NOAA Technical Memorandum NMFS-NWFSC-99

Viability Criteria

for the Lake Ozette Sockeye Salmon 

Evolutionarily Significant Unit

April 2009

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service
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This document should be referenced as follows:

Rawson, K., N.J. Sands, K.P. Currens, W.H. Graeber, M.H. 

Ruckelshaus, R.R. Fuerstenberg, and J.B. Scott. 2009. 

Viability criteria for the Lake Ozette sockeye salmon evolutionarily significant unit. U.S. Dept. Commer., NOAA Tech. 

Memo. NMFS-NWFSC-99, 38 p. 
NOAA Technical Memorandum NMFS-NWFSC-99

Viability Criteria

for the Lake Ozette Sockeye Salmon 

Evolutionarily Significant Unit

Kit Rawson,

1

 Norma Jean Sands, Kenneth P. Currens,

2

William H. Graeber,

3

 Mary H. Ruckelshaus,

Robert R. Fuerstenberg,

4

 and James B. Scott5

Northwest Fisheries Science Center

Conservation Biology Division

2725 Montlake Boulevard East

Seattle, Washington 98112

1 Tulalip Tribes

6700 Totem Beach Road

Tulalip, Washington 98271

2 Northwest Indian Fisheries Commission

6730 Martin Way East

Olympia, Washington 98516

3 Washington State Department of Natural Resources

Present affiliation: Entrix Inc.

148 Rogers Street Northwest, Suite 1

Olympia, Washington 98502

4 King County Department of Natural Resources and Parks

201 South Jackson Street, Suite 700

Seattle, Washington 98104

5 Washington Department of Fish and Wildlife

600 Capitol Way North

Olympia, Washington 98501

April 2009

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service
ii

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Table of Contents 

List of Figures...............................................................................................................................................v 

List of Tables ..............................................................................................................................................vii 

Executive Summary .....................................................................................................................................ix 

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

Methods ........................................................................................................................................................4 

PVA ..........................................................................................................................................................4 

Data ......................................................................................................................................................4 

Parameter Estimation ...........................................................................................................................5 

Testing the Assumptions of the Model.................................................................................................5 

Population Projection ...........................................................................................................................6 

Habitat-based Estimates of Adult Capacity..............................................................................................7 

Adult Capacity Based on Lake Productivity Estimates........................................................................7 

Adult Spawner Capacity Based on Spawning Habitat Availability .....................................................8 

Combining Results from the Analyses.....................................................................................................9 

Results and Recommendations...................................................................................................................11 

Abundance..............................................................................................................................................11 

PVA Analysis.....................................................................................................................................11 

Combined Analysis of Abundance Criteria........................................................................................11 

Productivity ............................................................................................................................................13 

Diversity .................................................................................................................................................14 

Spatial Structure .....................................................................................................................................14 

Conclusion ..................................................................................................................................................15 

References...................................................................................................................................................17 

Appendix A: Data and Diagnostics for Viability Analysis of Lake Ozette Sockeye Salmon.....................21 

Data.........................................................................................................................................................21 

Diagnostics.............................................................................................................................................23 

Appendix B: Data and Diagnostics for Viability Analysis of Lake Quinault Sockeye Salmon .................25 

Data.........................................................................................................................................................25 

Basic Data Analysis................................................................................................................................29 

iii
Diagnostics.............................................................................................................................................30 

Conclusions ............................................................................................................................................34 

Appendix C: “R” Functions Used for Simulation of Population Dynamics in PVA..................................37 

iv
List of Figures 

Figure 1. Flow chart showing how demographic and habitat-based analyses were combined with 

PVAs to derive planning ranges for equilibrium spawner abundance ..........................................................9 

Figure A-1. Graph for sigma2 and mu versus lag for the 30-year time series. ..........................................23 

Figure A-2. Normal probability plot of ln(Nt+1/Nt) for the hatchery-adjusted escapement analysis..........24 

Figure B-1. Time series of escapement and total run size for Lake Quinault sockeye salmon, 

1910–2005. .................................................................................................................................................25 

Figure B-2. Time series of escapement and total run size for Lake Quinault sockeye salmon, 

1973–2005. .................................................................................................................................................29 

Figure B-3. Graphs of σ2

 versus lag for the 96-year time series................................................................31 

Figure B-4. Graphs of σ

2

 versus lag for the 33-year time series................................................................31 

Figure B-5. Normal probability plot of ln(Nt+1/Nt) for escapement, 96-year time series...........................32 

Figure B-6. Normal probability plot of ln(Nt+1/Nt) for escapement, 33-year time series. .........................32 

Figure B-7. Graph of natural logarithm of lag 1 ratios of 4-year running sums of spawning 

escapements, 96-year time series................................................................................................................33 

Figure B-8. Time series of 4-year running sum of catch plus escapement divided by 4-year running 

sum of escapement for the previous 4 years...............................................................................................33 

Figure B-9. Graphs of catch plus escapement versus escapement.............................................................35 

Figure B-10. Trend in σ2

 computed for 20-year period with different starting dates. ...............................36 

v
vi
List of Tables 

Table 1. Annual population sizes, given natural logarithm of the population growth of μ = 0 and 

over a range of variance values, that are necessary for p < 0.05 and p < 0.01............................................12 

Table 2. Estimates of the natural logarithm of the rate of growth and its variance for the Lake 

Quinault sockeye salmon time series, 1910–2005 and 1973–2005, for Wesc, adjusted for hatchery 

influence, and adjusted for both hatchery and harvest influence ................................................................12 

Table A-1. Lake Ozette sockeye salmon data used in viability analysis and source of estimates.............22 

Table B-1. Catch and escapement data for Lake Quinault sockeye salmon, 1908–2005 ..........................26 

Table B-2. Estimates of μ and σ2

 for the two Lake Quinault sockeye salmon time series, 1910–2005 

and 1973–2005............................................................................................................................................30 

Table B-3. Estimates of σ

2

 and mean abundance for 20-year segments of the Quinault sockeye 

salmon time series.......................................................................................................................................36 

vii
viii
Executive Summary 

A salmon population is considered to be viable if it is expected to persist for at least 100 

years with a high probability. Population-based criteria necessary for viable salmonid 

populations (VSPs) include specific conditions of 1) abundance, 2) productivity, 3) diversity, and 

4) spatial structure. The Puget Sound Technical Recovery Team (PSTRT) developed viability 

criteria for the Lake Ozette sockeye salmon (Oncorhynchus nerka) evolutionarily significant unit 

(ESU), which is comprised of a single population. 

Abundance 

Following the general approach we previously applied to Puget Sound Chinook salmon 

(O. tshawytscha), we developed abundance criteria using two methods: a pure demographically 

based population viability analysis (PVA) and an estimate of the population numbers that the 

system’s available habitat could support if that habitat were in optimal condition. We then 

combined the PVA and habitat estimates, using an adaptation of a flow chart originally used in 

Columbia River salmon recovery planning, resulting in upper and lower bounds defining a 

planning range for the number of Lake Ozette sockeye salmon required for the population to be 

viable. 

The PVA analysis requires an estimate of the variance of the 4-year running sum of the 

population growth rate. We estimated this parameter using a 30-year data set (1977–2006) of 

available information for Lake Ozette sockeye salmon abundance. For some years where 

complete counts of fish were not available, we approximated the population numbers by 

expanding partial counts. In two cases, where there were no data available for a year, we 

estimated the abundance by interpolating between values for adjacent years. 

We estimated the variance of the growth rate using the “slope method,” which was 

developed for use with salmon populations where there is a great deal of uncertainty in annual 

abundance numbers. We conducted standard diagnostic tests and determined that the data met 

the assumptions of the method. To project the population’s extinction probability, we simulated 

abundance trajectories for 100 years using the estimated variance and assuming a stable (i.e., 

1:1) population growth rate. We added an additional constraint that the simulated population 

abundance could never exceed three times the initial population size. Whenever the population 

fell below a quasi-extinction threshold of 250 spawners summed over a 4-year period, that run 

was designated as going extinct. We ran simulations 10,000 times each for a range of starting 

population sizes between 10,000 and 800,000 (4-year running sum) in steps of 5,000. 

We also looked at two habitat-based estimates of the number of sockeye salmon the Lake 

Ozette system could support, one based on estimates of lake productivity and one based on the 

amount of available spawning habitat. We combined the habitat and PVA estimates using a flow 

chart that gives a range of population abundances for viability, with the lower end of the range 

ix
being the starting population size that results in an extinction probability of 0.05 with the PVA 

analysis and the upper end being the smaller of the two habitat-based capacity estimates and the 

PVA populations size with a 0.01 extinction probability. 

The Lake Ozette PVA analysis resulted in a population growth rate variance of 0.1. The 

population projection analysis using this variance gave a starting population size of 125,000 over 

a 4-year period (31,250 annual) for a 0.05 extinction probability and a size of 785,000 over 4 

years (196,250 annual) for a 0.01 extinction probability. From other work, we had a range of 

91,000 to 121,000 for population capacity based on available spawning habitat and numbers of 

adults much greater than this possible based on lake productivity alone. Therefore, combining 

the results using our flow chart, the viability abundance range for Lake Ozette sockeye salmon is 

31,250 to 121,000 for the annual population size. 

We also examined data from nearby Lake Quinault to compare with our results for Lake 

Ozette, because there is a longer time series and more careful measurement of abundance for 

Lake Quinault over the years. If we had estimated the variance of the population growth rate 

using the Quinault data, the viability abundance range for Lake Ozette sockeye salmon would 

have been 11,250 to 47,500 for the annual population size. In the end, despite a longer and more 

consistent data set for Lake Quinault, we chose to use the results from the Lake Ozette–specific 

data because there are important differences between the populations, especially age structure. 

PSTRT Recommendation: Based on currently available information, a viable sockeye 

population in Lake Ozette will range in abundance between 31,250 and 121,000 adult spawners. 

Productivity 

The PVA method used here assumes the population must be able to sustain itself. In 

other words, a viable population productivity, on average and after any introduced harvest, must 

be a 1:1 return of adults per spawner, after the viability level has been achieved. As a general 

rule of thumb, the population growth rate must be greater than 1:1 for the population to increase 

in size until the viable abundance threshold is achieved. Given the recent 8-year average Lake 

Ozette escapement of 4,600 and our abundance target range of 35,000 to 121,000, the growth 

rates would have to range between an average of 1.04 and 1.06 per year to achieve the 

abundance targets in 50 years, 1.02 to 1.03 to achieve them in 100 years, and 1.01 to 1.02 to 

achieve them in 200 years. 

PSTRT Recommendation: The growth rate for Lake Ozette sockeye salmon, once 

viability is achieved, should average 1. Until the ESU achieves viability, the growth rate must be 

greater than 1. 

Spatial Structure 

From the historical work done for the population characterization and identification, it is 

unclear whether the current distribution of Lake Ozette sockeye salmon between lakeshore and 

tributary spawners is the same as the historic structure. However, it appears that the spatial 

structure of Lake Ozette sockeye is becoming more tributary based, with less of the population 

spawning along the lakeshore and in fewer lakeshore sites than in the past. Such a confined 

x
spatial distribution increases the probability of catastrophic harm to the population and likely 

restricts the population to a narrower (more homogeneous) environmental suite that may reduce 

adaptive variation. Increasing the spatial structure of the population will reduce environmental 

risk and abet population variation. 

