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RESEARCH ARTICLE
Assessing recovery of spectacled eiders using
a Bayesian decision analysis
Kylee D. DunhamID
1
*
¤
, Erik E. Osnas
2
, Charles J. Frost
2
, Julian B. Fischer
2
, James
B. Grand
3
1School of Forestry and Wildlife Sciences, Alabama Cooperative Fish and Wildlife Research Unit, Auburn
University, Auburn, Alabama, United States of America, 2U.S. Fish & Wildlife Service, Migratory Bird
Management, Anchorage, Alaska, United States of America, 3U.S. Geological Survey, Alabama
Cooperative Fish and Wildlife Research Unit, Auburn University, Auburn, Alabama, United States of America
¤Current address: Department of Biological Sciences, University of Alberta, Edmonton, Alberta, Canada
*kylee583@gmail.com
Abstract
Assessing species status and making classification decisions under the Endangered Spe-
cies Act is a critical step towards effective species conservation. However, classification
decisions are liable to two errors: i) failing to classify a species as threatened or endangered
that should be classified (underprotection), or ii) classifying a species as threatened or
endangered when it is not warranted (overprotection). Recent surveys indicate threatened
spectacled eider populations are increasing in western Alaska, prompting the U.S. Fish and
Wildlife Service to reconsider the federal listing status. There are multiple criteria set for
assessing spectacled eider status, and here we focus on the abundance and decision analy-
sis criteria. We estimated population metrics using state-space models for Alaskan breeding
populations of spectacled eiders. We projected abundance over 50 years using posterior
estimates of abundance and process variation to estimate the probability of quasi-extinction.
The decision analysis maps the risk of quasi-extinction to the loss associated with making a
misclassification error (i.e., underprotection) through a loss function. Our results indicate
that the Yukon Kuskokwim Delta breeding population in western Alaska has met the recov-
ery criteria but the Arctic Coastal Plain population in northern Alaska has not. The methods
employed here provide an example of accounting for uncertainty and incorporating value
judgements in such a way that the decision-makers may understand the risk of committing a
misclassification error. Incorporating the abundance threshold and decision analysis in the
reclassification criteria greatly increases the transparency and defensibility of the classifica-
tion decision, a critical aspect for making effective decisions about species management
and conservation.
Introduction
The goal of the Endangered Species Act (ESA) [1] is to protect and recover imperiled species
and the ecosystems upon which they depend so federal protection is not necessary for main-
taining viability of the species. Recovery plans for species listed under the ESA are developed
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OPEN ACCESS
Citation: Dunham KD, Osnas EE, Frost CJ, Fischer
JB, Grand JB (2021) Assessing recovery of
spectacled eiders using a Bayesian decision
analysis. PLoS ONE 16(7): e0253895. https://doi.
org/10.1371/journal.pone.0253895
Editor: Guillaume Souchay, Office Franc¸ais de la
Biodiversite
´, FRANCE
Received: September 7, 2020
Accepted: June 16, 2021
Published: July 1, 2021
Copyright: This is an open access article, free of all
copyright, and may be freely reproduced,
distributed, transmitted, modified, built upon, or
otherwise used by anyone for any lawful purpose.
The work is made available under the Creative
Commons CC0 public domain dedication.
Data Availability Statement: All relevant data are
within the paper (Table 1) and the Supporting
Information files (Spectacled eider decision
analysis code).
Funding: Funding for this project was provided by
the Bureau of Land Management, the School of
Forestry and Wildlife Sciences at Auburn
University, and Ducks Unlimited Canada.
Competing interests: The authors have declared
that no competing interests exist.
to provide guidance regarding management actions and must include objective measurable
criteria to indicate when species reclassification (delisting or downlisting) is warranted. For
many species, the measurable criteria for reclassification are based on abundance, trend, and
extinction risk deemed appropriate by the species recovery team. Distinguishing when these
criteria are met is inherent in the concept of setting measurable objectives and has significant
implications for listed species and agencies tasked with their protection (e.g., U.S. Fish and
Wildlife Services [USFWS], National Marine Fisheries Service [NMFS]).
Recent surveys indicated spectacled eiders (Somateria fischeri), listed as threatened under
the ESA [2] have been increasing on one of their primary breeding grounds in Alaska, prompt-
ing the USFWS to consider population status relative to recovery criteria [3,4]. The global
population (i.e., the species) of spectacled eiders is listed and includes three distinct breeding
populations in Arctic Russia, northern Alaska along the Arctic Coastal Plain (ACP), and west-
ern Alaska on the Yukon-Kuskokwim Delta (YKD) [5]. The species can be considered for
delisting from threatened status following an analysis of continuous threats based on five fac-
tors ([1]; section 4(a)(1)(A-E)] and when each of the three breeding populations meets the
quantitative criteria outlined in the species recovery plan [3,4]. While the recovery plan sug-
gests that the three breeding populations meet the distinct population segment (DPS) criteria
[6], they were not formally designated as DPSs and thus, reclassification decisions must be
made for the entire species [2]. Based on aerial or nest surveys the populations can be assessed
by one of two sets of criteria: i) the minimum estimated breeding population size is 6,000
breeding pairs (or 12,000 breeding birds) designated by the 95% lower credible interval, and
the overprotection loss exceeds the underprotection loss as determined by an analysis of trend
data (10–15 years with 1 survey/year) and where loss functions are symmetrical around popu-
lation growth r= 0 with zero loss for both functions when r= 0, or ii) the minimum population
size is 10,000 breeding pairs over 3 surveys or the minimum estimate of abundance
exceeds 25,000 breeding pairs in any survey (see Criteria for delisting from threatened
status pp. 36–38 in [6]). Here, overprotection refers to the process of providing a species pro-
tection when it is not warranted, and underprotection refers to failing to provide protection
when it is warranted [6]. Based on limited aerial surveys of the breeding and the wintering
areas, the Russian breeding population is large (>100,000 breeding birds) and estimates sur-
pass the second criteria [7,8]. By comparison, the two breeding populations in Alaska repre-
sent a smaller portion of the global population and their status relative to these criteria are
unknown [3,4]. However, since listing, the YKD breeding population has increased in abun-
dance and may be close to meeting the first delisting criteria [3,4,6]. Determining if the Alas-
kan breeding populations have met the delisting criteria has wide-reaching implications for
the species conservation status.
