U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

NOAA Technical Memorandum NMFS-NWFSC-67

Cross Validation

of Quasi-extinction Risks

from Real Time Series:

An Examination of Diffusion

Approximation Methods

July 2005
NOAA Technical Memorandum

NMFS Series

The Northwest Fisheries Science Center of the National

Marine Fisheries Service, NOAA, uses the NOAA

Technical Memorandum NMFS series to issue informal scientific and technical publications when complete formal review and editorial processing are not

appropriate or feasible due to time constraints. Documents published in this series may be referenced in the

scientific and technical literature.

The NMFS-NWFSC Technical Memorandum series of

the Northwest Fisheries Science Center continues the

NMFS-F/NWC series established in 1970 by the

Northwest & Alaska Fisheries Science Center, which

has since been split into the Northwest Fisheries

Science Center and the Alaska Fisheries Science

Center. The NMFS-AFSC Technical Memorandum

series is now being used by the Alaska Fisheries

Science Center.

Reference throughout this document to trade names

does not imply endorsement by the National Marine

Fisheries Service, NOAA.

This document should be cited as follows:

Holmes, E.E., W.F. Fagan, J.J. Rango, A. Folarin, J.A.

Sorensen, J.E. Lippe, and N.E. McIntyre. 2005. Cross

validation of quasi-extinction risks from real time

series: an examination of diffusion approximation

methods. U.S. Dept. Commer., NOAA Tech. Memo.

NMFS-NWFSC-67, 37 p.
NOAA Technical Memorandum NMFS-NWFSC-67

Cross Validation

of Quasi-extinction Risks

from Real Time Series:

An Examination of Diffusion

Approximation Methods

E.E. Holmes, William F. Fagan1, Jessamy J. Rango2,

Ayoola Folarin2

, Jeffrey A. Sorensen2, Joyce E. Lippe2, and

Nancy E. McIntyre3

Northwest Fisheries Science Center

Conservation Biology Division

2725 Montlake Boulevard East

Seattle, Washington 98112

University of Maryland

Department of Biology

College Park, Maryland 20906

Arizona State University

Department of Biology

Tempe, Arizona 85287

Texas Tech University

Department of Biological Sciences

Lubbock, Texas 79409

July 2005

U.S. DEPARTMENT OF COMMERCE

Carlos M. Gutierrez, Secretary

National Oceanic and Atmospheric Administration

Vice Admiral Conrad C. Lautenbacher, Jr. USN (Ret), Administrator

National Marine Fisheries Service

William T. Hogarth, Assistant Administrator for Fisheries

1

2

3
Most NOAA Technical Memorandums NMFS-NWFSC

are available online at the Northwest Fisheries Science

Center web site (http://www.nwfsc.noaa.gov)

Copies are also available from:

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

phone orders (1-800-553-6847)

e-mail orders (orders@ntis.fedworld.gov)

ii
Table of Contents 

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

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

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

Acknowledgments........................................................................................................................................xi 

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

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

Estimating Parameters from Time Series of Counts: The Dennis Method...............................................5 

Estimating Parameters Using Running Sums: The Dennis-Holmes Method ...........................................7 

Cross-validating Predicted Declines Against Observations.....................................................................8 

Results.........................................................................................................................................................10 

Unbiased Quasi-extinction Estimates.....................................................................................................10 

Severe Declines and Actual Extinction Events Had Low Predictability................................................10 

Salmon and Nonsalmon Time Series Differ...........................................................................................13 

Discussion...................................................................................................................................................15 

References...................................................................................................................................................19 

Appendix A.................................................................................................................................................25 

Appendix B.................................................................................................................................................29 

iii
iv
List of Figures 

Figure 1. Schematic of a time series of population counts identifying data and population

sizes utilized in cross-validation analyses...................................................................................6 

Figure 2. Observed and predicted fraction of trajectories that are observed to reach 

quasi-extinction thresholds .......................................................................................................11 

Figure 3. Observed and predicted fraction of trajectories that reach quasi-extinction 

thresholds for fluctuating versus declining time series from the salmon data set.....................11 

Figure 4. Change in the predictability of population declines as the duration of the 

evaluation periods was increased..............................................................................................12 

Figure 5. Distribution of ln(Nt+1/Nt) ratios for populations that went extinct...........................................14 

v
vi
List of Tables 

Table 1. Estimated probabilities of observing a decline to 1 individual within the 10-year 

evaluation period for the populations that actually went extinct during the period. ...............13 

Table A-1. Summary of nonsalmon population time series used in cross-validation analyses. ................25 

Table B-1. Summary of salmon population time series used in cross-validation analyses.......................29 

vii
viii
Executive Summary 

Population viability analysis (PVA) has quickly become a widespread component of 

conservation planning for at-risk species. However, the quantitative utility of the PVA toolkit 

remains a strongly contested issue, with recent efforts turning from pure simulation studies to 

include direct assessments of the predictability of the dynamics of real populations. 

To explore further the efficacy of such extinction risk modeling, we employed a crossvalidation approach with long-term population censuses from 271 time series representing 46 

taxa, most of which were of past or present conservation concern (including 7 populations that 

actually went extinct). We used diffusion-approximation methods to estimate quasi-extinction 

risks for each population via two parameter-estimation techniques: the classical Dennis approach 

and the recently developed Dennis-Holmes approach. The latter technique can partition process 

error (environmental stochasticity) from nonprocess error (such as observation error). 

We found that quasi-extinction modeling that accounted for nonprocess error via the 

Dennis-Holmes approach more accurately matched realized population minima evident in the 

time series. Overall diffusion modeling correctly predicted the fraction of populations crossing 

quasi-extinction thresholds (>0 individuals). We also found little degradation of the 

predictability of quasi-extinction risks with lengthening prediction time horizons—from 10 to 30 

year horizons. At the same time, we found relatively low predictive ability for complete 

extinction events. With the exception of sockeye salmon, these events appeared to be due to 

declines that were well outside the normal distribution of year-to-year growth rates (i.e., some

anomalous event). For PVAs based on diffusion approximations, these results highlight both 

shortcomings (such as an absence of case-by-case certainty and the unpredictability of 

extinction) and successes (the ability to describe well the behavior of a collection of populations 

and species). 

ix
x
Acknowledgments 

Leah Gerber, Department of Biology, Arizona State University; Wendell L. Minckley, 

Department of Biology, Arizona State University; David Pearson, Department of Biology, 

Arizona State University; and Anne York, National Marine Mammal Laboratory, Seattle, guided 

us to or provided data sets. Steve Beissinger, Department of Integrative Biology, University of 

California at Berkeley; Dan Doak, Biology Department, University of California at Santa Cruz; 

Michelle Marvier, Biology Department, Santa Clara State University; Michelle McClure, 

Northwest Fisheries Science Center; and four anonymous referees offered comments and 

criticisms that improved the paper. 

xi
xii
Introduction 

An estimated 1,100–11,500 extinctions occur each year from a multitude of causes, most 

of which can be traced back to human impacts (Cox 1997). This loss of biodiversity has been 

called an “extinction crisis” (Soulé 1986), and in response to this crisis ecology has seen a surge 

of interest in the characterization of population vulnerability. However, biologists trying to 

develop ways to estimate extinction risks have encountered several logistical roadblocks. Most 

notably, we have precious few studies that provide long-term data detailing fluctuations in total 

population counts (Lawton 1996). Most population censuses have been conducted over a 

relatively short period (e.g., Orell 1989, Pistorius et al. 2000) or have been conducted only 

intermittently (e.g., Pierson and Turner 1998, Robertson and Jarvis 2000). As a consequence, 

long-term censuses of complete populations are relatively rare, meaning that conservation 

biologists must often use relatively short-term data to forecast population fates over longer time 

spans. Such forecasting has proved challenging because of the difficulties inherent in the 

accurate estimation of parameters underlying the dynamics of biological populations (Ludwig 

1996, Ludwig 1999, Fieberg and Ellner 2000, Holmes 2001, Ellner et al. 2002). 

Despite these difficulties, population viability analyses (PVAs) have now become a 

standard tool in conservation biology, with goals ranging from providing detailed guidance on 

management actions(Crouse et al. 1987) to simply characterizing the degree or nature of risk 

faced by populations(Morris et al. 1999, Fagan et al. 2001). Obtaining sufficiently detailed field 

data to parameterize models of population viability involves a challenging amount of work. 

Consequently, but unfortunately, for most species and situations, we lack the data required for all 

but the crudest PVAs. Indeed, it is telling that a recent synthesis found only 21 data sets (19 

species) with sufficient data for full PVA assessments(Brook et al. 2000). These data sets, 

which contained substantial detail on population size- or age-structure, life history, and 

demography, are far more characteristic of focused efforts by academic researchers than of the 

cash-strapped monitoring efforts by governmental wildlife agencies and nongovernmental 

organizations upon which so much modern conservation action depends. Though helpful when 

available, such detailed demography and basic population biology data are often lacking for 

species of conservation concern. As a result, any full assessment of the utility of PVAs must 

examine their performance when faced with less detailed information. 

Though still uncommon, long-term studies providing a continuous record of censuses, 

population counts, or estimates of population size occur more frequently than do in-depth 

demographic studies. Diffusion approximations (DAs) (e.g., Dennis et al. 1991, Holmes 2001) 

are one set of techniques that researchers have developed to estimate population vulnerability 

and extinction risk from limited data. The key to such approaches is the assumption of a simple 

stochastic exponential growth model and the estimation of the population growth rate and its 

variability from the year-to-year (or census-to-census) transitions in population size associated 

with such a model. These parameters, in combination with the most recent known population 

size, are then used to calculate the probability that a population will decline to extinction within a 

specified time frame. These models can also be used to discern additional information as well 
(Dennis et al. 1991), including profiles of quasi-extinction risk. Such profiles define the 

probability that a population will decline to each of a series of population sizes, of which 

extinction, or Nt=1, is but one of many potential values of interest (hence, “quasi-extinction”). 

Diffusion-approximation models provide a tool for estimating quasi-extinction risk, although 

such models may be constructed and parameterized in a variety of ways (Dennis et al. 1991, 

Lande et al. 1998, Engen and Saether 2000, Holmes 2001). One method of assessing the 

accuracy of DA models is to evaluate their performance in quantifying risk in real populations, 

as Ludwig (1999), Brook et al. (2000), and Ellner et al. (2002) have done. The general approach 

taken is a cross-validation analysis in which the first portion of a time series is used for 

estimating parameters, then the predictions of those parameterized models are evaluated by 

comparing them to the realized dynamics evident in the remaining portion of the time series. 

Brook et al. (2000) outlined the utility of applying cross-validation techniques to issues of 

extinction risk. They concluded that the good agreement between model predictions and realized 

dynamics evident in the evaluation portion of their time series was a strong endorsement of 

PVAs as a conservation tool. Ellner et al. (2002) criticized this conclusion, arguing that the 

results of Brook et al. (2000) fell far short of “predictive accuracy” and instead merely

demonstrated an absence of bias in ensemble—rather than species-level—estimates of

probabilities of quasi-extinction. 