PSTRT Recommendation: A viable sockeye salmon population in Lake Ozette 

includes multiple, spatially distinct and persistent spawning aggregations throughout the 

historical range of the population. Therefore, a viable population contains multiple spawning 

aggregations along the lake beaches, which are the known historical spawning areas. The 

certainty that the population achieves a viable condition would be further increased if spawning 

aggregations in one or more tributaries to the lake were also established. 

Diversity 

Expanding the distribution of sockeye salmon into different habitats may lead to 

increased life history diversity, including changes in age composition, morphology, and behavior 

that are different from that now observed in Lake Ozette. For example, such changes in life 

history could include residualism (i.e., the case where progeny of anadromous sockeye salmon 

carry out their whole life cycle in freshwater and do not become anadromous). 

PSTRT Recommendation: A viable Ozette sockeye salmon population includes one or 

more persistent spawning aggregations from each major genetic and life history group 

historically present within that population. As there is little information on historical diversity 

for Ozette sockeye, research is needed on current diversity types and retrospective analyses on 

the likely historical diversity range. A viable population of sockeye in Lake Ozette also 

maintains the historical genetic diversity and distinctness between anadromous sockeye salmon 

and resident kokanee salmon in Lake Ozette. 

The PSTRT’s viability criteria for Lake Ozette sockeye salmon specify a spatial structure 

for the population that emphasizes the population’s historic distribution and life history 

characteristics. Unfortunately, the historical distribution and life history diversity is not well 

documented. Recovery cannot rely solely on the present distribution of spawners within the lake 

and tributary system or on a simple increase in the tributary subpopulation to the exclusion of a 

lakeshore subpopulation. Of concern then, is that the present spatial structure and diversity of 

the population does not well represent the desired characteristics of the viable population. 

Our analyses and recommendations for viability criteria for all four VSP parameters were 

based on the best currently available information for Lake Ozette sockeye salmon. Although we 

attempted to address important sources of uncertainty in our analyses and recommendations, we 

were limited by the lack of good historical data. Likewise, because of this uncertainty, recovery 

strategies focusing exclusively on either tributary or beach spawners alone are also highly 

uncertain. The only practical solution to this uncertainty is an implemented adaptive 

management plan. Consequently, we recommend that the recovery plan include an adaptive 

management component that incorporates improved data monitoring and estimation. This will 

allow viability criteria to be reevaluated and, if warranted, revised as part of the adaptive 

management program. 

xi
xii
Introduction 

The Puget Sound Technical Recovery Team (PSTRT) was convened by the National 

Marine Fisheries Service to develop the technical basis for recovery plans for three Pacific 

salmon (Oncorhynchus spp.) evolutionarily significant units (ESUs) in Washington that are listed 

under the Endangered Species Act (ESA): Lake Ozette sockeye (O. nerka), Puget Sound 

Chinook (O. tshawytscha), and Hood Canal summer chum (O. keta). Key tasks of the PSTRT 

are to identify populations and describe the conditions of viable salmonid populations (VSPs) 

and ESUs. The foundation for accomplishing this for Pacific salmon is described by McElhany 

et al. (2000), who discuss delineating populations within an ESU, identify the key parameters 

used to describe the status of a population, define population viability as a probability of 

persistence over a specified time period, and discuss the means by which ESU delisting criteria 

can be based on alternative scenarios for the status of populations within the ESU. This PSTRT 

report identifies population and ESU viability criteria for the Lake Ozette sockeye salmon ESU. 

Based on the available information, the PSTRT has concluded that the Lake Ozette 

sockeye salmon ESU historically was comprised of a single population with several 

subpopulations (Currens et al. 2009). It follows that the ESU’s one population must be viable in 

order that the ESU be viable; that is, determining population viability criteria is also determining 

ESU viability for this ESU. The next step was to describe conditions of key population 

parameters consistent with long-term viability. The team considered the conditions necessary for 

a population to persist for at least 100 years with probabilities of 0.95 and 0.99, assuming no 

immigration or emigration, as bounds for population viability. Because Lake Ozette sockeye are 

currently not meeting viability criteria and because reliable estimates of historical abundance or 

productivity levels for the population are not available, the viability criteria will need to be 

reevaluated as measurements of abundance improve, recovery actions take effect, and 

consequences of recovery actions are evaluated and adapted. 

Following McElhany et al. (2000), we describe a population’s status using the four 

viability characteristics: abundance, productivity, diversity, and spatial structure (VSP criteria). 

Abundance is the number of individuals in the population at a given life stage or time; 

productivity or growth rate is the actual or potential ratio of abundance in the next generation to 

current abundance; diversity is the variety of genotypes, life histories, morphologies, and other 

characteristics expressed by individuals within a population; and spatial structure refers to how 

fish at any life stage are distributed among available or potentially available habitats. Our task 

with this report was to develop criteria for each of these characteristics, which considered 

together will describe a viable population and ESU. 

As scientific advisors, the PSTRT has several challenges in developing viability criteria 

that will be useful to planners, politicians, and the public. Viability criteria are not necessarily 

recovery goals. Rather, they collectively describe what we believe is necessary to maintain a 
viable population and ESU, independent of particular goals for direct or indirect societal benefits 

from the recovered population. 

Of the four VSP criteria, abundance is the most well developed in this report. We have 

used two approaches to determine abundance levels in developing the abundance viability 

criteria for the Lake Ozette sockeye salmon population. The first approach, utilizing population 

viability analysis (PVA) models, is demographically based. Using information derived from 

population census data combined with simple models of population dynamics, one can estimate 

extinction probabilities for the population, which can then be used to classify population status. 

In particular, recovered status can be assigned to those population conditions that result in a 

suitably low extinction probability. Dennis et al. (1991) first discussed the use of this approach 

for endangered species recovery planning. McElhany and Payne (in prep.) have developed an 

application to Pacific salmon, which we previously used for Puget Sound Chinook salmon 

(Ruckelshaus et al. 2002, Rawson et al. in prep.). 

Our second approach to abundance criteria is based on assessing the potential dynamics 

of the population as related to its natural environment or habitat. This approach requires a means 

of relating habitat quantity and condition to population performance in terms of abundance, 

which is challenging when data are scarce. However, the approach has appeal because, if such a 

linking model can be found, viability estimates can be bounded by reasonable estimates of the 

intrinsic potential of habitats to support sockeye salmon throughout their life cycle. With such 

an approach, it is possible to not only determine the abundance criterion for viability, but also to 

predict the likely contribution of suites of habitat recovery and protection actions to getting there. 

Mobrand (1997) described this type of approach in the context of recovery planning for 

listed Columbia River salmon. Two models linking changes in habitat to salmon population 

status, the Ecosystem Diagnosis and Treatment model (McConnaha 2001) and the Shiraz model 

(Sharma et al. 2005, Scheurell et al. 2006), have been applied to the Puget Sound Chinook 

salmon ESU. Both models are data intensive and therefore have not been applied to Lake Ozette 

sockeye salmon where the necessary information is not available. Instead, the PSTRT 

considered results from two habitat-based approaches available for Lake Ozette sockeye: 

1. The juvenile habitat rearing capacity approach estimates the capacity of Lake Ozette to 

produce sockeye salmon smolts, then determines how many returning adults would result 

from this number of smolts and how many spawners are needed to produce this number 

of smolts. 

2. The spawner habitat capacity approach estimates the maximum number of sockeye 

salmon spawners that lake beaches and tributary streams could accommodate based on 

the spawning habitat area and conditions. 

Because both the demographic and the habitat approaches have their own strengths and 

limitations, we explored both approaches to develop the viability criterion for Lake Ozette 

sockeye salmon abundance. The criterion is presented as a range, which is derived using 

information on both demographics and habitat. The demographics give us an estimation of a 

viable spawner abundance level and the habitat-based approach gives us capacity estimates 

(three estimates from the two approaches given above) which place an upper limit on viability 

estimates. 

2
Spatial structure is the distribution of individuals in habitats they use throughout their life 

cycle. A population with a broad spatial distribution at any life stage is more likely to persist 

than a population whose individuals are concentrated in a few locations. The contribution of 

spatial structure to population persistence results from three main processes: 1) reduced chance 

of catastrophic losses of the population (i.e., when groups of individuals are spread out in space), 

2) greater chance that locally extirpated or dwindling groups will be rescued by recolonization 

(i.e., when individual groups are close enough together), and 3) a greater opportunity for longterm demographic processes to buffer a population from future environmental changes. 

Collectively, these phenomena commonly are referred to as metapopulation processes. 

Because of the contrasting benefits of groups of individuals being close enough together for 

recolonization to occur and yet spread out enough so that all groups do not fall victim to the 

same catastrophe, spatial structure for a viable population should include multiple clusters of 

groups that are closely aggregated, with the clusters themselves being spread throughout the 

geographic area occupied by the population. 

Salmon exhibit considerable diversity within and among populations in their life history 

and their morphological, physiological, and genetic traits. In a spatially and temporally varying 

environment, there are three main reasons why diversity is important for species persistence: 1) 

diversity in life history allows a species to use a wider array of environments than a species 

lacking such diversity, 2) the more diverse the population, the more likely that some individuals 

will survive and reproduce in the face of environmental variation, and 3) genetically based 

diversity provides the raw material for surviving long-term environmental changes. Such 

diversity also allows the population to occupy, and thus potentially adapt to, a wider range of 

environmental conditions and to colonize or recolonize newly available habitats. Because 

salmon regularly face variability in the environments they inhabit, the contributions of diversity 

to population persistence are critical considerations. 

In this report, we provide for a viability planning range (upper and lower bounds) for the 

number of Lake Ozette sockeye salmon needed to achieve the abundance viability criterion given 

stable growth or productivity. The criteria for spatial structure and diversity for the population 

and ESU viability are also presented. 

3
Methods 

PVA 

The PVAs we conducted are based on the method of Holmes (2001), Holmes and Fagen 

(2002), and McElhany and Payne (in prep.). The approach uses an observed time series of 

abundances to estimate the growth rate (λ) and the variance of the natural logarithm of the 

growth rate (σ

2

). Assuming population dynamics will be restored in the future such that the 

growth rate is stable or increasing (λ ≥ 1) and the variance of the growth rate will remain the 

same as in the period of the observed time series, it is possible to estimate the minimum initial 

population size necessary to maintain the probability of extinction at or below a given level over 

a given number of years. Using this method, the viability criterion is for the population 

abundance to exceed the minimum size and for the growth rate to exceed λ = 1 over the specified 

time period. 

There were two steps in an analysis performed this way. The first step was to estimate σ

2

from the observed time series of abundance data using the slope method (Holmes 2001). The 

second was to project extinction risk of the population in the future, assuming that the time 

course of the population approximates a Brownian motion (Dennis et al. 1991). More details on 

the method are provided below in the subsections Parameter Estimation and Population 

Projection. 

Data 

Adult return estimates for Lake Ozette sockeye salmon are available for most years from 

1977 through 2003 (Haggerty et al. 2008) (Appendix A). These are derived from a variety of 

census methods and represent the number of adult sockeye entering Lake Ozette each year 

(Haggerty et al. 2008). Due to problems with fish counts at the weir, return estimates are not 

reported for some of the years in this time period. For those years, we interpolated adjacent 

years or used other information to fill in the missing years to create a complete time series for 

data analysis. Also, to bring the time series up to date, we used census information for 2004, 

2005, and 2006 provided by the Makah Tribe to create estimates of total run for those recent 

years. We describe methods we used to fill in estimates not provided by Haggerty et al. (2008) 

in Appendix A. 

