Modeling the Effects of Mortality on Sea Otter Populations 

Scientific Investigations Report 2010–5096

U.S. Department of the Interior

U.S. Geological Survey

Modeling the Effects of Mortality on 

Sea Otter Populations

By James L. Bodkin and Brenda E. Ballachey

Scientific Investigations Report 2010–5096

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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Suggested citation:

Bodkin, J.L., and Ballachey, B.E., 2010, Modeling the effects of mortality on sea otter populations: U.S. Geological 

Survey Scientific Investigations Report 2010–5096, 12 p.
iii

Contents

Abstract ..........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Methods...........................................................................................................................................................2

Results .............................................................................................................................................................4

Population Growth Rates ....................................................................................................................4

Additional Mortality..............................................................................................................................4

Maximum Sustainable Harvests ........................................................................................................5

Effects of Rates of Polygyny ...............................................................................................................8

Discussion ......................................................................................................................................................8

Assumptions ..........................................................................................................................................8

Spatial Considerations.........................................................................................................................9

Summary........................................................................................................................................................10

Acknowledgments.......................................................................................................................................10

References Cited..........................................................................................................................................10

Figures

Figure 1. Graph showing population trajectories over 20 years for sea otter 

populations exhibiting stable, moderate, and rapid rates of change 

using empirical estimates of age and sex specific reproduction and survival ...... 5

Figure 2. Graphs showing effects of additional sex and age specific mortality 

(removals) on rates of change in sea otter populations that are stable, 

increasing moderately, and increasing rapidly .......................................... 6

Figure 3. Graphs showing maximum annual sustainable rates of harvest for sea otter 

populations experiencing stable, moderate, and rapid growth, and maximum 

sustainable average annual harvest number for male only, and male to female 

ratios of 3:1 and 1:1. ........................................................................ 7

Tables

Table 1. Vital rates of sea otters used to generate population models representing 

stable (λ = 1.005), moderate (λ = 1.072), and rapid (λ = 1.145) rates of change ...... 3
iv

Conversion Factors and Acronyms

Conversion Factors

Multiply By To obtain

square kilometer (km2) 0.3861 square mile (mi2)

Acronyms

USGS United States Geological Survey

USFWS United States Fish and Wildlife Service

MMM Marine Mammals Management

MMPA Marine Mammals Protection Act
Modeling the Effects of Mortality on Sea Otter Populations

By James L. Bodkin and Brenda E. Ballachey

Abstract 

Conservation and management of sea otters can benefit 

from managing the magnitude and sex composition of human 

related mortality, including harvesting within sustainable 

levels. Using age and sex-specific reproduction and survival 

rates from field studies, we created matrix population models 

representing sea otter populations with growth rates of 1.005, 

1.072, and 1.145, corresponding to stable, moderate, and rapid 

rates of change. In each modeled population, we incrementally 

imposed additional annual mortality over a 20-year period 

and calculated average annual rates of change (λ). Additional 

mortality was applied to (1) males only, (2) at a 1:1 ratio 

of male to female, and (3) at a 3:1 ratio of male to female. 

Dependent pups (age 0–0.5) were excluded from the mortality. 

Maintaining a stable or slightly increasing population was 

largely dependent on (1) the magnitude of additional mortality, 

(2) the underlying rate of change in the population during 

the period of additional mortality, and (3) the extent that 

females were included in the additional mortality (due to a 

polygnous reproductive system where one male may breed 

with more than one female). In stable populations, additional 

mortality as high as 2.4 percent was sustainable if limited to 

males only, but was reduced to 1.2 percent when males and 

females were removed at ratios of 3:1 or 0.5 percent at ratios 

of 1:1. In moderate growth populations, additional mortality 

of 9.8 percent (male-only) and 15.0 percent (3:1 male 

to female) maximized the sustainable mortality about 

3–10 ten‐fold over the stable population levels. However, if 

additional mortality consists of males and females at equal 

proportions, the sustainable rate is 7.7 percent. In rapid growth 

populations, maximum sustainable levels of mortality as high 

as 27.3 percent were achieved when the ratio of additional 

mortality was 3:1 male to female. Although male-only 

mortality maximized annual harvest in stable populations, 

high male biased mortality in all simulations eventually led to 

low proportions of males, leading to instability in projected 

populations over time. Our findings identify the critical need 

to understand underlying rates of change that can be acquired 

only through frequent monitoring of managed populations. 

Models could be improved through better understanding of 

the effects of density and demographic and environmental 

stochasticity on sea otter vital rates. Although our primary 

objective was to provide information useful in managing 

harvests of sea otters, our findings have implications for 

the conservation and management of sea otter populations 

subjected to other sources of mortality that can be quantified, 

such as incidental, accidental, or illegal. 

