ORIGINAL ARTICLE

Bayesian analysis of multi-state data with individual covariatesfor estimating genetic effects on demography

Sarah J. Converse • J. Andrew Royle •

Richard P. Urbanek

Received: 4 February 2010 / Revised: 30 March 2011 / Accepted: 1 April 2011 / Published online: 24 April 2011

� Springer-Verlag (outside the USA) 2011

Abstract Inbreeding depression is frequently a concern

of managers interested in restoring endangered species.

Decisions to reduce the potential for inbreeding depression

by balancing genotypic contributions to reintroduced pop-

ulations may exact a cost on long-term demographic per-

formance of the population if those decisions result in

reduced numbers of animals released and/or restriction of

particularly successful genotypes (i.e., heritable traits of

particular family lines). As part of an effort to restore a

migratory flock of Whooping Cranes (Grus americana) to

eastern North America using the offspring of captive

breeders, we obtained a unique dataset which includes

post-release mark–recapture data, as well as the pedigree of

each released individual. We developed a Bayesian for-

mulation of a multi-state model to analyze radio-telemetry,

band-resight, and dead recovery data on reintroduced

individuals, in order to track survival and breeding state

transitions. We used studbook-based individual covariates

to examine the comparative evidence for and degree of

effects of inbreeding, genotype, and genotype quality on

post-release survival of reintroduced individuals. We

demonstrate implementation of the Bayesian multi-state

model, which allows for the integration of imperfect

detection, multiple data types, random effects, and

individual- and time-dependent covariates. Our results

provide only weak evidence for an effect of the quality of

an individual’s genotype in captivity on post-release sur-

vival as well as for an effect of inbreeding on post-release

survival. We plan to integrate our results into a decision-

analytic modeling framework that can explicitly examine

tradeoffs between the effects of inbreeding and the effects

of genotype and demographic stochasticity on population

establishment.

Keywords Breeding � Captive productivity � Genotype

quality � Grus americana � Inbreeding coefficient �Reintroduction � Whooping crane

Introduction

Conservation biologists are frequently concerned about the

potential effects of inbreeding on the viability of popula-

tions of rare species (e.g., Frankham 1995). Crnokrak and

Roff (1999) argued that high levels of inbreeding depres-

sion could be found in wild species, including avian spe-

cies, based on differences between inbred and outbred

individuals in demographic traits such as clutch size,

hatching success, nestling survival, fledgling survival, and

adult survival. However, few direct examinations of

inbreeding depression effects on wild population demog-

raphy have been carried out, and those studies that do exist

have not integrated state-of-the-art methods in demo-

graphic estimation, such as accounting for imperfect

detection and differences in individuals based on age and

breeding state. Even so, if inbreeding effects do occur in

wild species, and the degree of the effects can be estimated,

this information can be used to inform management of

captive and restored populations.

Communicated by W. L. Kendall.

S. J. Converse (&) � J. A. Royle

Patuxent Wildlife Research Center, U.S. Geological Survey,

12100 Beech Forest Road, Laurel, MD 20708, USA

e-mail: sconverse@usgs.gov

R. P. Urbanek

Necedah National Wildlife Refuge, U.S. Fish and Wildlife

Service, W7996 20th Street West, Necedah, WI 54646, USA

123

J Ornithol (2012) 152 (Suppl 2):S561–S572

DOI 10.1007/s10336-011-0695-0

An example species for which concerns about inbreed-

ing have influenced management is the Whooping Crane

(Grus americana). Whooping Cranes are listed as endan-

gered under the US Endangered Species Act and Canada’s

Species at Risk Act and, as of late 2008, there were fewer

than 400 individuals in the wild, and fewer than 600 total

individuals in existence (T. Stehn, US Fish and Wildlife

Service, unpublished data). Wild Whooping Cranes exist in

3 populations, including the Aransas–Wood Buffalo Pop-

ulation (AWBP), which breeds at Wood Buffalo National

Park, Canada, and winters at Aransas National Wildlife

Refuge, USA; the Florida Non-Migratory Population in

central Florida, USA; and the Eastern Migratory Popula-

tion (EMP), which migrates between Wisconsin and Flor-

ida, USA. The last 2 are the product of reintroductions

using chicks hatched in captivity.