Although one could take issue with Brook et al. (2000) for the inclusion of populations of 

relatively abundant species such as white-tailed deer (Odocoileus virginianus) and domestic 

sheep (Ovis aries) that are very well-studied ecologically but of much less interest from an 

extinction-risk perspective (Coulson et al. 2001), we find other details of their approach to be 

problematic. For example, the small size of their data set forced Brook et al. (2000) to combine 

evaluations of the performance of population viability models over different time frames within

the same analysis. Specifically, by examining model performance on the basis of “halves” of 

time series, Brook et al. (2000) combined extinction risk evaluations spanning only 6 years of 

data with evaluations spanning 28 years of data. Using half the data to parameterize and the 

other half to evaluate without regard for differences in time span (and hence variability) 

represented by those halved data sets complicates overall assessments of model performance. In 

addition, their method cannot be applied to species with nonoverlapping generations or other 

complicated life histories; these require a different approach (see Holmes 2001). A third and 

perhaps most important issue is that the analysis of Brook et al. (2000) involved only one species 

that actually went extinct. This limitation introduces a potential bias in that the dynamics of 

populations going extinct may differ from those that decline but do not go extinct. Despite these 

difficulties, Brook et al. (2000) provided a significant introduction to the issue of assessing the 

utility of extinction risk models via real data. Using data sets involving fewer species, Ludwig 

(1996) and Fieberg and Ellner (2000) have also conducted explorations of the utility of 

extinction risk modeling. These papers contrast with the optimistic conclusions of Brook et al. 

(2000), arguing that observation error and other uncertainties that plague real data make 

determinations of extinction risks rather futile exercises. In response to such criticisms, Brook 

et al. (2002) argue that despite its quantitative weaknesses, PVA remains a useful tool for 

conservation that is superior to alternative, often ill-formed resource management approaches 

that neglect potentially valuable data.

2
In this technical memorandum, we seek to contribute to a resolution of these PVA 

conflicts in six ways: 1) by using a substantially larger data set of populations, including several 

that have gone extinct; 2) by placing a greater emphasis on species that are of conservation 

interest; 3) by using a “sliding window” approach that standardizes the length of time series used 

in cross validation (instead of halving sets of varying lengths); 4) by contrasting two alternative 

approaches for parameter estimation (one of which can be used on species with nonoverlapping 

cohorts); 5) by restricting ourselves to the kinds of data (i.e., time series of counts) that are more 

typically available from monitoring programs; and 6) by studying the performance of DA 

techniques for data with high sampling error. 

3
Methods 

We conducted extensive literature searches to identify 49 time series of population 

censuses (representing 43 taxa) containing at least 21 years (20 transitions) of data (Appendix 

A). Gaps in the sequence of censuses were permissible. For this data set, we included only time 

series resulting from the application of standardized census techniques that provided an estimate 

of total size for wild populations. Six of these time series were from populations that were 

monitored as they actually went extinct. For populations monitored to extinction, we relaxed our 

restriction on time series length; the shortest such series we found involved an extinction in its 

14th year of monitoring. Seven of these 49 time series were also included in the analysis of 

Brook et al. (2000). 

An additional 222 time series (including one extinction) for four salmon species 

(Chinook, coho, steelhead, and sockeye) were collected from databases maintained by the 

National Marine Fisheries Service and the Pacific States Marine Fisheries Commission 

(Appendix B). Many of these time series involved species and stocks of conservation concern 

(Kareiva et al. 2000). These time series differ from the nonsalmon time series in a number of 

ways. First, salmon life history is characterized by long delays between birth and reproduction, 

combined with semelparity by most adults. These traits mean that counts of spawners in one 

year have no direct relationship with counts the next year. Second, the life history of salmon 

leads to striking boom-bust cycles in spawner count numbers—cycles that would be reflected to 

a much lesser degree in a total population count representing an integration of many age classes. 

Thus the variability in the censused class, spawners, is higher than that in the total population, 

and spawner variability does not directly reflect the underlying environmental variability 

affecting the total population’s trajectory. Third, salmon data are also plagued by unusually high 

observation error due not only to human variability, but also to variability in climate and runtiming that affect census accuracy (Hilborn et al. 1999, Dunham et al. 2001). For these reasons, 

the salmon time series include error structures considerably different than those present in the 

nonsalmon time series of Appendix A. We have therefore analyzed the two groups separately in 

order to contrast the accuracy of PVA predictions for data sets with high and low error. 

Observation error and cycles linked to age structure or other factors constitute types of 

“nonprocess” error. Historically, the need to disentangle such nonprocess errors from process 

errors (i.e, variability extrinsic to the population, such as environmental stochasticity) has 

represented a major stumbling block to conservation risk assessment and other areas of ecology 

(e.g., Carpenter et al. 1994, Ludwig 1996, Fieberg and Ellner 2000). To cope with highly 

corrupted data, Holmes (2001) developed a method to facilitate partitioning of the different error 

types from population time series. We compare this new method with more traditional DA 

approaches in our analyses, exploring their relative performance in data sets both with and 

without substantial nonprocess errors. 

Following Brook et al. (2000), we analyzed the time series using a cross-validation 

approach. We parameterized our extinction risk models from one portion of a time series, the 

4
estimation period, and then evaluated model performance over a subsequent portion, the 

evaluation period (Figure 1). We altered our methods of handling time series from those of 

Brook et al. (2000) in several key ways to increase standardization and internal consistency of 

our comparisons. Rather than halve each time series, we adopted a “sliding window” of 21 or 26 

years for the nonsalmon and salmon species, respectively. The difference in window size arose 

because of the need to filter the time series with high error, as detailed below. The first 11 years 

(16 years for salmon) in each window was the estimation period and was used to estimate model 

parameters. We then used the remaining years in the window to evaluate model performance. 

Note that our approach means that the estimation and evaluation periods of each window were 

effectively independent, because the only connection between the two fractions was that the final 

population size during the estimation period became the initial population size during the 

evaluation period. Sliding windows in which the evaluation period had missing data were 

excluded from analysis, but windows with missing data in the estimation period were allowed 

since the parameterization methods could cope with missing census years. To limit 

disproportionate representation by long time series, we used at most 10 sliding windows (picked 

at random) from any time series. To increase the independence of windows within a time series, 

we separated the start years of adjacent windows by at least 5 years (Figure 1). For example, a 

1960–1990 time series would be divided into 3 windows: 1960–1980, 1965–1985, 1970–1990. 

Estimating Parameters from Time Series of Counts: The Dennis 

Method 

Dennis et al. (1991) present a diffusion approximation approach for estimating extinction 

risks using time-series data. Diffusion approximations of population data derive from work on 

stochastic age-structured models (see Tuljapurkar 1982 and Dennis et al. 1991). Theory 

demonstrates that in the absence of density-dependence, changes in the size of a structured 

population behave asymptotically according to a stochastic discrete time model: 

( )

ε ( ) σ ω

μ ω ε ω

p p

t t p

 where is Normal 0,

N = N exp + , +

 (1) 

where Nt is the population size at time t, ω is the time gap between censuses (ω = 1 for annual 

censuses), μ is the underlying mean year-to-year population growth rate, and σp is the standard 

deviation of the distribution of year-to-year fluctuations in growth rate, termed the process error. 

Equation 1 can be approximated by a diffusion process; the diffusion process can then be used to 

estimate the statistical properties of the stochastic trajectories (such as distributions of extinction 

times, probability of reaching population thresholds, etc.) as a function of μ and σp (Tuljapurkar 

1982, Lande and Orzack 1988, Dennis et al. 1991). Dennis et al. (1991) discuss parameter 

estimation for the diffusion model and introduce a new estimation method that allows for 

missing years in the census time series used for parameterization. With the parameter estimates, 

a variety of extinction-related metrics can be calculated. One of these metrics, the probability 

that a population will reach a specified quasi-extinction threshold within a certain time frame, is 

widely used and forms the basis for our cross-validation analysis. Following prior usage, we 

refer to the combination of the Dennis et al. (1991) method for estimating parameters combined 

with DA for estimating risk metrics as the “Dennis method.” 

5
Figure 1. Schematic of a time series of population counts identifying data and population sizes utilized 

in cross-validation analyses. For nonsalmon time series (A), we used an “estimation period” 

and an “evaluation period” that were both 11 consecutive years in length (10 consecutive 

transitions). These two periods together form a “sliding window” that provides a snapshot of 

the population’s dynamics. Population size A1 is the initial population size for the first 

evaluation period, whereas population size B1 is the minimum population attained during the 

first evaluation period. In long time series, where it was possible to obtain more than one 

sliding window, windows were selected at random but always began at least 5 years later than 

its nearest neighbor (resulting in initial population size A2 and attained minimum population 

size B2). For salmon time series (B), we extended the estimation period to 16 years to 

accommodate the need to calculate running sums of population size. 

6
Estimating Parameters Using Running Sums: The Dennis-Holmes 

Method 

The Dennis method was developed for population processes of the form of Equation 1 

where the true population numbers, Nt, are observed. However, in many cases the observed 

counts are corrupted to some degree by nonprocess error (such as observation error) and 

researchers record instead a corrupted count, Ot, of the form: 

 and isf( , )

where is Normal(0, )

exp( ) ,

np np np

p p

t np t

t t p

O N

ε μ σ

ε σ ω

ε

N N exp(μω ε ), ω

=

+ = +

 (2) 

where Nt and Ot are the true and observed population numbers, respectively, and εp and εnp are 

the process and nonprocess error respectively. The distribution of εnp is unknown, and it has 

some unknown mean, μnp, and variance, . 2 σ np

One of the key differences between process and nonprocess error is that the nonprocess 

error does not feed back into the population process. Thus the variance due to nonprocess error 

does not grow with time. The most common example of nonprocess error is observation error in 

the counts themselves. However, other types of variability also act much like the model of 

Equation 2. For example, when the census includes only an age- or stage-specific subset of the 

population, the variance in this subset does not necessarily reflect the variance at the population 

level. Another example occurs when a clear relationship does not exist between the census count 

one year versus the next year, such as for insects with alternate-year cohorts or for sea-run 

salmon where the counts of returning adults in a given year are only weakly related to 

comparable counts the next year. A third common example of nonprocess error occurs when the 

population age structure has been perturbed, and the population is undergoing damped 

nonequilibrium cycles. 