Introduction

Sea otter (Enhydra lutris) populations in the North 

Pacific have experienced numerous large-scale fluctuations 

in abundance that date to prehistoric times. Periods of high 

and low abundance of sea otter remains in midden sites in 

the Aleutian archipelago suggest that harvests by indigenous 

peoples may have been responsible for reduced abundances 

that extended for centuries (Simenstad and others, 1978). 

Beginning in the 18th century with the large-scale commercial 

harvest for pelts, sea otters were systematically extirpated 

from most of their range from eastern Asia to northern Mexico 

(Lensink, 1962; Kenyon, 1969) despite an average annual 

harvest rate of less than 2 percent (Gorbics and Bodkin, 

2001). These harvests continued until late in the 19th century 

when as few as 13 separate populations, mostly in Alaska and 

numbering in total perhaps a few hundred individuals, were 

all that remained. In 1911, the International Fur Seal Treaty 

provided sea otters with protection from further commercial 

harvest, signaling the process of recovery that continued 

unabated until late in the 20th century, when growth rates 

again diminished in several populations. 

Remnant sea otter populations generally increased in 

numbers and expanded their range in Russia, Alaska, and 

California, with long-term annual rates of recovery ranging 

from about 5 to 13 percent (Bodkin and others, 1999). In the 

1970s, sea otters were successfully reintroduced in Southeast 

Alaska, Washington, and British Columbia (Jameson and 

others, 1982) and annual population growth rates among 

translocated populations ranged from 18 to 24 percent (Bodkin 

and others, 1999). Current rates of change in translocated 

populations range from 4.7 percent in Southeast Alaska to 

12.4 percent in British Columbia (Nichol and others, 2005; 

Esslinger and Bodkin, 2009; Laidre and others, 2009). The 

causes of the reduced population growth rates in Washington, 

Southeast Alaska, and British Columbia are largely unknown, 

but suitable unoccupied habitat remains in all areas.
2 Modeling the Effects of Mortality on Sea Otter Populations

More recently, three instances of decline have been well 

documented, all resulting from elevated mortality. In at least 

two instances, and possibly all three, declines can be linked to 

human activities. Beginning in the late 1970s, the California 

population entered a period of decline for several years, with 

elevated mortality incidental to fisheries impeding recovery 

until management actions were implemented (Wendell and 

others, 1986; Estes and others, 2003). In 1989, a large oil 

spill in Prince William Sound, Alaska, reduced the sea otter 

population by as many as several thousand animals (Garrott 

and others, 1993), with recovery delayed for at least 12 years 

(Ballachey and others, 1994; Bodkin and others, 2002). In 

the Aleutian Archipelago, following recovery to near pre-fur 

trade abundances, sea otter populations once again declined 

precipitously late in the 20th century, resulting from elevated 

mortality induced by killer whale (Orcinus orca) predation 

(Estes and others, 1998). This decline was potentially an 

indirect consequence of commercial whaling in the North 

Pacific during the 20th century, causing a shift in killer whale 

diet that eventually led to predation on sea otters (Springer and 

others, 2003). 

Harvest of sea otters by native Alaskans resumed over the 

past few decades under provision from the Marine Mammal 

Protection Act of 1972. Although the harvest is monitored 

by the U.S. Fish and Wildlife Service (Marine Mammals 

Management, Anchorage, Alaska) in terms of age and sex, the 

harvest is largely unregulated and the effects on population 

abundance have not been quantified. Additionally, an illegal 

take of unknown magnitude occurs over potential fisheries 

conflicts and for pelts throughout much of the species range 

(Bodkin, 2003).

Largely as a result of efforts to conserve and aid in the 

recovery of the species, extensive research has been conducted 

on sea otters over the past several decades (Riedman and 

Estes, 1990; Estes and Bodkin, 2002; Bodkin, 2003). 

Much of this research has focused on estimating vital rates 

(reproduction and survival) (Tinker and others, 2006). Studies 

have been conducted across a range of populations varying 

in status and trend (that is, near or below equilibrium density, 

and stable or increasing), providing empirical estimates of age 

and sex specific reproduction and survival rates suitable for 

constructing demographic models. Such models are amenable 

to exploring the effects of changing mortality or reproductive 

rates on population trajectories. 

Samuel and Foin (1983), using demographic model 

simulations, provide the only published information on 

levels of sustainable harvest, identifying harvest rates of 

less than 6 percent as sustainable, assuming that the targeted 

population was increasing at 14 percent annually. However, 

as they acknowledge, their models were limited by a lack 

of reliable data on critical life history attributes, such as age 

at first reproduction, and age and sex specific reproductive 

and survival rates. Additional demographic data, available 

from studies across the range of the sea otter, provide an 

opportunity to develop improved demographic models for 

sea otters. The reduced growth rates noted in several sea otter 

populations and the sea otter harvest in Alaska provide an 

impetus for development of models examining mortality. 