For Lake Ozette sockeye, we use the term “run size” and “escapement” synonymously 

over this time period, since there has been no harvest on Lake Ozette sockeye since at least 1973 

other than limited ceremonial harvest through 1980 (Haggerty et al. 2008). In this case 

escapement is not the same as spawning escapement, since there are limited surveys to verify 

actual spawning numbers. Because we also had data on the numbers of fish removed each year 

to provide eggs for an artificial production program in Umbrella Creek, we subtracted those 

4
numbers from the estimates of total escapement to estimate the number of fish that spawned 

naturally. 

Because of some uncertainties in the information for Lake Ozette sockeye salmon, 

especially lack of reliable information for the years before 1977, we looked at escapement and 

total recruitment data from other sockeye salmon populations along the Pacific coast from 

Bristol Bay in Alaska to the Washington coast for surrogate estimates of population trends and 

variability. In the end we chose to use local Lake Ozette data for PVAs. However, we also 

completed a detailed analysis for the much longer Lake Quinault run to compare variance and 

other population parameters because of the similar geographic location and ecology, similar 

proximity of the lake to the ocean, and similar ocean distribution of adults (Appendix B). 

Parameter Estimation 

The slope method (Holmes 2001) was developed to separate process error (the parameter 

of interest) from measurement error in the time series of abundance data for species such as 

salmon. In this method, the variance of population growth rates is estimated as the slope of the 

regression of the average growth rate over successive lags on the value of the lag, for one to four. 

Holmes and Fagan (2002) showed that the slope method produces reliable estimates of process 

error in the face of large measurement error when the population dynamics follow the 

assumptions of the model and also when the population dynamics follow other forms, including 

some of the density-dependent spawner-recruit relationships commonly found in salmon. We 

applied the slope method using 4-year running sums of abundance, based on the 4-year life cycle 

of Lake Ozette sockeye salmon, to express the returning run size. 

We used estimated variance (σ

2

) of growth rate two ways for the Lake Ozette population: 

using the time series of estimated natural origin (NOR) escapements and recruitment with an 

adjustment for hatchery fish. We did the same for Lake Quinault data, except that we added a 

third analysis—for the Lake Quinault time series only—adjusting for both hatchery fish and 

harvest effects. The first estimate uses the Holmes (2001) method directly to compute the 

variance of log(Nt+1/Nt) for a time series, where Nt is the running sum of natural origin 

escapement at time t. The second uses modifications described by McElhany and Payne (in 

prep.) to adjust for the fact that a portion of each year’s return is derived from first generation 

returns from hatchery releases that escape to natural spawning areas. The third estimate, used in 

the Lake Quinault analysis only, computes the variance of (Nt+1 + Ct+1)/Nt. Here Ct+1 is the 

running sum of the number of fish that would have returned to spawn in addition to Nt+1 had 

there been zero harvest. In both cases, we used 4-year-long unweighted running sums of the 

appropriate time series as the basic input data and lags of 1 through 4 years (τ = 4 in Holmes’ 

notation) for slope estimates. 

Testing the Assumptions of the Model 

Given the longer-term climatic cycles and ocean regime shifts that govern Pacific salmon 

population dynamics (Mantua et al. 1997, Pearcy 1992, 1997), variability increases with 

additional years of data, at least as time series length increases from very short to 30–40 years 

and as data span distinct ocean regimes. This is true even when the underlying process can be 

5
assumed to be Markovian (McElhany and Payne in prep.), as is the case for the simple model for 

which this technique was first developed. 

To determine if the assumptions underlying the slope method held for the Lake Ozette 

and Lake Quinault sockeye salmon data, we performed standard diagnostic tests (Holmes and 

Fagan 2002, McElhany and Payne in prep.). These are presented in Appendices A and B, 

respectively. None of these flagged a major problem for the 30-year time series for Lake Ozette 

or the 33-year time series for Lake Quinault, while the 96-year series for Lake Quinault failed 

several of the tests (Appendix B). 

The quasi-extinction threshold (NQET) is the population size below which extinction risk 

is mostly determined by depensatory effects and other factors not included in estimates of 

σ

2 from populations at higher abundance levels. There is no single accepted way to determine 

this parameter, and the outcome of PVA is highly sensitive to its value. Although a number of 

processes are important in setting NQET (Lande 1998), we considered only the potential loss of 

genetic diversity due to inbreeding. Studies of genetic diversity loss suggest that the probability 

of losing genetic diversity due to genetic drift increases rapidly at genetic effective population 

sizes (NE) less than 50 (Soule 1980) and that genetic drift can dominate over natural selection in 

accounting for changes in gene frequency in salmon populations smaller than 50 to 100 fish 

effective size (Gall 1987). Allendorf et al. (1997) recommended that Pacific salmon population 

sizes be above 500 to guard against long-term deleterious genetic change due to genetic drift and 

above 50 to guard against short-term change. We used the lower end of this range to derive our 

NQET. 

Typically the census number of fish in a salmon population (NC) is greater than the 

genetic effective size (Waples 1990). Assuming an NE of 50 for a full generation and assuming 

that NE = 0.2 NC, it follows that an equivalent NC = 250. Based on this, we use an NQET of 250 

spawners for a 4-year generation of Lake Ozette sockeye salmon in our analyses. 

Population Projection 

To project a population’s extinction probability, we assumed that a population grows at a 

lognormally distributed growth rate with a mean of λ = 1 and variance of σ

2

. The 

straightforward approach we used is described by McElhany and Payne (in prep.). We simulated 

population growth using functions written in “R” (R Development Core Team 2008, Appendix 

C). This program repeatedly simulates population trajectories for Y years, starting with a 

population size of N. The trajectory is assumed to go extinct if the population size ever falls 

below NQET during the Y years. We express population viability criteria as the number of 

salmon required for a naturally self-sustaining population to have a 0.95 or 0.99 probability of 

persistence over a Y = 100-year time period. Our projection method included the additional 

constraint that the population size can never exceed three times the initial population value in the 

model simulation. We estimated extinction probabilities by repeating the simulation 10,000 

times each for the value of N (4-year running sum population size) in steps of 5,000. 

6
Habitat-based Estimates of Adult Capacity 

Adult Capacity Based on Lake Productivity Estimates 

Adult capacity based on lake productivity can be expressed as either the maximum 

number of sockeye salmon adults that Lake Ozette could have produced from estimates of smolt 

capacity or the number of parent spawners needed to produce smolt capacity levels. This method 

assumes that no factor other than the capacity of the lake to produce juveniles is limiting and that 

all juvenile sockeye salmon will be anadromous. 

The first step, theoretically, in estimating adult capacity by food availability to juveniles 

in the lake is to estimate smolt capacity, although this number is never given in the following 

citations. A literature review suggests that salmon production in Lake Ozette is not limited by 

food availability. Haggerty (2006) states: 

All researchers, (Bortleson and Dion 1979, Dlugokenski et al. 1981, Blum 1988, 

Beauchamp and LaRiviere 1993) [see also Beauchamp et al. 1995] independent of 

methodologies, have concluded that Lake Ozette sockeye productivity and survival are 

not [currently] limited by food availability or competition. No direct estimates of total 

smolt production capacity of the lake have been developed. Blum (1988) used the Acre 

Plankton Index (API) model to estimate the carrying capacity of the lake, concluding the 

lake could support total adult sockeye runs in the range of 306,000 to 563,000 fish. 

Smolt capacity as used here is defined as the capacity of the lake to support juvenile 

salmon production based on the plankton productivity of the lake. The Plankton Acre Index 

(PAI, also referred to as API) was developed by the International Pacific Salmon Fisheries 

Commission (IPSFC 1972) to estimate the potential sockeye salmon rearing capacity of Fraser 

River system lakes based on zooplankton volume in two systems assumed to be at carrying 

capacity (Shuswap and Chilko lakes). 

Blum (1988) adapted the method to develop adult abundance capacity estimates for Lake 

Ozette. Not having zooplankton volume data, he used regressions with primary productivity 

indices available for both the Fraser River system lakes and Lake Ozette. The Ozette PAI 

estimates were derived from regressions on 1) just total dissolved solids (PAI = 0.4) and 2) total 

dissolved solids and chlorophyll a (PAI = 0.9). A PAI of 1 is equivalent to the ability of the lake 

to support 10 female spawners per acre (IPSFC 1972). Blum’s (1988) PAI estimates of 0.4 and 

0.9 result in estimates of 27,000 to 60,750 effective female spawners or 54,000 to 121,500 

spawners, assuming a female to male spawning ratio of 1:1. Blum (1988) also states that these 

estimates are based on an assumption of an effective spawn out of 3,000 eggs per female; 

unstated by Blum, the estimates also assume the same egg to smolt survival on Lake Ozette as 

experienced in the Fraser River system lakes used to develop the PAI regression equations. 

To get the total run estimates of 306,000 to 563,000 sockeye salmon adults, Blum (1988) 

used a linear regression analysis of total run sizes (Y) of Fraser River system lakes sockeye 

against mean escapements (X): 

Y = 3.79 X + 101734.77 (r2

 = 0.741, P < 0.01) (1) 

7
Blum notes that, on average, four recruits are produced per spawner in the Fraser River system 

lakes used; therefore, this same productivity is assumed when applying this regression to Lake 

Ozette sockeye. These estimates represent potential escapements and returns for Lake Ozette 

based on plankton productivity measures from the 1970s and 1980s. These potential abundances 

were not being achieved in either 1988 when Blum did his work or now; limiting factors other 

than lake capacity were and are controlling current abundances. Therefore, these abundances 

may be used as upper limits for our viability analysis. 

These estimates based on lake capacity give us two adult capacity estimates: spawners 

needed for smolt capacity (SSC), 54,000 to 121,500 spawners, and return from the smolt 

capacity (RSC), 306,000 to 563,000 adult returns. In making these estimates, Blum does not 

give actual smolt numbers or the survival estimates assumed. A 306,000 to 563,000 return from 

54,000 to 121,500 spawners, respectively, gives a total egg-to-adult return survival of 0.4% to 

0.3%, respectively, given the assumptions of 1:1 female to male spawners and 3,000 viable eggs 

per female. This total egg-to-adult survival could represent a freshwater survival of about 5% 

and 4%, respectively, and a marine survival of about 8% (this is the marine survival estimated 

for Fraser River system lakes sockeye salmon in recent years1

). Unfortunately, smolt capacity is 

never actually estimated, and therefore, it is difficult to separate the freshwater and marine 

survival rates. 

Adult Spawner Capacity Based on Spawning Habitat Availability 

Spawner capacity (SpC) is the maximum number of sockeye spawners that lake beaches 

and tributary streams could accommodate if no other factors were limiting. Haggerty (2006) 

developed new estimates of SpC for lake and tributary habitats; these are explained and reported 

in the Ozette recovery plan (Haggerty et al. 2009). Recent habitat inventories upon which these 

estimates are based are documented by Haggerty and Ritchie (unpubl. manuscr.) and Haggerty et 

al. (2008). 

Haggerty (2006) computed SpC for Allen’s, Olsen’s, Umbrella, and Baby Island beaches 

using various techniques to assess the amount of suitable spawning habitat available under 

recovered conditions and two methods for projecting the number of females per unit of habitat. 

For estimates of potential tributary spawner capacity, Haggerty (2006) used habitat surveys from 

1999 and 2000 to estimate stream length of suitable habitat in Big River and Umbrella and 

Crooked creeks. These were converted to suitable spawning area using two different methods. 