Whooping Cranes passed through a bottleneck during

the early twentieth century which reduced haplotype

diversity by approximately two-thirds (Glenn et al. 1999).

The AWBP, which is the source of all living Whooping

Cranes, was reduced to a low of 15 individuals in 1941.

Captive breeding of Whooping Cranes began in the 1960s,

with contributions of wild individuals (in the form of eggs

and wild-caught birds) to the captive population continuing

through the 1990s. The 2 largest captive breeding centers

are the US Geological Survey’s Patuxent Wildlife

Research Center (PWRC) in Laurel, Maryland, USA, and

the private International Crane Foundation (ICF), in Bar-

aboo, Wisconsin, USA. Several different studbooks, each

with different methods for assessing relatedness among

captive population founders, have been developed in order

to guide captive breeding decisions (Mirande 1995; Jones

et al. 2002). Studbooks are used to track the family lines of

individuals in the captive population and can be used to

produce sets of genetic statistics, including inbreeding

coefficients associated with the offspring of each potential

pairing of breeders. Captive breeding decisions have been

made with a goal of minimizing the potential for

inbreeding depression in the captive and released

populations.

There have been disproportionate contributions by

particular individuals and breeding pairs to the EMP (K.L.

Jones, University of Georgia, unpublished data) because

certain captive individuals are much more productive than

others. In order to minimize population mean kinship, and

with the ultimate goal of reducing the potential for

inbreeding depression in the EMP, two of the most pro-

ductive breeding pairs at PWRC were prevented from

producing for several years in the mid-2000s, resulting in

lower overall production. This decision could affect long-

term population viability in at least two ways. First,

because of demographic stochasticity, we expect a positive

relationship between the number of birds released and the

probability of successful establishment of the flock. This

has been demonstrated through modeling of the Florida

Non-Migratory Population (Moore et al. 2008) and

empirically for a number of different reintroduction pro-

jects (Wolf et al. 1996; Fischer and Lindenmayer 2000). In

addition, an effect of the decision to restrict the contri-

butions of the most productive pairs may be the reduction

of especially productive genotypes (i.e., heritable traits of

particular family lines) from the reintroduced population.

While there is a concern that the most successful geno-

types in a captive setting are not most successful in a wild

setting (see Frankham 2007 for a review), this is not

necessarily the case—it is possible that a positive rela-

tionship exists between the captive success and the wild

success of genotypes. If that is the case, a focus on bal-

ancing the genotypes of introduced animals, and thus

inhibiting reintroduction of the most successful captive

genotypes, may exact costs on the probability of suc-

cessfully establishing a population. However, there may be

a tradeoff if long-term viability is also compromised by

inbreeding effects.

These issues demonstrate the importance of integrating

genetic and demographic information into models that can

inform breeding and release decisions. To that end, we

wanted to provide empirical estimates that could be inte-

grated into such models, including demographic effects of

inbreeding and demographic effects of particular geno-

types, especially the most productive genotypes.

Therefore, we estimated the impacts of inbreeding on

post-release survival of Whooping Cranes in the EMP. We

also examined the impact of genotype on post-release

survival, by evaluating whether there were important dif-

ferences in individual survival as a function of parentage.

Finally, we examined whether there was a relationship

between captive productivity of dams and the post-release

survival of their offspring in order to examine whether

there is a link between the quality of a genotype in cap-

tivity and the quality of that genotype in the wild. We did

not examine a relationship between captive productivity of

sires and post-release survival of offspring (only of dams),

because the productivity of males in captivity is controlled

to a great degree by flock managers through extensive use

of artificial insemination. In the long term, it would be of

arguably greater interest to examine the impact of these

factors on post-release breeding success in addition to

survival, but because there has been little breeding in the

population during our study period, the dataset is not yet

adequate to support such an analysis.

In order to complete this work, we developed a Bayesian

multi-state model which could accommodate both live

resightings and dead recoveries (see also Barker et al.