When nonprocess error is present at high levels within a time series, the Dennis method 

highly overestimates the process error variance, (Holmes 2001). To circumvent these 

problems and generalize the DA approach for cases where nonprocess error is high, an 

alternative parameter estimation method (Holmes 2001, Holmes and Fagan 2002) was developed 

that separates process and nonprocess error. The method as presented in Holmes and Fagan 

(2002) involves an ad hoc running sum transformation of the data that is used to improve 

parameter estimation when working with the short time series (15–50 years) that are typical for 

real data. The appendix in Holmes and Fagan (2002) provides a more rigorous statistical 

discussion, without the transformation, for infinite time series. Tests of the running-sum method 

using simulated data (Holmes 2001, Hinrichsen 2002, Morris and Doak 2003, Holmes 2004) 

indicate that it can provide parameter estimates that are relatively unbiased even in the face of 

high sampling error and relatively short time series. 

2 σ p

7
Here, we merely outline the method’s key features. The reader is referred to previous 

papers (Holmes 2001, Holmes and Fagan 2002, Holmes 2002) for more in-depth discussions. 

Central to the method is the translation of a time series of counts into a time series of running 

sums by adding together several consecutive counts to yield 

∑=

= + −

i

Rt Nt i

1

1

L

 (3) 

where L is the filter length, and should take values between 3 to 6. We used L = 4 for both 

salmon and nonsalmon time series. For consistency with established usage among salmon 

conservation biologists, we refer to the application of DA using this method as the “DennisHolmes method.” The calculations of the risk metrics are essentially those in Dennis et al. 1991, 

whereas the parameter estimation methods are those in Holmes and Fagan (2002). 

Because they interfere with the calculation of the running sums, missing data (i.e., years 

with no census) require a different treatment in the Dennis-Holmes method than in the Dennis 

method. First, we eliminated from consideration all sliding windows in which data for 3 or more 

consecutive census years were missing. However, if one or two consecutive censuses were 

missing in the estimation period, the counts for those dates were linearly interpolated. This 

interpolation constitutes a standard step in the application of the Dennis-Holmes technique 

(Holmes and Fagan 2002). In contrast, sliding windows with missing data in the evaluation 

period were always excluded, because the missing data point could have been the population 

minimum for that window. In all cases, any analyses that compared the Dennis-Holmes and 

Dennis methods used identical sets of estimation and evaluation periods. 

Cross-validating Predicted Declines Against Observations 

Our cross-validation analyses addressed whether the predicted probability of reaching a 

given threshold within the evaluation period matched the frequency of declines actually 

observed. This probability is similar to the probability of extinction (to 1 individual) except that 

we instead used a series of quasi-extinction thresholds (xN0) where N0 is the population size at 

the start of the evaluation period and x is a proportion from 0 to 1. Lande and Orzack (1988) and 

Dennis et al. (1991) give analytical solutions for the probability of crossing a quasi-extinction 

threshold before some time horizon t. However, these analytical solutions implicitly assume that 

the time series is observed continuously. For cross-validation purposes we had to adjust these 

analytical solutions, because the actual time series are only observed at discrete times—generally 

once a year (Holmes and Fagan 2002). 

The Dennis method assumes that nonprocess error variability is minimal and attributes all 

variability to process error. In contrast, the Dennis-Holmes method assumes that some of the 

variability is nonprocess error, and partitions the variability between process and nonprocess 

error. These differences in the treatment of variability engender different predictions concerning 

the probability of observing quasi-extinction. To the extent that the nonprocess error in the data 

represents sampling error, the Dennis-Holmes method allows us to contrast the probability of 

observing quasi-extinction in our corrupted counts with the probability of true quasi-extinction 

(due to process error alone). When the observations are corrupted by sampling error, the 

8
probability of observing quasi-extinction is greater than the probability of actual quasiextinction. 

Using the estimated probabilities of observing declines, denoted and (from the 

Dennis and Dennis-Holmes methods respectively), we compared curves describing the fraction 

of windows that actually crossed various quasi-extinction thresholds during the evaluation period 

versus the fraction expected to do so given the estimated probabilities. We calculated the 

expected fractions by summing the estimated probabilities for all evaluation periods divided by 

the number of periods, m: 

PD

ˆ PHˆ

∑=

= iPi

m 1

ˆ expected fraction 

m 1 (4)

where is the or estimate for the i-th evaluation period. Pi

ˆ PD

ˆ PHˆ

Our study included three additional analyses addressing prominent issues in the study of 

extinction risk. For these comparative analyses, we used only the salmon data set because it had 

a sufficient number of long time series. First, we explored whether the accuracy of estimated 

quasi-extinction risks was influenced by the overall trend of the time series. We did this by 

examining separately those 62 salmon populations with overall declining trends and another 143 

salmon populations best described as fluctuating. We characterized those time series with an 

estimated median rate of growth 1.05 > exp( μˆ ) > 0.95 over the entire length of the time series as 

“fluctuating,” whereas “declining” time series were those with exp( μˆ ) < 0.95. Populations that 

were generally increasing (exp( μˆ ) > 1.05) were excluded. 

Second, to explore how the predictability of quasi-extinction risks degraded over time, 

we examined whether the bias in the estimated probability of quasi-extinction increased as one 

projected over longer periods of time. It is well known that the confidence intervals around 

probability of extinction estimates widen as the projection period increases (Dennis et al. 1991, 

Fieberg and Ellner 2000). Our analysis looked instead at whether there was a change in the 

mean tendency to overestimate or underestimate declines. For this analysis, we selected those 

salmon time series for which 46-year windows were available. These windows were divided 

into a 16-year estimation period, as before, followed by a 30-year period for evaluation. We

compared the predicted versus observed fraction of windows that reached quasi-extinction in the 

10, 20, or 30 years after the prediction period. In this way, the same estimation period was used 

for comparing 10-, 20-, and 30-year evaluation periods. 

Third, we expanded our analysis of estimation bias to examine the predictability of severe 

declines (defined as ≥95%) and extinctions. To do this, we examined the mean risk estimates for 

the subset of time series that experienced a severe decline or extinction during the evaluation 

period. Note that this analysis does not address the accuracy or precision of our probability 

estimates: that is something we cannot address without knowing the true underlying probabilities 

of decline (see Discussion section). Instead, this analysis addresses whether these severe events 

are unpredictable—whether because of the difficulties of estimating parameters for stochastic 

processes or simply because severe declines happen by chance. 

9
Results 

Unbiased Quasi-extinction Estimates 

For the nonsalmon time series, with low nonprocess error, parameters estimated via either 

the Dennis or the Dennis-Holmes approach gave good estimates of the frequency with which 

thresholds of various magnitudes were observed during the evaluation period (Figure 2). 

However, for the data with high nonprocess error (the salmon data set) the Dennis method 

underestimates the frequency of small and moderate declines and overestimates the frequency of 

large decline (Figure 2). This is the pattern expected when process error is severely 

overestimated (Holmes and Fagan 2002), as we would expect the Dennis method to do when 

nonprocess is high. By separating the process and nonprocess error, the Dennis-Holmes method 

provided an improved match for this data set. The Dennis-Holmes predictions followed the 

shape of the observed curve more closely, although there was a slight (though uniformly present) 

underestimation of the observed risk of quasi-extinction. This pattern is suggestive of a slight 

underestimation of μ. 

Analyses of the fluctuating and declining subsets of salmon stocks yielded similar results 

(Figure 3). In both types of time series, the Dennis method tended to underestimate the 

frequency of small and moderate declines and overestimate the frequency of large declines, 

whereas the Dennis-Holmes method more accurately captured the likelihood of both small and 

large declines. As the duration of the evaluation period was lengthened (Figure 4), we found no 

evidence that the bias in the predictability of quasi-extinction changed. Note that this is an 

analysis of bias only, it does not address the variability of the estimates, which theory indicates 

will increase with lengthened evaluation periods.

Severe Declines and Actual Extinction Events Had Low 

Predictability 

When we examined those time series segments actually exhibiting severe declines during 

the evaluation period, we found that we would have predicted relatively few of them to 

experience such declines on the basis of their dynamics during the preceding estimation period. 

For the trajectories that experienced a 95% decline in the evaluation period, the mean estimated 

probability of such a decline was only 9% with the Dennis-Holmes method. With the Dennis 

method, mean probability was 23%, but this method overestimated risks for the salmon data (see 

Figure 2), from which came the vast majority of our data on severe declines. There was a close 

correspondence between the Dennis-Holmes estimated probability and the fraction of evaluation 

periods that actually experienced a 95% decline (also 9%). This suggests that in our data set, the 

majority of severe declines were low probability events that do occur in populations that are 

otherwise at low risk. In other words, if the true risk of 95% decline were 9%, we would expect 

(as we did) that 9% of evaluation periods would experience such decline. Supporting this 

10
Figure 2. Observed and predicted fraction of trajectories that are observed to reach quasi-extinction 

thresholds. The evaluation periods were 10 years long for both data sets. The estimation 

periods were 11 years for the nonsalmon time series and 16 years long for the salmon time 

series. 

Figure 3. Observed and predicted fraction of trajectories that reach quasi-extinction thresholds for 

fluctuating versus declining time series from the salmon data set. Fluctuating time series 

were characterized as having an estimated median rate of growth (exp( μˆ )) between 1.05 and 

0.95 over the entire length of the time series. Declining time series were characterized by an 

estimated median rate of growth of less than 0.95. Windows were 26 years long with a 16-

year estimation period and 10-year evaluation period. 

11
Figure 4. Change in the predictability of population declines as the duration of the evaluation periods 

was increased. Only those salmon time series with at least 46 years of data were used. For 

each plot, the same estimation periods were used but the evaluation period was extended from 

10 to 20 to 30 years. 

12
interpretation, we found that the yearly declines (the ln(Nt+1/Nt) ratios) of the trajectories which 

experienced a 95% decline did not have obvious outliers. 

Seven of our time series captured actual extinction of a population (six nonsalmon 

populations plus Snake River sockeye). Like the estimates of severe decline, the estimated 

probabilities of extinction were very low for all species except sockeye salmon (Table 1). To 

examine whether the extinctions were outlier events, we examined the ln(Nt+1/Nt) ratios up to 

and including the extinction events. For all seven populations, the population dynamics were 

indicative of generally declining (or at least not increasing) populations (Figure 5). For six of the 

seven, the actual transitions to extinction were characterized by anomalously small ln(Nt+1/Nt) 

ratios (Figure 5). Since the estimated distribution of ln(Nt+1/Nt) is used to forecast declines, if the 

extinction event is anomalous, extinction itself will not be predicted based on the information in 

the estimation period. 

Table 1. Estimated probabilities of observing a decline to one individual within the 10-year evaluation 

period for the populations that actually went extinct during the evaluation period. 