Our objectives in this work were to: (1) construct 

population models using empirically derived estimates of 

age and sex-specific sea otter reproduction and survival, 

representing a range of population growth rates, (2) evaluate 

the effects of imposing additional male and female mortality 

on population trajectories, and (3) provide information useful 

for developing sustainable sea otter harvest or mortality 

management strategies. Although these population models 

were developed primarily to understand potential effects of 

harvest by humans on sea otter populations (generally referred 

to as harvest mortality in this report), the simulations are 

independent of causes of mortality and thus broadly applicable 

to conservation and management of sea otters. 

Methods

We obtained age and sex-specific reproductive and 

survival values for sea otters in Alaska from the published 

literature to generate three population models (table 1). In 

the first model, we used estimates of age and sex-specific 

reproduction and survival from populations that were at 

or near presumed equilibrium density (that is, stable). In 

the second, we used comparable vital rates estimated from 

populations that were rapidly increasing and presumed to 

be below equilibrium density (that is, rapid growth). When 

more than one estimate was available in the literature for any 

sex/age class, the lesser value was used for the equilibrium 

(stable) model, and the greater value was used for the 

rapidly increasing population (rapid growth) model. For 

the third model, vital rates from the rapid growth model 

were uniformly decreased for each age class to generate a 

population exhibiting a growth rate approximately midway 

between the stable and rapid growth rates (that is, moderate 

growth). Twenty-one age classes were used for each sex, 

with dependent pups aged 0–0.5 years and juveniles 0.5–1.5 

and 1.5–2 years. In all models, age classes greater than age 2 

represent 1 year each. We assumed that the sex ratio at birth 

was 1:1, females give birth to a single offspring, and the 

reproductive interval is 1 year. All models incorporated a 

polygynous reproductive system with each male potentially 

mating with as many as 10 females at each annual time step. 

Reproductive rates in the stable population for ages 2–4 

were from Prince William Sound (Bodkin and others, 1993), 

and ages 5–17 from Udevitz and others (1996) (reproduction 

was limited to these ages). Survival rates for dependent pups 

were from Amchitka Island (Monson and others, 2000), for 

ages 0.5–1.5 from Prince William Sound (Ballachey and 

others, 2003), and for ages 1.5–2 were the mean of ages 

0.5–1.5 and 2–3, adjusted for 6 months. Female survival rates 

for ages 2–20 were from Udevitz and Ballachey (1998) and 

male survival rates for ages 2–20 were from Udevitz and 

others (1996). All vital rates from Prince William Sound were 

independent of 1989 oil spill effects.
Methods 3

Primary differences in the vital rates we used in the 

three population models include reduced reproduction in 

young and aged females, and reduced survival in the young 

(<2 years) and aged (>15 years for females, >16 years 

for males) of both sexes in the stable model, compared to 

the rapid growth model. In comparison, the reproductive 

rates of prime age adults, and survival of females (ages 

2–11) and most males (ages 2–17) were relatively similar 

across models. Reproductive rates were lowest in the stable 

model particularly among individuals less than 8 years old, 

but were similar among females aged 9–16 years in each 

model, averaging 0.91 (table 1). In the stable model, female 

reproductive senescence began at age 17 and females did not 

reproduce after that age. In the stable model, survival rates of 

young females were 0.36 (age 0.5) and 0.15 (age 1.5) less than 

survival rates in the rapid growth model. Survival of females 

in the stable model declined steadily from ages 12 to 19, 

whereas female survival remained high in the moderate and 

rapid growth populations (0.90 and 0.96, respectively; table 1). 

Male survival rates in the first two age classes were 0.36 and 

0.375 less in the stable population than in the rapid growth 

population, but after age 2, male survival rates remained 

uniformly high until late in life (table 1). 

Table 1. Vital rates of sea otters used to generate population models representing stable (λ = 1.005), 

moderate (λ = 1.072), and rapid (λ = 1.145) rates of change.

[Reproductive rate: R, survival rate; S, stable and rapid growth rates were obtained from published values and the moderate 

rates represent the rapid growth rates reduced by 0.065. Age class: pups = 0–0.5 years, juveniles = 0.5–2.0 years. Stable rates 

from Bodkin and others (1993), Udevitz and others (1996, 1998), Monson and others (2000), and Ballachey and others (2003). 