Haggerty converted the tributary spawning area estimates to total spawners assuming 3 m2

 per 

female. The numbers of females for the lake and tributary estimates were converted to total fish 

assuming a 1:1 male:female ratio. Haggerty’s (2006) estimates of the SpC range from 11,000 to 

15,000 spawners for lake beaches and 80,000 to 106,000 spawners for the 3 tributaries, for an 

overall total range of 91,000 to 121,000 spawners for the basin. These are conservative estimates 

in the sense that, for both lake beaches and tributaries, potentially suitable spawning areas were 

not included in the calculations and these would increase the estimates if included (Haggerty 

2006, Haggerty et al. 2009). 

 

1

 Tim Tynan, National Marine Fisheries Service, Olympia, WA. Pers. commun., 9 April 2009. 

8
Combining Results from the Analyses 

We combined the results from the PVA estimates for viability levels and the habitatbased estimates for capacity according to a sequence of decision rules (Figure 1) adapted from an 

approach originally used in Columbia River recovery planning efforts (Ford et al. 2001, 

Ruckelshaus et al. 2002). Because of the significant uncertainty in each of the approaches, we 

used the estimates of viability and capacity to provide upper and lower bounds for the population 

abundance viability planning ranges rather than a point estimate. The upper and lower bounds 

are constrained by the different analyses. For example, the PVA estimate of the upper bound for 

abundance is estimated using an extinction probability of 0.01 (in contrast to the 0.05 used for 

the lower bound), but this is constrained by the maximum number of fish that could be supported 

Start with PVA, and 

upper range for SSC, 

RSC, and SpC 

Figure 1. Flow chart showing how demographic and habitat-based analyses were combined with 

PVAs to derive planning ranges for equilibrium spawner abundance (based on Ford et al. 2001). 

SSC = spawners needed to produce smolt capacity, RSC = return run size from smolt capacity, 

and SpC = spawner capacity. 

PVA (p = 0.05) PVA (p = 0.01) 

Is this 

> SpC, 

SSC, or 

RSC? 

Yes No 

min [SpC, SSC, RSC] PVA (p < 0.01) 

Lower end 

of planning 

range 

Upper end 

of planning 

range 

9
by the available spawning habitat or the available lake rearing capacity under unimpacted habitat 

conditions. This decision rule approach uses the independent analyses as a series of checks. In 

this case, the decision tree logic will not allow an upper bound for abundance derived from using 

demographic data that is greater than estimates of the spawner abundances the recovered habitat 

could support. 

We used the PVA results from the Lake Ozette data set in this decision tree process of 

combining PVA and habitat-based estimates of viable population sizes. However, because of 

missing data and other uncertainties in the available Lake Ozette data, we also computed PVA 

results for data from nearby Lake Quinault. We discuss the implications for the viability ranges 

if the PVA estimates from the Lake Quinault data were used instead of the direct Lake Ozette 

information. 

10
Results and Recommendations 

Abundance 

PVA Analysis 

The σ

2

 estimate, adjusted for the presence of hatchery fish, for the 30-year Lake Ozette 

time series was 0.1 for the natural escapement time series and 0.096 using the adjustment for the 

presence of hatchery fish. Shown below are estimates of the natural logarithm of the growth rate 

(μ) and its variance (σ

2

) for the Lake Ozette sockeye salmon time series, 1977–2007 (30 years) 

for NOR escapement (Wesc) and escapement adjusted for hatchery influence (Hat). 

Wesc Hat

μ 0.027 0.019 

σ

2 0.100 0.0960 

We used the 0.1 estimate of σ

2

 for further analysis. 

Determining minimum population sizes using the population projection simulation 

requires the following input variables be specified: population growth rate (λ or its natural 

logarithm μ), σ

2

, time period for the simulation in years (Y), extinction probability, and NQET. 

We set μ = 0 (indicating that the rate of population increase was stable, i.e., equal to zero) and 

simulated values of σ

2 from 0.04 to 0.12 in increments of 0.01 (Table 1). We used 100 years for 

Y and 0.05 and 0.01 for the extinction probabilities following McElhany et al. (2000). We ran 

10,000 replicated simulations for each trial parameter value, because we found that fewer 

replicates led to inconsistent results (i.e., smaller starting population sizes for higher variance in 

some cases). 

With the above input, we produced a table of minimum initial population sizes for ranges 

of μ and σ

2

 (Table 2). Given the estimated σ

2 of 0.10 for the 30-year Lake Ozette time series, 

the minimum population sizes for μ = 0 are approximately 31,250 for extinction probability p = 

0.05 and 196,250 with p = 0.01 (Table 1). 

Combined Analysis of Abundance Criteria 

With the results of the PVA analysis and the habitat-based capacity estimates, we applied 

the decision rules to generate a viable abundance range for the Lake Ozette sockeye salmon 

population. Based on Blum’s (1988) analyses, spawners needed to produce a smolt capacity 

(SmC) range 54,000–121,500 fish; returns from these spawners would range 306,000–563,000 

adults. Haggerty’s (2006) estimates of the spawner capacity (SpC ) range 11,000–15,000 for 

lake beaches and 80,000–106,000 for tributaries, for an overall total range of 91,000–121,000 for 

the basin. 

11
Table 1. Annual population sizes, given natural logarithm of the population growth of μ = 0 and over a 

range of variance (σ

2

) values, that are necessary for p < 0.05 and p < 0.01. Extinction is 

determined when the 4-year running sum of abundance declines to a Nqet of 250 fish or less over a 

100-year period. The estimated σ

2

 computed from available data for Lake Ozette sockeye salmon 

(Appendix A) is 0.09. The estimated σ

 2 computed from Lake Quinault data (Appendix B) is 

0.06. These lines are in bold in the table. Numbers were estimated using stochastic simulation 

modeling. 

p < 0.05 p < 0.01 

σ2 4-year Annual 4-year Annual

0.04 12,500 3,125 45,000 11,250

0.05 20,000 5,000 75,000 18,750

0.06 30,000 7,500 115,000 28,750

0.07 45,000 11,250 200,000 50,000

0.08 65,000 16,250 350,000 87,500

0.09 90,000 22,500 500,000 125,000

0.10 125,000 31,250 785,000 196,250

0.11 160,000 40,000 >800,000 >200,000

0.12 215,000 53,250 >800,000 >200,000

Table 2. Estimates of the natural logarithm of the rate of growth (μ) and its variance (σ

2

) for the Lake 

Quinault sockeye salmon time series, 1910–2005 (96 years) and 1973–2005 (33 years), for Wesc, 

adjusted for hatchery influence (HatAdj), and adjusted for both hatchery and harvest influence 

(HatHarAdj). 

Fixed Wesc HatAdj HatHarAdj

1910–2005 (96 years)

μ –0.011 –0.014 0.129

σ

2 0.163 0.159 0.175

1973–2005 (33 years)

μ 0.007 0.000 0.063

σ

2 0.041 0.038 0.061

Following the decision rules in Figure 1, the minimum abundance number is 31,250 from 

the PVA analysis for a 5% risk of extinction. The PVA estimate for the upper bound is 196,250 

(1% risk), but this is larger than the minimum of the upper range of the SSC, RSC, and SpC 

estimates. Thus the upper end of the viability planning range is determined by the minimum of 

the upper range of the SSC, RSC, and SpC estimates (Figure 1), which in this case is the SpC 

estimate of 121,000 spawners. Combining all of this, the current estimate of the viability 

planning range for Lake Ozette sockeye salmon is 31,250 to 121,000 spawners. It must be 

remembered that the spawning capacity of 121,000 is likely to be an underestimate if all 

potential beach and tributary sites were taken into consideration, not just ones currently being 

used (see Methods section). 

We also note that if the estimated variance of the Lake Quinault population was 

appropriate for Lake Ozette, then the viability planning range would be narrower and the total 

abundance value would be smaller. Both the upper and lower ends of the range would be 

determined by the PVA, and the range would be 11,250–47,500 spawners. 

12
One could argue that the Lake Quinault data set is preferable to the Lake Ozette data set 

for estimating σ

2

, because there is a much longer time series available and recent estimates 

appear to be more precise than those for Lake Ozette. However, fundamental differences 

between the systems suggest that the Lake Quinault analysis might not be reflective of the Lake 

Ozette population, and we chose to use the local data for estimating the viability range for Lake 

Ozette sockeye salmon. The principal reason for this choice is the substantial difference in the 

age structure of the two populations, with Lake Ozette sockeye returning almost exclusively at 

age 4, while Lake Quinault sockeye are typically split approximately evenly between age 3 and 

age 4. We would expect populations that are predominantly of a single age to exhibit greater 

variability than multiage populations, and this expectation is supported by the direction of the 

difference in the variance estimates of the two populations we examined. In addition, all Lake 

Quinault sockeye are tributary spawners while Lake Ozette exhibits both beach and tributary 

spawners. It is not known what effect this fundamental difference may have on variability in the 

growth rate of the populations. 

Thus we decided to use the available Lake Ozette data to estimate levels of the Lake 

Ozette population necessary for viability. We recognize that the current estimate of the variance 

includes a high level of uncertainty, which we expect will be greatly reduced in the future with 

improved estimates of spawning escapement. However, sampling for and estimation of Lake 

Ozette abundance and growth rates, and therefore variance, need to be improved in order to 

refine the estimates of viability abundance in the future. 

PSTRT Recommendation: Based on currently available information, a viable sockeye 

salmon population in Lake Ozette will range between 31,250 and 121,000 adult spawners. 

Productivity 

The PVA method used here assumes the population must be able to sustain itself (i.e., not 

be declining) at the viability abundance level. In other words, a viable population productivity, 

on average and after any introduced harvest, must be at a 1:1 return of adults per spawner, after 

the viability level has been achieved. The capacity estimates based on smolt capacity are derived 

from Fraser River system lakes sockeye salmon estimates that have a realized productivity of 

approximately four recruits per spawner; if lower productivities were realized, more spawners 

would be needed or fewer adults would return from a fixed smolt capacity, thus changing our 

adult capacity estimates. As a general rule of thumb, the λ must be greater than 1.0 for the 

population to increase in size until the viable abundance threshold is achieved. Given the recent 

8-year average Lake Ozette escapement of 4,600 and our abundance target range of 35,000 to 

121,000, the growth rates would have to range between an average of 1.04 and 1.06 per year to 

achieve the abundance targets in 50 years, 1.02 to 1.03 to achieve them in 100 years, and 1.01 

and 1.02 to achieve them in 200 years. 

PSTRT Recommendation: The growth rate for Lake Ozette sockeye salmon, once 

viability is achieved, should average 1. Until the ESU achieves viability, the growth rate must be 

greater than 1. 

13
Diversity 

Expanding the distribution of sockeye salmon into different habitats may lead to 

increased life history diversity, including changes in age composition, morphology, and behavior 

that are different from what is observed now in Lake Ozette. For example, such changes in life 

history could include residualism (i.e., the case where progeny of anadromous sockeye salmon 

carry out their whole life cycle in freshwater and thus do not become anadromous). 

Dramatic differences in diversity within the O. nerka species in Lake Ozette occur 

between the anadromous sockeye salmon population, which is listed under the ESA, and the 

resident kokanee salmon, which is not. The genetic differences are large enough between these 

two groups that they are designated as different ESUs (Gustafson et al. 1997). Interbreeding 

between the two is possible but genetic data indicate it is rare (Currens et al. 2009). Changing 

tributary habitats and expansion in the distribution of tributary spawning anadromous sockeye 

salmon could increase the likelihood of interbreeding, which would have the undesired impact of 

increasing homogeneity between the two groups. Any life history changes that do occur in the 

Lake Ozette sockeye population should be separately tracked and not confused with the 

genetically distinct kokanee salmon residing in Lake Ozette and its tributaries. Research is 

needed on current diversity types and retrospective analyses on the likely historical diversity 

range. 