Species 

Probability of Observing 

Extinction (Dennis) 

Probability of Observing 

Extinction (Dennis-Holmes) 

African wild dogs (Lycaon pictus) 0.103 0

Middle spotted woodpecker

(Dendrocopos medius) 

0 0

Golden plover (Pluvialis 

apricaria) 

0 0

Wood turtle (ALC) (Clemmys 

insculpta) 

0 0

Wood turtle (BLC) 0 0 

Snake River sockeye salmon 

(Oncorhynchus nerka) 

0.33 0.095

Red-cockaded woodpecker

(Picoides borealis) 

0.002 0

Salmon and Nonsalmon Time Series Differ 

Compared with the nonsalmon time series, salmon time series are substantially more 

variable and more likely to exhibit large percentage declines (Figure 2). The potential for 

precipitous declines underscores the extensive degree to which salmon data sets contain 

nonprocess error. The median nonprocess error variance for the salmon windows was 0.35 (with 

75% of the estimates between 0.11 and 1.26), compared to a median nonprocess error variance of

0.006 for the nonsalmon windows with (75% of the estimates between 0.0008 and 0.15). 

13
Figure 5. Distribution of ln(Nt+1/Nt) ratios for populations that went extinct. The crossed-through ratios

denote the final declines that marked the extinction events. The parameter μ is the underlying

mean year-to-year population growth rate from the diffusion approximation. 

14
Discussion 

Overall, our cross-validation analysis highlights several key results pertaining to the use 

of diffusion approximation methods for evaluating population vulnerability. Foremost, the 

relative matches between the diffusion approximation models and observed declines are a strong 

endorsement of this general approach to risk assessment. If diffusion approximations were poor 

descriptors of the underlying population processes, or if our conceptualization of process and 

nonprocess errors as drivers of population dynamics were inappropriate, this diffusion 

approximation with two parameters would not have allowed us to recapitulate the collection of

population declines as closely as we did (Figure 2). From a practical perspective, this success is 

especially noteworthy in that we used only count data. This paucity of data, which contrasts 

strongly with the extensive life history and detailed demography needed for full population 

viability analyses like those conducted by Brook et al. (2000), is fairly typical of the data 

limitation facing many species of conservation concern. Consequently, being able to use such 

limited data to forecast the expected frequency of population declines for a collection of species 

suggests that diffusion approximation techniques can aid conservation planning at the 

multispecies/multipopulation level. 

Both the Dennis and Dennis-Holmes parameterization methods are useful for predicting 

risk of decline to quasi-extinction levels, but for different kinds of species and data sets. The 

Dennis method performed well for time series with low nonprocess error; whereas for time series 

with high nonprocess error, it tended to underestimate the probability that small declines will be

observed and overestimate the probability of large declines. This is the expected pattern if

process error variance is overestimated for these data sets and suggests that indeed, because the 

Dennis method combines nonprocess error and process error variance together, it overestimates 

the process error variance when nonprocess error is high. In contrast, the Dennis-Holmes 

method, which separates process and nonprocess error variance, yielded close estimates of the 

observed declines for the salmon data — but with a tendency toward slight underestimation. 

Close fits were also observed for the collection of nonsalmon time series with relatively low 

nonprocess error. It should be noted that our analyses cross-validated the probability of 

observing a decline. The Dennis-Holmes method makes a distinction between declines due to 

process error alone versus due to both process error and nonprocess error. To the extent that the 

nonprocess error represents some type of observation error, this is the distinction between the 

probability of observing quasi-extinction and the probability of actual quasi-extinction. The 

Dennis method does not make such a distinction since all variability is attributed to process error. 

When observation error is high, the difference between the actual versus observed declines is 

significant (Figure 2, dotted versus solid black lines). 

Choosing between the different DA parameterization methods requires some judgment 

about the level of nonprocess error in the data. In those cases featuring relatively little 

nonprocess error (e.g., the nonsalmon time series in Appendix A), the Dennis-Holmes method 

yielded decline curves that closely matched the observed declines across species. However, this 

is an indication of a lack of bias and it does not address the level of variability in the estimates. 

15
In fact, the Dennis-Holmes parameterization method trades an improvement in bias problems for 

an increase in the variability of the parameter estimates. Simulations indicate that when the 

nonprocess error variance is less than the process error variance, the Dennis et al. (1991) 

parameterization methods will provide tighter—although slightly biased—estimates. But when 

nonprocess error is high, the biases become severe and trading lack of bias for increased 

variability is warranted. See Holmes (2002) for a discussion on selecting parameterization 

methods for a particular population using sensitivity analyses based on age-structured models. 

Our analyses looked primarily at whether our probability estimates were biased. It would 

have been interesting and compelling to examine the precision of the estimated probabilities, Pˆ , 

directly using our data set (i.e., to look at the relationship between the estimated and true risks). 

Unfortunately, this is not possible unless the underlying true parameters of each time series are 

known (i.e., the true P) or unless it is known that the collection of time series all have very 

similar, albeit unknown, underlying parameters (i.e., similar Ps). Likewise, it is uninformative to 

look for a relationship between specific estimated risk levels and the frequency of actual declines 

(i.e., were declines more likely when the estimated risks were higher), even though this appears 

to be a very natural analysis to do. To do such an analysis in a meaningful way, the true 

distribution of P (probability of decline) must be known. To see this, suppose that most of our 

populations have similar true probabilities of decline (we do not know if this is or is not the 

case), then the observed frequency of decline would be similar (i.e., would be approximately the 

true P) regardless of the estimated Pˆ and regardless of the precision of the Pˆ estimates. 

Although we could not examine precision with our data set, there is ample evidence that 

estimates of the probability of extinction (or quasi-extinction) tend to be highly uncertain with 

wide confidence intervals, particularly when the true probability is intermediate. This has been 

shown with simulations (Ludwig 1999, Fieberg and Ellner 2000, Ellner et al. 2002) and with 

calculations of the posterior probability distributions for risk metrics from real data (Holmes 

2004). 

However, the lack of bias that we observed in DA quasi-extinction probabilities suggests 

a way to circumvent the uncertainty problem. Rather than trying to attack the variability 

problem directly, the lack of bias suggests that we can use diffusion approximations to accurately 

estimate risk within groups rather than on a case-by-case basis. For example, say in a collection 

of 10 populations, we calculate that the mean probability of 90% decline in 10 years is 0.2. This 

estimate of the mean probability can be quite precise, since the variability of the mean is 1 / 10

less variable that the individual estimates. This analysis indicates that we should expect 2 of the 

10 populations to experience a severe decline in 10 years, although we cannot determine which 

two. This type of analysis also emphasizes that although mean risk within the collection is low, 

the probability is high that a few of the populations will experience severe declines. 

In contrast to the successes predicting proportional declines, the diffusion approximation 

model appeared to do poorly at predicting complete extinction events. Examining the population 

trajectories that experienced complete extinction (zero individuals), we found that both 

parameterization techniques (Dennis and Dennis-Holmes) appeared to do a distinctly poor job of 

signaling the real vulnerability of the populations (Table 1). Typically, the extinction-bound 

species, though declining, were expected to have a less than 1% risk of experiencing the 

pronounced drops they actually registered. In a collection of 271 time series with a 1% risk of 

16
extinction, we would expect approximately 3 extinctions rather than the 7 in our dataset. This 

might be explained by arguing that extinctions attract attention and thus were more likely to be 

documented. However, in six of the seven extinctions, the final extinction event, as reflected in 

the final Nt+1/Nt ratio, was of unusual magnitude (Figure 5) and was outside the normal 

distribution of year-to-year variability. The one exception was sockeye salmon. For this species, 

the Nt+1/Nt ratio associated with the final extinction event was within the prior range of year-toyear variability. This suggests some kind of anomalous final collapse. Though disconcerting 

from the perspective of population prediction, such sudden, catastrophic events do mirror our 

conceptual understanding of the extinction process (Simberloff 1986, Simberloff 1988, Caughley 

1994). Given this concept of extinction due to unpredictable catastrophic events, Coulson et al. 

(2001) have suggested that risk analyses should be used to predict decline to quasi-extinction 

levels that represent critical population sizes rather than decline to extinction, per se. 

For severe declines (95%) rather than complete extinction per se, we found that the Nt to 

Nt+1 ratios leading up to and immediately preceding the decline were well within the expected 

distributions and that the frequency of 95% declines in the data (9%) matched the expected 

probability from the DA model (also 9%). These observations suggest that the DA model was 

appropriately modeling the probability of severe decline. However, this did not translate into 

predictability of severe declines on a case-by-case basis. The mean probability of 95% decline 

for the windows that experienced a 95% decline was only 9%. These results emphasize that the 

very nature of stochastic processes means that the future is unpredictable and that severe declines

will occur due to chance even when the probability of such events is low. Obviously severe 

declines will be more common for those populations with higher underlying risks, but if the vast 

majority of populations are at relatively low risk of severe decline, the majority of severe 

declines will be observed to come from populations with low risk and thus appear unpredictable. 

This emphasizes the point that for populations experiencing stochastic growth and decline, low 

estimated risks, no matter how precise, are not a guarantee that severe declines will not occur—

indeed they most certainly will occur for some fraction of populations. Predicting the fraction of

populations that will experience a severe decline is possible; determining exactly which 

populations will experience such severe declines will not generally be possible—except in the 

case of populations undergoing rapid and drastic declines or populations with very low year-toyear variability. 

Overall, the results presented here highlight both successes and shortcomings of PVAs

based on diffusion approximations. Clearly, the lack of predictive certainty that these models 

afford on a case-by-case basis could be construed as a limitation of extinction risk modeling. 

However, there are lessons to learn from the general patterns that emerge from multipopulation 

and multispecies analyses for conservation planning (see also Fagan et al. 2001). In the present 

case, it is worth emphasizing the advantages of being able to describe well the behavior of a 

collection of populations and species. Conservation biology is increasingly adopting a 

multipopulation, multispecies perspective, a view that is necessitated both by the increasing 

numbers of species of conservation concern and by the general need to act quickly to halt or

reverse population declines. Often such action must take place in the absence of solid 

information on each component species, and from a practical perspective, broad brush 

multispecies conservation efforts may trade off case-by-case certainty for time. Although the 

knowledge that we will guess right “on average” may provide little solace when particular 

species or populations fail to persist, we must keep in mind that real population trajectories are 

17
stochastic and by their very nature unpredictable regardless of the sophistication and accuracy of 

one’s models. Taking a multipopulation approach may be the only viable means to achieve 

predictive power. 

18
References 

Andersen, M. E., and J. E. Deacon. 2001. Population size of Devils Hole pupfish (Cyprinodon diabolis) 

correlates with water level. Copeia 2001:224–228. 

Baker, W. W. 1983. Decline and extirpation of a population of red-cockaded woodpeckers in northwest 

Florida. In D. A. Wood (ed.), Red-Cockaded Woodpecker Symposium II, p. 44–45. State of 

Florida Game and Fresh Water Fish Commission, Tallahassee, FL. 

Bairlein, F. 1991. Population studies of white storks (Ciconia ciconia) in Europe. In C. M. Perrins, J. D. 

Lebreton, and G. J. M. Hirons (eds.), Bird population studies: Relevance to conservation and 

management, p. 207–229. Oxford University Press, Oxford. 