Species classification decisions are liable to two possible errors: i) failing to classify a species as
threatened or endangered that should be classified (underprotection), or ii) classifying a species
as threatened or endangered when it is not warranted (overprotection) [9]. Decision theory pro-
vides a framework for linking statistical inference on population metrics to the risk of making a
classification error based on statistical results, expected consequences of the possible decisions
(i.e., loss), and prior beliefs about the system [9–11]. The link between statistical inference and
decision making occurs through the specification of a loss function that expresses the cost associ-
ated with the decision and the true state of nature [11,12]. The spectacled eider classification
problem consists of three alternatives or decisions; i) to delist the species, ii) maintain current
(threatened) status, or iii) reclassify as endangered. Given the growth of the YKD population we
consider alternatives one and two to determine the optimal decision based on the quantitative
criteria. The analysis for considering reclassification from threatened to not warranted (i.e.,
delisting) is based on the specification of two loss functions which are symmetrical around a
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population growth of r= 0 (i.e., stable growth) as defined within the species recovery plan [6].
The symmetrical nature of these loss functions represents a choice made by the species recovery
team to minimize potential bias and represents a risk neutral approach for evaluating outcomes.
The first loss function represents the cost of underprotection and is calculated based on the risk
of the population falling below a quasi-extinction threshold in 50 years. This function is
grounded on the principle that species should be classified by the level of extinction risk. Extinc-
tion risk is nearly certain (1.0) when the population is declining rapidly and the risk of underpro-
tection decreases as the risk of extinction decreases and reaches 0 when the population is stable
or growing [6]. The second loss function represents the cost of overprotection and is simply the
mirror image of the first loss function. Thus, loss associated with this second function increases
as extinction risk decreases from 0, when the population is declining or stable, to its maximum
(1.0), when there is no risk of extinction. The risk of committing a misclassification error (i.e.,
under or over-protection) is therefore calculated as the risk associated with each loss function
integrated with the posterior distribution around the current population growth rate (r). For
spectacled eiders, the listing decision is based on the comparison of overprotection risk and
underprotection risk. Though alternative loss functions exist (see [9–12] for examples) the pri-
mary purpose of this study was to evaluate outcomes based on the established recovery criteria
to inform status decisions.
Our work focused on determining if the Alaskan breeding populations of spectacled eiders
have met the quantitative criteria outlined in the species recovery plan to consider delisting.
Thus, we constructed alternative population models to estimate population metrics required
to assess extinction risk, specifically, abundance, population growth rate, and process varia-
tion. Using these results, we conducted a decision analysis by calculating loss functions and
misclassification error related to a decision to delist or maintain the species threatened status.
We used alternative models to address concerns held by the USFWS about the effects of uncer-
tainty in detection and observation processes on the decision analysis. The results from this
study serve to inform classification decisions and conservation planning for Alaskan breeding
spectacled eiders. Our approach combining population models with loss functions and
accounting for uncertainty in observation processes is applicable to many species classification
decisions that require not only quantitative assessments of population status but also value
judgements and risk tolerance of decision makers.
Materials and methods
We went through the following steps when conducting this analysis and describe each step
in more detail in the sections below. First, we gathered detection adjusted abundance esti-
mates and standard errors from aerial surveys of the ACP and YKD breeding populations
of spectacled eiders from 2007 to 2019. We fit these data using Bayesian state-space models
to estimate abundance, population growth rate, and process variation for both populations.
We constructed 2 alternative models for the ACP breeding population and 4 alternative
models for the YKD breeding population to reflect uncertainties in detection and observa-
tion processes. As a first step to evaluate if the recovery criteria were met, we determined if
the lower 95% Bayesian credible interval (CRI) of abundance in 2019 was 12,000 breed-
ing birds for each model. We then generated the loss function and calculated the probabil-
ity of committing a misclassification error based on expected loss and the posterior of
mean population growth rate. The results serve to provide managers with a robust and
transparent assessment of spectacled eider status that may be used to inform species con-
servation decisions. All data and code used for this analysis are available in Table 1 and the
S1 Appendix, respectively.
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Survey methods
Aerial surveys have been flown annually since the early 1990’s to monitor both breeding popu-
lations of Alaskan spectacled eiders [3,13,14]. In most aerial surveys of waterfowl during the
breeding season, waterfowl are recorded in such a way as to distinguish breeding birds from
non-breeding birds. We used the number of indicated breeding birds which includes observa-
tions of single birds and pairs [3]. When aerial surveys are flown, spectacled eiders have typi-
cally been in pairs and in very few cases have flocks been documented on either breeding area.
Following guidelines regarding the temporal scope for analysis in the recovery plan, and to
include data from the most consistent sampling period across both study sites, we used survey
data from 2007 to 2019 for both populations.
Arctic coastal plain breeding population surveys. The ACP spans approximately 90,000
km
2
on the North Slope of Alaska bordering the Chukchi and Southern Beaufort Seas [13,14].
