction can never truly be zero for any wild population
(Shaffer 1990), but managment can strive to minimize the risk of extinction by
determining MVP and maintaining populations above that level. Based on the above
described model, I estimated that the MVP for lake sturgeon populations in the Great
Lakes basin was 80 individuals with approximately a 5% risk of extinction over 250
years. Few MVP’s have been determined for fish species, only 9 of 287 MVP’s were for

fish species in the original dataset compiled for the meta-analysis by Traill et al. (2007)

61

and only 1 of 102 for a study by Reed et al. (2003b). Those MVP’s that have been
estimated for fish species are generally larger than for the MVP estimated for lake
sturgeon, which could be related to different life history strategies between species or
different time frames used to estimate MVP. For example, the MVP for white-spotted
charr Salvelinus leucomaenis was estimated to be 250 with a 5% risk of extinction over
100 years (Morita and Yokota 2002), and Traill et al. (2007) predicted a standardized
MVP using a general linear mixed effects model for eight fish species to range from
approximately 200,000 to 2 million. The MVP for lake sturgeon was however
comparable to MVP’s for other long-lived species. The MVP was found to be 125
grizzly bears Ursos arctus horribilis for 100 years (Suchy et al. 1985), and about 100 for
a Japanese black bear Ursus thibetanusjaponicus population for 100 years with a 5% risk
of extinction (Horino and Miura 2000). A population of approximately 120 Asian
elephants Elephas maximus was determined to be the MVP with about a 5% risk of
extinction over 1,000 years (Armbruster et al. 1999).

Little empirical evidence is available relating levels of inbreeding to MVP;
therefore, modeling plausible scenarios is a useful strategy to explore possible effects.
Theory suggests that MVP can be increased by inbreeding depression by increasing the
population size needed to maintain viability, because individuals in an inbred population
have lower fitness than individuals in a non-inbred population of the same size (Amos
and Balmford 2001). For example, for red-cockaded woodpeckers, increased levels of
inbreeding depression resulted in increased risks of extinction using VORTEX (Haig et
al. 1993). Similarly, the MVP using VORTEX for the Atlantic Forest spiny rat Trinomys

eliasi was higher when inbreeding was included than when inbreeding wasn’t (Brito et al.

62

2003). Finally, population outputs were sensitive to inbreeding depression when
modeling the long-furred woolly mouse opossum Micoureus paraguayanus using the
program VORTEX which includes inbreeding depression via juvenile survival (Brito and
F onseca 2006). My study was unique because my study used a generalized individual
based model instead of VORTEX.

When genetic factors have been incorporated in the past, they have often been
incorporated using the program VORTEX (Caughley 1994). VORTEX uses lethal
equivalents or heterozygosity to implement inbreeding depression on juvenile survival
(rarely on any other fitness components; Marshall and Edwards-Jones 1998). Also, the
defaults are often used in VORTEX because inbreeding depression hasn’t been measured
for a lot of different types of species (e.g., bird species; Marshall and Edwards-J ones
1998). An alternative to VORTEX is a more generalized individual based model.
Individual based models (IBM) are useful because they track individuals through time
and because results can be given at both the individual and population levels. For
tracking inbreeding, using an IBM is more appropriate than a population model because
each individual has an inbreeding coefficient. Thus, tracking inbreeding at the individual
level allows for individual mortality instead of mortalities at the population level.
Overall, studies using IBMs with pedigrees are rare (Overall et al. 2005), but could be
very informative.

Some inbreeding depression scenarios explored in this analysis resulted in little or
no change to the MVP required to maintain persistence when compared to the scenario
without inbreeding depression. With inbreeding depression under the threshold scenario,

the MVP was the same as the MVP with no inbreeding depression for post YOY viability

63

for all thresholds. With gradual inbreeding depression for both YOY viability and
progeny number, the MVP increased only slightly to 85. Similar results were found in
other studies. For example, increased probabilities of extinction were not predicted for
the plant species B. cuneata with increased levels of inbreeding (Burgman and Lamont
1992). Inbreeding depression was thought not to increase extinction risks in Burgman
and Lamont’s model (1992) because of the random effects of environmental stochasticity.

However, some inbreeding depression scenarios explored did result in changes to
the predicted MVP required to maintain persistence. With threshold inbreeding
depression on progeny number, the MVP was 150, nearly twice the MVP with no
inbreeding depression. This result is similar to other findings where small increases in
inbreeding depression for survival and fecundity parameters consistent with mammal
species increased the risk of extinction for populations above the extinction risk for
simulations without inbreeding (Mills and Smouse 1994). Also, the probability of
extinction increased when inbreeding depression in the form of lethal equivalents on
juvenile mortality was included in simulation models of 20 species (Brook et al. 2002).
For the bird capercaillie Tetrao urogallus, the MVP with a 5% extinction risk was about
150 individuals with inbreeding depression manifested for juvenile survival in VORTEX
(Grimm and Storch 2000). Finally, the MVP including inbreeding depression on pup
mortality was 400 individuals for wolves Canis lupus in Scandinavia (N ilsson 2003).
Thus, I have predicted that inbreeding depression can increase extinction risk depending
upon how inbreeding depression is incorporated.

We found that gradual inbreeding depression via post YOY viability resulted in a

MVP of approximately ~1,800. Given the current lake sturgeon population sizes in the

64

Great Lakes basin, this scenario seems implausible because most populations are below
1,800 and have not spiraled to extinction during the recent generations at low abundance
(Hay-Chmielewski and Whelan 1997). I feel that this large MVP is due to the longevity
of lake sturgeon, and their ability to accumulate inbreeding over several generations.
This longevity leads to lake sturgeon being exposed to higher mortality rates due to the
accumulated inbreeding levels which results in high levels of extinction. In a sensitivity
analysis of a lake sturgeon population model (Schueller and Hayes in review; Chapter 1),
we found that post YOY mortality was the most sensitive parameter, whereby even small
increases in the mortality rate led to increased extinction rates and reduced abundance.
Sensitivity to post YOY survival has been found for other long-lived species (Boyce
1992). Thus, this model result makes sense given that even small increases in the post
YOY mortality rate resulted in large increases in the probability of extinction.

For the scenarios which incorporated inbreeding depression gradually, the
estimated MVP will be highly dependent on the slope of the fitness function. Because
the model outputs were hypersensitive to changes in the population parameters related to
survival (Chapter 1), the MVP for these scenarios will likely change with changes in
survival. For example, the model was most sensitive to post YOY mortality and the
MVP estimated with gradual inbreeding depression on post YOY mortality resulted in the
largest MVP needed for persistence. This example illustrates that the slope chosen for
these scenarios can greatly influence the outcome. Therefore, there is a critical need to
obtain better empirical estimates of inbreeding depression on sensitive population

parameters.

65

One important difference between my study and others is that I used an IBM and
the individual inbreeding coefficients were calculated through path analysis. The
inbreeding coefficient (fir) calculated in my study via path analysis is a direct probability
of inbreeding or of genes being identical by descent which is in contrast to studies using
effective population size or other proxies (Su et al. 1996). This allowed for those
individuals that were the most inbred to be subjected to reduced fitness instead of the
population as a whole being subjected to reduced fitness.

With threshold inbreeding on YOY viability, the MVP increased with decreasing
thresholds (Table 2.2). This outcome may be the result that purging would have on a
population. Although inbreeding depression reduces fitness, mortality of inbred
individuals prior to reproduction leads them to not contribute to the next generation.
Thus, these inbred individuals are “purged” from the population. This process can lead to
fitness levels being maintained or sometimes decreased in future generations (Hedrick
and Kalinowski 2000; Cmokrak and Barrett 2002; Keller and Waller 2002). Purging thus
can lead to situations where deleterious genes are lost and inbreeding depression is
reduced in future generations (Leberg and F irrnin 2007). I found that as the threshold
increased, the final mean inbreeding coefficient increased as did the percent of genes
retained. This is an example of purging where individuals with inbreeding coefficients
above the threshold experience mortality as YOY. This results in the removal of those
individuals with higher inbreeding coefficients, leading to lower mean inbreeding
coefficients than what would be expected without purging (Cmokrak and Barrett 2002).
My finding of purging is similar to findings from a meta-analysis where purging was

found to affect fitness of organisms including plants, mammals, mollusks, and insects

66

(Cmokrak and Barrett 2002), and to findings by Swindell and Bouzat (2006) where
inbreeding depression was likely reduced by purging for Drosophila melanogaster for
small population sizes.

Neither the final mean inbreeding coefficient nor the percent of genes retained
changed substantially for most of the scenarios which incorporated inbreeding depression
when compared to the scenario without inbreeding depression. However, for the
threshold scenarios for inbreeding depression affecting progeny number, the percent of
genes retained was about halved when compared to the scenario of no inbreeding
depression. Loss of abundance leads to the loss of genes generally, but the percent of
genes retained was lowest for the inbreeding depression with the highest MVP required.
Inbreeding depression via reduced progeny number means that fewer individuals are
contributing progeny, and thus fewer individuals are passing their genes to future
generations. This may explain why progeny number resulted in fewer genes being
retained while still requiring a larger MVP.

Demographic stochasticity often dominated the process of determining MVP for
lake sturgeon because the MVP was often the same or only slightly larger with
inbreeding depression (Table 2.2). For example, with the addition of inbreeding
depression for post YOY viability under threshold scenarios, the MVP was still 80.
However, MVP was influenced by inbreeding depression depending upon the scenario.
For example, with inbreeding under the threshold scenario, the (MVP for progeny number
was 150 or nearly twice the MVP with no inbreeding effects. Much discussion has
occurred over whether demographic stochasticity or genetic stochasticity is more

important or has a greater influence on long-term persistence (Lande 1988; Young 1991;

67

Frankham 1995a; Spielman et al. 2004). Based on the scenarios in my study, whether
demographic or genetic stochasticity dominate the determination of MVP and extinction
risk is dependent upon whether inbreeding depression was expressed as threshold or
gradual and whether inbreeding depression affected viability or progeny number. Thus,
my study doesn’t provide a clear picture of whether demographic or genetic stochasticity
dominates extinction risk. The focus, however, should not be on which factor
“dominates” the extinction process. Rather, efforts should be made to understand and
document how genetic and demographic factors jointly affect MVP.

Often, measuring inbreeding depression is difficult because of the many
environmental factors that impact populations and individuals (Pimm et al. 1988; Reed
and Bryant 2000). One factor I did not include was environmental stochasticity. When
inbreeding depression and environmental stochasticity act simultaneously, an inbreeding
vortex can occur whereby populations spiral to extinction at a quicker rate (Tanaka
2000). Thus, the incorporation of environmental stochasticity to this model could
increase rates of extinction for smaller population sizes via the inbreeding vortex.
Therefore, larger populations may need to be maintained for threatened and endangered
species to protect against an extinction vortex which could result from demographic
stochasticity, the plausible effects of inbreeding depression, and environmental
stochasticity. Environmental stochasticity wasn’t included in this model because of the
longevity of the lake sturgeon, and because the year to year variation in population
parameters would most likely not be large enough to cause differences in population
persistence over the long run (Benton et al. 1995). This is likely true because the

trajectory of the population parameters mimics the trajectory of the real world which

68

includes environmental effects. Moreover, Melbourne and Hastings (2008) showed that
environmental stochasticity was less of a factor for extinction risk if demographic
heterogeneity (random births and deaths) and stochasticity in sex ratio are included in the
model. This was especially true when population sizes are small or declining (Melbourne
and Hastings 2008). Thus, because my analysis explored smaller population sizes, the
sex ratio was allowed to vary, and demographic heterogeneity was included, including
environmental stochasticity would likely not have increased extinction risk substantially.

As a final caveat, as shown in Chapter 1, the outputs of the model were
hypersensitive to changes in the population parameters (e. g., YOY mortality and post
YOY mortality). Thus, if the baseline parameter values vary, then the minimum viable
population size as estimated above would likely change, potentially significantly. For
example, if either of the mortality rates are increased or decreased, the minimum viable
population size would increase or decrease, respectively. Thus, the estimate of minimum
viable population size is dependent upon the baseline parameters used, but can still be a
usefirl for management purposes if this aspect of uncertainty is taken into account.

RECOMMENDATIONS

Because this work looks at the plausible role that inbreeding depression may play
in the extinction process, this work should be used to guide experimental research
looking to measure the effects of inbreeding depression. Thus, if inbreeding depression
is manifesting itself in lake sturgeon or other long-lived species, inbreeding depression
should be most readily measured by reduced progeny number. Finally, if inbreeding
depression is resulting in purging of a population, then YOY viability should be

investigated.