2005; Kendall et al. 2006), multiple breeding states (i.e.,

unpaired, paired, and nester), and random effects, and

S562 J Ornithol (2012) 152 (Suppl 2):S561–S572

123

would also allow us to integrate both individual- and time-

dependent covariates into the modeling. This model has the

potential for extensive application to a wide variety of

demographic estimation problems. We provide a detailed

description of implementation of this model in WINBUGS

software (Gilks et al. 1996). Our results will support the

development of decision-analytic models (sensu Clemen

1996) which will allow for identification of optimal

breeding and release decision-making, while integrating

both genetic and demographic considerations, in order to

achieve the management objective of endangered species

conservation: long-term population viability.

Methods

Release program

Whooping Crane releases into the EMP began in 2001.

Birds were hatched at PWRC (beginning in 2001) and

ICF (beginning in 2005) in the spring of each year. Birds

hatched at PWRC were trained for ultralight aircraft-led

releases (ULR), training which consisted of early

imprinting of birds on costumed humans (such that they

will follow costumed breeding center staff and ultralight

pilots), and progressive familiarization and exercise behind

grounded ultralights operated by costumed humans. Birds

were shipped to Necedah National Wildlife Refuge

(NNWR), located in central Wisconsin, USA, in June or

July of their first year (i.e., at 1–2 months of age). Once at

NNWR, birds began training flights behind ultralights, and

were otherwise kept in pens on NNWR. Migration began

each year in October when birds were 4–5 months of age

and took up to several months, with birds flying short trips

behind the ultralights every day that weather allowed and

remaining in pens at secluded stop-over points at other

times. During the period of data collection covered by our

analysis, ultralight-led migrations terminated at Chas-

sahowitzka National Wildlife Refuge (CNWR) on Flor-

ida’s Gulf Coast. Birds remained there until they departed

of their own accord in the spring for the northward

migration. Until they departed in the spring, birds had

access to a pen and food (though they were not always

restricted to the pen). Additional details about ultra-light

led releases are provided in Urbanek et al. (2005) and

Urbanek et al. (2009).

Beginning in 2005, birds were hatched at ICF for direct

autumn release (DAR). These birds were also imprinted on

costumed humans, and shipped to a pen at NNWR, pri-

marily in early July (i.e., at \1–2 months of age). Birds

were then released directly on or near NNWR in their first

fall in the vicinity of previously released adult Whooping

Cranes, with the most desirable result being that the

released chicks would associate with the adult cranes and

follow them on their first southward migration.

Post-release, birds summered in and around NNWR,

with some birds migrating to and summering in points

farther afield, many of the latter in Michigan, USA.

Occasionally, birds that were located outside of the core

reintroduction area (on and around NNWR) during summer

were captured and relocated into the core area. In general,

released birds were able to migrate successfully on their

own after release. Northward and southward migration of

released birds occurred much more quickly than the

ultralight-led migration in the birds’ first fall, generally

over the course of a few weeks with the exception of birds

that spent at least part of the winter outside Florida (e.g.,

South Carolina, Tennessee). In Florida, birds used areas on

and near CNWR and throughout the west-central portion of

the state.

Through the 2007 year class, 114 birds were shipped

from PWRC for the ULR program and 23 birds were

shipped from ICF for the DAR program. Of these, 84

ULR program and 18 DAR program birds survived to

release and so entered our analysis. We defined release

for ULR birds as the time they began migrating north on

their own after their ultralight-led southward migration,

or, for DAR birds, the time they were released in

Wisconsin.

Birds began forming pairs in the spring of 2004, and

made the first nesting attempts in the spring of 2005.

Through the spring of 2009, of 41 nests containing eggs,

only 1, which was a renest, had successfully hatched (in

2006), and only 1 of the 2 chicks produced from that nest

successfully fledged.

Mark-resight and telemetry data

We used data collected from July 2001 through May 2008,

which included releases of 7 year classes. Birds were

affixed with colored leg bands while in pens at NNWR

prior to their first migration and with either radio or

satellite transmitters at NNWR or at the wintering site.