USFWS Division of Migratory Bird Management conducts annual aerial surveys sampling
nearly 60,000 km
2
of the ACP to monitor the distribution, abundance, and trend of bird spe-
cies. The ACP survey was flown annually following consistent methods from 2007 to 2019 [13,
14]. In 2015 and 2016, USFWS implemented double-observer techniques to estimate aerial
detection probabilities of spectacled eiders breeding on the ACP (for methodological details,
see [13]). We used detection-adjusted estimates of indicated breeding birds and error in our
analysis (Table 1).
Yukon-Kuskokwim delta breeding population surveys. The YKD of western Alaska
spans approximately 130,000 km
2
and borders the Bering Sea [3,4,9]. Aerial surveys of specta-
cled eiders have been conducted over 12,832 km
2
of YKD tundra wetland habitat annually
since 1988 [3] Additionally, ground-based surveys have been conducted annually on the YKD
since 1985 to estimate the numbers of nests for geese and eiders. This survey sampled ran-
domly selected plots within the core nesting area of spectacled eiders in the central coast zone
Table 1. Detection adjusted abundance estimates for Alaskan breeding populations of spectacled eiders (Soma-
teria fischeri) from 2007 to 2019 provided as data ( ^
yt^
, the mean observed number of breeding birds and σ^
yt^, the
estimated standard error for the number of breeding birds) in the observation model.
YKD
a
ACP
b
Number of breeding birds Number of breeding birds
Year ^
yt^σ^
yt^^
yt^σ^
yt^
2007 12,527 1,045 6,555 961
2008 14,580 1,273 7,733 939
2009 15,562 1,232 7,072 1,226
2010 13,491 1,056 6,892 987
2011 NA NA 10,562 1,258
2012 14,696 1,279 6,228 679
2013 16,178 1,238 9,995 1,302
2014 13,152 1,075 9,651 1,382
2015 5,714 494 7,745 969
2016 14,481 1,086 5,696 892
2017 16,727 1,368 5,951 1,073
2018 15,544 1,241 6,418 1,276
2019 15,111 1,137 5,108 725
There were no surveys flown in 2011 and thus no estimates are provided.
a
YKD metrics refer to the Yukon-Kuskokwim Delta breeding population.
b
ACP metrics refer to the Arctic Coastal Plain breeding population.
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encompassing 716 km
2
[3]. Estimates of nests and aerial observations among low, medium,
and high-density stratum on the YKD were used to calculate density-specific aerial visibility
correction factors (VCF) to account for incomplete detection on aerial surveys. Lewis et al. [4]
converted the aerial indices of spectacled eider abundance to annual estimates of breeding
abundance using the average density-specific visibility correction factors. The estimates gener-
ated for 2007–2019 were provided as observation data and error in our analysis (Table 1).
State-space models
Our first goal was to estimate mean population growth rate, �
r, and process or temporal varia-
tion in population growth rate σ
r
using detection adjusted abundance estimates from aerial
surveys of spectacled eiders on the YKD and ACP. We used Bayesian state-space models to
partition population dynamics into two components, the hidden state process and the observa-
tion model, and fit the process model to the time series of observations [15,16]. State-space
models simultaneously account for both process variation and observation error caused by
partial observability on surveys [15,16].
The spectacled eider recovery team was interested in understanding the effects of model
assumptions on population estimates and the decision analysis. Specifically, concerns were
raised about the use and effects of informative and noninformative priors on the model esti-
mates and decision analysis. Additionally, in 2015, a different observer conducted the eider
aerial surveys on the YKD. The abundance estimate for 2015 indicated that the population
dropped substantially from the previous year. However, upon closer inspection, the counts for
that year were significantly smaller than previous and following years [4] and estimates from
the nest counts for 2015 indicate no real decline in population size ([17], pg. 26 of report).
Finally, the detection-corrected population estimates were based on the mean detection across
years [4,13]; thereby assuming that detection is constant. The observation of the 2015 data on
the YKD as well as a large literature on population estimation (e.g., [18]), suggests that detec-
tion is rarely constant across years. Ignoring latent observation processes has been shown to
bias estimates of demographic parameters [19]. Given these concerns, we fit a total of 6 mod-
els: 2 for the ACP population and 4 for the YKD population. Models ACP1 and YKD1
included all available years of data between 2007 and 2019 and were initialized with ‘informa-
tive’ priors based on the species’ biology and expert opinion (Table 2). Model YKD2 included
all years of data between 2007 and 2019 and was initialized using noninformative priors
(Table 2). Model YKD3 was fit by excluding the 2015 population estimate and initializing the
model with informative priors. Finally, models ACP2 and YKD4 allowed for a latent observa-
tion process and used informative priors to provide estimates of VCF variance and an observer
effect (Table 2). Model parameters and prior distributions are described in Table 2. We worked
closely with the eider recovery team throughout all stages of the analysis including, but not
limited to considerable discussion regarding the choice of priors and alternative models. Sub-
sequently, informative priors were based on species biology and informally elicited expert
opinion from the recovery team.