69

Given that in some inbreeding depression scenarios the MVP was increased, I
recommend increasing the MVP to account for the possibility of inbreeding depression
for other threatened and endangered species in order to overcome both demographic
stochasticity and maintain genetic integrity. Because lake sturgeon are long-lived and
because of their life history characteristics (e.g., iteroparous), a much lower MVP may
have resulted when compared to most other species. Shorter life spans (e.g., those of
insects) most likely require populations of greater size to maintain population persistence
through time (Pimm et al. 1988; Boyce 1992). Therefore, other threatened and
endangered species, which don’t have long life spans, should have their populations
maintained at much higher levels, and those populations that are long-lived, with similar
population parameters to the baseline parameters used here, at least need populations
maintained above 80—150 individuals. Given the uncertainty in these parameter
estimates, larger population sizes may still be required for persistence.

Lake sturgeon long-term dynamics and persistence are dependent upon
maintaining populations which are above the minimum viable population size while also
maintaining genetic integrity. Thus, I recommend that populations should be maintained
above 80 to 150 individuals, for the given baseline parameters explored. These
recommendations should help to foster the protection of sustainable lake sturgeon
populations for the future by minimizing extinction risks due to both demographic
stochasticity and inbreeding depression. Also, estimation of MVP should help lake
sturgeon managers prioritize populations for future rehabilitation efforts, given extinction

risks. Given populations are below the MVP level, management efforts such as some

70

form of supplementation may be necessary to overcome demographic stochasticity and

maintain persistence.

71

Table 2.1. Baseline parameter values as determined from the literature and from lake

 

 

 

sturgeon biologists.
Parameter Parameter Value
Young of the year mortality rate 0.47 .
Mortality rate 0.05
Age at first maturation for females 20
Probability of mating for females 0.33
Age at first maturation for males 15
Probability of mating for males 0.5

 

72

Table 2.2. Minimum viable population size for no inbreeding depression, threshold
inbreeding depression, and gradual inbreeding depression for several fitness components,
and the final mean inbreeding coefficient and percent of genes retained at MVP for each
of the scenarios. For the percent of genes retained, simulations which went extinct were
assigned a zero. Means (i2 SE) are provided for percent of genes retained.

 

 

Final mean
inbreeding Percent genes
Inbreeding scenario Manifestation MVP coefficient retained
No inbreeding
depression Na 80 0.0913 7.63 (5.26, 10.01)
YOY viability 0.0625 125 0.0376 5.78 (3.69, 7.86)
0.125 100 0.0574 6.92 (4.65, 9.19)
0.25 80 0.0822 7.53 (5.17, 9.89)
Gradual 85 0.0902 7.28 (4.96, 9.60)
Post YOY viability 0.0625 80 0.0912 7.33(5.00, 9.66)
0.125 80 0.0951 7.49 (5.13, 9.84)
0.25 80 0.0921 7.43 (5.08, 9.77)
Gradual 1,800 0.0942 0.29 (-0.19, 0.78)
Progeny number 0.0625 150 0.0834 4.12 (2.34, 5.90)
0.125 150 0.0809 4.13 (2.35, 5.90)
0.25 150 0.0894 4.03 (2.27, 5.79)
Gradual 85 0.0877 7.28 (4.96, 9.61)

 

73

 

Initialize population I

 

 

 

"'1

Random breeding I

 

_I_

Offspring produced I

 

 

 

"l

 

Mortality of individuals
Loop over years I

 

 

Update age of each individual I

CL

 

 

 

I Calculate individual inbreeding coefficients

 

l

 

End of simulation, calculate population level outputs:
-Percent of extinct populations

~Percent of increasing populations

0Percent of genes retained

-Final mean inbreeding

 

 

 

Figure 2.1. Model structure for simulations of lake sturgeon demographic and genetic
parameters.

74

100 -

    

 

 

90 -
80 -
a 70 -
E
3 60 .
5
8 50 I
o
E 40 -
9" 30 - -0—No Inbreeding
20 . "Ir-Threshold 0.125progeny number
10 - -I -Thresh01110.125Y0Y viability
0 ' I I I I
0 50 100 150 200
Initial Abundance

Figure 2.2. Percent of extant populations across a range of initial population sizes
(persistence curves) under the scenarios of no inbreeding, threshold inbreeding
depression as reduced progeny number at the threshold 0.125, and threshold inbreeding
depression as decreased YOY viability at the threshold 0.125.

75

—O—No Inbreeding
14 - - - - Threshold 0.] 25 progeny number
. - ° ° ° ° Threshold 0.1 ZSYOY viability

 

Percent of Genes Retained

 

 

 

0 50 100 150 200

Initial Abundance

Figure 2.3. Percent of genes retained across a range of initial population sizes under the
scenarios of no inbreeding, threshold inbreeding depression as reduced progeny number
at the threshold 0.125, and threshold inbreeding depression as decreased YOY viability at
the threshold 0.125. Percent of genes retained represent all simulations, including
populations with no survivors. Error bars (i2 SE) for each scenario are represented in the
same line type for each scenario. Simulations with no survivors were considered to have
no genes retained.

76

0.50 -

 

 

 

 

 

-0—No Inbreeding
0.45 -

a. 0 40 --A--Threshold 0.125progeny number

= . ‘

=5 -I -Threshold 0.1253'011' viability

g 0.35 -

i-

3 0.30 -

g 0.25 "l

a

29 0.20 -

E 0.15 .

E: 0.10 .1 ...... -- i
0'03 u — — -" "‘- —- — fl
0.00 i i i .

0 50 100 l50 200

Initial Abundance

Figure 2.4. Final mean inbreeding across a range of initial population sizes under the
scenarios of no inbreeding, threshold inbreeding depression as reduced progeny number
at the threshold 0.125, and threshold inbreeding depression as decreased YOY viability at
the threshold 0.125. Final inbreeding coefficients only represent extant populations at the
end of the 250 year simulation duration; populations with no survivors were not assigned
an inbreeding coefficient.

77

EVALUATION OF STOCKING STRATEGIES FOR LAKE STURGEON:
TRADEOFF S BETWEEN DEMOGRAPHIC STOCHASTICITY AND GENETIC

INTEGRITY

ABSTRACT-Lake sturgeon were once abundant throughout the Great Lakes basin, but
have been reduced to less than one percent of historic levels due to habitat degradation
and overexploitation. Current management strategies suggest stocking as a tool to
increase abundance, but this strategy also has genetic implications. The objective of this
study was to determine the number of individuals that should be stocked in order to
maintain long-term persistence of population abundance while maintaining the smallest
genetic impact. An individual based model of demographics and genetics was used to
explore scenarios which included three initial population sizes, two different
supplementation time frames, varying sex ratios, variance in family size, and different
percentages of the adult population contributing progeny for supplementation. All
stocking scenarios resulted in reduced extinction risk, increased population sizes,
increased gene retention, and reduced inbreeding over time. Stocking over long time
frames was only necessary for larger population sizes. A skewed sex ratio and unequal
family size had little impact on the genetics of populations. Reduced numbers of adults
contributing progeny reduced the proportion of genes retained and increased inbreeding.
To the extent logistically possible, supplementing larger populations over longer time
frames and capturing the greatest number of adults from the population for

supplementation purposes are the most important considerations for maintaining genetic

integrity.

78

INTRODUCTION

Lake sturgeon Acipenserfulvescens are a long-lived species that was once
abundant throughout the five Great Lakes and the Great Lakes drainage basin in the
United States and Canada (Birstein et al. 1997; Hay-Chmielewski and Whelan 1997;
Smith and Baker 2005). Currently, lake sturgeon restoration is a priority throughout the
Great Lakes basin, where sturgeon have been reduced to less than 1% of historic levels
due to habitat degradation, overharvest, and fragmentation of spawning populations
(Johnson et al. 1998; Auer 1999; Holey et a1. 2000; McQuown et al. 2003). Factors that
have contributed to the decline of lake sturgeon in the past continue to contribute to
declines in abundance and impede restoration where populations have been extirpated.
Therefore, extensive management efforts aimed at restoration and protection of the
imperiled lake sturgeon have been developed. Lake sturgeon restoration plans have been
completed by Michigan (Hay-Chmielewski and Whelan 1997), Wisconsin (WDNR
2008), and Ontario (OMNR 2006), although considerable uncertainty exists as to the best
course of action for lake sturgeon restoration. Stocking, habitat improvement, and
reduced exploitation are all part of the overall strategy for lake sturgeon management.
However, stocking is often the only option available for rehabilitation; because
exploitation is already reduced and habitat improvement is unlikely in the short-term
given dams are one of the major habitat impediments. In addition, stocking can result in
relatively rapid achievement of population abundance goals as outlined in lake sturgeon
management plans.

Stocking is a management tool which has been used for lake sturgeon

rehabilitation, either through the use of traditional hatchery methods or through stream-

79

side rearing practices, a form of supportive breeding (Hay-Chmielewski and Whelan
1997). Supportive breeding generally refers to using local, wild adults to produce
progeny (Ryman and Laikre 1991; Ruzzante et al. 2001; Duchesne and Bematchez 2002).
Those progeny are then released back into the wild population from which they came, as
opposed to traditional hatchery rearing which involves domesticated brood stock.
Supportive breeding increases survival (Ryman and Laikre 1991), and is the type of
supplementation generally used for lake sturgeon populations given that adults are much
too large and long-lived to easily house in a traditional hatchery setting.

As supportive breeding programs are implemented for lake sturgeon,
rehabilitation efforts need to consider reducing genetic risks such as inbreeding (Waples
1994) or loss of unique alleles. Inbreeding occurs when individuals who are closely
related mate, and most readily occurs in small populations where random mating often
results in breeding among related individuals (Hedrick and Kalinowski 2000; Brook et al.
2002; Keller and Waller 2002). Inbreeding is often thought to result in a decrease in an
individual’s fitness relative to non-inbred offspring, resulting in inbreeding depression.
Inbreeding depression can be manifested in any traits related to fitness (e. g., survival,
fecundity; Cmokrak and Roff 1999; Hedrick and Kalinowski 2000; Amos and Balmford
2001), but has been difficult to demonstrate empirically (Newman and Pilson 1997).
Lake sturgeon populations in the Great Lakes basin are greatly reduced in numbers, but
the genetic diversity of these populations has not yet been depressed (DeHaan et al.
2006). As such, care must be taken when stocking in order to avoid an accrual of

inbreeding.

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Supportive breeding is thought to result in tradeoffs between abundance, or
demographics, and genetic integrity such as inbreeding and gene retention of a
population. While supplementation is often focused on increasing population abundance,
supplementation can result in the loss of genetic variability and increased inbreeding in a
population thereby reducing genetic integrity (Ryman and Laikre 1991; Tessier et al.
1997; Hansen et al. 2000; Lynch and O’Hely 2001; Brown and Day 2002). However,
supplementing over multiple generations could lead to increased genetic integrity,
increased gene retention and reduced inbreeding accrual, if the population size is larger in
the long-term (Wang and Ryman 2001; J ager 2005). Thus, while demographic
stochasticity has been argued to be a more influential driving force with respect to
probability of extinction than genetic factors, inclusion of both demographic stochasticity
and genetics in population management strategies has been advocated (Lande 1988;
Lande 1998).

When supplementing a population, several recommendations have been made to
minimize genetic impacts. Some of these recommendations include supplementing over
long time frames, maintaining a 1:1 sex ratio of males to females contributing progeny,
equalizing progeny contributions from families or matings, and using large numbers of
adults selected from the population for breeding purposes (F rankham 1995b; Wang et al.
2002; Miller and Kapuscinski 2003; Fraser 2008). Supplementing a population over a
longer time frame is thought to result in greater genetic integrity and less generational
change in allele frequencies and diversity (Miller and Kapuscinski 2003; Page et al.
2005) because more adults will have the opportunity to contribute genes to progeny. A

sex ratio varying from an equal number of males and females has been shown to reduce

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the effective population size and increase relatedness (Miller and Kapuscinski 2003; Page
et al. 2005) which could lead to increased inbreeding among progeny and an increased
risk of losing alleles (Fraser 2008). For example, a skewed sex ratio resulted in increased
inbreeding for the Japanese flounder Paralichthys olivaceus (Oota and Matsuishi 2005)
and reduced genetic diversity for Atlantic salmon Salmo salar L. in Spain (Machado-
Schiaffino et al. 2006). Unequal family size or high levels of variance in the number of
progeny produced per mating pair has been shown to reduce genetic diversity (Allendorf
1993; Page et al. 2005; Fraser 2008). If one family contributes most of the progeny that
are released, then relatedness is increased and genes will be lost. Finally, using the
largest percentage of mature mates from a population as possible will reduce inbreeding
and increase the retention of alleles (Miller and Kapuscinski 2003; Page et al. 2005)
because more adults will have the opportunity to contribute progeny and thus genes.
Using the greatest number of mature adults will help to prevent loss of rare alleles (Miller
and Kapuscinski 2003). Thus, to maintain the highest levels of genetic integrity meaning
reduced inbreeding and reduced loss of alleles, a widely held expectation is that
supplementation practices with longer time frames, a 1:1 sex ratio, equal family
contributions, and using a large percentage of mature fish will result in progeny with
relatively higher levels of genetic variability and lower levels of inbreeding.