Attempts were made to capture released birds and replace

transmitters periodically, although this was not always

possible. The lead biologist (R.P. Urbanek) plus several

technicians monitored released birds with detections made

based on either transmitter signals, or if transmitters stop-

ped working, on colored leg bands. The focus of tracking

was on maintaining a sense of where all individuals were at

all times, which resulted in, in most cases, multiple loca-

tions weekly. However, we used monthly detections in the

multi-state model, that is, birds were either detected or not

in each month of the study period. When birds were

detected, location, activity, and social interactions were

noted. Periodically, birds were also located dead, although

J Ornithol (2012) 152 (Suppl 2):S561–S572 S563

123

not always immediately if their transmitter was not work-

ing and/or the signal was not easily located. For birds that

were found dead, the lead biologist estimated mortality

date to at least monthly precision, based on when birds

were last seen alive and on necropsy information. In just

one case, a known mortality could not be localized to a

month (rather to a multiple-month period), so we assumed

that mortality occurred during the month the bird was last

observed. Permanent removals from the population (e.g.,

because a bird was seriously injured) were also treated as

mortalities.

Living birds were classified in each time period that

they were detected as either unpaired, paired, or nester.

Whether they occupied the unpaired or paired state was

determined by the lead biologist based on observations

of social interactions between individuals; pairs were

defined as an association between 2 birds of the opposite

sex, who demonstrated territorial defense, copulation,

and/or nest building behaviors. For the nester state, birds

that laid eggs in a given year were assigned to this state

beginning in April and remained in that state through the

following March (i.e., a nester was classified as a nester

for an entire year, and no transitions were allowed into

our out of the nester state in months other than April).

Birds were assumed to change their age class each year

in June (e.g., birds occupy the first age class from release

until the following June, the second age class until the

June after that, etc.). However, we defined only 5 ages:

0, 1, 2, 3, and 4?; this age structure has been used

elsewhere for Whooping Cranes (Moore et al. 2008;

Moore et al. 2011).

Genetic information

Three different studbooks, which record individual pedi-

grees for all members of the captive population, were

compiled for Whooping Cranes using (1) historical

knowledge of the apparent relatedness of individuals that

founded the captive population, and (2) similarity coeffi-

cients based on microsatellite DNA profiles (Jones et al.

2002). Birds were collected from the AWBP to establish

the captive population between 1967 and 1998. Originally,

individuals collected from different composite nesting

areas (CNAs; distinct nesting territories at Wood Buffalo

National Park, Canada, to which nesting pairs return

annually) were assumed to be unrelated (Mirande 1995).

Information derived from leg banding data, based on bands

put on juveniles at AWBP from 1977 to 1988 (Canadian

Wildlife Service and U.S. Fish and Wildlife Service 2005)

was used to develop a studbook (the LG studbook; Jones

et al. 2002) which integrated information on known rela-

tionships between birds in different CNAs. For example, a

pair from one CNA might have hatched a chick that was

banded, and that chick was then known to have become a

member of a breeding pair at another CNA. If both these

pairs contributed a founder, these founders would be

known to be related.

However, because of the severe bottleneck that

Whooping Cranes passed through, an assumption of unre-

latedness in founder birds that were not known to be related

based on banding data is not valid, and estimates of

inbreeding calculated from the LG studbook will be min-

imum measures of inbreeding. Therefore, 11 microsatellite

loci were assessed to more thoroughly determine related-

ness among founders (Jones et al. 2002). Two different

methods were used to assess relatedness, producing 2 dif-

ferent microsatellite-generated studbooks, including the

number of allelic positions shared between 2 individuals

divided by the total number of positions assessed (pro-

ducing the AS studbook; Blouin et al. 1996) and the more

complex method producing the QG studbook (Queller and

Goodnight 1989), which measures relatedness based on

whether individuals share alleles at a higher or lower than

average rate. As expected, integration of microsatellite

information into the studbooks substantially increased the

assessed relatedness of birds in the captive breeding pop-

ulation (Jones et al. 2002).

Various statistics are calculable based on the studbooks,

including the coefficient of inbreeding, an index of the

relatedness of an individual’s parents. Despite the avail-

ability of studbooks integrating microsatellite data, captive

breeding of Whooping Cranes has been and is still largely

managed to minimize the inbreeding coefficient arising

from the LG studbook, 0 B I - LG B 1. The result is that

there is essentially no variation in inbreeding coefficient in

the reintroduced population based on the LG studbook

measures (all offspring have inbreeding values &0).