Survival rates for rapid growth reduced by 0.065 and fecundity held stable, to achieve moderate growth (λ = 1.072). Rates for 

rapid growth from Bodkin and others (1993), Monson and DeGange (1995), Monson and others (2000), and Ballachey and 

others (2003)]

Age class

(years)

Growth rate

Stable Moderate Rapid

R Female (S) Male (S) R Female (S) Male (S) R Female (S) Male (S)

0–0.5 0.00 0.47 0.47 0.00 0.77 0.77 0.00 0.83 0.83

0.5–1.5 0.00 0.75 0.53 0.00 0.84 0.84 0.00 0.9 0.9

1.5–2 0.00 0.91 0.85 0.00 0.9 0.85 0.00 0.96 0.91

2–3 0.22 0.92 0.86 0.35 0.9 0.85 0.37 0.96 0.91

3–4 0.64 0.92 0.86 0.60 0.9 0.85 0.64 0.96 0.91

4–5 0.6 1.00 0.86 0.68 0.9 0.85 0.73 0.96 0.91

5–6 0.73 1.00 0.86 0.94 0.9 0.85 1.00 0.96 0.91

6–7 0.81 1.00 0.86 0.88 0.9 0.85 0.94 0.96 0.91

7–8 0.85 1.00 0.86 0.88 0.9 0.85 0.94 0.96 0.91

8–9 0.87 1.00 0.86 0.88 0.9 0.85 0.94 0.96 0.91

9–10 0.89 0.81 0.86 0.88 0.9 0.85 0.94 0.96 0.91

10–11 0.9 0.81 0.86 0.88 0.9 0.85 0.94 0.96 0.91

11–12 0.9 0.81 0.86 0.88 0.9 0.85 0.94 0.96 0.91

12–13 0.9 0.81 0.86 0.88 0.9 0.85 0.94 0.96 0.91

13–14 0.91 0.81 0.86 0.88 0.9 0.85 0.94 0.96 0.91

14–15 0.91 0.81 0.86 0.88 0.9 0.85 0.94 0.96 0.91

15–16 0.91 0.81 0.86 0.88 0.9 0.85 0.94 0.96 0.91

16–17 0.6 0.00 0.86 0.88 0.9 0.85 0.94 0.96 0.91

17–18 0.00 0.00 0.00 0.88 0.9 0.85 0.94 0.96 0.91

18–19 0.00 0.00 0.00 0.88 0.9 0.85 0.94 0.96 0.91

19–20 0.00 0.00 0.00 0.88 0.00 0.00 0.94 0.00 0.00
4 Modeling the Effects of Mortality on Sea Otter Populations

Each of the three population models was initialized 

with the vital rates as described above and with an assumed 

population size of 1,000 individuals with a stable age 

distribution. We used published estimates of variance for 

vital rates when available and assumed standard deviations 

of 0.10 of the mean when estimates were not available to 

generate different sets of vital rates for each simulation. Each 

model simulation was replicated 500 times to estimate growth 

rates without imposing any additional mortality. Density 

dependence and demographic and environmental stochasticity 

were not included in the simulations. The initial simulations 

provided average annual rates of change over 20 years for the 

three population models (stable, moderate, and rapid growth). 

We next imposed additional incremental mortality to 

simulate a hypothetical harvest that varied with respect to 

sex ratio. We considered harvests that were (1) male only, 

(2) 1:1 ratio of male to female and (3) 3:1 ratio of male to 

female. Additional mortality was imposed as a proportion of 

individuals in each age class with the exception of dependent 

pups (ages 0–0.5), which were excluded. Mortality rates were 

incrementally increased from values that allowed for positive 

growth until growth rates turned negative (λ < 1.00). For each 

level of additional mortality, we calculated the average annual 

rate of change in the population (λ), the average annual harvest 

over 20 years (reported as the proportion of all non-pups in 

the population), the harvest number at year 20, the ending 

population size, and the proportion of males in the population 

after 20 years. The average annual harvest rate was calculated 

as the sum of all animals harvested in a year divided by the 

total number of non-pup individuals in the population for 

that year and averaged over the 20 years of simulations. For 

example, a male only harvest rate of 10 percent applied to all 

non-pup male age classes in a total population of 1,000 would 

equate to the removal of 31 males in 1 year, or 3.1 percent 

of the total population. This annual harvest rate was then 

averaged over 20 years and then divided by the proportion of 

non-pups in the population in year 20. For example, assuming 

an average annual harvest of 3.1 percent and non‐pups account 

for 77 percent of this total population, this would equate 

to a corrected average annual harvest rate of 4.03 percent 

(3.1/0.77). To calculate maximum sustainable harvest levels 

for each population, we required that the mean and final 

harvest number were approximately equal, the population size 

in year 20 ≥ 1000, and the average annual rate of change (λ) 

was > 1.00. To evaluate the effect of the assumed degree of 

polygyny (1:10 ratio of male to female), we altered the degree 

of polygyny to 1:2, 1:4, 1:6, and 1:20 ratios of male to female 

in our maximum sustainable harvest models (where λ ≥ 1.0 

and with polygyny initially set at 1:10 ratio of male to female). 