We modeled the log initial abundance as the log of the point estimate for abundance in
2007 the first year of our time series, with a standard Normal prior either 0.1 or 0.5 to generate
an informative or noninformative distribution, respectively. The prior for mean population
growth rate (r) is Normal with mean 0 with standard deviation is 0.1 or 0.5 for models with
informative or noninformative priors, respectively (S1 Fig in S2 Appendix). The standard devi-
ation for informative priors for initial abundance and population growth rate were based on
the initial abundance estimate and input from species experts. The prior distribution for tem-
poral variation in population growth (here, process variance) was Gamma distributed and
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based on shape and rate parameters with a range of values between approximately 0.005 and 1
for models using informative priors and a range of values between 0.005 and 10 for models
using noninformative priors (S2 Fig in S2 Appendix). Comparisons of the informative and
noninformative priors with their respective models’ posterior distributions for rand process
variance are included in the supplementary material (S2 Appendix) for transparency (S3 and
S4 Figs in S2 Appendix). Descriptions of the priors for latent observation processes are
described in further detail in the text below.
Each of the six state-space models described population growth as
logðNtþ1Þ ¼ logðNtÞ þ rtð1Þ
where N
t
is the number of breeding birds in year t,r
t
is population growth rate, and
rtNormalð�
r;s2
rÞ:ð2Þ
The observation model relates the true population size N
t
to the observations correspond-
ing to the detection-adjusted abundance indices for each breeding area. For models ACP1 and
YKD1, YKD2, and YKD3, our observation process was
^
ytNormalðNt;^s^ytÞ ð3Þ
Table 2. Model descriptions, parameters, and prior distributions used to model population dynamics of spectacled eiders (Somateria fischeri) breeding on the Arc-
tic Coastal Plain (ACP) and Yukon-Kuskokwim Delta (YKD).
Model Model Description Parameters Prior
Distributions
ACP1 Informative priors based on expert opinion and species biology log(N
2007
)Normal (8.78, 0.1)
�
r
�Normal (0, 0.1)
s2
rGamma (3, 20)
ACP2 Informative priors (see above) and includes latent variation in the observation process log(N
2007
)Normal (8.78, 0.1)
�
r
�Normal (0, 0.1)
s2
rGamma (3, 20)
σ
d
Gamma (1, 10)
YKD1 Informative priors based on expert opinion and species biology log(N
2007
)Normal (9.43, 0.1)
r
t
Normal (0, 0.1)
s2
rGamma (3, 20)
YKD2 Noninformative (diffuse) priors log(N
2007
)Normal (9.43, 0.5)
�
r
�Normal (0, 0.5)
s2
rGamma (3, 2)
YKD3 Informative priors with 2015 observation removed log(N
2007
)Normal (9.43, 0.1)
�
r
�Normal (0, 0.1)
s2
rGamma (3, 20)
YKD4 Informative priors and includes latent variation in the observation process in the form of random effects and includes a
fixed effect for the new observer in 2015
log(N
2007
)Normal (9.43, 0.1)
�
r
�Normal (0, 0.1)
s2
rGamma (3, 20)
σ
d
Gamma (1, 10)
Β Gamma (15.5, 0)
Here, we describe each model, the relevant parameters, and the respective prior distributions. The parameters include, N
2007
– population size in 2007, �
r
�– mean
population growth rate, s2
r– process variance, s2
d– standard deviation of annual VCF, and β–the fixed effect of a new observer. For the Normal distributions we report
the mean and the standard deviation on the log scale. The Gamma distributions are reported with the shape and rate parameters. For the process variance parameter
(s2
r) we report the prior distributions for the standard deviation.
https://doi.org/10.1371/journal.pone.0253895.t002
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where the observations, ^
yt, were the detection-adjusted abundance point estimates of specta-
cled eiders from the aerial surveys on the respective breeding grounds (i.e., ACP and YKD) [3,
14] (Table 1). Annual observation error from aerial survey sampling (^s^
yt) was provided as data
(see similar approach in [20]) (Table 1).
An alternative observation model was required to account for the latent observation pro-
cesses for models ACP2 and YKD 4. For the ACP, we simply added a multiplicative random
effect (d
t
) to population size (N
t
) and the associated prior for the variance of this effect (σ
d
) in
the observation model
^
ytNormal Nt
dt
;^s^
yt
ð4Þ
logðdtÞ Normalð0;sdÞ ð5Þ
sdGammað1;10Þ:ð6Þ
In this model, d
t
is the (unmeasured) year-specific deviation in the VCF. Positive deviations
mean that fewer birds were observed ( ^
yt) relative to the population (N
t
). For the YKD, we
modeled the observation process with the same random effect but added a fixed effect for the
new observer in 2015
logðdtÞ Normalðbxt;sdÞ ð7Þ
where x
t
is an indicator equal to zero in all years except 2015, when it is 1, and βis a fixed effect
regression parameter for the effect on VCF in 2015 due to a new observer. We used a prior for
βinformed by our knowledge of the number of eider nests estimated from ground-based sur-
veys in 2015 [17].
b1Gammað15:5;9Þ ð8Þ
We derived the parameters for this distribution by matching the mean and standard devia-
tion based on the ratio of twice the estimated nests reported for 2015 (e.g., the expected num-
ber of breeding birds, 15,584 ±2,472, [17]) to the estimate of indicated breeding birds derived
from the VCF-corrected aerial data for 2015 (5,714 ±494) which results in a ratio with mean
2.73 and standard deviation 0.49. With this information, we generated a Gamma prior for β−1
with the shape parameter 15.5 and rate parameter 9 which has a mean of 1.72 and standard
deviation of 0.44 to limit the range of expected values from this ratio on the log scale.
The prior for σ
d
in both the ACP and YKD models was chosen to reflect a belief that annual
deviations in detection are most likely small but could be large with low probability. Combin-
ing Eqs (5) and (6) results in a prior distribution for the VCF deviations, d
t
, where 50% of |d
t
|
<0.04 and 99% are <0.44. This is an extremely informative prior and implies most deviations
are small but large deviations (>0.04) can occur and very large deviations (>0.44) very rarely
occur. In the absence of direct measures of annual VCFs, we believe this is a reasonable prior.