Given the longevity of lake sturgeon and the difficulty in directly determining the
effects of supplementation, I used a modeling approach to explore the consequences of
management actions (Boyce 1992). My objective was to determine the number of
individuals that should be stocked in order to achieve population abundance goals while

maintaining the smallest genetic impact. This was accomplished through the use of an

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individual based model of demographics and genetics. Long-term persistence of
populations was determined by probability of extinction and mean population size.
Genetic integrity was determined by both individual inbreeding coefficients and the
percent of genes retained within the population.

Although general advice is available for supplemental stocking practices (Miller
and Kapuscinski 2008; Fraser 2008) and specific recommendations have been made for
lake sturgeon in the Great Lakes basin (Rob Elliot, personal communication) deviations
from such advice is common in practice. Because of this, I explored the genetic and
demographic consequences of varying time frame of supplementation, differences in the
sex ratio of adults contributing to the stocked progeny, number of progeny per mating
released, and percentage of mature adults used for mating. From this model, the numbers
of individuals that needed to be stocked to achieve a target population size or to retain a
target level of genetic integrity were determined. This exploration, of supplementation
options will help to determine which stocking strategies are best for the long-term
persistence and genetic integrity of lake sturgeon populations.

METHODS
Model Development

An individual based-model was developed that incorporated demographic and
genetic processes. Lake sturgeon exhibit a polygamous mating system which was
represented based on available data whereby female lake sturgeon mature at
approximately 20 years of age and spawn approximately once every 3 years, and male
lake sturgeon mature at approximately 15 years of age and spawn approximately every

other year (Auer 1999; Bruch 1999; Billard' and Lecointre 2001; DeHaan 2003; Nichols

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et al. 2003). Once an individual reached the minimum age for maturity then the
individual was assigned a random number distributed Uniforrn(0,1) each year. If that
random number was less than the probability of mating, then that individual returned to
the river to mate that year. Empirical data from Black Lake, Michigan, lake sturgeon
suggest that reproductive success is not related to the length or weight of the adult
sturgeon, therefore, the size of individual fish wasn’t included in this individual-based
model (DeHaan 2003). For each fish returning to spawn, the number of potential mates
or batches of offspring, B, for each spawning male and female was based on empirical
data from Black Lake, MI (Figure B]; DeHaan 2003). Random ntunbers of batches
were generated using a discrete form of the exponential distribution by:

B = 1 + integer(-2 * ln(l - U(0, 1)) .
This distribution represents the number of mates from empirical data (Figure B. 1;
DeHaan 2003). The batches for the males and females were randomly shuffled, and
female batches were paired with male batches. This process allowed random matings
between individuals, and allowed individuals to mate with multiple other individuals as
has been observed in lake sturgeon. In this model, any batches produced by a male or
female without a pair, or mate, were deleted. This distribution allows for a large number
of mates as the uniform distribution approaches one; however, the number of mates is
decreased based on how the batches are paired with mates. Thus, extremely large
numbers of mates is unlikely.‘ The number of progeny, P, created (at the end of the
summer) from each mating pair, or batch, was generated using an exponential equation of
the form:

P = integer(l * (-ln(l - U(O,l))))

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producing a distribution of numbers of offspring similar to that seen in Black Lake, MI
(DeHaan 2003). This distribution was based on the empirical number of progeny per
adults as reported by DeHaan (2003; Figure B2). The empirical distribution was based
on a parentage analysis whereby progeny in a sample were assigned to parents. Only
about 25% of progeny were assigned to parents, however. Because of this, the empirical
nturrber of progeny per parent should be treated cautiously. Because the number of
progeny was modified by varying the YOY mortality rate to match observed population
sizes and trajectories, this distribution was judged to be appropriate.

The sex of offspring was randomly determined with an equal probability.
Following birth, age-specific mortality rates were applied to each individual sturgeon.
Mortality rates were set up in the model such that a random number between 0 and 1 was
generated for each individual and if that random number was less than the specified level
of mortality, then that individual suffered mortality. As such, demographic stochasticity
was implicitly incorporated into the model because the death of each individual was
randomly determined. The mortality rate from the end of the summer through the winter
to the end of the first year is unknown. Therefore, this mortality rate was varied to
produce population growth rates that mimic observed growth rates for existing
populations. This technique has proven useful in previous studies and provides a means
to develop management advice even though parameter values are uncertain (Vaughn and
Saila 1976; Hayes and Taylor 1990; Heppell et al. 2000). All parameter values were
developed from literature review and further review by local Great Lakes sturgeon
experts. Mortality after the first year was set to 0.05 based on Baker (1980). Henceforth,

young of the year mortality will be referred to as such, and mortality after the first year

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will be referred to simply as “mortality.” Young of the year and post young of the year
mortality rates have been treated this way by past elasticity studies for other sturgeon
species (Gross et al. 2002).

Individual inbreeding coefficients were determined using path analysis of the
individual’s pedigree implemented in the IN BREED procedure available in SAS® (SAS
Institute Inc., 2003). From a pedigree, the inbreeding coefficient ([2) for an individual
was determined by summing all of the unique paths (P) through a common ancestor (A)

as

fx =21";— (1+fA)

where n was the number of ancestors in the path ande was the inbreeding coefficient of
ancestor A (Wright 1922). Lake sturgeon are polyploid with a ploidy level of eight
(Blacklidge and Bidwell 1993). Polyploidy is thought to mask inbreeding depression;
however this effect has not been shown for other polyploid species such as salmon
species Oncorhynchus sp. (Wang et al. 2002). Therefore, I assumed polyploidy of lake
sturgeon did not affect the accrual of inbreeding or inbreeding depression. This approach
allowed for the tracking of overall individual inbreeding levels and accrual of inbreeding
rather than specifying certain alleles as deleterious.

Gene retention from the founding population was tracked based on a one locus
system whereby each individual at the start of the simulations had two unique,
hypothetical alleles at one locus (MacCluer et al. 1986). The hypothetical locus was
assumed to be inherited as a Mendelian trait. As mating occurred between individuals,

some alleles were lost from the population before they could be passed on to offspring.

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Random loss of unique alleles results in genetic differentiation among populations and
determines the percentage of founders that have contributed genes to the population. The
loss of unique alleles can be described through a technique called gene drop analysis
(MacCluer et al. 1986; Hedrick and Miller 1992), which tracks all unique alleles that are
retained or lost from the population through time (Haig et al. 1993). Thus, the percent of
remaining alleles at the end of each simulation can then be expressed as the number of
remaining alleles over the number of unique alleles at the beginning of the simulation
which is two times the initial population size.
Stocking scenarios

For the baseline stocking scenarios, I ran simulations which represented the ideal
situation for maintaining genetic diversity as described by the literature (Frankham 1995;
Wang et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005; Fraser 2008). All adult
males and females entering the spawning stream were selected for mating and bred in a
1:1 sex ratio. Although this is an idealized situation, it does occur in practice in some
situations. Equal numbers of offspring were produced from each mating, and the
offspring were randomly assigned sex and one gene from each parent. From these
potential progeny, a specific number were randomly supplemented. Although stocking of
lake sturgeon in the Great Lakes generally occurs in the fall, my model represented those
individuals that survive over winter. If supplementation occurs in the fall, then numbers
need to be scaled to reflect overwinter survival. The survival rate from stocking to the
following spring has been estimated as 40% for the population in Black Lake, MI

(Crossman 2009).

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l explored three situations representing different populations in need of
supplementation. These scenarios reflect a range of population sizes representative of
lake sturgeon in the Great Lakes basin and thus, are relevant to current management.
Moreover, a major objective was to determine if different stocking strategies would be
required for different starting conditions. In the first scenario, the population was less
than the minimum viable population size (MVP, which was defined as a population with
approximately a 5% extinction risk over 250 years Shaffer 1981; Boyce 1992). Many
populations are below their MVP in the Great Lakes basin, and are in need of
rehabilitation to offset their inherent decline (Hay-Chmielewski and Whelan 1997).
Moreover, populations less than the MVP are likely at high risk of inbreeding because
they are small populations (Hedrick and Kalinowski 2000; Brook et al. 2002; Keller and
Waller 2002). The MVP for lake sturgeon in the Great Lakes basin was estimated to be
approximately 80 individuals (Schueller and Hayes in prep; Chapter 2). Accordingly, I
simulated a population size of 50 with a 3% decline in population size over time
(l=0.97). This scenario will be referred to as “less than MVP”.

The second scenario represented populations slightly above MVP but stable.
Although such populations have minimal risk of extinction in the short run, they have
substantial risk of accruing excess inbreeding. Thus, many management plans have
objectives to increase the abundance of lake sturgeon populations in this condition. For
this scenario, I simulated populations of 100 individuals with a stable growth rate over
time (71=1.0). This scenario will be referred to as “brink of MVP”.

In the final scenario, I considered larger, declining populations. Although large

populations have a lower risk of extinction and accrual of inbreeding, supplementation is

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a useful tool to offset declines and prevent the population from eventually reaching MVP.
Thus, I simulated populations of 250 individuals with a declining population growth rate
over time (h=0.97). This scenario will be referred to as “large, declining”.

I simulated stocking over two different time frames for each population scenario
in order to test the influence of this aspect of supplementation on genetic integrity (Wang
et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005). First, stocking occurred over
a relatively long time frame of 25 years, which is approximately one generation for lake
sturgeon. I termed this strategy “trickle” because in general a relatively small number of
young sturgeon would need to be stocked each year. Because the duration of
supplementation was large relative to the spawning interval, both males and females
would likely be available multiple times over the course of the supplementation program.
In the second time frame, stocking occurred for 4 years, which is approximately the time
needed to allow all mature individuals to be available for mating at least once. I termed
this strategy “pulse” because stocking occurs in a very brief period at the beginning of the
simulation. For each scenario, I determined the number of individuals that would need to
be stocked to offset declines or increase the population abundance to target levels.

We explored several additional factors to determine their impact on genetic
integrity in each supplementation scenario. These factors included: different sex ratios,
unequal family sizes, and reduced numbers of adults sampled for breeding purposes
(Wang et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005; Fraser 2008). One
level of stocking was chosen for each population size and time frame stocked (6 total),
and each of the following scenarios was run against those six baseline scenarios to

evaluate the impact on gene retention and inbreeding accrual. For each population size

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and time frame stocked, the sex ratio was varied from 1:1 and was allowed to range up to
5:1 and 10:1 (males per female). Thus, for a sex ratio of 10:1, up to 10 males could
create progeny with one female. The simulation represents a female’s eggs being divided
into 10 lots where one male fertilizes each lot. This is the recommended strategy when
mating a female with more than one male (Miller and Kapuscinski 2003). Eggs from
each female were broken into lots, and then males were randomly paired with lots, with
any excess males not contributing to reproduction. This allowed for a sex ratio of up to
10 males per female. Because males spawn at a younger age and more frequently, in
practice more males are often available for supplementation purposes. However, the
number of males and females available each year were random in my simulation (and in
nature). Thus, sex ratios were designed to be a constraint rather than an exact number,
and in some years could be as low as 1:1 in practice.

For each population size and time frame stocked, unequal family contributions
were tested by allowing up to a fivefold difference in the number of progeny per mating.
For each mating, the number of progeny was randomly determined from a uniform
distribution where the largest number of progeny that could be produced was five times
the smallest number of progeny that could be produced. Thus, a range in progeny
production up to a fivefold difference could occur. Finally, for each population size and
time frame stocked, decreased numbers of adults contributing progeny was tested by only
sampling 20% of the mature adult population for breeding purposes.

Lake sturgeon have been shown to reproduce naturally even if their gametes have

been collected for supplementation purposes (Crossman 2008); therefore, all adults used

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to create progeny for supplementation purposes were also allowed to reproduce naturally
in the model.
Simulations and outputs

A simulation duration of 250 years was used as this allowed time for transient
responses to dissipate. For each scenario, 250 simulations were run to provide precise
estimates of the mean response and the variance across the factors explored. A yearly
time step was used in all simulations. The percent of extinct populations, mean final
abundance, average individual inbreeding coefficient in the final year, and percent of
unique alleles retained were recorded for each simulation run of 250 years. The mean
final abundance was the average abundance including zeroes for those populations that
went extinct. The average individual inbreeding coefficient was the average inbreeding
coefficient for progeny produced in the final year. No uncertainty estimates could be
provided for the inbreeding coefficients because only the mean was an output for the
model. The average percent of unique alleles retained was the average percent of genes
retained including zeroes for those populations that went extinct. For the percent of
extinct populations and the average percent of genes retained, confidence intervals were
calculated as:

(estimate i 2*SE)* 100

where the SE = (pq/n) A (1/2), p = (percent of extinct populations or genes retained/ 100),
q = l-p, and n=number of simulations. A confidence interval for the mean final
abundance was given as the estimate :1: 2*SE where the SE = (o/n) A (1/2). The mean
final abundance and the average percent of genes retained were used as opposed to the

median because the mean and median were very similar in value, even with zeroes

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included. Simulations were assumed to have current environmental and demographic
conditions, which remained constant into the future. For all of the outputs, functions
were fitted to smooth the relationship between the output and the total number stocked
over the supplementation period. This was then used to estimate the number of
individuals to stock in order to attain a specific benchmark (e.g., a population size of 250,
inbreeding level below 0.01 ). The total number of individuals supplemented to reach a
target was the number of years in the time frame multiplied by the number of individuals
each year. This should be useful for lake sturgeon managers, who will be able to
determine the approximate number of individuals that would need to be stocked. in order
to achieve a defined goal or objective.
RESULTS

As intended in the baseline simulations without stocking, mean abundance for the
less than MVP and large, declining scenarios declined from the starting population size
over the 250 year time frame. Mean abundance in the brink of MVP scenario remained
near the starting value of 100. In the two declining populations, a substantial proportion
of the populations went extinct, while in the brink of MVP scenario, no populations went
extinct (Table 3.1). The percent of genes retained was highest in the brink of MVP
scenario, followed the less than MVP scenario, and finally by large, declining
populations (Table 3.1). In all scenarios, the mean inbreeding coefficient increased over
time, reaching approximately 0.13 to 0.14 in the two scenarios with declining
populations, and 0.068 in the brink of MVP scenario.