PSTRT Recommendation: A viable Lake Ozette sockeye salmon population includes 

one or more persistent spawning aggregations from each major genetic and life history group 

historically present within that population. Since there is little historical diversity information 

for Lake Ozette sockeye, research is needed on current diversity types and retrospective analyses 

on the likely historical diversity range. A viable population of sockeye in Lake Ozette also 

maintains the historical genetic diversity and distinctness between anadromous sockeye salmon 

and resident kokanee salmon in Lake Ozette. 

Spatial Structure 

From the historical work done for population characterization and identification (Currens 

et al. 2009), it is unclear whether the current spatial structure of Lake Ozette sockeye salmon is 

the same as the historic structure. Based on the available information of current spawning 

activity, however, it appears that the spatial structure of Lake Ozette sockeye is becoming more 

tributary-based, with less of the population spawning along the lakeshore and in fewer lakeshore 

sites than in the past. Such a confined spatial distribution increases the probability of 

catastrophic harm to the population and probably restricts the population to a narrower (more 

homogeneous) environmental suite that may reduce adaptive variation. Increasing the spatial 

structure of the population will reduce environmental risk and abet population variation. 

PSTRT Recommendation: A viable sockeye salmon population in Lake Ozette includes 

multiple, spatially distinct and persistent spawning aggregations throughout the historical range 

of the population. Therefore, a viable population contains multiple spawning aggregations along 

the lake beaches, which are the known historical spawning areas. The certainty that the 

population achieves a viable condition would be further increased if spawning aggregations in 

one or more tributaries to the lake were also established. 

14
Conclusion 

The PSTRT’s viability criteria for Lake Ozette sockeye salmon specify a spatial structure 

for the population that emphasizes the population’s historic distribution and life history 

characteristics. Unfortunately, the historical distribution and life history diversity are not well 

documented. Little is known about the distribution of the historic (pre-1950s) population, and 

the role played by Lake Ozette tributaries in the spatial structure of the species. Data available 

since the 1950s (and prior to adult returns from the tributary hatchery programs) indicate that the 

population was generally lake-centric, mainly shoreline spawners with some smaller contribution 

by the tributaries. Research is needed on current diversity types and retrospective analyses on 

the likely historical diversity and spatial ranges. In the meantime, under the recovery process, it 

is advantageous to increase spatial distribution from where it was when the ESU was listed. The 

recovery of multiple persistent spawning aggregations along the lakeshore and in tributaries can 

only increase the robustness of the population. 

Recovery cannot rely solely on the present distribution of spawners within the lake and 

tributary system or on a simple increase in the tributary subpopulation2

 to the exclusion of a 

lakeshore subpopulation. Managing the transition from current population attributes to the 

attributes of the viable population will require care and attention to the status of the various 

components of the population and to habitat and watershed conditions in the tributaries and the 

lake. Care must be taken to begin the process of habitat recovery in the lake at the same time as 

restoration proceeds in the tributaries so that the attributes of the remaining lake aggregations are 

not lost altogether. 

Of concern then, is that the present spatial structure and diversity of the population does 

not well represent the desired characteristics of the viable population. Currently, the population 

is not well-distributed, either within the tributaries or the lake or across the watershed. This 

relatively confined spatial structure (considering both the distribution of spawners and the 

abundance of each of the spawning groups) probably also confines the expression of life history 

diversity, especially if the adaptive regime experienced by the fish is limited. Moreover, given 

the population’s present limited distribution, the risks from severe environmental events and 

from more general environmental degradation are high. 

Our analyses and recommendations for viability criteria for all four VSP parameters were 

based on the best currently available information for Lake Ozette sockeye salmon. Although we 

attempted to address important sources of uncertainty in our analyses and recommendations, we 

were limited by the lack of good historical data (e.g., spawner abundances, distribution over lake 

beaches and between lake and tributary spawning areas, and life history diversity). Likewise 

because of this uncertainty, recovery strategies focusing exclusively on either tributary or beach 

spawners alone are also highly uncertain. The only practical solution to this uncertainty is an 

implemented adaptive management plan. Consequently, we recommend that the recovery plan 

include an adaptive management component that incorporates improved data monitoring and 

estimation. Better data about the sockeye salmon population in Lake Ozette is essential to being 

 

2

 Subpopulation refers here to distinct spawning aggregations and does not necessarily imply a more rigorous 

genetic distinction. 

15
able to recognize changes in the status as a result of recovery actions and will allow reanalysis of 

the population to get better estimates of annual results. This will allow viability criteria to be 

reevaluated and, if warranted, revised as part of the adaptive management program. 

16
References 

Allendorf, F. W., D. Bayles, D. L. Bottom, K. P. Currens, C. A. Frissell, D. Hankin, J. A. Lichatowich, 

W. Nehlsen, P. C. Trotter, and T. H. Williams. 1997. Prioritizing Pacific salmon stocks for 

conservation. Conserv. Biol. 11(1):140–152. 

Beauchamp, D. A., and M. G. LaRiviere. 1993. An evaluation of competition and predation as limits to 

juvenile sockeye salmon production in Lake Ozette, Washington. Final Report to Makah Tribe, 

Makah Fisheries Management, Neah Bay, WA. 

Beauchamp, D. A., M. G. LaRiviere, and G. L. Thomas. 1995. Evaluation of competition and predation 

as limits to the production of juvenile sockeye salmon in Lake Ozette. N. Am. J. Fish. Manag. 

15:121–135. 

Blum, J. P. 1988. Assessment of factors affecting sockeye salmon (Oncorhynchus nerka) production in 

Ozette Lake, WA. Master’s thesis. Univ. Washington, Seattle. 

Bortleson, G. C., and N. P. Dion. 1979. Preferred and observed conditions for sockeye salmon in Ozette 

Lake and its tributaries, Clallam County, Washington. Water-Resources Investigations 78-64. 

U.S. Dept. Interior, U.S. Geological Survey, Tacoma, WA. 

Currens, K. P., R. R. Fuerstenberg, W. H. Graeber, K. Rawson, M. H. Ruckelshaus, N. J. Sands, and 

J. B. Scott. 2009. Identification of an independent population of sockeye salmon in Lake Ozette, 

Washington. U.S. Dept. Commer. NOAA Tech. Memo. NMFS-NWFSC-96. 

Dennis, B., P. L. Munholland, and J. M. Scott. 1991. Estimation of growth and extinction parameters for 

endangered species. Ecol. Monogr. 61:115–143. 

Dlugokenski, C., W. Bradshaw, and S. Hager. 1981. An investigation of the limiting factors to Lake 

Ozette sockeye salmon production and a plan for their restoration. U. S. Fish and Wildlife 

Service, Fisheries Assistance Office, Olympia, WA. 

Ford, M. P., C. Budy, C. A. Busack, D. Chapman, T. Cooney, T. Fisher, J. Geiselman, T. Hillman, J. 

Lukas, C. Pevan, C. Toole, E. Weber, and P. Wilson. 2001. Upper Columbia River steelhead 

and spring Chinook salmon population structure and biological requirements. Final rep., Upper 

Columbia River Steelhead and Spring Chinook Salmon Biological Requirements Committee, 14 

December 1999. Northwest Fisheries Science Center, Seattle, WA. Online at http://www 

.nwfsc.noaa.gov/assets/11/4291_06162004_180804_steel_chinook_popstr.pdf [accessed 31 

March 2009]. 

Gall, G. A. E. 1987. Inbreeding. In N. Ryman and F. Utter (eds.), Population genetics and fishery 

management, p. 47–87. University of Washington Press, Seattle. 

Gustafson, R. G., T. C. Wainwright, G. A. Winans, F. W. Waknitz, L. T. Parker, and R. S. Waples. 1997. 

Status review of sockeye salmon from Washington and Oregon. U.S. Dept. Commer., NOAA 

Tech. Memo. NMFS-NWFSC-33. 

17
Haggerty, M. J. 2006. Development of Lake Ozette sockeye recovery goals. Technical memorandum 

June 21, 2006. (Available from Makah Fisheries Management, P.O. Box 115, Neah Bay, WA 

98357.) 

Haggerty, M., R. Furfey, M. Hollenbach, T. Hooper, M. Longenbaugh, M. Plummer, B. Trask, T. Tynan, 

and R. Wheeler. 2009. Proposed recovery plan for Lake Ozette sockeye salmon (Oncorhynchus 

nerka). NMFS, Northwest Regional Office, Salmon Recovery Division, Seattle, WA. Online at 

http://www.nwr.noaa.gov/Salmon-Recovery-Planning/Recovery-Domains/Puget-Sound/ 

Ozette-Plan.cfm [accessed 10 April 2009]. 

Haggerty, M. J., and A. C. Ritchie. Unpubl. manuscr. Lake Ozette tributary habitat conditions: A 

summary of Ozette watershed baseline habitat inventory data, 2004. Funding from FY 1999 

Bureau of Indian Affairs Watershed Projects-Jobs in the Woods Program. Submitted to Makah 

Indian Tribe. (Available from Makah Fisheries Management, P.O. Box 115, Neah Bay, WA 

98357.) 

Haggerty, M. J., A. C. Ritchie, J. G. Shellberg, M. J. Crewson, and J. Jalonen. 2008. Draft Lake Ozette 

sockeye limiting factors analysis. Prepared for Makah Indian Tribe and NOAA Fisheries Service 

in cooperation with Lake Ozette Sockeye Steering Committee, Neah Bay, WA. Online at 

http://www.nwr.noaa.gov/Salmon-Recovery-Planning/Recovery-Domains/Puget-Sound/ 

Draft-Ozette-LFA.cfm [accessed 10 April 2009]. 

Holmes, E. E. 2001. Estimating risks in declining populations with poor data. Proc. Natl Acad. Sci. 

USA 98(9):5072–5077. 

Holmes, E. E., and W. F. Fagan. 2002. Validating population viability analysis for corrupted data sets. 

Ecology 83(9):2379–2386. 

IPSFC (International Pacific Salmon Fisheries Commission). 1972. Proposed program for restoration 

and extension of the sockeye and pink salmon stocks of the Fraser River. (IPSFC replaced by 

Pacific Salmon Commission.) Online at http://www.psc.org [accessed 31 March 2009]. 

Lande, R. 1998. Demographic stochasticity and Allee effect on a scale with isotropic noise. Oikos 

83:353–358. 

Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis. 1997. A Pacific interdecadal 

climate oscillation with impacts on salmon production. Bull. Am. Meteorol. Soc. 78(6):1069–

1079. 

McConnaha, W. E. 2001. Role of ecosystem diagnosis and treatment procedure in subbasin and species 

recovery planning. Northwest Power Planning Council, Fish and Wildlife Division, Portland, 

OR. 

McElhany, P., and J. Payne. In prep. Setting viability criteria for Pacific salmonids using abundance 

data. (Available from P. McElhany, NWFSC, 2725 Montlake Blvd. E., Seattle, WA 98112.) 

McElhany, P., M. Ruckelshaus, M. J. Ford, T. C. Wainwright, and E. Bjorkstedt. 2000. Viable salmonid 

populations and the recovery of evolutionarily significant units. U.S. Dept. Commer., NOAA 

Tech. Memo. NMFS-NWFSC-42. 

Mobrand, L. E., J. A. Lichatowich, L. C. Lestelle, and T. S. Vogel. 1997. An approach to describing 

ecosystem performance “through the eyes of salmon.” Can. J. Fish. Aquat. Sci. 54:2964–2973. 