We fit the state-space models in a Bayesian framework implementing Markov chain Monte
Carlo methods (MCMC, [21]) to sample the posterior distributions in JAGS 3.3.0([22], using
the jagsUI package in R [23]). We ran three MCMC chains for 100,000 iterations, set thin to 2,
discarded 70,000 iterations as burn-in, and ran 5,000 iterations in the JAGs adaptive phase.
We checked convergence using the Gelman-Rubin statistic [24] and all results were satisfac-
tory (all ^
R<1.01).
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Decision analysis
The basic elements in statistical decision analyses include θ, the state of nature which affects
the decision process, and Θis the set of all possible states of nature [11,12]. The decisions or
actions are denoted by a, and all possible actions considered may be denoted A. The loss func-
tion, L(θ,a) describes the loss associated with taking action afor each θstate of nature and the
function is defined for ðy;aÞ 2 YA. Following Berger [12] and Williams and Hooten [11],
the general notation for Bayesian expected loss is:
EyjyLðy;aÞ ¼ ZY
Lðy;aÞ½yjydy:ð9Þ
In this analysis we consider two possible states of nature based on the recovery criteria, the
first is that the population is declining (r<0) and the second is that the population is stable or
increasing (r0). Additionally, there are two alternative actions (a) which refer to delisting or
maintaining the threatened status. The recovery team chose symmetric loss functions around
r= 0 to represent equivalent loss associated with providing too little (underprotection) or too
much (overprotection) protection to the species based on the classification of threatened or not
warranted [6,9]. The loss functions refer to the decision to delist when the population is declining
(i.e., underprotection) and for the decision to maintain the threatened status when the population
is stable or increasing (i.e., overprotection). The loss associated with delisting spectacled eiders is
equivalent to the probability of reaching a quasi-extinction threshold of 250 breeding birds within
50 years, given a projection using the abundance and process variation estimates from the state
space model(s) over a range of population growth rates with a zero-loss occurring once r= 0.
Loss is set to zero once r= 0 because the recovery team decided that the decision to delist is cor-
rect when the population is stable or increasing. Based on the decision to equalize errors we set
the loss function for overprotection to reflect the underprotection loss function as specified by
the USFWS [6] and described in Taylor et al [9]. The overprotection loss function is thus the loss
incurred when the decision is to maintain the threatened status and the population is stable or
increasing and there is zero loss when the population is declining because the decision to main-
tain the status is correct. In classification decisions, expected loss (e.g., under or over-protection
loss) is also known as the conditional risk of committing a classification error. For this classifica-
tion decision, expected loss or risk of committing a classification error is conditional on the pos-
terior distribution of mean population growth rate generated from the state-space model(s).
We generated the underprotection loss function by projecting abundance for 50 years over all
possible values of population growth denoted rs (all possible values of the state of nature, Θ). The
range of rs was set from -0.4 to 0.4 because the posterior distribution of mean rproduced from
the state-space models fell within these limits. First, initial abundance is chosen from the poste-
rior distribution of N
2019
(see Table 3 for values); (ii) process variance σ
r
is selected from the pos-
terior distribution generated in the state-space model; (iii) r0is pulled from N(rs,σ
r
) for each year;
(iv) the population is projected forward for 50 years, when N falls below 250 breeding birds the
run is assigned a 1 and if it does not reach this threshold within 50 years the run is assigned a 0;
and (v) steps i-iv are repeated 10,000 times, and the number of times N falls below the quasi-
extinction threshold is saved. The probability of committing a classification error is calculated as
the sum of the expected loss for the decision to delist (underprotection loss) for r<0 and for the
decision to maintain status (overprotection loss) for r0 multiplied by the probability of that
value of rfrom the posterior distribution on mean population growth. This results in a single
value (i.e., loss or the risk of committing a classification error) for each decision (i.e., to delist or
maintain threatened status). Based on the specification of our loss functions and decision criteria,
the optimal decision minimizes underprotection loss in favor of maximizing overprotection loss.
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Results
Our results indicate that estimates of abundance and misclassification error are sensitive to
uncertainty, but conclusions broadly remain consistent. Specifically, in each case the YKD
population met the recovery criterion, whereas the smaller ACP population did not meet
either the abundance threshold or the requirements for misclassification error (Table 3, Figs 1
and 2). The low abundance estimate combined with a highly variable and slightly decreasing
population growth rate at the posterior mean for the ACP breeding population increase the
risk of quasi-extinction. For the ACP breeding population, an underprotection error is more
likely if the decision is to delist than an overprotection error if the decision is to maintain
threatened status. The YKD breeding population is larger than the ACP population, and for
each alternative model the lower 95% CRI of the 2019 abundance estimate met the threshold
of 12,000 breeding birds. However, similar to the ACP population results, the posterior of
mean population growth rate for the YKD was uncertain and centered nearly at zero for each
model (Table 3). While overprotection loss for the YKD population is larger than underprotec-
tion loss for each alternative model, there is still considerable uncertainty in population met-
rics when the low estimate from 2015 is included in the data and detection is assumed
constant (Models YKD1, YKD2).
Arctic coastal plain population
Analysis of the ACP data indicates the population has not met any of the recovery criteria
(Table 3). When assuming constant detection, estimated posterior mean abundance for the
ACP population in 2019 was 5,355 breeding birds (95% CRI 4,106–6,589; Model ACP1,
Table 3. Posterior estimates of population metrics and misclassification error for both Alaskan breeding populations of spectacled eiders (Somateria fischeri).