Stocking decreased the extinction risk to zero with only a few individuals stocked

for all of the scenarios, thus no table was provided. Stocking increased the mean

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abundance for all scenarios, with higher stocking rates producing higher mean ending
populations (Table 3.2). Although the number of sturgeon that needed to be stocked per
year was higher under the pulse stocking strategy than the trickle stocking strategy to
achieve a specified mean ending population, the total number of sturgeon stocked over
the course of the entire stocking program was similar (Table 3.2). For example, under the
less than MVP scenario, to reach an abundance of 250 individuals, approximately 475
individuals would need to be stocked over the course of either the pulse or trickle
strategies (Table 3.2). Stocking also increased the percent of genes retained (Table 3.3),
and decreased the mean final inbreeding coefficient (Table 3.4). As with mean
population abundance, the pulse stocking strategy required more individuals stocked per
year than the trickle strategy, but the total number stocked was in most cases similar for
the duration of the stocking program to achieve a specified target (Table 3.3; Table 3.4).
Two exceptions to this were for large, declining populations, where the trickle strategy
required somewhat fewer individuals stocked over the course of the entire stocking
program when compared to the pulse scenario to retain an equivalent percentage of genes
(Table 3.3), and for the mean inbreeding coefficient» within the brink of MVP scenario
where the trickle strategy required substantially more individuals stocked over the course
of the entire stocking program (Table 3.4). For example, to maintain a population below
an average inbreeding coefficient level of 0.03, 925 individuals would need to be stocked
over the course of the time period for the trickle strategy while only 74 would need to be
stocked for the pulse strategy (Table 3.4).

Skewing the sex ratio toward a greater males to female ratio did not substantially

affect the demographic characteristics of the stocked population or the genetics of the

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population for all of the scenarios when compared to a 1:1 sex ratio. All sex ratios
explored resulted in increased population sizes, more genes retained, and reduced
inbreeding when compared to no stocking. For all scenarios, skewing the sex ratio did
not result in large differences in the percent of genes retained or the accrual of inbreeding
for either the pulse or trickle time frames (Table 3.5).

Unequal family sizes, so that some families had more progeny than others, did not
affect the demographic characteristics of the stocked population and did not significantly
affect the genetics of the population for all of the scenarios when compared to equal
family sizes. Unequal family sizes still resulted in increased population size, more genes
retained, and reduced inbreeding when compared to no stocking. For all scenarios,
unequal family sizes did not result in large differences in the percent of genes retained or
the accrual of inbreeding for either the pulse or trickle time frames (Table 3.6).

Decreasing the percent of adults contributing progeny for stocking did not affect
the demographic characteristics relative to stockings where all returning adults
contributed gametes, but did require more individuals be produced from each mating to
achieve abundance goals. When the percent of adults contributing progeny was reduced
to 20% of the spawning run, stocking still resulted in increased population size, more
genes retained, and reduced inbreeding when compared to no stocking. In the pulse
stocking strategy, no discemable impact of using a lower percentage of the spawning run
was evident for gene retention or final mean inbreeding (Table 3.7). Reducing the
percent of adults contributing progeny for stocking purposes under the trickle strategy
resulted in a decreased percent of genes retained and a coincident increase in the

inbreeding coefficient (Table 3.7).

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DISCUSSION

Overall, stocking was beneficial under all scenarios explored in this analysis both
demographically and genetically. Without stocking, lake sturgeon populations were at
risk of extinction, had smaller population sizes, reduced gene retention, and increased
inbreeding accrual. With stocking, the extinction risk was considerably decreased, with
nearly all populations remaining extant even with small numbers of individuals being
stocked. Stocking is generally suggested as a management tool in order to avoid
extinction and increase abundance (Ryman and Laikre 1991 ). In these scenarios,
stocking greatly decreased the risk of extinction and allowed for much larger population
sizes when compared to scenarios with no stocking. However, stocking has been
cautioned against because of the possibility of inbreeding, inbreeding depression, and
reduced gene retention (Ryman and Laikre 1991; Tessier et al. 1997). For these scenarios
with stocking, gene retention increased and inbreeding accrual decreased which is in
contrast to expected results given much of the prevailing advice. In my simulations, I
considered two situations where the population was experiencing a decline. As shown in
my baseline simulations without stocking, declining populations had a rapid loss of
genetic diversity and higher levels of inbreeding. As such, stocking was beneficial
because losses of genetic integrity due simply to greatly reduced population size were
offset. Thus, it is important to consider not just the final amount of inbreeding and loss
of genes, but to determine how this relates to how these measures of genetic integrity
would change without stocking (i.e., with continued population decline).

The most appropriate stocking strategy has been found to be dependent upon the

population size and population trajectory (Duchesne and Bematchez 2002). All of the

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populations explored in my study were relatively small and declining, and all benefited
both demographically and genetically from supplementation using the best genetic
practices recommended (Wang et al. 2002; Miller and Kapuscinski 2003; Page et al.
2005; Fraser 2008). Improved supplementation practices can reduce genetic
consequences of supplementation (Tessier et al. 1997). Eldridge and Killebrew (2008)
found non-significant decreases in genetic integrity with the implementation and
expansion of a supplementation program for Chinook salmon Oncorhynchus rshawytscha
in the Stillaguamish River over several generations. All three plausible lake sturgeon
population scenarios resulted in improved demographic and genetic outputs with
stocking, which is most likely due to increased population sizes over time. Jager (2005)
predicted higher gene retention with supplementation using a demographic and genetic
individual based model for white sturgeon Acipenser transmontanus. Supplementing
over multiple generations could lead to increased genetic integrity, if the population size
is larger in the long-term (Wang and Ryman 2001; Jager 2005). Additionally, the life
history strategy of the lake sturgeon could have contributed to the increased genetic
integrity with supplementation. Given that the probability of survival to maturity is low
for each individual, the probability that two related individuals would survive and mate to
produce progeny is likely low. Also, males and females reach maturity at different ages
and reproduce at different intervals (Hay-Chmielewski and Whelan 1997), which would
reduce the probability that an individual would encounter a related individual on the
spawning grounds. Thus, with larger population sizes in the long-term and without

mating between related individuals due to life history characteristics, the accrual of

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inbreeding would be lower and gene retention would be higher than in species with
different life histories.

Supplementing over a 25-year time frame was not found to be better for avoiding
extinction, attaining a target mean population size, retaining genes, or for reducing
inbreeding than stocking over a 4-year time frame when using recommended genetic
practices (Wang et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005; Fraser 2008)
for less than MVP and brink of MVP, but not for large, declining. If the total numbers of
individuals stocked over the two time frames were approximately equal for the less than
MVP and brink of MVP scenarios, the two strategies (pulse and trickle) were equally as
effective. However, for the brink of MVP scenario, greater numbers of individuals
needed to be stocked with the trickle scenario in order to be below a desired level of
inbreeding. Thus, the genetic recommendation of stocking over a longer time frame
(Wang et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005) may not be necessary
for smaller population sizes given the scenarios explored, especially given the financial
constraints of most management agencies. Thus, the pulse strategy is recommended as a
means to more rapidly achieve conservations goals, and would most likely cost less
because of the shorter time frame needed for collection of gametes on rivers. For large,
declining populations, supplementing using the trickle scenario resulted in a greater
percent of genes retained over the long-term than supplementing using the pulse scenario.
Also, for the large, declining populations, greater numbers of individuals needed to be
stocked under the pulse scenario in total in order to achieve the desired mean final
population size, percent of genes retained, and mean final inbreeding coefficient. Thus,

the genetic recommendation of stocking over a longer time frame (Wang et al. 2002;

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Miller and Kapuscinski 2003; Page et al. 2005) may be more important for larger
populations in order to retain larger percentages of genes.

Skewing the sex ratio and unequal family sizes did not lead to an impact in either
the inbreeding coefficient or the percent of genes retained for populations less than MVP,
on the brink of MVP, or for large, declining populations under the conditions explored.
This is not what was expected given the genetic guidelines set out for effective stocking
practices (Wang et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005; Fraser 2008).
However, this may be simply due to much larger population sizes in the long-term given
that supplementation could lead to increased genetic integrity, if the population size is
larger in the long-term (Wang and Ryman 2001; Jager 2005). This is in contrast to
findings by Oota and Matsuishi (2005) who found that skewing the sex ratio, from 1;], of
adults contributing progeny through stocking practices resulted in increased inbreeding
coefficients using data for the Japanese flounder. However, this is not in contrast to
findings by Jager (2005) who used an individual based model of demographics and
genetics and who found that unequal family sizes did not affect the genetic integrity of
white sturgeon populations. These findings may also be due to nearly all adults still
having the opportunity to spawn and contribute progeny to the future during these
simulations given that the percent of mature adults contributing progeny was held
constant. Thus, even though the sex ratio was skewed or the family sizes were unequal,
most adults were still able to contribute progeny and thus genes thereby reducing the
impact of sex ratio and family size on the retention of genes and the accrual of
inbreeding. Finally, these findings may also be due to low probabilities of surviving to

adulthood and encountering a related individual to mate with. This may be especially

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true for the two scenarios that were declining, and would result in higher gene retention
and lower inbreeding accrual over time.

For the skewed sex ratios, gametes were mixed in a way that would not allow for
sperm competition. Often, stocking for management purposes uses milt that has been
mixed or milt is sequentially added to eggs (Campton 2004; Wedekind et al. 2007).
Sperm competition is then possible whereby one male’s sperm may fertilize a large
proportion of the eggs available (Miller and Kapuscinski 2003). This dissertation does
not address that issue, although, I concur with recommendations (Wedekind et al. 2007)
to avoid mixing of gametes prior to fertilization to eliminate the possibility of sperm
competition which could increase relatedness among progeny and result in gene loss over
time.

The greater the percent of mature adults contributing progeny to the supplemented
population, the less likely inbreeding will accrue and the greater the retention of genes for
the trickle scenarios explored. This finding is what would be expected given the
recommended genetic practices for supplementation (Wang et al. 2002; Miller and
Kapuscinski 2003; Page et al. 2005). Duchesne and Bematchez (2002) found that the
size of the hatchery population was the most pivotal parameter controlling inbreeding.
The greater the number of adults contributing progeny in a hatchery setting, the lower the
risk of inbreeding accrual (Duchesne and Bematchez 2002). Given these results,
managers should collect as many mature adults as possible for mating purposes. This
practice should help to reduce inbreeding accrual and help to retain genes in the

population.

99

Based on the high levels of coancestry (probability that genes are identical by
descent between two individuals; Bila et al. 1999; Perrin and Mazalov 1999; Wang and
Ryman 2001) between progeny produced for supplementation purposes, the mean
inbreeding coefficient was expected to be much higher with supplementation as
compared to no supplementation. Coancestry increases the risk of inbreeding with
mating in future generations (Bila et al. 1999; Perrin and Mazalov 1999). My results are
counterintuitive, but are most likely a function of the initial population sizes that were
explored and the life history of the lake sturgeon. Because the population sizes that were
explored were small and declining, the chance of surviving to reproductive age and
mating with a related individual who has also survived to reproductive age is low. Thus,
inbreeding would not accrue even though the coancestry of individuals supplemented into
the population may be relatively high. Male and female lake sturgeon also do not reach
sexual maturity at the same age or mate at the same interval, therefore, the probability of
encountering a related individual may be low because of the life history of the species.
Again, this would lead to lower levels of inbreeding accrual than one would expect given
coancestry levels.