Beamesderfer, R. C. P., H. A. Schaller, M. P. Zimmerman, C. P. Petrosky, O. P. Langness, and L. LaVoy. 

1998. Spawner-recruit data for spring and summer Chinook salmon populations in Idaho, 

Oregon, and Washington. In D. R. Marmorek and C. N. Peters (eds.), Plan for analyzing and 

testing hypotheses (PATH): Retrospective and prospective analyses of spring/summer Chinook. 

ESSA Technologies Ltd., Vancouver, BC. 

Becker, P. H. 1991. Population and contamination studies in coastal birds: The common tern Sterna 

hirundo. In C. M. Perrins, J. D. Lebreton, and G. J. M. Hirons (eds.), Bird population studies: 

Relevance to conservation and management, p. 433–460. Oxford University Press, Oxford. 

Bennetts, R. E., W. A. Link, J. R. Sauer, and P. W. Sykes, Jr. 1999. Factors influencing counts in an 

annual survey of snail kites in Florida. Auk 116:316–323. 

Brook, B. W., and J. Kikkawa. 1998. Examining threats faced by island birds: A population viability

analysis on the Capricorn silvereye using long-term data. J. Appl. Ecol. 35:491–503. 

Brook, B. W., M. A. Burgman, H. R. Akcakaya, J. J. O’Grady, and R. Frankham. 2002. Critiques of 

PVA ask the wrong questions: Throwing the heuristic baby out with the numerical bath water. 

Conserv. Biol. 16:262–263.

Brook, B. W., J. J. O’Grady, A. P. Chapman, M. A. Burgman, H. R. Akçakaya, and R. Frankham. 2000. 

Predictive accuracy of population viability analysis in conservation biology. Nature 404:385–

387. 

Cabot, D. 1996. Performance of the roseate tern population breeding in North-West Europe — Ireland, 

Britain and France, 1960–94. Biol. and the Environ.: Proc. R. Irish Acad. 96B(2):55–68. 

Carpenter, S. R., K. L. Cottingham, and C. A. Stow. 1994. Fitting predator prey models to time series 

with observation errors. Ecology 75:1254–1264. 

Caughley, G. 1994. Directions in conservation biology. J. Anim. Ecol. 63:215–244. 

19
Christian, C. S., T. E. Lacher, Jr., M. P. Zamore, T. D. Potts, and G. W. Burnett. 1996. Parrot

conservation in the Lesser Antilles with some comparison to the Puerto Rican efforts. Biol. 

Conserv. 77:159–167. 

Coulson, J. C., and C. S. Thomas. 1985. Changes in the biology of the Kittiwake Rissa tridactyla: A 31-

year study of a breeding colony. J. Anim. Ecol. 54:9–26. 

Coulson, J. C., G. M. Mace, E. Hudson, and H. Possingham. 2001. The use and abuse of population 

viability analysis. Trends Ecol. Evol. 16:219–221. 

Cox, G. W. 1997. Conservation biology: Concepts and applications (2nd ed.). Wm. C. Brown Publishers, 

Dubuque, IA.

Crouse, D. T., L. B. Crowder, and H. Caswell. 1987. A stage-based population model for loggerhead sea 

turtles and implications for conservation. Ecology 68:1412–1423. 

Davis, P. E. and I. Newton. 1981. Population and breeding of red kites in Wales over a 30-year period. 

J. Anim. Ecol. 50:759–772.

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

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

Dunham, J. B., B. E. Rieman, and K. Davis. 2001. Sources and magnitude of sampling error in redd 

counts for bull trout Salvelinus confluentus. N. Am. J. Fish. Manag. 21:343–352.

Ellner, S. P., J. Fieberg, D. Ludwig, and C. Wilcox. 2002. Precision of population viability analysis. 

Conserv. Biol. 16:258–261.

Engen, S., and B. E. Saether. 2000. Predicting the time to quasi-extinction for populations far below 

their carrying capacity. J. Theor. Biol. 205:649–658.

Fagan, W. F., E. Meir, J. Prendergast, A. Folarin, and P. M. Kareiva. 2001. Characterizing vulnerability

to extinction for 758 species. Ecol. Lett. 4:132–138. 

Fieberg, J., and S. P. Ellner. 2000. When is it meaningful to estimate an extinction probability? Ecology 

81:2040–2047. 

Fish Passage Center. 2002. Chinook data. Online at http://www.fpc.org/adultsalmon/adultqueries/ 

Adult_Table_Submit.html [accessed 17 June 2002]. 

Foley, P. 1994. Predicting extinction times from environmental stochasticity and carrying capacity. 

Conserv. Biol. 8:124–137. 

Garber, S. D., and J. Burger. 1995. A 20-year study documenting the relationship between turtle decline 

and human recreation. Ecol. Appl. 5:1151–1162. 

Gerber, L. R., D. P. De Master, and P. M. Kareiva. 1999. Grey whales and the value of monitoring data 

in implementing the U.S. Endangered Species Act. Conserv. Biol. 13:1215–1219. 

Gilmartin, W. G., and L. L. Eberhardt. 1995. Status of the Hawaiian monk seal (Monachus 

schauinslandi) population. Can. J. Zool. 73:1185–1190. 

20
Ginsberg, J. R., G. M. Mace, and S. Albon. 1995. Local extinction in a small and declining population: 

Wild dogs in the Serengeti. Proc. R. Soc. Lond. Ser. B Biol. Sci. 262:221–228. 

Hilborn, R., B. G. Bue, and S. Sharr. 1999. Estimating spawning escapements from periodic counts: A 

comparison of methods. Can. J. Fish. Aquat. Sci. 56:888–896. 

Hinrichsen, R. A. 2002. The accuracy of alternative stochastic growth rate estimates for salmon 

populations. Can. J. Fish. Aquat. Sci. 59:1014–1023.

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

USA 98:5072–5077. 

Holmes, E. E. 2004. Beyond theory to application and evaluation: Diffusion approximations for 

population viability analysis. Ecol. Appl. 14:1272–1293. 

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

Ecology 83:2379–2386. 

Jouventin, P., and H. Weimerskirch. 1991. Changes in the population size and demography of southern 

seabirds: Management implications. In C. M. Perrins, J. D. Lebreton, and G. J. M. Hirons (eds.), 

Bird population studies, p. 297–314. Oxford University Press, Oxford. 

Kareiva, P., M. Marvier, and M. McClure. 2000. Recovery and management options for spring/summer 

Chinook salmon in the Columbia River Basin. Science 290:977–979. 

Komdeur, J. 1996. Breeding of the Seychelles Magpie Robin (Copsychus sechellarum) and implications 

for its conservation. Ibis 138:485–498. 

Lande, R., S. Engen, and B. E. Saether. 1998. Extinction times in finite metapopulation models with 

stochastic local dynamics. Oikos 83:383–389. 

Lande, R., and S. H. Orzack. 1988. Extinction dynamics of age-structured populations in a fluctuating 

environment. Proc. Natl. Acad. Sci. USA 85:7418–7421. 

Lawton, J. H. 1996. Population abundances, geographic ranges, and conservation: 1994 Witherby

Lecture. Bird Study 43:3–19. 

Loery, G., and J. D. Nichols. 1985. Dynamics of a black-capped chickadee population. Ecology

66:1195–1203. 

Ludwig, D. 1996. Uncertainty and the assessment of extinction probabilities. Ecol. Appl. 6:1067–1076. 

Ludwig, D. 1999. Is it meaningful to estimate a probability of extinction? Ecology 80:298–310. 

Marmorek, D. R., and C. N. Peters (eds.). 1998. Plan for analyzing and testing hypotheses (PATH): 

Retrospective and prospective analyses of spring/summer Chinook. ESSA Technologies Ltd., 

Vancouver, BC. 

Masatomi, H. 1987. Population dynamics of red-crowned cranes in Hokkaido since the 1950s. In

Proceedings of the 1987 International Crane Workshop, p. 297–299. International Crane 

Foundation, Baraboo, WI. 

21
Meyer, A. H., B. R. Schmidt, and K. Grossenbacher. 1998. Analysis of three amphibian populations 

with quarter-century long time-series. Proc. R. Soc. Lond. Ser. B Biol. Sci. 265:523–528. 

Milner-Gulland, E. J., T. N. Coulson, and T. H. Clutton-Brock. 2000. On harvesting a structured 

ungulate population. Oikos 88:592–602. 

Moore, N. W. 1991. The development of dragonfly communities and the consequences of territorial 

behaviour: A 27-year study on small ponds at Woodwalton Fen, Cambridgeshire, United 

Kingdom. Odontologica 20:203–231. 

Morris, W., D. Doak, M. Groom, P. Kareiva, J. Fieberg, L. Gerber, P. Murphy, and D. Thomson. 1999. 

A practical handbook for population viability analysis. The Nature Conservancy, Washington, 

DC. 

Morris, W., and D. Doak. 2003. Quantitative conservation biology: Theory and practice of population 

viability analysis. Sinauer Press, Sunderland MA. 

Newton, I. 1998. Population limitation in birds, p. 1–27 and 449–480. Academic Press, San Diego, CA. 

Nicholls, A. O., P. C. Viljoen, M. H. Knight, and A. S. van Jaarsveld. 1996. Evaluating population 

persistence of censused and unmanaged herbivore populations from the Kruger National Park, 

South Africa. Biol. Conserv. 76:57–67. 

Orell, M. 1989. Population fluctuations and survival of great tits Parus major dependent on food 

supplied by man in winter. Ibis 131:112–117. 

Packer, C., S. Altizer, M. Appel, E. Brown, J. Martenson, S. J. O’Brien, M. Roelke-Parker, R. HofmannLehman, and H. Lutz. 1999. Viruses of the Serengeti: Patterns of infection and mortality in 

African lions. J. Anim. Ecol. 68:1161–1178. 

Parr, R. 1992. The decline to extinction of a population of golden plover in North-East Scotland. Ornis 

Scand. 23:152–158. 

Peters, C. N., Marmorek, D. R., Parnell, I. (eds.). 1999. PATH Decision analysis report for Snake River 

fall Chinook. Prepared by ESSA Technologies, Ltd., Vancouver, B.C. 

Peterson, M. J, and N. J. Silvy. 1996. Reproductive stages limiting productivity of the endangered 

Attwater’s prairie chicken. Conserv. Biol. 10:1264–1276.

Peterson, R. O., N. J. Thomas, J. M. Thurber, J. A. Vucetich, and T. A. Waite. 1998. Population 

limitation and the wolves of Isle Royale. J. Mammal. 79:828–841. 

Pettersson, B. 1985. Extinction of an isolated population of the middle spotted woodpecker 

Dendrocopos medius (L.) in Sweden and its relation to general theories on extinction. Biol. 

Conserv. 32:335–353. 

Pierson, E. A., and R. M. Turner. 1998. An 85-year study of saguaro (Carnegiea gigantica) 

demography. Ecology 79:2676–2693. 