ACP1
a
ACP2
a
YKD1
b
YKD2
b
YKD3
b
YKD4
b
Abundance
Posterior mean 5355 6401 15054 15047 15388 16113
Posterior SD 629 1510 1104 1118 908 2249
95% CRI 4106–6589 3766–9750 12903–17212 12863–17253 13595–17175 12313–21352
Population growth rate ‘r’
Posterior mean -0.016 -0.005 0.009 0.013 0.013 0.016
Posterior SD 0.043 0.043 0.068 0.137 0.023 0.037
95% CRI -0.103–0.072 -0.092–0.082 -0.124–0.0143 -0.263–0.287 -0.035–0.062 -0.065–0.091
Process variation
Posterior mean 0.158 0.142 0.323 0.479 0.073 0.123
Posterior SD 0.061 0.064 0.064 0.137 0.038 0.073
95% CRI 0.057–0.293 0.039–0.288 0.219–0.468 0.284–0.814 0.017–0.161 0.026–0.305
Loss
Underprotection 0.181 0.108 0.145 0.282 0.0002 0.011
Overprotection 0.072 0.088 0.218 0.357 0.0061 0.068
Here, we report the mean (posterior mean), standard deviation (posterior SD), and 95% Bayesian credible intervals (95% CRI) for each parameter and model.
Consideration for reclassification from threatened to recovered requires that both populations must reach or exceed the abundance threshold (N 12,000 breeding
birds), and overprotection loss must be greater than underprotection loss. Abundance estimates and misclassification error rates for the ACP population do not support
the decision to delist. Alternatively, all four models for the YKD population support delisting based on population metrics meeting the reclassification criteria in the
species recovery plan.
a
ACP metrics refer to the Arctic Coastal Plain breeding population.
b
YKD metrics refer to the Yukon-Kuskokwim Delta breeding population.
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Table 3, S5 Fig in S2 Appendix). When we allowed detection to vary across years, estimated
mean abundance in 2019 was 6,401 (3,766–9,750; Model ACP2, Table 3, S5 Fig in S2 Appen-
dix). Based on estimated abundance in 2019 for either model, the ACP population has not met
Fig 1. Posterior estimates of abundance for spectacled eider populations breeding on the Arctic Coastal Plain (ACP) and Yukon-Kuskokwim Delta (YKD) of
Alaska. We fit 2 alternative models for the ACP breeding population and four alternative models for the YKD breeding population. Models ACP1 and YKD1 included
all available years of data between 2007 and 2019 and were initialized with ‘informative’ priors based on the species’ biology and expert opinion. Model YKD2 included
all years of data between 2007 and 2019 and was initialized using noninformative priors. Model YKD3 was fit by excluding the 2015 population estimate and initializing
the model with informative priors. Finally, models ACP2 and YKD4 allowed for a latent observation process and used informative priors to provide estimates of VCF
variance and an observer effect. Gray circles represent the annual mean abundance and gray ribbons represent the 95% credible interval (CRI). The black dashed line is
the population threshold of 12,000 breeding birds identified in the species recovery plan.
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Fig 2. Loss functions and posterior distributions of population growth rate (r) generated from state-space models of abundance for spectacled eiders breeding on
the Arctic Coastal Plain (ACP) and Yukon Kuskokwim Delta (YKD). Loss functions were generated using the probability of quasi-extinction given population size,
growth rate, and process variation. The dotted line represents the under-protection loss function (i.e., loss if decision were to delist given negative population growth)
and the solid line is the over protection loss function (i.e., loss if the decision were to maintain status given positive population growth). Gray distributions show the
posterior density of population growth rate (r) estimated by a Bayesian state-space model for the time series from 2007 to 2019. As part of the recovery criteria,
spectacled eiders will be considered for delisting if overprotection (value in solid line box) is greater than underprotection (value in dashed line box). Greater
overprotection error indicates that we are more likely to provide too much protection to the species than we are to provide too little protection to thespecies.
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the abundance threshold (95% CRI ¼^
N12,000 breeding birds) (Fig 1). The posterior mean
for mean growth rate of the ACP population was negative (�
r¼ 0:016 or -0.005) with wide
credible intervals (95% CRI: -0.103 to 0.072; -0.092 to 0.082) for models assuming constant
and variable detection, respectively (Table 3). Furthermore, underprotection loss for the ACP
population was greater than overprotection loss in both models (Table 3,Fig 2).
Yukon-Kuskokwim delta population
We fit four alternative models to the YKD breeding population data. In each case, estimates
of abundance exceeded the decision threshold and overprotection loss exceeded underpro-
tection loss, indicating the population has met the recovery criteria. Model YKD1 includes
all data points between 2007 and 2019 and was initialized with informative priors (see State-
space models section in Materials and methods). Estimated posterior mean abundance
from model YKD1 in 2019 was 15,054 breeding birds (95% CRI 12,903 to 17,212) (Table 3).
The 95% lower CRI of abundance in 2019 is above 12,000 breeding birds indicating the
YKD breeding population met the abundance threshold criterion (Fig 1 and S6 Fig in S2
Appendix). The posterior mean for mean population growth rate of the YKD population
was �
r= 0.009 with a wide credible interval (95% CRI -0.124 to 0.143) (Table 3,Fig 2). Over-
protection loss was 1.5 times that of underprotection loss based on the YKD1 model
(Table 3,Fig 2).