Therefore, we focused our attention on the measures of

inbreeding from the microsatellite studbooks, which give a

different picture of inbreeding in the captive and released

populations, and which vary substantially across released

individuals. An individual’s inbreeding coefficient based

on both the AS studbook, 0 B I - AS B 1, and the QG

studbook, -1 B I - QG B 1 increase with greater relat-

edness of the parents.

Multistate modeling

We model the state of individual i at time t, Zi,t, conditional

on the state at the previous time period (i.e., state transi-

tions are first-order Markovian) and we assume that the

state-transition probabilities depend on previous state, as

well as factors that are individual- and time-specific.

Because the state-space is discrete, we denote the state

model by the following short-hand notation for describing

a categorical random variable:

S564 J Ornithol (2012) 152 (Suppl 2):S561–S572

123

Zi;tjZi;t�1�Cat Ti;t;Zi;t�1

� �ð1Þ

where i specifies the individual and t specifies the time

period (i.e., month) and Ti;t;Zi;t�1is the vector of state-

transition probabilities for individual i, at time t - 1, given

that individual i was in state Zi;t�1 at time t - 1. Equiva-

lently, the state an individual occupies in month t, depen-

dent on the state in the previous month, is a multinomial

trial with multinomial cell probabilities Ti;t;Zi;t�1:

The observation of individuals is described by variable

Xi,t which is 1 if individual i is observed at time t and 0

otherwise. We specify a model for Xi,t such that,

Xi;tjZi;t�BernðpZi;tÞ ð2Þ

where detections arise from a Bernoulli distribution with

detection probability, p, which depends only on the state an

animal occupies when detected (though we note that

detection probability could easily be made to depend on

individual and time as well; see further comments on this

issue below).

We defined states 1:5 in the model: unpaired (1),

paired (2), nester (3), newly dead (4), and unobservable

dead (5). Birds only occupied the newly dead state in the

month that they died, and were observable in that state. In

the following month, they transitioned deterministically

into the unobservable dead state. Use of a newly dead

state to model mortality in a multi-state context was

previously described by Lebreton et al. (1999). The state

transition probabilities Ti;t;Zi;t�1

� �were then specified as a

function of conditional state transitions (c) and survival

(u) as follows:

ð3Þ

The last two rows in this matrix ensure that a bird can

occupy the newly dead state in only one time period, we

can then use the observation model to ensure that birds

are only recoverable in the first month they die (in

practice, birds are recovered after their first month dead,

but the month of death is determined as described

above). Note that the left-most 0 in the top row

restricts movement directly from the unpaired to the

nester state.

Generally, we can use a multinomial logit function to

model the c parameters to ensure that the state transition

probabilities sum to 1. This can be achieved by speci-

fying, for example, for transitions out of the paired

state:

c 2;1ð Þ;i;t ¼p 2;1ð Þ;i;t

1þ p 2;1ð Þ;i;t þ p 2;3ð Þ;i;tð4aÞ

and

c 2;3ð Þ;i;t ¼p 2;3ð Þ;i;t

1þ p 2;1ð Þ;i;t þ p 2;3ð Þ;i;tð4bÞ

and

c 2;2ð Þ;i;t ¼ 1� c 2;1ð Þ;i;t � c 2;3ð Þ;i;t ð4cÞ

such that we calculate the probability of remaining in a

state by subtraction. We then specify models for the pusing a log function, such as:

logðp 2;1ð Þ;i;tÞ ¼ b 2;1ð Þ: ð5Þ

More simply, if only 2 transitions from a particular state

are possible, one of these can be modeled directly as a logit

function. For example (for transitions out of the unpaired

state):