18
Pearcy, W. G. 1992. Ocean ecology of North Pacific salmonids. Washington Sea Grant Program. 

University of Washington Press, Seattle. 

Pearcy, W. G. 1997. Salmon production in changing ocean domains. In D. J. Stouder, P. A. Bisson, R. J. 

Naiman, and M. G. Duke (eds.), Pacific salmon and their ecosystems: Status and future options, 

p. 331–352. Chapman and Hall, New York. 

R Development Core Team. 2008. R: A language and environment for statistical computing. R 

Foundation for Statistical Computing. Vienna, Austria. ISBN 3-900051-07-0. Online at 

http://www.R-project.org [accessed 1 April 2009]. 

Rawson, K., K. P. Currens, R. Fuerstenberg, W. Graeber, M. Ruckelshaus, N. J. Sands, and J. B. Scott Jr. 

In prep. Combining demographic and habitat-based approaches to triangulate on viability criteria 

for Puget Sound Chinook salmon populations. (Available from K. Rawson, Tulalip Tribes, 6700 

Totem Beach Road, Tulalip, WA 98271.) 

Ruckelshaus, M., K. P. Currens, R. Fuerstenberg, W. Graeber, K. Rawson, N. J. Sands, and J. Scott. 

2002. Planning ranges and preliminary guidelines for the delisting and recovery of the Puget 

Sound Chinook salmon evolutionarily significant unit. Puget Sound Technical Recovery Team. 

Online at http://www.nwfsc.noaa.gov/trt/puget_docs/trtpopesu.pdf [accessed 1 April 2009]. 

Scheuerell, M. D., R. Hiliborn, M. H. Ruckelshaus, K. K. Bartz, K. M. Lagueux, A. D. Haas, and K. 

Rawson. 2006. The Shiraz model: A tool for incorporating anthropogenic effects and fishhabitat relationships in conservation planning. Can. J. Fish. Aquat. Sci. 63:1596–1607. Online 

at http://article.pubs.nrc-cnrc.gc.ca/RPAS/rpv?hm=HInit&afpf=f06-056.pdf&journal=cjfas& 

volume=63 [accessed 1 April 2009]. 

Sharma, R., A. B. Cooper, and R. Hilborn. 1997. A quantitative framework for analysis of habitat and 

hatchery practices on Pacific salmon. (Available from Columbia River Inter-Tribal Fish 

Commission, 729 NE Oregon St., Suite 200, Portland, OR.) 

Soule, M. E. 1980. Thresholds for survival: Maintaining fitness and evolutionary potential. Conserv. 

Biol. 4:324–327. 

Waples, R. S. 1990. Conservation genetics of Pacific salmon III. Estimating effective population size. 

J. Hered. 81:277–289. 

19
20
Appendix A: Data and Diagnostics for Viability 

Analysis of Lake Ozette Sockeye Salmon 

Data 

Run size values from Haggerty et al. (2008, their Appendix B) in Table A-1 below are the 

medians of several values, as explained there. The escapement numbers given are the run size 

minus the broodstock take. Years with no run size estimates available were filled in by 

expanding weir counts (Haggerty et al. 2008, their Table 3.5) by the average ratio of weir counts 

to overall system estimates (Haggerty et al. 2008, their Appendix B). Because the expansion 

factor seemed to be generally larger before 1991 and smaller after that, we used the pre-1991 

average of 2.37 for the years before 1991 and the post-1991 average of 1.46 for the later years. 

We also used a factor of 1.46 to expand weir count data for 2004, 2005, and 2006 provided to us 

by Caroline Peterschmidt of the Makah Tribe. By this method, we were able to fill in all years 

except 1985 and 1987, for which there were no weir counts available; they were estimated as the 

average of the escapement from the year before and the year after. Note that in each case, one of 

the two years averaged was also an estimate for missing data, but based on the expansion factor. 

Estimates of the natural origin (NOR) fraction of the total escapement were derived from 

NOR estimates of the Umbrella Creek returns provided by the Makah Tribe to reflect the 

proportion of the total Ozette return that are NOR. 

The broodstock take given in Table A-1 is from Haggerty et al. (2008, their Appendix C 

and Table 3.9), but reflects only the NOR portion of the broodstock take. Prior to 2000, the 

broodstock take was from the beaches and was all NOR. From 2000 on, the broodstock take was 

from Umbrella Creek returns and included both NOR and hatchery origin fish. We used the 

NOR proportions given us by the Makah Tribe (see previous paragraph) to determine the NOR 

fish in the broodstock take. 

From the escapement time series in Table A-1, estimates of variance (σ

2

) and growth rate 

(μ) can be computed using the methods described for the Lake Quinault data analysis (Appendix 

B) as shown below, providing estimates of μ and σ

2

 for natural escapement (Tesc), NOR 

escapement (Wesc), and hatchery adjusted escapement (Hat). 

Tesc Wesc Hat

μ 0.033 0.027 0.019 

σ

2 0.098 0.100 0.096 

Tesc estimates use the time series of estimated total natural escapement, including both 

NOR and hatchery-origin fish that escape to natural spawning areas. Wesc estimates use the 

21
Table A-1. Lake Ozette sockeye salmon data used in viability analysis and source of estimates. Years 

where we estimated the escapement are italicized. 

Escapement NOR 

Year Spawning Broodstock fraction Escapement data source 

1977 2,752 0 100% Haggerty et al. 2008, Appendix B 

1978 2,398 0 100% Haggerty et al. 2008, Appendix B 

1979 1,335 0 100% Haggerty et al. 2008, Appendix B 

1980 1,054 0 100% Haggerty et al. 2008, Appendix B 

1981 858 0 100% Haggerty et al. 2008, Appendix B 

1982 4,131 0 100% Haggerty et al. 2008, Appendix B 

1983 828 14 100% Expanded from weir count 

1984 2,474 0 100% Haggerty et al. 2008, Appendix B 

1985 2,054 40 100% Interpolated 

1986 1,566 43 100% Expanded from weir count 

1987 5,542 123 100% Interpolated 

1988 9,696 193 95% Haggerty et al. 2008, Appendix B 

1989 1,520 6 95% Haggerty et al. 2008, Appendix B 

1990 709 33 95% Haggerty et al. 2008, Appendix B 

1991 1,932 175 95% Haggerty et al. 2008, Appendix B 

1992 4,010 109 95% Haggerty et al. 2008, Appendix B 

1993 320 32 92% Expanded from weir count 

1994 949 54 93% Haggerty et al. 2008, Appendix B 

1995 363 94 63% Expanded from weir count 

1996 3,931 200 95% Haggerty et al. 2008, Table 3.6 

1997 1,404 263 79% Haggerty et al. 2008, Table 3.6 

1998 1,882 88 91% Haggerty et al. 2008, Table 3.6 

1999 2,620 29 84% Haggerty et al. 2008, Table 3.6 

2000 4,851 170 87% Haggerty et al. 2008, Table 3.6 

2001 4,151 149 93% Haggerty et al. 2008, Table 3.6 

2002 3,822 116 88% Haggerty et al. 2008, Table 3.6 

2003 4,876 193 99% Haggerty et al. 2008, Table 3.6 

2004 6,461 190 92% Expanded from weir count

2005 2,997 144 77% Expanded from weir count

2006 3,044 29 63% Expanded from weir count

time series of estimated NOR escapements obtained by applying the estimated NOR fraction to 

the estimated total escapement. Hat estimates use the adjustment for hatchery fish in progeny 

escapement as described for the Lake Quinault data analysis (Appendix B). Unlike the Quinault 

system, there is no harvest on Ozette sockeye salmon. 

22
Diagnostics 

We examined three diagnostic tests. 

1. Slope of σ

2

(τ) versus τ (the lag) is linear. 

The slope method assumes the relationship of σ

2

 to τ is linear. Visual inspection of the 

graph for the Hat adjustment suggests this is the case for the data in Figure A-1. 

2. Distribution of ln(Nt+1/Nt) is approximately normal. 

The slope method also assumes that the distribution of the natural logarithm of the 4-year 

running sums, lagged one year, is approximately normal. The data used in all three of these 

analyses fit this assumption well. For example, for the Hat analysis, results of three statistical 

tests, giving the coefficient value and probability (p) and testing the Ozette sockeye salmon data 

for normality, were as follows. 

Coefficient p

Shapiro-Wilk 0.9786 0.8431 

Skewness 0.2567 0.5520 

Kurtosis 0.5193 0.4286 

The p values are all high, indicating no identifiable deviation from normality (Figure A-2). 

3. No temporal trend in ln(Nt+1/Nt) or recruits per spawner. 

The Ozette time series is also relatively stationary over the 30-year period used here, 

which satisfies another assumption of the slope method. 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1234

sigma 2 mu

Lag (τ)

Value of σ2 or 

μ

Figure A-1. Graph for sigma2

 (σ

2

) and mu versus lag for the 30-year time series. 

23
-3

-2

-1

0

1

2

3

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Normal quantile

Hat

Figure A-2. Normal probability plot of ln(Nt+1/Nt) for the Hat analysis. 

24
Appendix B: Data and Diagnostics for Viability 

Analysis of Lake Quinault Sockeye Salmon 

Data 

The time series of escapement and catch plus escapement for Lake Quinault sockeye 

salmon, 1908–2005, is shown in Figure B-1 and the available data are given in Table B-1. 

Larry Gilbertson, biologist for the Quinault Indian Nation (QIN), supplied the data in 

Table B-1, along with the following explanations:3

Harvest. The harvest estimates come from historic and current records and catch 

accounting systems. The estimate for 1908 came from an article in the New York 

Sun Times (July 19, 1908). The estimates for 1910–1952 came from a Washington 

Department of Fisheries (WDF) publication (R. S. Robison, 1953, The Quinault 

River Indian Fishery with statistics of the catch.). Harvest numbers for 1910–1934 

were estimated based on an average of 7.5 fish per case of 48 half-pound cans. The 

estimates for 1935–1952 came from the WDF catch reporting system. The 

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1910 1918 1926 1934 1942 1950 1958 1966 1974 1982 1990 1998

Esc Tot Run

Number of fish

Figure B-1. Time series of escapement (Esc) and total run size (Tot Run) for Lake Quinault sockeye 

salmon, 1910–2005. 

 

3

 Larry Gilbertson, Quinault Indian Nation, Taholah, WA. Pers. commun., August 2006. 

25
Table B-1. Catch and escapement data for Lake Quinault sockeye salmon, 1908–2005. The number and 

percentage of hatchery fish in the escapement are also given. 