The software program RAMAS® Metapop 5.0.3 (Akçakaya, 

2005) was used to perform all model simulations. 

Results

The stable age/sex distribution generated from each 

population prior to any additional mortality resulted in a sex 

ratio of 0.40:0.60 male to female in the stable population, and 

0.46:0.54 male to female in the moderate and rapid growth 

populations. This resulted largely from lower male survival 

in juvenile age classes in the stable population compared to 

the moderate and rapid growth populations. The final age 

distribution included 0.26 dependent pups (ages 0–0.5) in the 

stable population, and 0.21 in the moderate and rapid growth 

populations. 

Population Growth Rates 

The vital rates used in these models, estimated from 

sea otter populations at or near equilibrium density (stable) 

and from rapid growth populations, yielded average annual 

rates of change of 1.005 and 1.145, respectively (fig. 1). A 

third population with intermediate growth was achieved by 

multiplying the rapid growth vital rates by 0.935 in each age 

class, resulting in an average annual rate of change of 1.072, 

considered to be moderate growth (fig. 1).

Additional Mortality

The effects of additional mortality on growth rates in the 

modeled populations were largely dependent on three factors: 

(1) the magnitude of additional mortality, (2) the rate of 

population change prior to the additional mortality, and (3) the 

sex composition of the additional mortality (fig. 2). In a stable 

population, additional annual mortality of about 0.5 percent 

that included females at a 1:1 ratio or of 1.2 percent at a male 

to female ratio of 3:1 resulted in population decline (λ<1.00) 

(fig. 2A). If additional mortality is constrained to males only, 

harvest rates of more than 2.4 percent resulted in population 

decline. As additional annual mortality of only males exceeded 

this rate, λ decreased rapidly, largely as a result of reduced 

proportions of males in the population. After 20 years of a 

male harvest of 2.4 percent annually, the proportion of males 

in the population equaled 34 percent, compared to 40 percent 

without a harvest. The annual average rate of change (λ) 

declined linearly with mortality rates when both males and 

females were included in the harvest, independent of the 

underlying growth rate in the population (fig. 2A).

In a population exhibiting moderate growth (fig. 2B), 

additional annual male mortality of more than 9.8 percent 

resulted in λ<1.00. As mortality of males only exceeded this 

rate, λ decreased largely as a result of reduced proportions 
Results 5

Figure 1. Population trajectories over 20 years for sea otter populations exhibiting stable, 

moderate, and rapid rates of change using empirical estimates of age and sex specific 

reproduction and survival. Error bars represent +1 standard deviation from the mean.

tac10-5153_fig 01 POPULATION SIZE (± 1 STANDARD DEVIATION)

20,000

15,000

10,000

5,000

1,000

0

YEAR

0 5 10 15 20

Stable (λ = 1.005)

Moderate (λ = 1.072)

Rapid (λ = 1.145)

of males in the population, with the proportion of males 

after 20 years equaling 27 percent compared to 46 percent 

without a harvest. If females at a 1:1 ratio were included in 

the additional mortality, λ decreased to ≤1.00 when average 

annual mortality exceeded 7.7 percent. When males and 

females were harvested at a 3:1 ratio, additional mortality 

resulted in λ ≤ 1.00 at a mortality rate of 15.0 percent (fig. 2B). 

In a population exhibiting rapid growth (fig. 2C), 

additional male only mortality of more than about 

8.5 percent annually resulted in low proportions of males in 

the population. Although λ remained positive (1.04) at an 

average annual male mortality of 8.5 percent, the proportion 

of males after 20 years equaled 14 percent compared to 

46 percent without a harvest. Further increases in male only 

annual mortality led to both negative λ values and reduced 

average annual harvests (fig. 2C). If females at a 1:1 ratio 

were included in the additional mortality, λ was ≤ 1.00 when 

average annual mortality exceeded 16.2 percent. When males 

and females were included at a 3:1 ratio, additional mortality 

resulted in λ≤1.00 at a mortality rate of about 27 percent 

(fig. 2C). 

Maximum Sustainable Harvests

Maximum sustainable harvests were dependent on 

the underlying rate of change in the population and the sex 

composition of the harvest (fig. 3), and ranged from about 

0.5 to 27 percent. For stable populations near equilibrium 

density, male only harvests allowed a maximum sustainable 

harvest of 18 individuals per year out of a population of 

1,000 individuals. This resulted in an average annual harvest 

rate of 2.4 percent of the non-pup population and a final 

abundance that exceeded initial abundance. Although an 

average annual harvest rate of about 4 percent also resulted 

in a positive λ, the population abundance in year 20 was less 

than the initial abundance (fig. 2A). Inclusion of females in 

the harvest reduced the maximum average annual harvest 

rates to 1.2 and 0.5 percent at male to female ratios of 3:1 and 

1:1, with maximum average sustainable annual harvests of 

nine and four individuals, respectively. Average annual rates 

of change over the 20-year period at maximum sustainable 

harvest rates ranged from 1.002 for male only harvests 

to 1.001 when females were included. At all maximum 

sustainable mortality rates, the proportion of males in the 

population after 20 years exceeded 0.34. 
6 Modeling the Effects of Mortality on Sea Otter Populations

Figure 2. Effects of additional sex and age specific mortality (removals) on rates of change in sea otter 

populations that are stable (λ= 1.005), increasing moderately (λ=1.072), and increasing rapidly (λ=1.145). 