logit c 1;2ð Þ;i;t

� �¼ b 1;2ð Þ ð6aÞ

and

c 1;1ð Þ;i;t ¼ 1� c 1;2ð Þ;i;t ð6bÞ

Specifically for Whooping Cranes in the EMP, we

modeled state transition probabilities as a function of the

state, sex, and, for unpaired birds, the age of the individual,

where age was 0, 1, 2, 3, or 4? years. We also included a

random effect of month. This effect applied over

83 months for the transitions between the unpaired and

paired states, but for transitions into and out of the nester

state, because these were only allowed to occur in April,

the random effect applied over just 7 months, i.e., in 7

Aprils. Transitions into and out of the nester state were not

allowed in all other months. We specified:

logit c 1;2ð Þ;i;t

� �¼ b 1;2ð Þ;sexi

þ b 1;2ð Þ;agei;tþ b 1;2ð Þ;t; ð7aÞ

where b 1;2ð Þ;t�Norm bð1;2Þ; rð1;2Þ� �

; and for (q,r) = (2,1),

(2,3), (3,1), and (3,2):

log p q;rð Þ;i;t� �

¼ b q;rð Þ;sexiþ b q;rð Þ;t ð7bÞ

where the b q;rð Þ;t are intercepts for each of the state tran-

sitions, r(q,r) are transition-specific standard deviations of

the monthly random effect normal hyper-distributions, the

b q;rð Þ;sexiare fixed effects of sex for each of the state tran-

sitions, and the b 1;2ð Þ;agei;tare age-specific effects of each of

the 5 age classes on transition from the unpaired to the

paired state.

Note that, although, as described below, we included a

release type effect (ULR vs. DAR) in the models of sur-

vival, we did not consider this effect for state transitions.

J Ornithol (2012) 152 (Suppl 2):S561–S572 S565

123

This was because no DAR birds had left the unpaired state

during the period our analysis covers, as the DAR program

was not initiated until 2005 and the DAR birds were on

average much younger than the ULR birds. Also, for the

transitions out of the paired and nester states, we did not

estimate age effects because most of the birds in those

states were in only the 3 and 4? age classes.

For survival, we built basic logit models with survival as

a function of state, age, sex, and release type, and again, we

also included a random effect of month. The model for

unpaired survival, u 1ð Þ;i;t; was:

log it u 1ð Þ;i;t

� �¼ a 1ð Þ;agei;t

þ a 1ð Þ;sexiþ a 1ð Þ;releasetypei

þ a 1ð Þ;t;

ð8aÞ

where a qð Þ;t�Norm aðqÞ; rðqÞ� �

and for paired (q = 2) and

nester (q = 3) survival:

log itðu qð Þ;i;tÞ ¼ a qð Þ;sexiþ a qð Þ;t: ð8bÞ

Again, we did not include release type effects in the

paired and nester state models because only ULR birds

occupied those classes during the period our analysis

covers, and we did not consider age effects because birds in

those states were primarily in the older age classes.

The survival models (for all states) also had one other

parameter associated with a genetic variable. We used

6 different genetic variables, including measures of

inbreeding from the AS studbook, I-AS, and the QG

studbook, I-QG (from Jones et al. 2002) as well as dam,

sire, breeding pair, and dam productivity (a surrogate for

genotype quality). We standardized each of the inbreeding

values to have mean 0 and standard deviation 1. For the

dam effect, we identified 24 different dams that had

contributed chicks to our dataset, then we fit the 24 dam-

specific effects adamið Þ as random effects, where dam-

specific effects were assumed Normð0; rdamÞ: For sire, there

were 23 males that had contributed chicks to our dataset,

and the asireiwere assumed Normð0; rsireÞ: There were 30

unique combinations of dam and sire (i.e., breeding pair)

represented in our dataset; while breeding individuals have

only a single social mate (with whom they are housed)

extensive use of artificial insemination results in a greater

number of pairs than breeding individuals of either sex.