Year Harvest Escapement Run size Hatchery Hatchery % 

1908 75,000 72,059 147,059 0 0.0% 

1910 65,250 62,691 127,941 0 0.0% 

1911 30,465 29,270 59,735 0 0.0% 

1912 70,500 67,735 138,235 0 0.0% 

1913 263,198 252,877 516,075 0 0.0% 

1914 184,110 176,890 361,000 0 0.0% 

1915 367,260 352,858 720,118 0 0.0% 

1916 154,725 148,657 303,382 0 0.0% 

1917 69,120 66,409 135,529 0 0.0% 

1918 37,350 35,885 73,235 0 0.0% 

1919 18,660 17,928 36,588 2,566 7.0% 

1920 15,665 15,051 30,716 2,566 8.4% 

1921 38,850 22,892 61,742 0 0.0% 

1922 288,195 249,545 537,740 2,625 0.5% 

1923 156,810 176,503 333,313 6,756 2.0% 

1924 125,595 141,042 266,637 5,432 2.0% 

1925 49,695 20,854 70,549 2,791 4.0% 

1926 25,935 24,918 50,853 1,490 2.9% 

1927 84,300 80,994 165,294 2,184 1.3% 

1928 30,000 28,824 58,824 4,937 8.4% 

1929 66,735 64,118 130,853 4,381 3.3% 

1930 323,040 310,372 633,412 3,362 0.5% 

1931 127,140 122,154 249,294 3,697 1.5% 

1932 213,945 205,555 419,500 2,792 0.7% 

1933 101,310 97,337 198,647 3,240 1.6% 

1934 74,400 71,482 145,882 5,264 3.6% 

1935 95,094 91,365 186,459 5,747 3.1% 

1936 39,060 37,528 76,588 5,257 6.9% 

1937 71,890 69,071 140,961 3,899 2.8% 

1938 113,594 109,139 222,733 2,460 1.1% 

1939 17,127 16,455 33,582 3,641 10.8% 

1940 280,422 269,425 549,847 3,730 0.7% 

1941 509,140 489,174 998,314 1,446 0.1% 

1942 155,247 149,159 304,406 1,986 0.7% 

1943 37,410 35,943 73,353 2,378 3.2% 

1944 54,686 52,541 107,227 1,889 1.8% 

1945 60,129 57,771 117,900 2,135 1.8% 

1946 68,068 65,399 133,467 2,145 1.6% 

1947 156,941 150,786 307,727 2,391 0.8% 

1948 74,631 71,704 146,335 2,288 1.6% 

1949 207,473 199,337 406,810 2,072 0.5% 

1950 91,008 87,439 178,447 1,816 1.0% 

1951 62,442 59,993 122,435 718 0.6% 

1952 29,928 28,754 58,682 0 0.0% 

1953 15,644 15,031 30,675 0 0.0% 

1954 107,579 103,360 210,939 0 0.0% 

26
Table B-1 continued. Catch and escapement data for Lake Quinault sockeye salmon, 1908–2005. The 

number and percentage of hatchery fish in the escapement are also given. 

Year Harvest Escapement Run size Hatchery Hatchery % 

1955 62,417 59,969 122,386 0 0.0% 

1956 112,646 108,229 220,875 0 0.0% 

1957 43,545 41,837 85,382 0 0.0% 

1958 32,036 30,780 62,816 0 0.0% 

1959 25,288 24,296 49,584 0 0.0% 

1960 40,159 38,584 78,743 0 0.0% 

1961 34,551 33,196 67,747 0 0.0% 

1962 18,828 18,090 36,918 0 0.0% 

1963 89,674 86,157 175,831 0 0.0% 

1964 26,210 25,182 51,392 0 0.0% 

1965 21,648 20,799 42,447 0 0.0% 

1966 58,872 56,563 115,435 0 0.0% 

1967 37,556 36,083 73,639 0 0.0% 

1968 58,010 55,735 113,745 0 0.0% 

1969 30,576 29,377 59,953 0 0.0% 

1970 5,987 5,752 11,739 0 0.0% 

1971 9,701 9,321 19,022 0 0.0% 

1972 16,185 15,550 31,735 0 0.0% 

1973 12,369 15,200 27,569 0 0.0% 

1974 25,629 25,000 50,629 0 0.0% 

1975 73,612 60,487 134,099 0 0.0% 

1976 14,904 26,420 41,324 0 0.0% 

1977 30,400 34,900 65,300 774 1.2% 

1978 21,022 28,586 49,608 1,826 3.7% 

1979 4,666 60,800 65,466 5,865 9.0% 

1980 16,653 30,000 46,653 4,964 10.6% 

1981 21,743 32,949 54,692 2,002 3.7% 

1982 15,329 30,909 46,238 4,266 9.2% 

1983 679 11,546 12,225 4,046 33.1% 

1984 947 48,550 49,497 3,118 6.3% 

1985 24,736 58,700 83,436 3,313 4.0% 

1986 1,894 20,516 22,410 3,607 16.1% 

1987 24,347 57,186 81,533 1,861 2.3% 

1988 18,186 49,492 67,678 168 0.2% 

1989 2,691 22,017 24,708 88 0.4% 

1990 10,106 41,536 51,642 0 0.0% 

1991 6,158 48,820 54,978 0 0.0% 

1992 9,797 47,162 56,959 0 0.0% 

1993 33,681 59,832 93,513 0 0.0% 

1994 1,194 14,407 15,601 0 0.0% 

1995 828 22,147 22,975 0 0.0% 

1996 2,230 45,527 47,757 231 0.5% 

1997 3,690 30,973 34,663 894 2.6% 

1998 5,476 18,801 24,277 705 2.9% 

1999 760 5,967 6,727 111 1.6% 

2000 250 18,364 18,614 70 0.4% 

27
Table B-1 continued. Catch and escapement data for Lake Quinault sockeye salmon, 1908–2005. The 

number and percentage of hatchery fish in the escapement are also given. 

Year Harvest Escapement Run size Hatchery Hatchery % 

2001 284 21,302 21,586 0 0.0% 

2002 21,800 50,000 71,800 0 0.0% 

2003 37,131 56,612 93,743 1,292 1.4% 

2004 6,973 39,942 46,915 2,076 4.4% 

2005 517 12,022 12,539 1,773 14.1% 

estimates for 1953–1965 were taken from WDF Statistical Reports and the Joint 

Biological Statement (U.S. v Washington). Estimates for 1966–1970 were taken 

from reports prepared by the U.S. Fish and Wildlife Service, Fisheries Assistance 

Office, for the QIN. Estimates for 1975–2005 were taken from the QIN catch 

reporting system. Harvest numbers for the earlier years were also cited in various 

publications and government reports (e.g., annual reports of the U.S. Bureau of 

Indian Affairs agent at Taholah) that differ from the estimates reported by Robison. 

Escapement. We have escapement estimates made directly from counts for two 

time periods, 1921–1925 and 1973–2005. The early estimates were made from 

weir counts at a Bureau of Fisheries weir constructed at the mouth of Lake 

Quinault. Escapement estimates since 1973 have been made using acoustic 

methods in Lake Quinault. The weir counts were “corrected” for days that the weir 

was not operated and for years when the weir started operations late or ended 

operations early. The estimates for other years were based on assuming a fixed 

harvest rate (see below). 

Harvest rates. The basic structure of the fishery was established in 1915, based on 

recommendations contained in a report by Special Agent Dorrington of the U.S. 

Indian Service. Fishing ground locations were formally established with specific 

gear limitations for each. This basic structure has survived to the present and is still 

enforced. A system of fishing seasons and schedules was also established early in 

the period of record. As a result, the fishery operated in a fairly consistent way 

from 1915 through 1978. Much of the structure was already in place prior to 1915 

and was enforced by the power of tradition. After 1978, management was changed 

from a set-season-gear-restriction approach to an escapement goal approach. The 

harvest rates during 1921–25 (mean = 0.56) and 1973–1978 (mean = 0.46) can be 

used to represent the “norm” for the fishery. Interestingly, the overall mean of 0.51 

is near the level of federal policy for stocks under federal management in the early 

1900s (e.g., sockeye salmon in Alaska). This was not Dorrington’s intent; it is just 

a fortuitous result of the structured fishery. 

Hatchery contribution. Hatchery releases of sockeye salmon have occurred in 

Lake Quinault from two facilities during two time periods. The U.S. Bureau of 

Fisheries operated a hatchery on Lake Quinault from 1914 to 1947. The QIN has 

operated a facility on the lake since 1972. Broodstock for the bureau hatchery came 

mostly from spawning grounds distant from the facility. A few adults were taken at 

the facility toward the end of its operation, but the on-station egg takes amounted to 

28
only 10–12% of the total each year. Broodstock for the QIN hatchery has come 

from spawning grounds. The fingerling releases from the bureau hatchery were fed 

fry held into the summer period prior to release. The fingerling releases from the 

QIN facility were fish fed for accelerated growth and released in early summer as 0-

age smolts. 

The only direct estimates of return rates for the sockeye salmon releases comes 

from the 0-age smolt releases from the QIN facility. Marked fish from the 1973–

1976 broodyear releases were recorded during catch sampling. These data were 

used to estimate a total brood year return rate of approximately 0.01. Survival of 

fry and fingerlings from the bureau facility were likely on the low side of the 

published range. The hatchery practices were not advanced and there was little sign 

of success; for example, after three decades of operation, only a small hatchery run 

had been developed (only ≈100 females/year). The 0-age smolt rate was used for 

yearlings simply for lack of something better. The return rate for QIN facility fry is 

based on midlevel survival. This was chosen because of improved hatchery 

practices and decreased competition from natural origin (NOR) fry. A high survival 

rate was not used because of degraded habitat conditions. 

Based on the above, the time series from 1973 through 2005 (Figure B-2) includes the 

best time series of data having independent estimates of both harvest and escapement. 

Basic Data Analysis 

We estimated the variance of the growth rate (σ

2

) in three ways: 1) using the time series 

of estimated natural origin spawning escapements (Wesc), 2) using this time series with an 

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

1973 1977 1981 1985 1989 1993 1997 2001 2005

Esc Tot Run

Number of fish

Figure B-2. Time series of Esc and Tot Run for Lake Quinault sockeye salmon, 1973–2005. 

29
adjustment for hatchery (HatAdj), and 3) using the time series of total recruitment adjusted for 

both hatchery and harvest (HatHarAdj). The first and second estimates use Holmes’ (2001) 

method directly. The third estimate, HatHarAdj, uses a modification (McElhany and Payne in 

prep.) to account for productivity that would not be evident from looking at escapement data 

alone. 

In all cases, 4-year-long unweighted running sums of the appropriate time series were 

used as the basic input data and lags of 1 through 4 years (τ = 4 in Holmes’ notation) were used 

for the slope estimates. The HatAdj estimate requires average age of reproduction as an input 

parameter and, lacking specific data for the Quinault population, we used an average age of 3.5 

years. A Microsoft Excel spreadsheet was developed to compute these estimates rather than the 

SimSalmon computer program, because the spreadsheet approach facilitates manipulation of the 

data to conduct the diagnostic tests. 

The computations were conducted on the entire 1910–2005 (96-year) time series and on 

the 1973–2005 (33-year) subset, during which time we have independent estimates of 

escapement and catch. 

For the 96-year time series, σ

2

 was estimated to be between 0.159 and 0.175 for the 

Wesc, HatAdj, and HatHarAdj analyses (Table B-2). For the 33-year time series, σ

2

 was 

estimated to be between 0.038 and 0.061 for the three analyses (Table B-2). 

Diagnostics 

We examined seven diagnostic tests, which look at assumptions of the method, suggested 

by Paul McElhany as follows. 

1. Slope of σ

2 (τ) versus τ is linear. 

Visual inspection suggests that the relationship of σ

2

(τ) versus τ is linear for both series 

(Figure B-3 and Figure B-4). For the three, 96-year HatAdj analyses, there is a possible 

deviation from linearity at τ = 4. Reducing the maximum lag to 3 from 4 for the 96-year time 

series would increase the estimates of σ

2

. 

Table B-2. Estimates of μ and σ

2

 for the two Lake Quinault sockeye salmon time series, 1910–2005 (96 

years) and 1973–2005 (33 years). 