Pistorius, P. A., M. N. Bester, and S. P. Kirkman. 2000. Evaluation of age- and sex-dependent rates of 

tag loss in southern elephant seals. J. Wild. Manag. 64:373–380. 

22
Ragen, T. J., and D. M. Lavigne. 1997. The Hawaiian monk seal. In J. Twiss and R. Reeves (eds.), 

Marine mammals, Vol. 2. Smithsonian Institution Press, Washington, DC. 

Reed, J. M., and L. W. Oring. 1993. Long-term population trends of the endangered Ae’o (Hawaiian 

stilt, Himantopus mexicanus knudseni). Trans. West. Sect. Wildl. Soc. 29:54–60. 

Robertson, A., and A. M. Jarvis. 2000. Oxpeckers in north-eastern Namibia: recent population trends 

and the possible negative impacts of drought and fire. Biol. Conserv. 92:241–247. 

Runyoro, V. R., H. Hofer, H. E. B. Chausi, and P. D. Moehlman. 1995. Long term trends in the 

herbivore populations of the Ngorongoro Crater, Tanzania. In A. R. E. Sinclair and P. Arcese 

(eds.), Serengeti II: Dynamics, management, and conservation of an ecosystem, p. 146–168. 

University of Chicago Press, Chicago. 

Saether, B. E., S. Engen, A. Islam, R. McCleery, and C. Perrins. 1998. Environmental stochasticity and

extinction risk in a population of a small songbird, the great tit. Am. Nat. 151:441–450. 

Simberloff, D. 1986. The proximate causes of extinction. In D. M. Raup and D. Jablonski (eds.), 

Patterns and processes in the history of life, p. 259–276. Springer-Verlag, Berlin. 

Simberloff, D. 1988. The contribution population and community biology to conservation science. Ann. 

Rev. Ecol. Syst. 19:473–511. 

Solomon, B. D. 1998. Impending recovery of Kirtland’s Warbler: Case study in the effectiveness of the 

Endangered Species Act. Environ. Manag. 22:9–17. 

Soulé, M. E. 1986. Conservation biology: The science of scarcity and diversity. Sinauer Press, 

Sunderland, MA. 

Spencer, D. L., and C. J. Lensink. 1970. The muskox of Nunivak Island. J. Wildl. Manag. 34:1–15. 

StreamNet. 2002. Salmon data. Online at http://www.streamnet.org [accessed June 2002]. 

Tuljapurkar, S. D. 1982. An uncertain life: Demography in random environments. Theor. Popul. Biol. 

35:227–294. 

Whitehouse, A. M, and A. J. Hall-Martin. 2000. Elephants in Addo National Park, South Africa: 

Reconstruction of the population’s history. Oryx 34:46–55. 

York, A. E. 1985. Estimation of numbers of pups born on St. Paul Island during 1977 and 1978. In P.

Kozloff (ed.), Fur seal investigations, 1982, p. 16–19. U.S. Department of Commerce, Seattle. 

York, A. E., and J. R. Hartley. 1981. Pup production following harvest of female northern fur seals. 

Can. J. Fish. Aquat. Sci. 38:84–90. 

York, A. E., R. G. Towell, R. R. Ream, J. D. Baker, C. W. Fowler, and B. W. Robson. 2000. Population 

assessment, Pribilof Islands, Alaska. In B. W. Robson (ed.), Fur seal investigations, 1998, p. 7–

26. U.S. Department of Commerce, Seattle. 

Zollinger, R., and G. Müskens. 1994. Population dynamics and lifetime reproductive success in 

sparrowhawks Accipiter nisus in a Dutch-German study area. In B. U. Meyburg and R. D. 

Chancellor (eds.), Raptor conservation today, p. 77–85. Pica Press, London. 

23
24

 
Appendix A 

Table A-1. Summary of nonsalmon population time series used in cross-validation analyses. 

Species 

Type of organism

Location of study population 

Number of 

transitions 

Unit of census References

Connochaetes taurinus(Wildebeest)

Mammal Ngorongoro Crater,

Tanzania 

21 Total

population 

Runyoro et al. 1995 

Ovibos moschatus (Musk ox) 

Mammal Nunivak Island, Alaska 24 Total 

population 

Spencer and Lensink 1970 

Ursus arctos horribilis (Grizzly bear) 

Mammal Yellowstone National

Park 

28 Adult

females 

Foley 1994 

Cervus elaphus (Red deer) 

Mammal Isle of Rum, UK 21 Females Milner-Gulland et al. 2000 

Cervus elaphus (Red deer) 

Mammal Isle of Rum, UK 21 Females Milner-Gulland et al. 2000 

Canis lupus (Wolves) 

Mammal Isle Royale National 

Park, Michigan 

24 Total

population 

Peterson et al. 1998 

Panthera leo(Lion) 

Mammal Ngorongoro Crater,

Tanzania 

22 Total

population 

Packer et al. 1999 

Telespiza cantans (Laysan finch) 

Bird Laysan Island, Hawaii 24 Total 

population 

Dennis et al. 1991 

Grus Americana (Whooping crane) 

Bird Aransas, Texas 51 Total

population 

Dennis et al. 1991 

Parus major (Great tit) 

Bird Wytham Wood, UK 30 Total 

population 

Saether et al. 1998 

Zosterops lateralis chlorocephala (Heron Island silvereye) 

Bird Great Barrier Reef,

Australia 

25 Total

population 

Brook and Kikkawa 1998 

25
Table A-1. Summary of nonsalmon population time series used in cross-validation analyses. Continued. 

Species 

Type of organism

Location of study population 

Number of 

transitions 

Unit of census References 

Dendroica kirtlandii(Kirtland’s warbler) 

Bird Northern half of 

Michigan’s lower peninsula 

22 Singing

males 

Dennis et al. 1991, Solomon 1998 

Milvus milvus (Red kite) 

Bird Wales 29 Total

population 

Davis and Newton 1981 

Rostrhamus sociabilis (Snail kite) 

Bird Wetlands in central and 

southern Florida 

25 Total

population 

Bennetts et al. 1999 

Somateria mollissima (Eider) 

Bird Wadden Sea Coast, 

Germany

33 Breeding

pairs 

Becker 1991 

Tympanuchus cupido attwateri (Attwater’s prairie chicken) 

Bird Coastal Prairie,

Louisiana and Texas 

29 Total

population 

Peterson and Silvy 1996 

Ciconia ciconia (White stork) 

Bird Baden-Wurttenberg,

Germany

38 Breeding

pairs 

Newton 1998, Bairlein 1991 

Ciconia ciconia (White stork) 

Bird Oldenburg/NW

Germany

60 Breeders Bairlein 1991 

Fulmarus glacialoides(Antarctic fulmar) 

Bird Pointe Geologie

Archipelago, Adele Land, in Antarctic zone

25 Total

population 

Jouventin and Weimerskirch 1991 

Sterna dougallii (Roseate terns) 

Bird main colonies in 

Ireland, Britain, and France 

34 Breeding

pairs 

Cabot 1996 

Rana temporaria (European frog) 

Amphibian Bern, Switzerland 27 Spawn 

clumps 

Meyer et al. 1998 

Cyprinodon diabolis (Devils Hole pupfish) 

Fish Devils Hole, Nevada 24 Total 

population 

Andersen and Deacon 2001 

Euphydryas editha bayensis (Jasper Ridge checkerspot) 

Butterfly Jasper Ridge, California 26 Females Nicholls et al. 1996 

26
Table A-1. Summary of nonsalmon population time series used in cross-validation analyses. Continued. 

Species 

Type of organism

Location of study population 

Number of 

transitions 

Unit of census References 

Euphydryas editha bayensis (Jasper Ridge checkerspot) 

Butterfly Jasper Ridge, California 26 Females Nicholls et al. 1996 

Ischnura elegans (Blue-tailed damselfly)

Odonate Woodwalton Fen,

Cambridgeshire, UK 

26 Male

territories 

Moore 1991 

Sympetrum striolatum(Common darter) 

Odonate Woodwalton Fen,

Cambridgeshire, UK 

26 Male

territories 

Moore 1991 

Coenagrion puella (Azure damselfly)

Odonate Woodwalton Fen,

Cambridgeshire, UK 

25 Male

territories 

Moore 1991 

Lestes sponsa (Emerald damselfly)

Odonate Woodwalton Fen,

Cambridgeshire, UK 

24 Male

territories 

Moore 1991 

Rissa tridactyla (Kittiwake) 

Bird North Shields, Tyne and 

Wear, UK 

33 Nests with

eggs 

Coulson and Thomas 1985 

Amazona vittata (Puerto Rican parrot) 

Bird Puerto Rico 20 Total

population 

Dennis et al. 1991, Christian et al. 1996 

Copsychus seychellarum(Seychelles magpie robin) 

Bird Fregate Is, Seychelles 21 Total 

population 

Komdeur 1996 

Eschrichtium robustus(California gray whale) 

Mammal California 23 Total

population 

Gerber et al. 1999 

Callorhinus ursinus (Northern fur seal) 

Mammal St. George Island, 

Alaska 

43 Pups York et al. 2000, York 1985, 

York and Hartley 1981 

Callorhinus ursinus (Northern fur seal) 

Mammal St. Paul Island, Alaska 43 Pups York et al. 2000, York 1985, 

York and Hartley 1981 

Callorhinus ursinus (Northern fur seal) 

Mammal San Miguel Island, 

California 

24 Pups York et al. 2000, York 1985, 

York and Hartley 1981 

Zalophus californianus (California sea lion) 

Mammal California 20 Pups York et al. 2000, York 1985, 

York and Hartley 1981 

Parus atricapillus (Black-capped chickadee) 

Bird Litchfield and Morris, 

Connecticut 

23 Winter

population 

Loery and Nichols 1985 

27
Table A-1. Summary of nonsalmon population time series used in cross-validation analyses. Continued. 

Species 

Type of organism

Location of study population 

Number of 

transitions 

Unit of census References 

Monachus shauinslandi (Hawaiian monk seal) 

Mammal Hawaiian Islands minus 

Midway

20 Total

population (almost) 

Gilmartin and Eberhardt 1995, Ragen and Lavigne 1997 

Accipiter nisus (Northern sparrowhawk) 

Bird Germany 22 Total

population 

Zollinger and Müskens 1994 

Himantopus mexicanus knudseni(Hawaiian stilt) 

Bird Hawaiian Islands minus 

Kauai--Niihau 

22 Total

population (almost) 

Reed and Oring 1993 

Grus japonesis (Red-crowned crane) 

Bird Hokkaido, Japan 35 Total

population 

Masatomi 1987 

Loxodonta africana (African elephant) 

Mammal Addo National Park, 

South Africa 

68 Total

population 

Whitehouse and Hall-Martin 2000 

Melospiza melodia (Song sparrow) 

Bird Mandarte Island, British 

Columbia 

20 Territorial

females 

Ludwig 1999 

Lycaon pictus(African wild dog) 

Mammal Serengeti Plains,

Tanzania 

19 Adults +

yearlings 

Ginsberg et al. 1995 

Dendrocopos medius (Middle spotted woodpecker) 

Bird Southern Sweden 14 Adults Pettersson 1985 

Pluvialis apricaria (Golden plover) 

Bird Kerloch, NE Scotland 17 Total 

population 

Parr 1992 

Clemmys insculpta (Wood turtle) 

Reptile South-central

Connecticut 

19 Total

population 

Garber and Burger 1995 

Clemmys insculpta (Wood turtle) 

Reptile South-central

Connecticut 

19 Total

population 

Garber and Burger 1995 

Picoides borealis (Red-cockaded woodpecker) 

Bird Tall Timbers Research

Station, Florida 

14 Adults Baker 1983 

28
Appendix B 

Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. 