Additional mortality occurs annually over 20 years as a proportion of individuals in each age/sex class 

except dependent pups. Additional mortality was applied to males only, and at male to female ratios of 3:1 

and 1:1. As harvest levels rise sufficient to reduce λ to 1.0, declines in average annual harvest over time are 

particularly evident in graphs B and C. Note differences in scales on x axis. tac10-5153_fig02

A. Stable

B. Moderate

C. Rapid

1.20

1.15

1.10

1.05

1.00

0.95

0.90

0.85

1.20

1.15

1.10

1.05

1.00

0.95

0.90

1.20

1.15

1.10

1.05

1.00

0.95

0.90

AVERAGE ANNUAL GROWTH RATE (λ)

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16 18 20

0 5 10 15 20 25 30 35

AVERAGE ANNUAL HARVEST, AS PERCENTAGE OF NON-PUPS IN POPULATION

Male only

3:1 male to female

1:1 male to female
Results 7

Figure 3. Maximum annual sustainable rates of harvest for sea otter populations experiencing stable, moderate, 

and rapid growth (A), and maximum sustainable average annual harvest number (B) for male only, and male to female 

ratios of 3:1 and 1:1. Initial population size is 1000, and results were constrained to model outputs where λ> 1.00 and 

final harvest number equaled the average annual harvest. 

tac10-5153_fig 03

A.

B.

30

25

20

15

10

5

200

150

100

50

0

Male only male:female 3:1 male:female 1:1 

SEX RATIO OF HARVEST

MAXIMUM AVERAGE SUSTAINABLE HARVEST NUMBER MAXIMUM SUSTAINABLE HARVEST RATE, IN PERCENT

Stable

Moderate

Rapid
8 Modeling the Effects of Mortality on Sea Otter Populations

In a population of 1,000 exhibiting moderate growth, 

a male only harvest of 100 individuals per year was 

sustainable (fig. 3) with an average annual rate of change 

of 1.01; however, the proportion of males in the population 

after 20 years was 0.27. With a harvest ratio of 3:1 male to 

female, a sustainable harvest rate was 15 percent, resulting 

in an average annual harvest of 107 individuals with a final 

proportion of males of 0.34. If the harvest ratio was 1:1, the 

maximum sustainable annual harvest was 67 individuals, with 

a final male proportion of 0.46.

In these simulations, maximum sustainable annual 

harvest rates and average harvest number were greatest in 

populations exhibiting rapid growth (fig. 3). In a population 

of 1,000 exhibiting rapid growth, an average annual male 

only harvest of up to 8 percent did not reduce λ and allowed 

an average annual harvest of 283 individuals (fig. 2C). 

However, at an annual harvest rate of 8.5 percent, removal of 

120 individuals was sustainable (fig. 3) with λ =1.04 but, the 

proportion of males in the population after 20 years was 0.14. 

When females were included at a ratio of 3:1 male to female, 

a maximum average sustainable harvest rate of 27 percent was 

possible, with an average annual harvest of 191 individuals 

and a 20-year average annual growth rate of 1.00. For this 

harvest simulation, the proportion of males after 20 years had 

declined to 0.28. At a 1:1 sex ratio, the maximum sustainable 

annual harvest rate was 16.2 percent with a maximum average 

annual sustainable harvest of 144 individuals, and a final male 

proportion of 0.46. 

Effects of Rates of Polygyny

Results presented above (figs. 1–3) assume a mating 

ratio of 1:10 male to female. As we decreased the degree 

of polygyny from the assumed value to a minimum of 

1:2 male to female (presumably much too conservative), 

we observed negative rates of change in seven of the nine 

maximum sustainable harvest simulations (all simulations 

except moderate and rapid growth at 1:1 harvest ratios). At 

a polygyny ratio of 1:4 male to female, growth stabilized 

with λ ≥ 1.00 in the stable population under all maximum 

harvest simulations, but populations declined in mixed sex 

harvests in moderate and rapid growth models. At polygyny 

rates of 1:6 male to female, we observed declines in the 

moderate growth population with male only harvest and in the 

rapid growth population with a 3:1 harvest. We detected no 

diminishment in λ as polygyny increased to the 1:20 ratio of 

male to female but did detect increased rates of change in the 

moderate and rapid growth populations with the higher levels 

of polygyny. 