Rearing individuals in captivity may result in unwanted consequences when the
individuals are released into the wild. With captive rearing, individuals with specific
traits may be inadvertently selected over others, and those traits may not be advantageous
in the wild (e.g. large body size, run time; Lynch and O’Hely 2001 ). With captive
rearing, selection may be decreased or changed to select for traits that are not
advantageous in the wild, for instance in situations with reduced predation (Lynch and

O’Hely 2001). However, this model did not explore the effects of domestication, and I

100

assume limited domestication selection on lake sturgeon while in captivity given the short
time frame of rearing.

This model assumed that all supplemented progeny had the same demographic
parameters as the naturally produced progeny in the future. All supplemented progeny
had the same mortality rates and produced progeny at the same rate as progeny produced
in the wild. Many studies show that mortality rates are higher for stocked fish and that
stocked fish produce lower numbers of offspring than their wild counterparts (Miller and
Kapuscinski 2003; Araki et al. 2007a; Araki et al. 2007b). However, the differences that
result in survival and future reproductive success from supplemented versus stocking
using broodstock are difficult to distinguish, and supplemented individuals may not
experience the same mortality and reduced reproductive success of individuals stocked
using broodstock (Miller and Kapuscinski 2003). For example, Araki et al. (2007b)
found that supplemented fish didn’t have lower reproductive success when compared to
wild fish. Given that the lifetime performance of lake sturgeon produced by
supplemental stocking is unknown relative to naturally produced individuals, experiments
evaluating this possibility would be very valuable.

Overall, these results suggest that demographic stochasticity may be the more
important factor with respect to retaining genes and populations. Lande (1988)
advocated that demographic stochasticity was the more important force in extinction
processes for small population sizes. Generally, these populations faced an extinction
risk if they were not supplemented, and given that supplementation did not result in large

decreases in gene retention or increases in inbreeding using the recommended genetic

101

practices, avoiding extinction resulting from demographic stochasticity seemed to be the
more pressing issue.
MANAGEMENT IMPLICATIONS

Depending upon the population size and trajectory, different numbers of
individuals need to be stocked in order to move a population towards rehabilitation. For
lake sturgeon populations less than MVP or on the brink of MVP, relatively few
individuals need to be stocked in order to maintain both positive population trajectories
and reduced genetic impacts. For larger, declining populations, more individuals need to
be stocked if a short time frame is used. How many fish should be stocked is dependent
upon the target, when you stock, and overwinter mortality rates. For example, the
number that needs to be stocked in the fall each year is the recommended stocking
number (which accounts for over winter mortality) divided by the actual over winter
survival for the population. If you wanted to supplement a population below MVP under
the pulse scenario, so that the population size in the long-term was on average 500
individuals, and if the over winter survival was 0.40% (Crossman et al. 2009), then you
would need to stock (244/0.40=610) 610 individuals in the fall each year (Table 3.2).
This strategy should be used when determining how many to stock to achieve specific
population sizes, percent of genes retained, and mean final inbreeding coefficients.

Based on the scenarios explored, if all recommended genetic practices cannot be
followed, some recommendations appear more important than others with respect to
maintaining genes and reducing inbreeding. First, if supplementing a larger population,
supplementing over a longer time frame is recommended for the retention of genes over

the long term. Second, capturing the greatest number of adults from the population for

102

supplementation purposes seems to be the most crucial recommendation for retaining
genes and reducing inbreeding accrual. Third, sex ratio and family size variation have
smaller effects on the genetics of populations, thus, following these genetic guidelines is
less crucial.

Many lake sturgeon populations are in need of rehabilitation, and supplementation
is one potential management tool. My analyses show that supplementing populations can
increase the retention of unique genes and decrease inbreeding, and achieve target
population sizes with reduced risks of extinction when compared to not supplementing
the population. However, other limitations, such as reduced spawning habitat
availability, may influence the need to stock if the limitation can’t be remedied. Thus,
this study has provided advice on how many to stock and what genetic guidelines are
important, but it is up to the managers to determine goals and objectives for populations

of interest and then take actions to meet those goals and objectives.

103

 

Table 3.1. The percent of extinct populations (:1: 2 SE), percent of genes retained (i 2
SE), and mean final inbreeding coefficient for baseline conditions with no stocking at the

 

 

end of 250 years.
Percent of Mean final
extinct Percent of genes inbreeding
Scenario popplations retained coefficient
34.4 4.64
Less than MVP (30.1, 38.6) (2.76, 6.52) 0.1388
0 10.05
Brink of MVP (0, 0) (7.36, 12.74) 0.0683
22.4 0.89
Large, declining (18.7, 26.1) (0.05, 1.74) 0.1303

 

104

Table 3.2. The number stocked per year under the trickle scenario, the total stocked under
the trickle scenario, the number stocked per year under the pulse scenario, and the total
stocked under the pulse scenario for each of the population types in order to achieve the
desired mean final population size. Numbers stocked per year were obtained using
interpolation using a linear equation, and total stocked was estimated as the number
stocked per year before rounding times the number of years stocked. The first line under
each scenario is the baseline with no stocking.

Mean final Number

population stocked per Trickle

Number
stocked per Pulse

 

 

 

Scenario size year-Trickle Total year-Pulse Total

Less than MVP-no

stocking 22 0 0 0 0

Less than MVP 50 2 60 18 70
100 7 166 43 171
150 1 1 273 68 272
200 15 380 93 372
250 19 487 118 473
350 28 700 169 674
500 41 1,020 244 977

Brink of MVP—no

stocking 110 0 0 0 0

Brink of MVP 150 2 53 17 66
200 6 141 38 152
250 9 230 60 238
350 16 406 102 410
500 27 671 167 667

Large, declining-

no stocking 6 0 0 0 0

Large, declining 50 47 1,183 365 1,461
100 105 2,617 772 3,089
150 162 4,051 1,179 4,717
200 219 5,485 1,586 6,345
250 277 6,919 1,993 7,973
350 391 9,786 2,807 11,228
500 564 14,088 4,028 16,112

 

105

 

Table 3.3. The number stocked per year under the trickle scenario, the total stocked
under the trickle scenario, the number stocked per year under the pulse scenario, and the
total stocked under the pulse scenario for each of the population types in order to achieve
the desired percent of genes retained. Numbers stocked per year were obtained using
interpolation using a power function, and total stocked was estimated as the number
stocked per year before rounding times the number of years stocked. The first line under

each scenario is the baseline with no stocking.

 

 

 

 

Percent of Number Number
genes stocked per Trickle stocked per Pulse
Scenario retained year-Trickle Total year-Pulse Total
Less than MVP-no
stocking 4.64% 0 0 0 0
Less than MVP 5% 0 6 1 4
10% 2 40 11 45
25% 11 265 68 272
35% 20 496 119 478
50% 38 944 212 847
Brink of MVP-no
stocking 10.05% 0 0 0 0
Brink of MVP 10% 0 0 1 2
25% 16 406 100 400
3 5% 30 759 1 81 724
50% 54 1,352 313 1,253
Large, declining-
no stocking 0.89% 0 0 0 0
Large, declining 5% 36 906 296 1,184
10% 96 2,394 736 2,944
25% 324 8,105 2,405 9,622
35% 503 12,570 3,705 14,820
50% 798 19,955 5,851 23,404

 

106

Table 3.4. The number stocked per year under the trickle scenario, the total stocked

 

under the trickle scenario, the number stocked per year under the pulse scenario, and the
total stocked under the pulse scenario for each of the population types in order to achieve
the desired mean final inbreeding coefficient. Numbers stocked per year were obtained
using interpolation using a Weibull function, and total stocked was estimated as the
number stocked per year before rounding times the number of years stocked. The first
line under each scenario is the baseline with no stocking.

 

 

 

 

Mean final Number Number
inbreeding stocked per Trickle stocked per Pulse
Scenario coefficient year-Trickle Total year-Pulse Total
Less than MVP-no
stocking 0. 1 3 88 0 0 0 0
Less than MVP 0.125 0 12 3 13
0.100 3 68 17 69
0.075 8 190 45 181
0.050 18 450 100 401
0.025 44 1,100 227 908
Brink of MVP-no
stocking 0.0683 0 0 0 0
Brink of MVP 0.050 0 4 4 14
0.040 3 83 9 36
0.030 37 925 18 74
0.025 1 1 1 2,778 26 104
Large, declining-
no stocking 0.1303 0 0 0 0
Large, declining 0.125 0 0 4 17
0.100 0 8 31 125
0.075 3 74 102 409
0.050 16 393 270 1,082
0.025 82 2,038 739 2,954
0.010 310 7,744 1,703 6,81 1

 

107

Table 3.5. The percent of genes retained (i2 SE) and mean final inbreeding coefficient
for skewed sex ratios for each population size and stocking strategy. For each initial
population size or scenario, baseline outputs are included for no stocking.

 

 

 

 

 

S . Stocking Sex ratio Percent of genes Mean final
cenarro . . inbreeding
strategy (Males.Females) retained .
coefficrent
Less than No
MVP Stocking - 4.64 (2.76, 6.52) 0.1388
Pulse 1:1 13.85 (9.47, 18.22) 0.0975
5:1 13.63 (9.29,17.97) 0.0943
10:1 14.25 (9.83,l8.67) 0.0893
Trickle 1:1 15.62 (11.03, 20.21) 0.0804
5:1 15.89 (11.26, 20.51) 0.0881
10:1 15.64 (11.04, 20.23) 0.0819
Brink of No
MVP Stocking - 10.05 (7.36, 12.74) 0.0683
Pulse 1:1 13.51 (9.19, 17.83) 0.0565
5:1 12.96 (8.72, 17.21) 0.0565
10:1 13.84 (9.47, 18.21) 0.0558
Trickle 1:1 15.85 (11.23, 20.47) 0.0482
5:1 14.98 (10.47, 19.50) 0.0504
10:1 15.43 (10.86, 20.00) 0.0486
Large, No
declining Stocking - 0.89 (0.05, 1.74) 0.1303
Pulse 1:1 4.77 (2.08, 7.47) 0.0425
5:1 4.99 (2.23, 7.74) 0.0405
10:1 4.70 (2.03, 7.38) 0.0503
Trickle 1:1 17.27 (12.49, 22.06) 0.013
5:1 17.11 (12.35, 21.88) 0.0144
10:1 16.62 (11.91,21.33) 0.0154

 

108

 

Table 3.6. The percent of genes retained (i2 SE) and mean final inbreeding coefficient
for unequal family sizes for each population size and stocking strategy. None indicates
equal family size, and up to 5x indicates that family size could vary up to five times
higher than the baseline family size. For each initial population size or scenario, baseline
outputs are included for no stocking.

 

 

 

 

S . Stocking Variance in Percent of genes Mean final
cenarro . . . inbreeding
strategy family srze retained .
coefficrent
Less than No
MVP Stocking - 4.64 (2.76, 6.52) 0.1388
Pulse None 13.85 (9.47, 18.22) 0.0975
Up to 5x 12.90 (8.66, 17.14) 0.0951
Trickle None 15.62 (11.03, 20.21) 0.0804
Up to 5x 15.95 (11.32, 20.58) 0.0845
Brink of No
MVP Stocking - 10.05 (7.36, 12.74) 0.0683
Pulse None 13.51 (9.19, 17.83) 0.0565
Up to 5x 13.73 (9.38, 18.09) 0.0531
Trickle None 15.85 (11.23, 20.47) 0.0482
Up to 5x 14.75 (10.27, 19.24) 0.0487
Large, No
declining Stocking - 0.89 (0.05, 1.74) 0.1303
Pulse None 4.77 (2.08, 7.47) 0.0425
Up to 5x 5.04 (2.27, 7.81) 0.0474
Trickle None 17.27 (12.49, 22.06) 0.0130
Up to 5x 17.51 (12.71, 22.32) 0.0119

 

109

 

Table 3.7. The percent of genes retained (i2 SE) and mean final inbreeding coefficient
for reduced numbers of adults used for mating purposes for each population size and
stocking strategy. One hundred percent indicates all adults contributing progeny for
stocking purposes, and 20% indicates only 20% of mature adults contributing progeny for
stocking purposes. For each initial population size or scenario, baseline outputs are
included for no stocking.