These breeding pair effects, apairi; were modeled as

Normð0; rpairÞ: Finally, we also examined the relationship

between a dam’s genotype quality, as measured by her

productivity as a captive breeder, and the survival of her

offspring. We used the number of chicks that a dam had

contributed to EMP releases (defined as chicks shipped to

Wisconsin from the breeding centers); we also standard-

ized this variable as described above. Note that the coef-

ficients for the genetic variables were not superscripted

with q; we did not estimate separate effects for the different

states. We then ran 6 separate models, one with each of the

different genetic effects, and, for inference, examined the

posterior distributions of the genetic effects: Inbreeding-

AS, with parameter aI�ASi; Inbreeding-QG, with parameter

aI�QGi; Dam, with parameter rdam, Sire, with parameter

rsire, Pair, with parameter rpair, and Dam Productivity, with

parameter aprodi: We based our inference on these genetic

effect parameter estimates, their magnitude, direction, and

95% credible intervals. Conceivably model selection could

be used to rank these 5 models, but we did not carry out

formal model selection because we were primarily inter-

ested not in which model was best but in the effect esti-

mates and their uncertainty, which we plan ultimately to

integrate into decision-support models for informing

breeding and release decisions in this population (see

‘‘Discussion’’). Moreover, we note the substantial diffi-

culties associated with model selection, as described by

Link and Barker (2006) and Millar (2009), which will only

be increased by the inclusion of random effects.

Finally, detection probabilities varied only by state, and

were modeled on the logit scale, resulting in 4 parameters:

s(1), s(2), s(3), and s(4). For state 4, the detection probability

is, more precisely, the probability of dead recovery in the

month an animal dies. We did originally attempt to build

models with additional structure on p (in particular, time

and individual random effects), but found that these models

were very slow to converge, which indicated to us that our

data could not support this additional structure.

We specified uniform prior distributions, Unif(-10,10)

for all parameters except for r(q), …, r(q,r), rdam, rsire, and

rpair, which had prior distributions Unif(0,10). Analyses of

the 6 different models (Inbreeding-AS, Inbreeding-QG,

Dam, Sire, Pair, and Dam Productivity) were conducted

using the computational software WinBUGS (Gilks et al.

1996). For each of 3 independent Markov chains, we ran

7,000 samples (14,000 samples for the Dam, Sire, and Pair

models, which, containing an additional random effect,

required additional samples to obtain good convergence)

after discarding an initial 2,000 samples (4,000 samples for

the Dam, Sire, and Pair models), for a total of 15,000

samples (30,000 samples for the Dam, Sire, and Pair

models) from which we made inference. These sampling

parameters were adequate to obtain good model conver-

gence, based on visual inspection of the chains and on R_

generally \1.2 as recommended by Gelman et al. (2004).

Individuals for which data were missing were dropped

from the analysis; these included 2 wild-hatched individ-

uals and 3 other individuals for whom inbreeding coeffi-

cients were not available.

To implement the model in WinBUGS, data input

included 2 matrices, each of dimension ‘number of

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123

individuals’ by ‘number of months’. One was a matrix of

detections (X), this matrix was equal to ‘NA’ (i.e., missing

or irrelevant data) before a bird entered the dataset (i.e.,

before it was released), ‘1’ when a bird was detected, and

‘0’ when a bird was not detected. If a bird was known to

have died (i.e., was recovered dead), X was ‘1’ in the

month of mortality, and ‘0’ thereafter. The second matrix

was a state matrix (Z), which was equal to ‘1’, ‘2’, ‘3’, or

‘4’ if a bird was detected in the unpaired, paired, nester, or

dead states, respectively, in a given month, and ‘NA’

otherwise. If a bird was observed in the dead state in

1 month (i.e., was recovered dead and death occurred in the

given month), then in subsequent months the individual’s

state became ‘5’—birds in this state were dead but unob-

servable. We also specified 2 vectors of length ‘individu-

als’: vector F recorded the month of release and vector

L specified either the month an individual was known to

have died or, for individuals not recovered dead, the end of

the study period; these vectors bounded the likelihood for

each individual. Additional input data included the number

of individuals (i) and months (t) in the dataset, as well as

the various individual- and time-dependent covariates used

in modeling. An R (R Development Core Team 2004)

script, using the library R2WinBUGS (Sturtz et al. 2005),

and input data files necessary to run the ‘‘Dam’’ model can

be obtained from the first author.

Results

Our analysis included data on 102 released individuals.

Thirty-five of those birds were known to have entered the

paired state at some point during the study period, and 26 of

those were further known to have entered the nester state.