Fixed Wesc HatAdj HatHarAdj

1910–2005 (96 years)

μ –0.011 –0.014 0.129

σ

2 0.163 0.159 0.175

1973–2005 (33 years)

μ 0.007 0.000 0.063

σ

2 0.041 0.038 0.061

30
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1234

Lag (τ)

WEsc HatOnly HatHar

Value of 

σ2 or 

μ

Figure B-3. Graphs of σ

2

 versus lag for the 96-year time series. 

0

0.05

0.1

0.15

0.2

0.25

0.3

1234

Lag (τ)

WEsc HatOnly HatHar

Value of 

σ 2 or 

μ

Figure B-4. Graphs of σ

2

 versus lag for the 33-year time series. 

2. Distribution of ln(Nt+1/Nt) is approximately normal. 

Inspection of a normal probability plot of the natural log interannual ratios of the 4-year 

running sums shows significant deviation from a normal distribution in some cases. For 

example, the 96-year HatHar adjusted series (Figure B-5) differs from normality at p = 0.06 by 

the Shapiro-Wilk test and has a coefficient of skewness significantly different from 0 at p = 0.02. 

The comparable series for the 33-year period (Figure B-6) fits the normal distribution 

better, with a Shapiro-Wilk coefficient at p = 0.63 and a skewness coefficient different from 0 at 

p = 0.2. 

31
-3

-2

-1

0

1

2

3

4

-0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5

Normal quantile

Lake Quinault 1910–2005 — HatHar

Figure B-5. Normal probability plot of ln(Nt+1/Nt) for escapement, 96-year time series. 

-3

-2

-1

0

1

2

3

-0.4 -0.2 0 0.2 0.4 0.6 0.8

Normal quantile

Lake Quinault 1973–2005 — HatHar

Figure B-6. Normal probability plot of ln(Nt+1/Nt) for escapement, 33-year time series. 

3. No temporal trend in ln(Nt+1/Nt). 

A graph of the time series of ln(Nt+1/Nt), adjusted for hatchery and harvest effects, 

appears to be stationary, although there seems to be a reduction in the absolute values of the 

extreme high and low values going forward in the 96-year time period (Figure B-7). 

32
4. No temporal trend in preharvest recruits per spawner. 

A graph of the 4-year running sum of recruits (catch plus escapement) divided by the 4-

year running sum of NOR spawners 4 years earlier shows a cyclic pattern (high every 7–10 

years) with decreasing recruits per spawner overall over time (Figure B-8). 

-1

-0.5

0

0.5

1

1.5

2

1913 1933 1953 1973 1993

Lag 1 Hat-Har adj. RS ratio

Lag 1 Hat-Har adj. RS ratio 

Figure B-7. Graph of natural logarithm of lag 1 ratios of 4-year running sums of spawning escapements, 

96-year time series. The year on the x-axis is the final year of the running sum in the 

denominator. 

0

2

4

6

8

10

12

14

1913 1921 1929 1937 1945 1953 1961 1969 1977 1985 1993

Recruits per spawner

Figure B-8. Time series of 4-year running sum of catch plus escapement (t+4) divided by 4-year running 

sum of escapement (t) for the previous 4 years. The x-axis is labeled with the final year of the 

escapement running sum. 

33
5. No density dependence. 

To look for density dependence, we examined the size of the return from the size of the 

spawning abundance. Assuming an average age of 4 years, we compared escapement in year t 

with the catch plus escapement 4 years later for the years 1910–2001; there is a definite pattern 

of density dependence (Figure B-9 upper graph). If we only look at recent abundance (1973–

2001), although the range of escapements and returns is much reduced, the pattern of density 

dependence is still notable, but much less pronounced (Figure B-9 lower graph). 

6. No temporal trend or changes in σ

2

. 

Estimates of σ

2

 for 20-year segments of the 1910–2005 time series range from 0.020 to 

0.432 (Table B-3). The estimates from the Wesc, HatAdj, and HatHar series are nearly identical 

for the 1910–1969 period because every estimate of total returns before 1973 used the constant 

0.845 catch to escapement ratio (Table B-1). The magnitude of Wesc and the total return are 

both positively correlated with σ

2

 (computed with the HatHar correction) at p < 0.05, and this 

coincides with a downward trend in both abundance and σ

2

 over time until about 1960 

(Figure B-10). However for the recent period, σ

2

 appears to be stationary (Figure B-10). 

7. Data should not encompass regime shifts. 

Major regime shifts (long-term changes in overall survival or productivity) could affect 

the estimate of σ

2

, which is meant to be the variance of growth rate on a relatively short-term 

basis. There is no good statistical test for this, but any major regime shifts should be apparent 

from a graph of the escapement over time (Figure B-10). There appears to be an earlier period of 

higher abundance, followed by a more recent period of lower abundance. The 1973–2005 period 

encompasses part of this more recent period of low abundance and appears to be within a single 

production regime. 

Conclusions 

The Quinault Lake sockeye salmon provide one of the longest data sets available within 

or near our domain. However, only the data from 1973 through the present are useful for 

estimating the variance in growth rate during a period of stable growth. 

The 1973–2005 data series for Lake Quinault appears to be a reliable data set and is 

usable for our purpose. The relationships of σ

2 to τ are approximately linear, the time series of 

the log growth rate and recruits per spawner appear to be stationary, the natural log ratios of the 

4-year running sums are approximately normally distributed, and there is no indication of major 

regime shifts. 

34
0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

0 100,000 200,000 300,000 400,000 500,000 600,000

All spawners y = t

NOR return y = t +4

0

20,000

40,000

60,000

80,000

100,000

120,000

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000

All spawners y = t

NOR return y = t +4

Figure B-9. Graphs of catch plus escapement (t+4) versus escapement (t). The upper graph is for the 

entire time series, 1910–2001, and the lower graph is the same plot with the axes reduced to 

emphasize the recent year time series, 1973–2001, with triangles representing those years and the 

small diamonds being early years that fall in the same range within the graph. In both graphs, the 

linear line is the replacement line (i.e., 1:1 return per spawner). 

35
Table B-3. Estimates of σ

2

 and mean abundance for 20-year segments of the Quinault sockeye salmon 

time series. 

σ2

 estimate Mean abundance 

Years Wesc HatAdj HatHarAdj

NOR 

escapement

Total 

return 

1910 1929 0.432 0.424 0.417 100,928 208,918 

1920 1939 0.236 0.228 0.224 95,990 200,679 

1930 1949 0.284 0.272 0.278 132,070 272,622 

1940 1959 0.097 0.096 0.097 104,434 214,380 

1950 1969 0.054 0.054 0.054 47,911 97,904 

1960 1979 0.054 0.054 0.145 33,744 65,617 

1970 1989 0.048 0.049 0.092 30,785 49,278 

1980 1999 0.029 0.020 0.036 33,705 44,908 

1986 2005 0.072 0.070 0.118 33,592 43,531 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1900 1920 1940 1960 1980 2000

Start of 20-year period

σ

2

Figure B-10. Trend in σ

2

 (HatHar) computed for 20-year period with different starting dates. 

36
Appendix C: “R” Functions Used for Simulation 

of Population Dynamics in PVA 

This appendix provides the computer code for the “R” functions. (Note: The default 

values for these functions are not necessarily the values used in our runs; see Methods section of 

this report.) 

Dennis <- function(mu=0, Q=.1, NZero=10000, T=100, QET=250, 

Maxn=3*NZero, randomMax=FALSE) { 

 # mu = log growth rate, Q = variance of mu 

 N <- NULL 

 n <- NZero 

 eta <- rnorm(T, 0, sqrt(Q)) 

 z <- rnorm(T, 0, sqrt(Q)) 

 for (i in 1:T) { 

 n <- n * exp(mu + eta[i]) 

 if (n < QET) n <- 0 

 if (n > Maxn) 

 if (randomMax) n <- MaxN*exp(z[i]) else n <- Maxn 

 N <- c(N,n) 

 } 

 return(N) 

 } 

Dennis.Repeat <- function(NRuns=10000, NZero=10000, mu=0, QET=250, 

 Q=.1, Maxn=3*NZero) { 

 Extinct <- NULL 

 for (i in 1:NRuns) { 

 Pop <- Dennis(T=100, mu=mu, QET=QET, NZero=NZero, Q=Q, 

 Maxn=Maxn, randomMax=FALSE) 

 p <- min(Pop) 

 if (p <= 0) 

 Extinct <- c(Extinct, TRUE) 

 else Extinct <- c(Extinct, FALSE) 

 } 

 E <- sum(Extinct) 

 return (c(NZero, E/NRuns)) 

 } 

NZero.Test <- function(Low=10000, High=150000, Step=5000, Q=.1, 

QET=250, NRuns=10000) { 

 NZero <- Low 

 Output.NZero <- NULL 

 Output.ExtProb <- NULL 

 while (NZero <= High) { 

37
38

 Output.NZero <- c(Output.NZero, NZero) 

 ep <- Dennis.Repeat(NRuns=NRuns, NZero=NZero, Q=Q, QET=QET, 

 Maxn=3*NZero) 

 Output.ExtProb <- c(Output.ExtProb, ep[2]) 

 NZero <- NZero + Step 

 } 

 Output <- 

data.frame("NZero"=Output.NZero,"ExtProb"=Output.ExtProb) 

 return(Output) 

 } 
Recent NOAA Technical Memorandums

published by the

Northwest Fisheries Science Center

NOAA Technical Memorandum NMFS-NWFSC98 Johnson, L.L., G.M. Ylitalo, M.S. Myers, B.F. Anulacion, J. Buzitis, W.L. Reichert, and T.K. Collier. 

2009. Polycyclic aromatic hydrocarbons and fish health indicators in the marine ecosystem in Kitimat, British 

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Scott. 2009. Identification of an independent population of sockeye salmon in Lake Ozette, Washington. 

U.S. Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-96, 18 p. NTIS number PB2009-108060. 

95 Harms, J.H., J.A. Benante, and R.M. Barnhart. 2008. The 2004–2007 hook and line survey of shelf 

rockfish in the Southern California Bight: Estimates of distribution, abundance, and length composition. 

U.S. Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-95, 110 p. NTIS number PB2009-106740.

94 Fleischer,G.W., K.D. Cooke, P.H. Ressler, R.E. Thomas, S.K. de Blois, and L.C. Hufnagle. 2008. The 

2005 integrated acoustic and trawl survey of Pacific hake, Merluccius productus, in U.S. and Canadian 

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number PB2009-104774.

93 Keller, A.A., B.H. Horness, E.L. Fruh, V.H. Simon, V.J. Tuttle, K.L. Bosley, J.C. Buchanan, D.J.

 Kamikawa, and J.R. Wallace. 2008. The 2005 U.S. West Coast bottom trawl survey of groundfish resources off Washington, Oregon, and California: Estimates of distribution, abundance, and length composition. U.S. Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-93, 136 p. NTIS number PB2008-113766.

92 Levin, P.S., M.J. Fogarty, G.C. Matlock, and M. Ernst. 2008. Integrated ecosystem assessments. U.S. 

Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-92, 20 p. NTIS number PB2008-113765.

91 Wainwright, T.C., M.W. Chilcote, P.W. Lawson, T.E. Nickelson, C.W. Huntington, J.S. Mills, K.M.S. 

Moore, G.H. Reeves, H.A. Stout, and L.A. Weitkamp. 2008. Biological recovery criteria for the Oregon 

Coast coho salmon evolutionarily significant unit. U.S. Dept. Commer., NOAA Tech. Memo. NMFS-

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Most NOAA Technical Memorandums NMFS-NWFSC are available online at the

Northwest Fisheries Science Center web site (http://www.nwfsc.noaa.gov).