 

 

 

 

. Percentage of Mean final

S . Stocking Percent of genes . .
cenarro Strategy adult retained inbreeding
contribution coefficient

3;?” No Stocking - 4.64 (2.76, 6.52) 0.1388

Pulse 100% 13.85 (9.47, 18.22) 0.0975

20% 13.24 (8.96, 17.53) 0.0921

Trickle 100% 15.62 (11.03, 20.21) 0.0804

20% 13.37 (9.07, 17.68) 0.0886

Brink of MVP No Stocking - 10.05 (7.36, 12.74) 0.0683

Pulse 100% 13.51 (9.19, 17.83) 0.0565

20% 13.57 (9.24, 17.90) 0.0562

Trickle 100% 15.85 (11.23, 20.47) 0.0482

20% 14.92 (10.42, 19.43) 0.0490

Larger No Stocking - 0.89 (0.05, 1.74) 0.1303

declimng

Pulse 100% 4.77 (2.08, 7.47) 0.0425

20% 4.53 (1.90, 7.16) 0.0465

Trickle 100% 17.27 (12.49, 22.06) 0.0130

20% 15.94 (11.31, 20.57) 0.0156

 

110

CONCLUSIONS

Overall, this dissertation explored which population parameters are important for
long-term persistence and the likely fate of populations with and without management
intervention. If managers focus on the population parameters that will have the most
impact on lake sturgeon persistence and genetic integrity, then managers should focus on
reducing post YOY mortality rates. The estimated MVP range (estimated both with and
without inbreeding depression) of 80-150 individuals provides guidance for populations
at high risk of extinction, but the sensitivity of population outputs to changes in the
baseline parameters needs to be accounted for. Without some form of management,
populations below this level are unlikely to persist. Simulations indicate that stocking
even small numbers of fingerlings can offset population declines, leading to greater
abundance and genetic integrity. For the scenarios explored, stocking is generally
beneficial for both abundance and genetic integrity, especially for small and declining
populations.

The sensitivity analysis of the individual based model demonstrated that lake
sturgeon population persistence and genetic integrity was hypersensitive to changes in
most of the population parameters including young of the year mortality, mortality, age at
first maturation for females, and the probability of mating for females. Changes in these
parameters were essentially driving population outputs. The post YOY mortality rate
was the most sensitive of all of the population parameters for the outcomes of interest.
Lake sturgeon persistence was relatively insensitive to both age at first maturation for
males and the probability of mating for males. Changes in these parameters had

relatively little impact on population outputs.

111

Sensitivity was not linear for any of the outputs across the range of plausible
values explored. In many previous sensitivity analyses, all of the model parameters are
held at a nominal value and one parameter at a time is changed by :tIO% (or less) to
determine which parameters most strongly influence model predictions (McCarthy et al.
1996; Essington 2003). However, in my sensitivity analyses, I varied model inputs
across a broader range of values, which helped to delineate the shape of the sensitivity
curve, depicting a richer picture of model sensitivity. This sensitivity analyses helped to
determine which parameters were most sensitive and in what range those parameters have
the greatest influence on model outcomes.

I found that the use of any sensitivity analysis information for species
management and conservation is dependent upon the initial population sizes that are
explored. The outputs for the model were found to have joint sensitivity meaning that the
outputs were related to one another. The joint sensitivity between final mean inbreeding
and percent of genes retained indicated that for a given level of inbreeding, the percent of
genes retained for the initial population size of 200 was much less than for the initial
population size of 50. The differences in the functions for the two initial population sizes
may be because the initial population size of 50 was more prone to extinction than the
initial population size of 200. Generally, the differences observed between the two
population sizes indicated that sensitivities were dependent upon initial population size.
Therefore, parameter perturbation (for example, reduced mortality rate) will have a
different demographic and genetic effect depending upon the population size, which will

be important for management.

112

For naturally reproducing populations, without management, the minimum viable
population size for lake sturgeon with no inbreeding depression was estimated at
approximately 80 individuals with a 5% chance of extinction over 250 years for the
baseline parameters used. The MVP allows managers to estimate extinction risks and
identify populations for conservation (Shaffer 1981), but should acknowledge how the
results of the sensitivity analysis would affect the estimate of MVP. This work is unique
because few MVP’s have been determined for fish species; only 9 of 287 MVP’s were
for fish species in the original dataset compiled for a large meta-analysis by Traill et al.
(2007) and only 1 of 102 for a meta-analysis by Reed et al. (2003b).

Minimum viable population size was also estimated for several possible
inbreeding depression scenarios. Some inbreeding depression scenarios explored in this
analysis resulted in little or no change to the MVP required to maintain persistence when
compared to the scenario without inbreeding depression. With inbreeding depression, the
MVP was the same as the MVP with no inbreeding depression for post YOY viability for
all thresholds. With gradual inbreeding depression for both YOY viability and progeny
number, the MVP increased only slightly to 85. However, some inbreeding depression
scenarios explored did result in changes to the predicted MVP required to maintain
persistence. Inbreeding depression on progeny number resulted in an MVP of 150,
nearly twice the MVP with no inbreeding depression. With threshold inbreeding on
YOY viability, the MVP increased with decreasing thresholds. Thus, I have predicted
that inbreeding depression can increase extinction risk, but the impact of inbreeding

depended upon which life stage was influenced by inbreeding depression.

113

 

Much discussion has occurred over whether demographic stochasticity or genetic
stochasticity is more important or has a greater influence on long-term persistence (Lande
1988; Young 1991; Frankham 1995a; Spielman et al. 2004). My study doesn’t provide a
clear picture of whether demographic or genetic stochasticity dominates extinction risk,
because some estimated MVPs did change with the incorporation of inbreeding
depression and some didn’t. Based on the scenarios in my study, whether demographic
or genetic stochasticity dominated the determination of MVP and extinction risk was
dependent upon how inbreeding depression was expressed (threshold versus gradual) in
the model and how fitness was reduced.

In many cases, management of lake sturgeon is likely to proceed using
supplementation as the primary strategy because of impediments to habitat improvement.
Recently, stocking has been cautioned against because of the possibility of inbreeding
and inbreeding depression (Wang et al. 2002). However, for the scenarios explored, my
results show that stocking reduced extinction risk, increased population size, increased
gene retention, and decreased inbreeding accrual for all of the scenarios explored when
compared to no stocking. While supplementation is expected to increase abundance and
reduce extinction risk, supplementation is not expected to increase gene retention nor
reduce inbreeding accrual. The genetic integrity of supplemented populations was
thought to benefit because stocking reduced extinction risk and resulted in larger
population sizes in the long-term. Some evidence suggests that this may be the case, if
population sizes are larger in the future (Wang and Ryman 2001).

Supplementing over a 25-year time frame was not found to be better for avoiding

extinction, attaining a target mean population size, retaining genes, or for reducing

114

 

inbreeding than stocking over a 4-year time frame when using recommended genetic
practices (Wang et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005) for
population sizes less than MVP or on the brink of MVP. If the total numbers of
individuals stocked over the two time frames were approximately equal for the less than
MVP and brink of MVP scenarios, the two strategies were equally as effective for the
scenarios explored. Thus, the genetic recommendation of stocking over a longer time
frame (Wang et al. 2002; Page et al. 2005) may not be necessary for smaller population
sizes, especially given the financial constraints of most management agencies. For
larger, declining populations, supplementing using the 25-year time frame resulted in a
greater percent of genes retained over the long-term than supplementing using the shorter
time frame. Thus, the genetic recommendation of stocking over a longer time frame
(Wang et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005) may be more
important for larger populations in order to retain larger percentages of genes.

Skewing the sex ratio and unequal family sizes did not lead to an impact in either
the inbreeding coefficient or the percent of genes retained for populations less than MVP,
on the brink of MVP, or for larger, declining populations given the conditions explored.
This is not what was expected given the genetic guidelines set out for effective stocking
practices (Wang et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005; Fraser 2008).
However, this may be simply due to much larger population sizes in the long-term given
that supplementation could lead to increased genetic integrity, if the population size is
larger in the long-term (Wang and Ryman 2001; Jager 2005). These findings may also be
due to nearly all adults still having the opportunity to spawn and contribute progeny to

the future during these simulations given that the percent of mature adults contributing

115

 

progeny was held constant. Thus, even though the sex ratio was skewed or the family
sizes were unequal, most adults were still able to contribute progeny and thus genes
thereby reducing the impact of sex ratio and family size on the retention of genes and the
accrual of inbreeding. Finally, these findings may also be due to low probabilities of
surviving to adulthood and encountering a related individual to mate with. This may be
especially true for the two scenarios that were declining, and would result in higher gene
retention and lower inbreeding accrual over time.

However, reduced numbers of adults contributing progeny did result in a decrease
in genetic integrity when compared to using more adults for progeny production for the
scenarios explored. The greater the percent of mature adults contributing progeny to the
supplemented population, the less likely inbreeding will accrue and the greater the
retention of genes for supplementation over a longer time frame. This finding is what
would be expected given the recommended genetic practices for supplementation (Wang
et al. 2002; Miller and Kapuscinski 2003; Page et al. 2005).

Overall, these results suggest that demographic stochasticity may be the more
important factor with respect to retaining genes and populations. Lande (1988)
advocated that demographic stochasticity was the more important force in extinction
processes for small population sizes. Generally, these populations faced an extinction
risk if they were not supplemented, and given that supplementation did not result in large
decreases in gene retention or increases in inbreeding using the recommended genetic
practices, avoiding extinction resulting from demographic stochasticity seemed to be the
more pressing issue.

MANAGEMENT IMPLICATIONS

116

The sensitivity analysis indicated that reducing the mortality or increasing
survival of lake sturgeon will have the largest impact on population persistence.
Reductions in mortality can be accomplished through reducing and regulating harvest,
both legal and illegal (Beamesderfer and Farr 1997). Increases in YOY survival can be
accomplished through stocking or supportive breeding via stream-side rearing. Each of
these practices have been suggested in past lake sturgeon rehabilitation strategies
(Beamesderfer and Farr 1997; Hay-Chmielewski and Whelan 1997). Second,
maintaining lake sturgeon persistence and genetic integrity is dependent upon
maintaining populations which are above the minimum viable population size. Thus, I
recommend that populations should be maintained above 80 to 150 individuals. These
recommendations should help to foster the protection of sustainable lake sturgeon
populations for the future by minimizing extinction risks due to both demographic
stochasticity and inbreeding depression. Also, estimation of MVP should help lake '
sturgeon managers prioritize populations for future rehabilitation efforts, given extinction
risks. For populations below the MVP level, management efforts such as some form of
supplementation may be necessary to overcome demographic stochasticity and maintain
persistence.

Supplementing populations using appropriate genetic guidelines was shown to
increase the retention of unique genes and decrease inbreeding, and achieve target
population sizes with reduced risks of extinction when compared to not supplementing
the population for the scenarios explored. Thus, I recommend supplementing those
populations at high risk of extinction or populations showing sustained decline.

Depending upon the population size and trajectory, different numbers of individuals need

117

 

to be stocked in order to move a population towards rehabilitation. For lake sturgeon
populations less than MVP or on the brink of MVP, relatively few individuals need to be
stocked in order to maintain both positive population trajectories and reduced genetic
impacts. For larger, declining populations, more individuals need to be stocked if a short
management time horizon is used. The number that needs to be stocked in the fall each
year is the recommended stocking number (which accounts for over winter mortality)
divided by the actual over winter survival for the population. For example, if you wanted
to supplement a population below MVP under the pulse scenario, so that the population
size in the long-term was on average 500 individuals, and if the over winter survival was
0.40% (Crossman et al. 2009), then you would need to stock (244/0.40:610) 610
individuals in the fall each year. This strategy should be used when determining how
many to stock to achieve specific population sizes, percent of genes retained, and mean
final inbreeding coefficients. This study provides specific advice on how many to stock
and what genetic guidelines are important, but it is up to the managers to determine goals
and objectives for populations of interest and then take action to meet those goals and
objectives.

If all recommended genetic practices cannot be followed, some recommendations
appear more important than others with respect to maintaining genes and reducing
inbreeding for the scenarios explored. First, if supplementing a larger population,
supplementing over a longer time frame is recommended for the retention of genes over
the long term. Second, capturing the greatest number of adults from the population for
supplementation purposes seems to be the most crucial recommendation for retaining

genes and reducing inbreeding accrual. Third, sex ratio and family size variation have

118

 

smaller effects on the genetics of populations, thus, following these genetic guidelines is
less crucial.
FUTURE RESEARCH

Many research tracks would be useful for enhancing the conservation of lake
sturgeon in the Great Lakes basin. The impacts of dams and value of dam removal, or
the potential impact of food web changes on the diet of lake sturgeon are just a couple of
examples of areas of inquiry that would be valuable. Focusing on topics that emerge
directly from my research, I feel two areas should take priority. For empirical research,
researchers should try to measure inbreeding depression in lake sturgeon, most likely
focusing on YOY mortality or progeny numbers produced. This research would be
important because it will help to estimate the effects of inbreeding depression on long-
terrn population persistence for lake sturgeon. Given the longevity of lake sturgeon and
model results, measuring inbreeding depression in YOY mortality and progeny numbers
would be most feasible because these measurements occur over a relatively short time
period. Also, this research will add greatly to the literature on inbreeding depression in
wild populations for fish species because few studies have addressed inbreeding
depression in wild populations of fish species, especially long-lived species.

Lastly, based on the stocking strategies chapter and using the individual based
model developed, future work could explore outbreeding depression, caused by stocking
individuals from another population. Outbreeding depression is a reduction in fitness due
to the loss of locally adapted gene complexes (Edmands 2007). This research is
important because it will address an important issue with direct management

implications. If outbreeding depression is found to be important, then only fish from the

119

same spawning location or closely related locations should be used for supplementation
purposes. However, if outbreeding depression is not found to be important, then
individuals for supplementation purposes could be obtained from any population of lake
sturgeon. Thus, understanding how outbreeding depression may influence the long-term
dynamics of lake sturgeon populations is important for population persistence, as well as,

determining which populations should provide progeny for supplementation purposes.