Discussion 

Managers of wildlife resources have a responsibility 

for conserving and sustaining resources, and pursue various 

strategies to meet management objectives, including habitat 

conservation and manipulation (Poole and Mowat, 2005), 

management of movements (Beier and Noss, 1998), and 

reproduction (DeNicola and others, 1997). Most commonly, 

however, it is mortality, often human related, that provides the 

means for active management of populations (Strickland and 

others, 1996). Population management can include various 

objectives, including increasing or decreasing population 

abundance, or maximizing rates of harvest by humans or 

productivity in the population (Caughley, 1977). One widely 

applied population management tool is the demographic model 

based on life history attributes in a Leslie matrix (Caughley, 

1977). Although acquisition of empirically derived age and 

sex-specific reproduction and survival rates required by such 

models can be time and labor consuming, particularly for 

long-lived species, application of those values in demographic 

models to guide conservation and manage populations is 

relatively straight-forward (Johnson, 1996).

Assumptions

We created three sea otter demographic models using age 

and sex-specific reproduction and survival rates obtained from 

field studies of populations that simulated stable, moderate, 

and rapid rates of population growth. We then applied 

additional incremental mortality to each simulation to evaluate 

effects on population growth rates. Although model outcomes 

illustrate clear effects of additional mortality, particularly as 

maximum sustainable levels are approached and exceeded, 

it is important to recognize and evaluate the assumptions 

inherent in this approach.

Perhaps most importantly, we assumed that the vital rates 

used in each model simulation remained constant and within 

the bounds estimated from field studies, and that annual rates 

of change in the population prior to additional mortality are 

constant. However, this certainly is not always true, based 

on long-term studies of wildlife around the globe (Gaillard 

and others, 1998; Wisdom and others, 2000), including sea 

otters specifically (Tinker and others, 2006). Rather, the 

underlying vital rates, particularly survival, tend to vary on 

temporal and spatial scales that are specific to individual 

species’ life histories, and often reflect environmental and 

ecological conditions. Thus, although the model outcomes we 

present here can be useful for guiding mortality management 

of sea otters, it is essential that managers recognize the need 

to incorporate accurate rates of change in the application 
Discussion 9

of the types of models we describe. Permitting the high 

rates of additional mortality sustainable in a rapid growth 

population, if the rate of change declines, could clearly result 

in a declining population through unsustainable additional 

mortality. For example, prior to 1994, the sea otter population 

in Southeast Alaska was increasing at about 18 percent 

per year (Bodkin and others, 1999). A survey conducted in 

2002–03 showed that the annual growth rate since 1994 was 

reduced to 5 percent or less (Esslinger and Bodkin, 2009). If 

mortality had been managed on the higher growth rate, the 

sea otter population in Southeast Alaska may have declined in 

abundance as a consequence of excessive harvest during the 

long interval between surveys.

We also assumed that additional mortality (that is, 

harvests or incidental mortality) rates are known, accurate, 

and applied to each age and sex as prescribed. Our models 

also assume that females with dependent pups are not included 

in the additional mortality. Again, to some extent, these 

assumptions may not be true. Mortality can be undetected 

or unreported and novel sources of mortality can emerge 

to supplement known sources of mortality that are being 

managed. At least in the case of sea otters, it seems likely 

that reported mortality (for example, harvests or incidental 

fisheries take) will underestimate actual mortality to the extent 

that such sources remain undetected or under-reported. Thus, 

it would seem prudent to incorporate some level of undetected 

managed mortality into models used for management. 

Frequent estimates of trend in rates of population change also 

would serve to evaluate the potential effects of undetected or 

underestimated mortality.

In male only mortality models, we detected a strong 

adverse effect on population trajectory beyond maximum 

sustainable rates from about 2 to 9 percent (fig. 2). We 

assumed a ratio of 1 male to 10 females to represent the 

level of polygyny in each of our models. The rapid declines 

likely arise from diminishing proportions of males in the 

population and the assumed polygyny we imposed in the 

models. Reducing polygyny to ≤ 1:4 (male to female) resulted 

in declining populations under maximum sustainable male 

biased mortality models in the moderate and rapid growth 

populations, but not in the stable population. Assuming a 

higher degree of polygyny (for example, 1:20 ratio of male 

to female) can increase population sizes under male only 

harvests but also can result in even lower proportions of males 

after 20 years. These results suggest a conservative approach 

(that is, 1:10 ratio of male to female or less) is warranted until 

additional research provides empirical data on the degree of 

polygyny in this species. Because of the effects of sex-specific 

mortality on rates of population change, the sex composition 

of managed mortality should be determined and incorporated 

into future models. Further, such models could incorporate 

the appropriate functional response to changing levels of 

polygyny, particularly if sex-biased mortality leads to highly 

skewed sex ratios. 