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Chinook California Merced River (Fall) 61115 Chinook California Tuolumne River (Fall) 61116 Chinook California Stanislaus River (Fall) 61117 Chinook California Cosumnes River (Fall) 61121 Chinook California American River (Fall) 61122 Chinook California Feather River (Fall) 61123 Chinook California Yuba River (Fall) 61129 Chinook California Butte Creek (Spring) 61131 Chinook California Deer Creek (Fall) 61136 Chinook California Mill Creek (Fall) 61137 Chinook California Battle Creek (Fall) 90010 Chinook California San Joaquin River (Fall) 61118 Chinook Lower Columbia River Big Creek (Fall) 57497 Chinook Lower Columbia River Clackamas River (Spring) 50312 Chinook Lower Columbia River Clackamas River (Fall) 50990 Chinook Lower Columbia River Clackamas River N Fork (Fall) 50010 Chinook Lower Columbia River Clatskanie River (Fall) 50982 Chinook Lower Columbia River Cowlitz River (Fall)(tule) 105030 Chinook Lower Columbia River Elochoman River (Fall)(tule) 103050 Chinook Lower Columbia River Gnat Creek (Fall) 50007 Chinook Lower Columbia River Kalama River (Fall)(tule) 110050 

29
Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. Continued.

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Chinook Lower Columbia River Klickitat River (Fall)(tule) 131030 Chinook Lower Columbia River Lewis River (Fall)(bright) 113030 Chinook Lower Columbia River Lewis River E Fork (Fall)(tule) 113040 Chinook Lower Columbia River Plympton Creek (Fall) 50005 Chinook Lower Columbia River Washougal River (Fall)(tule) 116050 Chinook Lower Columbia River White Salmon River (Fall)(tule) 128050 

Chinook Lower Columbia River Wind River (Fall)(tule) 121002 Chinook Lower Columbia River Youngs River (Fall) 50276 Chinook Middle Columbia River (Spring) American River (Spring) 61466 Chinook Middle Columbia River (Spring) Beaver Creek (Spring) 50178 Chinook Middle Columbia River (Spring) Bull Run Creek (Spring) 52055 Chinook Middle Columbia River (Spring) Clear Creek (Spring) 52054 Chinook Middle Columbia River (Spring) Granite Creek (Spring) 52053 Chinook Middle Columbia River (Spring) John Day River (Spring) 50148 Chinook Middle Columbia River (Spring) John Day River M Fork (Spring) 50167 Chinook Middle Columbia River (Spring) John Day River N Fork (Spring) 50158 Chinook Middle Columbia River (Spring) Mill Creek (Spring) 50177 Chinook Middle Columbia River (Spring) Warm Springs River (Spring) 50175 Chinook Middle Columbia River (Spring) Wind River (Spring) 122050 Chinook Upper Columbia River (Spring) Chiwack River (Spring) 60044 Chinook Upper Columbia River (Spring) Chiwawa River (Spring) 60057 Chinook Upper Columbia River (Spring) Entiat River (Spring) NWFSCb 

Chinook Upper Columbia River (Spring) Icicle Creek (Spring) 60063 

Chinook Upper Columbia River (Spring) Icicle Creek (Spring) 143031 

Chinook Upper Columbia River (Spring) Icicle Creek (Spring) 60827 

Chinook Upper Columbia River (Spring) Little Wenatchee River (Spring) 60059 Chinook Upper Columbia River (Spring) Little Wenatchee River (Spring) 60826 Chinook Upper Columbia River (Spring) Lost River (Spring) 60046 

30
Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. Continued.

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Chinook Upper Columbia River (Spring) Methow River (Spring) NWFSCb Chinook Upper Columbia River (Spring) Nason Creek (Spring) 60061 

Chinook Upper Columbia River (Spring) Twisp River (Spring) 60048 

Chinook Upper Columbia River (Spring) Wenatchee River (Spring) NWFSCb 

Chinook Upper Columbia River (Spring) White River (Spring) 60058 Chinook Upper Columbia River (Spring) White River (Spring) 60825 Chinook Upper Columbia River (Summer/Fall) Hanford Reach (Fall) M 1998c Chinook Upper Columbia River (Summer/Fall) Methow River (Summer) 60042 Chinook Upper Columbia River (Summer/Fall) Okanogan River (Summer) 60040 

Chinook Upper Columbia River (Summer/Fall) Similkameen River (Summer) 60041 

Chinook Upper Columbia River (Summer/Fall) Wenatchee River (Summer) 60055 

Chinook Snake River (Spring/Summer) Alturas Lake Ck (Spring) 41012 Chinook Snake River (Spring/Summer) Bear Creek B 1998d 

Chinook Snake River (Spring/Summer) Bear Creek (Clearwater) (Spring) 41068 Chinook Snake River (Spring/Summer) Bear Valley Creek (Spring) 41028 Chinook Snake River (Spring/Summer) Beaver Creek (Spring) 41036 Chinook Snake River (Spring/Summer) Big Creek (Spring) 41044 Chinook Snake River (Spring/Summer) Big Creek Upper 41045 Chinook Snake River (Spring/Summer) Big Sheep Creek (Spring) 50121 Chinook Snake River (Spring/Summer) Brushy Fork (Spring) 41078 Chinook Snake River (Spring/Summer) Camas Creek (Spring) 41048 Chinook Snake River (Spring/Summer) Cape Horn Creek (Spring) 41033 Chinook Snake River (Spring/Summer) Catherine Creek (Spring) 54594 Chinook Snake River (Spring/Summer) Catherine Creek N Fork (Spring) 57510 Chinook Snake River (Spring/Summer) Catherine Creek S Fork (Spring) 57511 Chinook Snake River (Spring/Summer) Crooked Fork (Spring) 41076 Chinook Snake River (Spring/Summer) Elk Creek (Spring) 41030 Chinook Snake River (Spring/Summer) Grande Ronde River (Spring) 57512 

31
Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. Continued.

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Chinook Snake River (Spring/Summer) Hayden Creek (Summer) 41024 Chinook Snake River (Spring/Summer) Herd Creek (Summer) 41018 Chinook Snake River (Spring/Summer) Imnaha River (Spring) B 1998d 

Chinook Snake River (Spring/Summer) Imnaha River (Spring) 50124 Chinook Snake River (Spring/Summer) Johnson Creek (Summer) B 1998d Chinook Snake River (Spring/Summer) Johnson Creek (Summer) 41060 Chinook Snake River (Spring/Summer) Knapp Creek (Spring) 41035 Chinook Snake River (Spring/Summer) Lake Creek (Summer) 41059 Chinook Snake River (Spring/Summer) Lemhi River (Spring) 41023 Chinook Snake River (Spring/Summer) Lookingglass Creek (Spring) 57513 Chinook Snake River (Spring/Summer) Loon Creek (Summer) 41038 Chinook Snake River (Spring/Summer) Lostine Creek (Spring) 57514 Chinook Snake River (Spring/Summer) Lower Salmon River NWFSCb Chinook Snake River (Spring/Summer) Lower Valley Creek NWFSCb Chinook Snake River (Spring/Summer) Marsh Creek (Spring) B 1998d Chinook Snake River (Spring/Summer) Marsh Creek (Spring) 41031 Chinook Snake River (Spring/Summer) Minam River (Spring) B 1998d Chinook Snake River (Spring/Summer) Minam River Upper (Spring) 50074 Chinook Snake River (Spring/Summer) Minam River Lower (Spring) 50097 Chinook Snake River (Spring/Summer) Moose Creek (Spring) 41071 Chinook Snake River (Spring/Summer) Newsome Creek (Spring) 41088 Chinook Snake River (Spring/Summer) Poverty Creek B 1998d Chinook Snake River (Spring/Summer) Red River (Spring) 41084 Chinook Snake River (Spring/Summer) Salmon River E Fork (Spring) 41015 Chinook Snake River (Spring/Summer) Salmon River E Fork (Summer) 41016 Chinook Snake River (Spring/Summer) Salmon River S Fork (Summer) 41056 Chinook Snake River (Spring/Summer) Salmon River Upper (Spring) 41001 Chinook Snake River (Spring/Summer) Salmon River Upper (Summer) 41002 

32
Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. Continued.

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Chinook Snake River (Spring/Summer) Secesh River (Summer) 41058 Chinook Snake River (Spring/Summer) Selway River (Spring) 41062 Chinook Snake River (Spring/Summer) Sulphur Ck (Spring) B 1998d 

Chinook Snake River (Spring/Summer) Sulphur Creek (Spring) 41026 Chinook Snake River (Spring/Summer) Valley Ck Upper (Spring) 41008 Chinook Snake River (Spring/Summer) Valley Ck Upper (Summer) 41009 Chinook Snake River (Spring/Summer) Wallowa Creek (Spring) 50119 Chinook Snake River (Spring/Summer) Wenaha River S Fork (Spring) 50120 Chinook Snake River (Spring/Summer) White Cap Creek (Spring) 41066 Chinook Snake River (Spring/Summer) Yankee Fork (Summer) 41005 Chinook Snake River (Spring/Summer) Yankee W Fork (Summer) NWFSCb Chinook Snake River (Spring/Summer) Yankee W Fork (Spring) 41006 Chinook Snake River Basin (Fall) Snake River Basin P 1999e Chinook Upper Willamette River McKenzie River above Leaburg Dam ODFWf Chinook Upper Willamette River McKenzie River (Spring) 57319 

Chinook Upper Willamette River Molalla River (Fall) 50999 Chinook Upper Willamette River Santiam River S (Fall) 50017 Chinook Upper Willamette River Santiam River N (Fall) 50019 Chinook Upper Willamette River Willamette River (Fall) 50987 Chinook Oregon Coast Bear Creek (Chetco) (Fall) 50568 Chinook Oregon Coast Buck Creek (Alsea) (Fall) 52076 Chinook Oregon Coast Clear Creek (Fall) 50445 Chinook Oregon Coast Coquille River S Fork (Fall) 50541 Chinook Oregon Coast Coquille River N Fork (Fall) 50549 Chinook Oregon Coast Coquille River E Fork (Fall) 53494 Chinook Oregon Coast Coquille River M Fork (Fall) 53498 Chinook Oregon Coast Cronin Creek (Newhalem) (Fall) 50412 Chinook Oregon Coast Deep Creek (Chetco) (Fall) 50569 

33
Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. Continued.