120

APPENDIX A

Table A. 1. Sensitivity, S, of percent of extinct populations for each of the parameters for
an initial population size of 50 where R, is the model response for the altered parameter,
R, is the model response for the nominal parameter, Pa is the altered parameter, and P" is
the nominal parameter.

 

 

Parameter Pn Pa Rn Ra S

Young of the year mortality rate 0.47 0.32 34.4 1.2 3.02
0.47 0.35 34.4 3.8 3.48
0.47 0.38 34.4 10.0 3.70
0.47 0.41 34.4 12.8 4.92
0.47 0.44 34.4 19.2 6.92

0.47 0.50 34.4 56.2 9.93
0.47 0.53 34.4 61.6 6.19
0.47 0.56 34.4 74.2 6.04
0.47 0.59 34.4 78.4 5.01
0.47 0.62 34.4 91.4 5.19

 

Mortality rate 0.05 0.035 34.4 0.0 3.33
0.05 0.04 34.4 0.0 5.00
0.05 0.045 34.4 4 2 8.78

0.05 0.055 34.4 84.8 14.65
0.05 0.06 34.4 98.2 9.27
0.05 0.065 34.4 99.2 6.28

 

Age at first maturation for

females 20 14 34.4 3.0 3.04
20 16 34.4 6.8 4.01
20 18 34.4 19.8 4.24
20 22 34.4 49.6 4.42
20 24 34.4 67.2 4.77
20 26 34.4 74.0 3.84

 

Probability of mating for females 0.33 0.231 34.4 91.8 -5 .56
0.33 0.264 34.4 65.8 -4.56
0.33 0.297 34.4 57.2 -6.63
0.33 0.363 34.4 20.4 -4.07

 

0.33 0.396 34.4 6.8 -4.01

0.33 0.429 34.4 2.8 -3.06

Age at first maturation for males 15 11 34.4 20.0 1.57
15 12 34.4 26.4 1.16

15 13 34.4 29.4 1.09

15 14 34.4 32.4 0.87

15 16 34.4 31.4 -1.31

15 17 34.4 42.4 1.74

15 18 34.4 47.0 1.83

15 19 34.4 52.0 1.92

 

121

Table A.1 (cont’d).

 

Probability of mating for males

0.5
0.5
0.5
0.5
0.5
0.5

122

0.35
0.4
0.45
0.55
0.6
0.65

34.4
34.4
34.4
34.4
34.4
34.4

77.8
59.8
41.0
29.4
25.8
20.0

-4.21
-3.69
-1.92
-1.45
-1.25
-1.40

 

Table A2. Sensitivity, S, of average percent of genes retained for each of the parameters
for an initial population size of 200 where Ra is the model response for the altered

parameter, R,2 is the model response for the nominal parameter, Pa is the altered

parameter, and P" is the nominal parameter. NR represents no response because of

computing limitations.

 

 

 

 

 

Parameter ' Pn Pa Rn Ra S
Young of the year mortality rate 0.47 0.33 9.487 19.289 -3.47
0.47 0.36 9.487 17.055 -3.41
0.47 0.39 9.487 15.087 -3.47
0.47 0.42 9.487 12.752 -3.24
0.47 0.45 9.487 10.801 -3.25
0.47 0.48 9.487 8.831 -3 .25
0.47 0.51 9.487 6.996 -3.09
0.47 0.54 9.487 5.451 -2.86
0.47 0.57 9.487 4.019 -2.71
0.47 0.60 9.487 2.621 -2.62
0.47 0.63 9.487 1.819 -2.37
Mortality rate 0.05 0.035 9.487 NR
0.05 0.04 9.487 29.412 -10.50
0.05 0.045 9.487 18.580 -9.58
0.05 0.055 9.487 3.527 -6.28
0.05 0.06 9.487 1.075 -4.43
0.05 0.065 9.487 0.560 -3.14
Age at first maturation for
females 20 14 9.487 22.481 -4.57
20 16 9.487 17.292 -4.11
20 18 9.487 13.071 -3.78
20 22 9.487 6.998 -2.62
20 24 9.487 5.012 -2.36
20 26 9.487 3.598 -2.07
Probability of mating for females 0.33 0.231 9.487 2.135 2.58
0.33 0.264 9.487 3.816 2.99
0.33 0.297 9.487 6.355 3.30
0.33 0.363 9.487 12.961 3.66
0.33 0.396 9.487 16.753 3.83
0.33 0.429 9.487 20.487 3.86

 

123

Table A2 (cont’d).

 

 

Age at first maturation for males 15 11 9.487 9.858 -0.15
15 12 9.487 9.739 -0.13
15 13 9.487 9.660 -0.14
15 14 9.487 9.713 -0.36
15 16 9.487 9.811 0.51
15 17 9.487 9.286 -0.16
15 18 9.487 9.135 -0.19
15 19 9.487 8.8155 -0.27
Probability of mating for males 0.5 0.35 9.487 7.147 0.82
0.5 0.4 9.487 8.405 0.57
0.5 0.45 9.487 9.134 0.37
0.5 0.55 9.487 9.842 0.37
0.5 0.6 9.487 9.635 0.08
0.5 0.65 9.487 9.767 0.10

 

124

 

 

Table A.3. Sensitivity, S, of the percent of increasing populations for each of the
parameters for an initial population size of 200 where Ra is the model response for the
altered parameter, R,, is the model response for the nominal parameter, Pa is the altered
parameter, and P" is the nominal parameter. NR represents no response because of
computing limitations.

 

Parameter Pn Pa Rn Ra S
Young of the year mortality rate 0.47 0.33 46.2 99.8 -3.89
0.47 0.36 46.2 100 4.98

0.47 0.39 46.2 99.2 -6.74
0.47 0.42 46.2 93.8 -9.68
0.47 0.45 46.2 67.8 -10.99
0.47 0.48 46.2 30.8 -15.67

 

 

 

0.47 0.51 46.2 8.8 -9.51
0.47 0.54 46.2 0.8 -6.60
0.47 0.57 46.2 0 -4.70
0.47 0.60 46.2 0 -3.62
0.47 0.63 46.2 0 -2.94
Mortality rate 0.05 0.035 46.2 NA
0.05 0.04 46.2 100 -5.82
0.05 0.045 46.2 100 -11.65
0.05 0.055 46.2 0 -10.00
0.05 0.06 46.2 0 -5.00
0.05 0.065 46.2 0 -3.33
Age at first maturation for
females 20 14 46.2 100 -3.88
20 16 46.2 99.8 -5.80
20 18 46.2 95 -10.56
20 22 46.2 5 -8.92
20 24 46.2 0.2 -4.98
20 26 46.2 0 -3.33
Probability of mating for females 0.33 0.231 46.2 0 3.33
0.33 0.264 46.2 0 5.00

0.33 0.297 46.2 2.2 9.52
0.33 0.363 46.2 94.8 10.52
0.33 0.396 46.2 99.8 5.80

 

0.33 0.429 46.2 100 3.88

Age at first maturation for males 15 11 46.2 50.6 -0.36
15 12 46.2 51.4 -0.56

15 13 46.2 52 -0.94

15 14 46.2 48.4 -0.71

15 16 46.2 47.4 0.39

15 17 46.2 38.4 -1.27

15 18 46.2 34.8 -1.23

15 19 46.2 28.2 -1.46

 

125

Table A3 (cont’d).
Probability of mating for males

0.5
0.5
0.5
0.5
0.5
0.5

126

0.35
0.4
0.45
0.55
0.6
0.65

46.2
46.2
46.2
46.2
46.2
46.2

7.4
23.6
35.8
50.8
47.4

51

2.80
2.45
2.25
1.00
0.13
0.35

 

Table A.4. Sensitivity, S, of the final mean inbreeding for each of the parameters for an
initial population size of 200 where Ra is the model response for the altered parameter, Rn
is the model response for the nominal parameter, Pa is the altered parameter, and P" is the
nominal parameter. NR represents no response because of computing limitations.

 

 

 

 

 

 

Parameter Pn Pa Rn Ra S
Young of the year mortality rate 0.47 0.33 0.0413 0.0220 1.57
0.47 0.36 0.0413 0.0241 1.78
0.47 0.39 0.0413 0.0262 2.15
0.47 0.42 0.0413 0.0309 2.37
0.47 0.45 0.0413 0.0359 3.07
0.47 0.48 0.0413 0.0407 -0.68
0.47 0.51 0.0413 0.0490 2.19
0.47 0.54 0.0413 0.0570 2.55
0.47 0.57 0.0413 0.0683 3.07
0.47 0.60 0.0413 0.0816 3.53
0.47 0.63 0.0413 0.0939 3.74
Mortality rate 0.05 0.035 0.0413 NR
0.05 0.04 0.0413 0.0147 3.22
0.05 0.045 0.0413 0.0223 4.60
0.05 0.055 0.0413 0.0724 7.53
0.05 0.06 0.0413 0.1670 15.22
0.05 0.065 0.0413 NR
Age at first maturation for
females 20 14 0.0413 0.0196 1.75
20 16 0.0413 0.0247 2.01
20 18 0.0413 0.0312 2.45
20 22 0.0413 0.0476 1.53
20 24 0.0413 0.0594 2.19
20 26 0.0413 0.0664 2.03
Probability of mating for females 0.33 0.231 0.0413 0.0942 -4.27
0.33 0.264 0.0413 0.0722 -3.74
0.33 0.297 0.0413 0.0505 -2.23
0.33 0.363 0.0413 0.0302 -2.69
0.33 0.396 0.0413 0.0246 -2.02
0.33 0.429 0.0413 0.0208 -l.65
Age at first maturation for males 15 11 0.0413 0.0392 0.19
15 12 0.0413 0.0395 0.22
15 13 0.0413 0.0389 0.44
15 14 0.0413 0.0382 1.13
15 16 0.0413 0.0387 -0.94
15 17 0.0413 0.0397 -0.29
15 18 0.0413 0.0394 -0.23
15 19 0.0413 0.0405 -0.07

 

127

Table A.4 (cont’d).

 

Probability of mating for males

0.5
0.5
0.5
0.5
0.5
0.5

128

0.35
0.4
0.45
0.55
0.6
0.65

0.0413
0.0413
0.0413
0.0413
0.0413
0.0413

0.0491
0.0409
0.0395
0.0385
0.03 89
0.0383

-0.63
0.05
0.44
-0.68
-0.29
-0.24

 

Table A5. Sensitivity, S, of average percent of genes retained for each of the parameters
for an initial population size of 50 where Ra is the model response for the altered
parameter, R" is the model response for the nominal parameter, Pa is the altered

gameter, and P,, is the nominal parameter.

 

 

 

 

 

 

Parameter Pn Pa Rn Ra S
Juvenile mortality rate 0.47 0.32 4.638 17.052 -8.39
0.47 0.35 4.638 13.626 -7.59
0.47 0.38 4.638 10.964 -7.12
0.47 0.41 4.638 8.824 -7.07
0.47 0.44 4.638 6.860 -7.51
0.47 0.50 4.638 2.182 -8.30
0.47 0.53 4.638 1.810 -4.78
0.47 0.56 4.638 0.734 -4.40
0.47 0.59 4.638 0.726 -3.30
0.47 0.62 4.638 0.190 -3.00
Adult mortality rate 0.05 0.035 4.638 40.152 -25.52
0.05 0.04 4.638 28.088 -25.28
0.05 0.045 4.638 14.974 -22.29
0.05 0.055 4.638 0.532 -8.85
0.05 0.06 4.638 0.036 -4.96
0.05 0.065 4.638 0.016 -3.32
Age at first maturation for
females 20 14 4.638 16.20 -8.31
20 16 4.638 12.036 -7.98
20 18 4.638 7.364 -5.88
20 22 4.638 2.822 -3.92
20 24 4.638 1.324 -3.57
20 26 4.638 0.834 -2.73
Probability of mating for females 0.33 0.231 4.638 0.228 3.17
0.33 0.264 4.638 1.254 3.65
0.33 0.297 4.638 2.120 5.43
0.33 0.363 4.638 7.516 6.21
0.33 0.396 4.638 11.506 7.40
0.33 0.429 4.638 15.228 7.61
Age at first maturation for males 15 11 4.638 6.490 -1.50
15 12 4.638 6.162 -1.64
15 13 4.638 5.686 -1.69
15 14 4.638 5.080 -1.43
15 16 4.638 4.520 -0.38
15 17 4.638 3.628 -1 .63
15 18 4.638 3.172 -1.58
15 19 4.638 2.140 -2.02

 

129

Table A5 (cont’d).