We did not incorporate catastrophes, environmental or 

demographic stochasticity, or density dependence into the 

mortality simulations. Our intent in this work is to produce 

examples of an approach to improve the management of 

sea otter mortality. It is our premise that incorporation of 

these types of processes would do little to enhance the 

demonstration of demographic models as a management tool. 

Additionally, we have little empirical data from which to 

estimate and incorporate such processes into the models. We 

suggest that as data from field studies are acquired through 

additional research, that those processes and sources of 

uncertainty be explicitly incorporated into future models as 

feasible. Examples of such processes might include mortality 

associated with catastrophic pollution events, such as the 

1989 Exxon Valdez oil spill (Ballachey and others, 1994), or 

density-dependent reductions in population size and growth 

rate (Bodkin and others, 2000). However, managing mortality 

for an annual average rate of change approximating 1.0, 

as in our simulations, would tend to moderate any densitydependent effects on vital rates.

Spatial Considerations

The geographical scale at which sea otter populations are 

managed remains an important, although largely unexplored 

issue. As noted by Gorbics and Bodkin (2001), the annual 

harvest rate during the commercial fur trade of the 18th and 

19th centuries averaged only about 1.5 percent per year of 

the global sea otter population. Over that time, range-wide 

reductions and extirpations occurred not simply because of 

excessive harvest, but because the harvest was not allocated 

proportional to the abundance and distribution of sea otters. 

This resulted in the serial depletion of otters beginning in the 

western Pacific that systematically expanded eastward across 

the Aleutian Archipelago and southward along North America, 

as harvested populations became either reduced to unprofitable 

densities or became locally extinct. The process of serial 

depletion was facilitated by the relatively sedentary nature 

of sea otters. Annual home range sizes of adult sea otters are 

relatively small, with male territories ranging from 4 to 11 km2

and adult female home ranges from a few to 24 km2 (Garshelis 

and Garshelis, 1984; Ralls and others, 1988; Jameson, 1989). 

When additional mortality is spatially concentrated in areas 

equal to or smaller than the cumulative home range of the 

managed population, local depletion, potentially leading 

to serial depletion, may occur. Therefore, it is essential to 

consider the spatial scales at which sea otter mortality is 

managed. 
10 Modeling the Effects of Mortality on Sea Otter Populations

At least two general approaches to the issue of spatial 

distribution of mortality are evident. One approach is to 

assure that mortality is spatially distributed proportional 

to sea otter abundance. In this case, the size of the area 

managed is of relatively little consequence provided that it is 

large enough to support a self sustaining population (that is, 

adequate numbers of individuals in each age and sex class). A 

second approach to managing mortality would be to identify 

subunits within geographic areas that display demographically 

distinct population trends and manage mortality according 

to those differences in rates of population change (Tinker 

and others, 2008). Models, such as those we created, can 

incorporate meta‐population analysis, but will require new 

data on movement and dispersal rates among subpopulations, 

particularly among juvenile age classes. In either case, 

mortality management will be facilitated by relatively frequent 

surveys of distribution and abundance at spatial scales 

consistent with managed sources of mortality.

Summary

Sea otter populations are subjected to a variety of human 

related sources of mortality that are amenable to management. 

We developed demographic models that represent stable, 

moderate, and rapid rates of change in sea otter populations 

and applied additional age and sex-specific mortality in each 

model. Our methods and results identify important ways 

in which sea otter conservation and management can be 

improved through modeling. In addition to the magnitude 

of the additional mortality, two other factors were important 

in determining the effect of additional mortality on the 

population. One was the underlying rate of change in the 

population, that is, populations that were increasing could 

sustain higher mortality than stable populations. The second 

was the sex ratio of the additional mortality, as high levels of 

male only mortality eventually resulted in low proportions 

of males in the population and instability in population 

projections. Our findings illustrate the essential need to obtain 

frequent information on the rates of change in managed 

populations, and the magnitude and sex composition of 

additional mortality. It also will be important to consider the 

spatial scales at which additional mortality is occurring to 

avoid the potential for serial depletion across populations. 

Although the models we describe may be most suitable for 

harvest management, other sources of quantifiable mortality, 

such as incidental, accidental, or illegal, can readily be 

incorporated into this modeling approach. 

Acknowledgments

This work was supported by the U.S. Geological Survey, 

Alaska Science Center. Doug Burn, Brian Hatfield, Kim 

Kloecker, Karen Oakley, Joel Schmutz, Tim Tinker, and Mark 

Udevitz contributed valuable suggestions to improve the 

manuscript. 

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Bodkin and Ballachey— Modeling Effects of Mortality on Sea Otter Populations—Scientific Investigations Report 2010–5096