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Chinook Oregon Coast Dry Creek (Sixes) (Fall) 53505 Chinook Oregon Coast Emily Creek (Chetco) (Fall) 53516 Chinook Oregon Coast Grant Creek (Yaquina) (Fall) 52074 Chinook Oregon Coast Humbug Creek (Newhalem) (Fall) 50414 Chinook Oregon Coast Lake Creek (Siuslaw) (Fall) 52078 Chinook Oregon Coast Middle Creek (Coquille) (Fall) 53492 Chinook Oregon Coast Millicoma River W Fork (Coos) (Fall) 52080 Chinook Oregon Coast Moon Creek (Nestucca) (Fall) 50452 Chinook Oregon Coast Niagara Creek (Nestucca) (Fall) 50570 Chinook Oregon Coast Siuslaw River N Fork (Fall) 50498 Chinook Oregon Coast Sunshine Creek (Siletz) (Fall) 50572 Chinook Oregon Coast Tillamook River (Fall) 50568 Chinook Oregon Coast Salmon Creek (Coquille) (Fall) 52082 Chinook Oregon Coast Umpqua River S (Fall) 66899 Chinook Oregon Coast Wilson River N Fork (Fall) 50445 Chinook Puget Sound Cedar River (Summer) 60645 Chinook Puget Sound Green/Duwamish River NWFSCb 

Chinook Puget Sound Hood Canal (Summer)/(Fall) 61992 Chinook Puget Sound Hood Canal SE NWFSCb Chinook Puget Sound Nisqually River (Summer) 60677+61583 

Chinook Puget Sound Nooksack River 60586 Chinook Puget Sound Puyallup River 60665 Chinook Puget Sound Samish River NWFSCb 

Chinook Puget Sound Sauk River (Summer) 61470 Chinook Puget Sound Sauk River (Spring) 61471 Chinook Puget Sound Skagit River Lower (Fall) 61475 Chinook Puget Sound Skagit River (Spring) NWFSCb Chinook Puget Sound Skagit River (Spring) HMU NWFSCb 

34
Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. Continued.

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Chinook Puget Sound Skagit River S Fork 60606 Chinook Puget Sound Skagit River Upper (Summer) 61474 Chinook Puget Sound Skokomish River 60689 Chinook Puget Sound Snohomish River 60638 Chinook Puget Sound Sound South NWFSCb 

Chinook Puget Sound Stillaguamish River 60611 Chinook Puget Sound Suiattle River (Spring) NWFSCb Chinook Puget Sound White River (Spring) NWFSCb Chinook Puget Sound White River 60674 Steelhead Lower Columbia River Clackamas River (Summer) (N Fork Dam) 50316 

Steelhead Lower Columbia River Clackamas River (Winter) (N Fork Dam) 50320 

Steelhead Middle Columbia River Bear Creek (John Day) 57526 Steelhead Middle Columbia River Beech Creek (John Day) 57530 Steelhead Middle Columbia River Beech Creek E Fork (John Day) 57531 Steelhead Middle Columbia River Big Wall Creek (John Day) 57533 Steelhead Middle Columbia River Camp Creek (John Day) 54587 Steelhead Middle Columbia River Canyon Creek (John Day) 57536 Steelhead Middle Columbia River Cottonwood Creek (John Day) 54597 Steelhead Middle Columbia River Deep Creek (John Day) 57538 Steelhead Middle Columbia River Deer Creek (John Day) 50094 Steelhead Middle Columbia River Fields Creek (John Day) 54598 Steelhead Middle Columbia River Kahler Creek (John Day) 54599 Steelhead Middle Columbia River McClellan Creek (John Day) 50104 Steelhead Middle Columbia River Murderers Creek (John Day) 50106 Steelhead Middle Columbia River Parrish Creek (John Day) 50109 Steelhead Middle Columbia River Riley Creek (John Day) 50111 Steelhead Middle Columbia River Tex Creek (John Day) 50114 Steelhead Middle Columbia River Umtilla River (Summer) 50515+57508 

35
Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. Continued.

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Steelhead Middle Columbia River Wind Creek (John Day) 50118 Steelhead Upper Columbia River Wenatchee River and Tribs 180072 Steelhead Snake River Camp Creek (Imnaha) 54589 Steelhead Snake River Crow Creek (Grande Ronde) 54575 Steelhead Snake River Devils Run Creek (Grande Ronde) 54567 Steelhead Snake River Elk Creek (Grande Ronde) 54569 Steelhead Snake River Five Points Creek (Grande Ronde) 50023 Steelhead Snake River Fly Creek (Grande Ronde) 50026 Steelhead Snake River McCoy Creek (Grande Ronde) 50025 Steelhead Snake River Meadow Creek (Grande Ronde) 50024 Steelhead Snake River Peavine Creek (Grande Ronde) 54565 Steelhead Snake River Phillips Creek (Grande Ronde) 50022 Steelhead Snake River Prairie Creek (Grande Ronde) 54564 Steelhead Snake River Swamp Creek (Grande Ronde) 54573 Steelhead Snake River Wallowa River (Grande Ronde) 54572 Steelhead Upper Willamette River McKenzie River (Summer) 54595 Steelhead Upper Willamette River Santiam River N Late (Winter) 51005 Steelhead Upper Willamette River Santiam River S (Summer) (Foster Dam) 50902 Steelhead Upper Willamette River Santiam River S (Winter) (Foster Dam) 51004 Steelhead Upper Willamette River Willamette River (Winter) (Will Falls 

Dam)

50305 

Steelhead Upper Willamette River Willamette River (Summer) (Will Falls 

Dam)

50945 

Steelhead Klamath Mountains Province Rogue River (Summer) 51222 Steelhead Klamath Mountains Province Rogue River (Winter) 51223 Steelhead Oregon Coast Umpqua River N (Summer) 50512 Steelhead Oregon Coast Umpqua River N (Winter) 50513 

36
Table B-1. Summary of salmon population time series used in cross-validation analyses. StreamNet (2002) refers to the S

numbers as of summer 2002. Continued.

Species Evolutionarily significant unit Stock 

StreamNet # or reference

Steelhead Puget Sound Baker River (Skagit) (Winter) 60896 Steelhead Puget Sound White River (Puyallup) (Winter) 60900 Chum Columbia River Grays River W Fork WDFWg 

Chum Columbia River Grays River WDFW Chum Columbia River Hardy Creek WDFW Chum Columbia River Crazy J WDFW Chum Columbia River Hamilton WDFW Chum Columbia River Hamilton Springs WDFW Sockeye Snake River Snake River mainstem FPCh 

a Type: dc = dam count, peak = one time peak count of spawners or carcasses, redds = redd count along an index reach, rpm = redds pe

count (an estimate of the total number of spawers), unk = unknown. 

b Northwest Fisheries Science Center c Marmorek and Peters 1998d Beamesderfer et al. 1998 e Peters et al. 1999 f Oregon Dept. of Fish and Wildlife g Washington Dept. of Fish and Wildlife h Fish Passage Center (2002) 

37

Most NOAA Technical Memorandums NMFS-NWFSC are available online at the

Northwest Fisheries Science Center web site (http://www.nwfsc.noaa.gov).

Recent NOAA Technical Memorandums NMFS

published by the

Northwest Fisheries Science Center

NOAA Tech. Memo.

NMFS-NWFSC66 Good, T.P., R.S. Waples, and P. Adams (editors). 2005. Updated status of federally listed ESUs of West

Coast salmon and steelhead. U.S. Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-66, 598 p. NTIS

number pending.

65 Fleischer, G.W., K.D. Cooke, P.H. Ressler, R.E. Thomas, S.K. de Blois, L.C. Hufnagle, A.R. Kronlund,

J.A. Holmes, and C.D. Wilson. 2005. The 2003 integrated acoustic and trawl survey of Pacific hake,

Merluccius productus, in U.S. and Canadian waters off the Pacific coast. U.S. Dept. Commer., NOAA

Tech. Memo. NMFS-NWFSC-65, 45 p. NTIS number pending.

64 Ferguson, J.W., G.M. Matthews, R.L. McComas, R.F. Absolon, D.A. Brege, M.H. Gessel, and L.G.

Gilbreath. 2005. Passage of adult and juvenile salmonids through federal Columbia River power system

dams. U.S. Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-64, 160 p. NTIS PB2005-104828.

63 Williams, J.G., S.G. Smith, R.W. Zabel, W.D. Muir, M.D. Scheuerell, B.P. Sandford, D.M. Marsh,

R.A. McNatt, and S. Achord. 2005. Effects of the federal Columbia River power system on salmonid

populations. U.S. Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-63, 150 p. NTIS PB2005-107352.

62 Krahn, M.M., M.J. Ford, W.F. Perrin, P.R. Wade, R.P. Angliss, M.B. Hanson, B.L. Taylor,

G.M. Ylitalo, M.E. Dahlheim, J.E. Stein, and R.S. Waples. 2004. 2004 Status review of Southern

Resident killer whales (Orcinus orca) under the Endangered Species Act. U.S. Dept. Commer., NOAA

Tech. Memo. NMFS-NWFSC-62, 73 p. NTIS PB2005-106089.

61 Berejikian, B.A., and M.J. Ford. 2004. Review of relative fitness of hatchery and natural salmon. U.S.

Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-61, 28 p. NTIS PB2005-106090.

60 Ford, M.J., T.A. Lundrigan, and P.C. Moran. 2004. Population genetics of Entiat River spring Chinook

salmon. U.S. Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-60, 45 p. NTIS PB2004-107039.

59 Sloan, C.A., D.W. Brown, R.W. Pearce, R.H. Boyer, J.L. Bolton, D.G. Burrows, D.P. Herman, and

M.M. Krahn. 2004. Extraction, cleanup, and gas chromatography/mass spectrometry analysis of

sediments and tissues for organic contaminants. U.S. Dept. Commer., NOAA Tech. Memo. NMFSNWFSC-59, 47 p. NTIS PB2004-105739.

58 Beechie, T.J., E.A. Steel, P. Roni, and E. Quimby (editors). 2003. Ecosystem recovery planning for

listed salmon: an integrated assessment approach for salmon habitat. U.S. Dept. Commer., NOAA Tech.

Memo. NMFS-NWFSC-58, 183 p. NTIS PB2004-105734.

57 Rogers, J.B. 2003. Species allocation of Sebastes and Sebastolobus sp. caught by foreign

countries from 1965 through 1976 off Washington, Oregon, and California, USA. U.S. Dept. Commer.,

NOAA Tech. Memo. NMFS-NWFSC-57, 117 p. NTIS PB2004-105737.