Model YKD2 included all data points between 2007 to 2019 and was initialized with non-
informative priors. Estimated posterior mean abundance for 2019 from model YKD2 was
15,047 (95% CRI 12,863 to 17,253), which exceeds the abundance threshold (Table 3,Fig 1
and S6 Fig in S2 Appendix). The posterior mean of mean population growth rate was �
r=
0.013 and 95% CRI of -0.263 to 0.287. The posterior mean for process variation in this
model was 0.479 (95% CRI of 0.280 to 0.801). Both the posterior mean growth rate and pro-
cess variance are larger than those produced when using biologically realistic informative
priors (Fig 2). Overprotection loss again exceeded underprotection loss and the risk of com-
mitting an overprotection error was 1.26 times that of the risk of committing an underpro-
tection error.
Model YKD3 was initialized with informative priors and the 2015 data point was removed
from the time series and treated as a missing data point similar to 2011 when no survey was
conducted. The abundance estimate for 2019 from model YKD3 was also above the threshold,
with a posterior mean of 15,388 and 95% CRI of 13,595 to 17,175 (Table 3,Fig 1 and S6 Fig in
S2 Appendix). The posterior of mean population growth rate was substantially more precise
than posterior distributions produced by YKD1 and YKD 2. The posterior mean of mean pop-
ulation growth was 0.013 with 95% CRI of -0.035 to 0.062 (Fig 2). The posterior mean process
variation was only 0.073 (95% CRI of 0.017 to 0.161), significantly lower than estimates from
YKD1 and YKD2 (Table 3). Overprotection loss exceeded underprotection loss, however, in
this case the risk of committing an overprotection error was 30.5 times that of the risk of com-
mitting an underprotection error for model YKD3.
Finally, Model YKD4 included all data, informative priors for all parameters and latent vari-
ation in VCF. The posterior mean abundance for YKD4 in 2019 was 16,113 (95% CRI of
12,313 to 21,352) just satisfying the abundance threshold and substantially wider than the
other models (Table 3,Fig 1 and S6 Fig in S2 Appendix). The posterior mean of mean popula-
tion growth rate was 0.016 and 95% CRI of -0.065 to 0.091. For process variation, the posterior
mean for YKD4 was 0.123 and 95% CRI of 0.026 to 0.305. Overprotection loss exceeded
underprotection loss and the risk of committing an overprotection error given model YKD4
was 6.18 times that of the risk of committing an underprotection error.
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Discussion
We constructed a series of models to assess the status of two breeding populations of specta-
cled eiders in Alaska and determine if the populations had met the species recovery goals. Our
results demonstrated that the ACP population of spectacled eiders has not met the quantitative
criteria required to consider delisting; however, the YKD breeding population has met the
recovery criteria. Our application of a decision analysis in conjunction with a population
assessment is an example of a robust methodology for informing species classification deci-
sions based on population estimates in addition to value judgements and risk tolerance. Fur-
thermore, our approach including alternative models offered an opportunity to explore the
effects of uncertainty not only on population estimates but also on the risks associated with
species classification decisions.
When using population metrics (abundance, trends, demographic rates, etc.) for species
classifications, harvest regulations, or other management actions, it is important to consider
the accuracy and precision of those estimates and the influence those estimates may have on a
decision [25]. A considerable portion of variation in the YKD population growth rates and
process variation can be attributed to the negative bias introduced by the 2015 data and assum-
ing constant VCFs across years (Tables 1and 2,Fig 2). Beginning in 2015, a new observer was
assigned to conduct the aerial surveys and VCF values tended to be elevated in years with new
observers which in conjunction with low counts biased the abundance estimate low [4]. Fur-
thermore, the VCF accounted for nesting density and spatial variation but did not account for
temporal variation in detection or a fundamental change in study design (i.e., a new observer).
Removing the biased abundance estimate from 2015 (model YKD3) or accounting for tempo-
ral variation in detection (model YKD4) had a considerable effect on the precision of popula-
tion metrics and on the risk of committing an overprotection error. There is considerable
information to suggest that the perceived decline in 2015 was the result of an unaccounted-for
change in observation process and not a true decline in population size or growth rate. In addi-
tion to the abnormally low counts and the evidence of unmodeled variation in observation
processes from this analysis, estimates from the YKD nest plot survey estimated greater than
7,000 nests (14,000 breeding birds) in 2015 ([17], pg. 26 of report). This analysis highlights two
important points: (i) in models where we use a constant VCF and do not account for temporal
variation or observer changes, residual variation in the data is captured by the process varia-
tion term [26,27] and it is biased high related to the year-specific variance in the VCF; there-
fore, (ii) the extinction risk, loss functions, and risks of committing a misclassification error
reported here are also biased high. By extending the analysis to consider multiple models and
assumptions, we explicitly incorporated the effects of uncertainty into the decision analysis
and population assessment and provide decision makers with transparent results. Importantly,
we note that the results consistently showed that the ACP population did not meet the recov-
ery criteria and the YKD population did meet the recovery criteria, regardless of the underly-
ing model assumptions.
By fitting models ACP2 and YKD4 that included year-specific variation in detection (VCF)
as a random effect (both models) and fixed effects for systemic changes in study design (e.g.,
novice observers; model YKD4) we were able to account for latent variation in observation
processes. In the context of N-mixture models, Zhao and Royle [19] found that assuming con-
stant detection when in fact detection varied annually caused biased estimates of demographic
parameters. They also found that fitting a model with latent random effects for detection even
with only one survey replicate per year reduced bias in demographic estimates. This is consis-
tent with our state-space models using the eider data and latent effects for detection where we
found that when a greater proportion of variation is attributed to the latent observation
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process, it results in a lower estimate of process variance, more precise estimates of mean
growth rate, and reduced precision of the population estimates (Models ACP2 and YKD4,
Table 3, S5 and S6 Figs in S2 Appendix). The results of Zhao and Royle [19] and our explora-
tions suggest that not accounting for such variation in detection, either by direct measurement
or by modelling the effect through a latent process, may cause abundance estimates to be too
precise and our demographic parameters to be biased; thus, biasing population viability analy-
ses. The former leads to overconfidence in the population estimate and incorrect decisions
based on abundance thresholds, and together, both lead to biased estimates of extinction risk.