 

Probability of mating for males

0.5
0.5
0.5
0.5
0.5
0.5

130

0.35
0.4
0.45
0.55
0.6
0.65

4.638
4.638
4.638
4.638
4.638
4.638

0.660
1.746
3.168
5.196
6.248
7.342

2.86
3.12
3.17
1.20
1.74
1.94

 

Table A6. Sensitivity, S, of the percent of increasing populations for each of the

parameters for an initial population size of 50 where Ra is the model response for the
altered parameter, Rn is the model response for the nominal parameter, Pa is the altered
parameter, and P,, is the nominal parameter.

 

 

 

 

 

 

Parameter Pn Pa Rn Ra S
Young of the year mortality rate 0.47 0.32 9.2 87 -26.50
0.47 0.35 9.2 71 -26.31
0.47 0.38 9.2 59.2 -28.38
0.47 0.41 9.2 40.8 -26.91
0.47 0.44 9.2 22.2 -22.14
0.47 0.50 9.2 2.2 -11.92
0.47 0.53 9.2 1.2 -6.81
0.47 0.56 9.2 0 -5.22
0.47 0.59 9.2 0 -3.92
0.47 0.62 9.2 0 -3.13
Mortality rate 0.05 0.035 9.2 100 -32.90
0.05 0.04 9.2 99.2 -48.91
0.05 0.045 9.2 76.2 -72.83
0.05 0.055 9.2 0 -10.00
0.05 0.06 9.2 0 -5.00
0.05 0.065 9.2 0 -3.33
Age at first maturation for
females 20 14 9.2 86.2 -27.90
20 16 9.2 66.0 -30.87
20 18 9.2 29.4 -21.96
20 22 9.2 2.2 -7.61
20 24 9.2 0.4 -4.78
20 26 9.2 0 -3.33
Probability of mating for females 0.33 0.231 9.2 0.0 3.33
0.33 0.264 9.2 0.4 4.78
0.33 0.297 9.2 2.0 7.83
0.33 0.363 9.2 29.0 21.52
0.33 0.396 9.2 57.6 26.30
0.33 0.429 9.2 79.4 25.43
Age at first maturation for males 15 11 9.2 21.8 —5. 14
15 12 9.2 19.2 -5.43
15 13 9.2 18.6 -7.66
15 14 9.2 13.4 -6.85
15 16 9.2 8.0 -1.96
15 17 9.2 4.4 -3.91
15 18 9.2 3.6 -3.04
15 19 9.2 1.6 -3.10

 

131

 

Table A6 (cont’dL

 

Probability of mating for males

0.5
0.5
0.5
0.5
0.5
0.5

132

0.35
0.4
0.45
0.55
0.6
0.65

9.2
9.2
9.2
9.2
9.2
9.2

1.4
4.4
12.4
20.0

26

3.33
4.24
5.22
3.48
5.87
6.09

 

Table A.7. Sensitivity, S, of the final mean inbreeding for each of the parameters for an
initial population size of 50 where Ra is the model response for the altered parameter, R,
is the model response for the nominal parameter, Pa is the altered parameter, and P" is the
nominal parameter. NR indicates no response because none of the populations persisted
long enough to determine a final mean inbreeding.

 

 

 

 

 

Parameter Pn Pa Rn Ra S
Young of the year mortality rate 0.47 0.32 0.1388 0.0845 1.23
0.47 0.35 0.1388 0.0960 1.21
0.47 0.38 0.1388 0.1072 1.19
0.47 0.41 0.1388 0.1124 1.49
0.47 0.44 0.1388 0.1277 1.25
0.47 0.50 0.1388 0.1547 1.79
0.47 0.53 0.1388 0.1707 1.80
0.47 0.56 0.1388 0.1236 -0.57
0.47 0.59 0.1388 0.2038 1.83
0.47 0.62 0.1388 0.1643 0.58
Mortality rate 0.05 0.035 0.1388 0.0427 2.31
0.05 0.04 0.1388 0.0586 2.89
0.05 0.045 0.1388 0.0921 3.36
0.05 0.055 0.1388 0.1996 4.38
0.05 0.06 0.1388 0.7083 20.52
0.05 0.065 0.1388 NR
Age at first maturation for
females 20 14 0.1388 0.0868 1.25
20 16 0.1388 0.1018 1.33
20 18 0.1388 0.1181 1.49
20 22 0.1388 0.1825 3.15
20 24 0.1388 0.1906 1.87
20 26 0.1388 0.1619 0.55
Probability of mating for females 0.33 0.231 0.1388 0.167 -0.68
0.33 0.264 0.1388 0.2023 -2.29
0.33 0.297 0.1388 0.1667 -2.01
0.33 0.363 0.1388 0.1094 -2.12
0.33 0.396 0.1388 0.1008 -1.37
0.33 0.429 0.1388 0.0896 -1.18

 

133

Table A.7 (cont’d).

 

 

Age at first maturation for males 15 11 0.1388 0.1362 0.07
15 12 0.1388 0.1398 -0.04

15 13 0.1388 0.1331 0.31

15 14 0.1388 0.1466 -0.84

15 16 0.1388 0.1458 0.76

15 17 0.1388 0.1279 -0.59

15 18 0.1388 0.1377 -0.04

15 19 0.1388 0.1535 0.40

Probability of mating for males 0.5 0.35 0.1388 0.1770 -0.92
0.5 0.4 0.1388 0.1597 -0.75

0.5 0.45 0.1388 0.1341 0.34

0.5 0.55 0.1388 0.1378 -0.07

0.5 0.6 0.1388 0.1269 -0.43

0.5 0.65 0.1388 0.1226 -0.39

 

134

 

 

 

 

 

3’ —"

a; 2 -

I:

'5 —

a

Q M
m I I fi- - -

-004 -003 '002 '00] 001 002 003 004

 

 

 

'8 ‘ YOY mortality

Mortality
Age of female maturation
-10 - .
— ' Female mating prob.

' ' Age of male maturation
_12 . Male mating prob.

 

 

 

 

Percent parameter change

Figure A. 1. Percent change in parameter versus sensitivity, S, for average percent of
genes retained for lake sturgeon with an initial population size of 200.

135

 

 

 

I
P
A

Sensitivity

 

 

YOY mortality
—"Mortality

Age of female maturation \
— Female mating probability
Age of male maturation

- - Male mating probability

 

 

 

 

-30 J
Percent parameter change

Figure A.2. Percent change in parameter versus sensitivity, S, for percent of increasing
populations for lake sturgeon with an initial population size of 200.

136

 

YOY mortality 15 ..
Mortality

Age of female maturation
— ' Female mating prob.

Age of male maturation
" ' Male mating prob.

 

 

  
  

 

 

Sensrtrvrty
I

 

 

 

-0.4 -0.2 , ’ f . 0.2 - - 04
.._. / / ' /
-5-
/
/
-10.
-15.

Percent parameter change

Figure A.3. Percent change in parameter versus sensitivity, S, for final mean inbreeding
for lake sturgeon with an initial population size of 200.

137

 

15-

 

5. —

fl ‘-
I I I W (7(SL.__I I

 

 

 

 

 

41.4 -0.3 _-. -0.2 " -0.1 ‘5', — - 0.1 - 0.2 "' 0.3 0.4
\ \ T
\ l
l
9 45‘ .'
m I
5 -25 « -
U) I
l
I
'35 T '
YOY mortality ,'
Mortality

 

—Age of female maturation .45 -
— " Female mating prob.
—Age of male maturation
' ' ' Male mating prob.

 

-55 -
Percent parameter change

Figure A.4. Percent change in parameter versus sensitivity, S, for percent of extinct
populations for lake sturgeon with an initial population size of 50.

138

 

YOY mortality

 

 

Mortality 30 -
Age of female maturation ‘
— - Female mating probability
— e of nude maturation ‘
' - ' ale mating probability ‘
20 a I
I
\
g“ i
>
:2 10' ‘.
m — — —
5 ’ ——' ’— ‘/
m

“fir-I...

I I r I i T: I ~ I I
-0.4 -0.3 -0.2 -0.1 Y; _—_- 0.2 I}: 0.3 0.4

-10

 

 

I

_/ -20

.30 .
Percent parameter change

 

Figure A.5. Percent change in parameter versus sensitivity, S, for average percent of
genes retained for lake sturgeon with an initial population size of 50.

139

Sensitivity
3° .
£

45- I

25-

-75 .

|
|

I‘/-_—-—
/‘ _

l

 

\ . -
"Pf—4C" ____I __I -
2

1 "' 0.3 0.4

-0.

0.

45.7

 

YOY mortality

— Mortality

Age of female maturation
— ' Female mating prob.
Age of male maturation
Male mating prob.

 

 

 

Percent parameter change

Figure A.6. Percent change in parameter versus sensitivity, S, for percent of increasing
populations for lake sturgeon with an initial population size of 50.

140

 

——YOY mortality 25
Mortality T

—Age of fimale maturation

— ' Fe male mating prob.

' ' 'Age of male maturation 20 q

— Male mating prob.

15'

10'

ivi

t

- Sensi
h

 

0.1

b
a.
b
u
5
N
l
.5
I
e
N
e
u
c
:5

\-5‘ /
\/

-10 J

 

Percent parameter change

Figure A.7. Percent change in parameter versus sensitivity, S, for final mean inbreeding
for lake sturgeon with an initial population size of 50.

141

APPENDIX B

Table B. 1. Baseline population parameter values for each of the three plausible scenarios
explored. All under scenario means that the parameter value was used for all three
scenarios.

 

 

Parameter Scenario Value
Age at first reproduction (male) All 15
Age at first reproduction (female) All 20
Post YOY mortality All 0.05
Probability of spawning each year (male) All 0.5
Probability of spawning each year (female) All 0.33
YOY mortality Less than MVP 0.47
Brink of MVP 0.45
Large, declining 0.67

 

142

I Model

0.3 . Cl Empirical

Frequency
.6 E .= 5
'- ’JI N ’JI

P

a

'JI
4

 

 

 

l 2 3 4 5 6 7 8 91011121314

Number of batches
Figure B. 1. The frequency of the number of batches, B, randomly assigned to males and
females in the model using a random uniform distribution and the

equation B = 1 + integer(-2 *ln(1- U(O,l)). The frequency of number of mates per
individual from empirical data from DeHaan (2003).

143

.3
’.h

0.45

I Model
0.4

D Empirical

Frequency

 

0 l 2 3 4 5 6 7 8 9 1011121314151617181920212223
Number of progeny

Figure B2. The frequency of the number of progeny for an individual male or female
from the model and from empirical data (DeHaan 2003).

144

Mean final population size M939 final POPUMiOfl Size

Mean final population size

W .5 U 05
O O O O
C) O O O
J l I I

200 1

 

._.n
O
C) O
1

O

600 -
500 '
400 -
300 ‘

N

C)

O
l

 

a...
O
O

U W T Y 7 U

200 400 600 800 1,000 1,200

 

O

600 a

M

O

O
n

W b
O O
O O
1 n

200 a
100 .

200 400 600 800

 

 

O

U I ‘I

5,000 10,000 15,000
Number Stocked

Figure B3. The number of individuals that need to be stocked using the trickle strategy
in order to attain a mean final population size for each scenario as determined by
interpolation using a linear function where a) less than MVP, b) brink of MVP, and c)

large,

declining.

145

0.6 '
0.5 ' I
0.4
0.3
0.2
0.1 ' I

0.0 .P

0 200 400 600 800 1,000

 

Mean percent of genes retained
I

_o 9
U1 0‘
I I
o

p
w
1

ent of genes retained
p o
m A

 

en:
99
QI—I
H

q
G
q
a

Mean p
O

500 1,000 1,500

0.6 -
0.5 . A
0.4 -
0.3 .
0.2 -
0.1 . A

0.0 I f I I I
0 5,000 10,000 15,000 20,000 25,000

Number Stocked

 

 

Mean percent of genes retained
D

Figure B4. The number of individuals that need to be stocked using the trickle strategy
in order to attain a mean percent of genes retained for each scenario as determined by
interpolation using a power function where a) less than MVP, b) brink of MVP, and c)

large, declining.

146

Mean final inbreeding

Mean final inbreeding

Mean final inbreeding

0.14
0.12 :L
0.10 -
0.08 r
0.06 ‘
0.04 '
0.02 -

 

 

0.00

0.08
0.07
0.06
0.05
0.04 r
0.03 ‘
0.02 .
0.01 ‘

 

I I I

800 1,000 1,200

I I I

200 400 600

 

0.00

0.14
0.12
0.10
0.08
0.06 t
0.04 ‘
0.02 "

 

I I I I I I

500 1,000 1,500 2,000 2,500 3,000

A
A

 

0.00
0

I I I I I

2.000 4,000 6,000 8,000 10,000
Number Stocked

Figure B5. The number of individuals that need to be stocked using the trickle strategy
in order to attain a mean final inbreeding level for each scenario as determined by
interpolation using a Weibull function where a) less than MVP, b) brink of MVP, and 0)

large, declining.

147

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