While further research and consideration of how to treat this type of data when year-specific
detection is not measured may be warranted, using informed priors based on expert judge-
ment or auxiliary data for unmeasured processes seems a reasonable approach to improve con-
servation decisions. In any case, measurement of year-specific detection probability would
increase the ability to appropriately account for uncertainty in both the observation and popu-
lation process; thereby, leading to less biased population parameters and better management
decisions.
We followed the decision analysis approach outlined in the spectacled eider recovery plan
and in Taylor et al. [9] to quantitatively assess spectacled eider populations against recovery
criteria. These criteria include the loss associated with a listing decision and an abundance
threshold based on the lower 95% credible interval (i.e., 2.5 percentile) of the posterior distri-
bution of abundance. Certain properties of the current recovery criteria, however, might be
reevaluated as the recovery plan is revised to ensure that they reflect the current risk values of
the decision makers. First, using loss has been proposed for endangered species listing deci-
sions and other natural resource management problems, but has not yet been widely adopted
[10,11,28]. We agree with this approach as it offers a transparent and logically coherent
framework for making species classification decisions [11,12]. However, we wonder if the
choice of symmetrical loss functions around zero mean population growth with zero loss at
r= 0 and a shape determined by a population viability analysis directly reflect the risk values of
the decision makers. Loss functions can take many shapes that represent risk attitudes but can
be difficult to elicit [11], and we suggest that the current loss functions might be improved or
at least reevaluated. Second, setting loss equal to zero when r= 0 does not accurately reflect the
extinction risk of the population which predicates the underprotection loss function. Specifi-
cally, when r0 there is still a non-zero risk of the population declining below the quasi-
extinction threshold within the 50-year period and this risk is not accounted for in the current
calculation of loss. Third, the abundance threshold criteria seem redundant to a criterion
based on population viability because viability is based on growth rate, stochasticity in growth
rate (here process variance), and current abundance. Importantly, the abundance threshold
criteria is sensitive to the posterior variance in abundance, and in the absence of year-specific
detection estimates, we may be greatly underestimating this variance. Furthermore, choosing
an abundance threshold implies a loss function for abundance. The current 2.5 percentile
threshold (the lower bound of a 95 percent credible interval) implies that overestimates are 39
times worse than underestimates of abundance under a linear loss function (see Table 2 of
[11]). While it is certainly reasonable that overestimating a listed species’ abundance is worse
than underestimating, using the same threshold as is widely used for statistical hypothesis test-
ing, which is often devoid of any applied decision context, might be reconsidered. Even though
the abundance threshold might seem simple and value-free, there is an implied value judgment
for risk tolerance of the decision maker. If the variance in the abundance estimate is much
larger than previously thought, it could influence decisions regarding status.
Decision-makers are often tasked with choosing conservation or management actions
despite uncertainty. The methods employed here provide an example of accounting for
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uncertainty in such a way that incorporates both science and value-based judgements to
inform decision-makers about the risk of committing a misclassification error [28]. Account-
ing for the uncertainty in population dynamics and observation processes in the population
assessment and decision analysis allowed us to explore the impacts of those uncertainties in a
robust and transparent manner. The combined strengths in these approaches provide a robust
framework for formally linking ecological inference to conservation and management deci-
sions under considerable uncertainty [9–11,29]. We believe our approach is a reasonable
method for capturing risk of listing decision alternatives with careful thought and explicit defi-
nitions of the loss functions and risk tolerance. Future applications may consider explicitly
modeling the effects of different decisions on future population outcomes and incorporate
these predictions with loss functions thereby representing decision makers’ risk tolerances to
better inform listing status decisions. This analysis adds to the growing support for decision-
theoretic approaches in applied ecology and conservation, and further emphasizes the impor-
tance of exploring the effects of uncertainty on making endangered species classification
decisions.
Supporting information
S1 Appendix. Spectacled eider decision analysis R and Jags code.
(RMD)
S2 Appendix. Spectacled eider decision analysis supplementary figures.
(DOCX)
Acknowledgments
We would like to thank David Koons, Conor McGowan, Christopher Lepczyk, Ash Abebe,
Anna Tucker, Abigail Lawson, Kate Martin, and several anonymous reviewers for providing
reviews that made this manuscript stronger. We also thank the members of the spectacled
eider recovery team for their valuable insight throughout. Any use of trade, firm, or product
names is for descriptive purposes only and does not imply endorsement by the U.S.
Government.
Author Contributions
Conceptualization: James B. Grand.
Data curation: Erik E. Osnas, Charles J. Frost, Julian B. Fischer.
Formal analysis: Kylee D. Dunham, Erik E. Osnas.
Methodology: Kylee D. Dunham, Erik E. Osnas, Charles J. Frost, Julian B. Fischer, James B.
Grand.
Project administration: James B. Grand.
Supervision: James B. Grand.
Writing – original draft: Kylee D. Dunham, Erik E. Osnas, Julian B. Fischer, James B. Grand.
Writing – review & editing: Kylee D. Dunham, Erik E. Osnas, Charles J. Frost, Julian B.
Fischer, James B. Grand.
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