Sixty-eight birds were known to have died during the study

period. ULR birds were included in the analysis from 7

release cohorts (2001 n = 5; 2002 n = 16; 2003 n = 16;

2004 n = 13; 2005 n = 19; 2006 n = 1; and 2007 n = 14).

DAR birds were included from 3 cohorts (2005 n = 4; 2006

n = 4; and 2007 n = 10). The low number in the 2006 ULR

cohort was due to a mortality event which occurred at the

wintering site in Florida, where all but one of the year’s

chicks was killed by an apparent lightning strike to a pen;

one individual escaped and was free roaming in Florida

until its death a few months later (Fig. 1).

Of greatest interest are the estimates of the genetic

effects on survival. Based on the IAS measure, the effect of

inbreeding was 0.02 (95% CI = -0.36, 0.39; Table 1);

54% of the mass of this posterior distribution was \0.

Based on the IQG measure, the estimate was -0.15 (95%

CI = -0.51, 0.22; Table 1); 78% of the mass of this

posterior distribution was \0. This suggests that there is

virtually no effect of inbreeding based on the IAS measure

but that there is some indication of a negative effect of

inbreeding on survival based on the IQG measure. We

present predicted annual survival probabilities, based on

the Inbreeding-QG model, for unpaired birds with

inbreeding coefficients across the range of values for birds

in our dataset (Fig. 2). Annual survival probabilities of the

offspring of the various dams, sires, and pairs are shown in

Figs. 3, 4, and 5, respectively; these figures suggest much

greater sampling uncertainty within individuals (or pairs)

versus variation between individuals (or pairs) which is not

surprising given the sample size of chicks from each

individual or pair. Finally, the effect of dam productivity

on post-release success was 0.20 (95% CI = -0.18, 0.60;

Table 1); 84% of the mass of the posterior distribution was

greater than 0. Predicted annual survival probabilities for

the offspring of dams with productivity (i.e., number of

offspring contributed to the EMP) across the range of birds

in our dataset are provided (Fig. 6).

Basic demographic patterns in this reintroduced popu-

lation are also of interest. Birds appeared to have sub-

stantially higher survival in the paired and nester states,

which suggests a benefit of pairing, though these birds are

also older, on average, than unpaired birds (Table 2; all

estimates are based on the Inbreeding-AS model but these

estimates varied little across the 5 different models).

Annual state transition probabilities also showed inter-

esting patterns. First, from the paired state, birds were

much more likely to become nesters than to become

unpaired (Table 2). This suggests that pairing is a good

indicator of future nesting. Second, transitions out of the

nester state were near 0 (Table 2), such that birds that

nested once were likely to continue to nest in subsequent

years.

We note that estimated transitions from the unpaired

into the paired state were lowest, as expected, in the 0-year-

old age class, but also were highest in the 3-year-old age

class (b 1;2ð Þ;age¼0 : b 1;2ð Þ;age¼4þ; Table 1). An indication of a

Fig. 1 States and state transitions used to model demographics of

Whooping Cranes (Grus americana) in the Eastern Migratory

Population, reintroduced to the eastern United States

J Ornithol (2012) 152 (Suppl 2):S561–S572 S567

123

higher pairing probability in 3-year-old versus 4?-year-old

birds is consistent with patterns observed in the Florida

Non-Migratory Population (Moore et al. 2008).

Finally, we also note an indication of lower survival

in the DAR cranes as compared to the ULR cranes

(a 1ð Þ;releasetype; Table 1) in the unpaired state. When con-

verting monthly to annual survival (based on estimates

from the Inbreeding-AS model), the survival estimate was

0.90 (95% CI = 0.83, 0.96) for unpaired ULR birds and

0.84 (95% CI = 0.65, 0.97) for unpaired DAR birds.

Discussion

A seminal paper by Lande (1988) suggested that the

importance of demographic factors would generally out-

strip the importance of genetic factors in determining the

fate of endangered species. This argument caused extensive

controversy within the conservation genetics community

(see Frankham et al. 2002 for a review). However, Lande

went on to emphasize the importance of understanding

the ‘‘interaction of demographic and genetic factors in

Table 1 Selected parameter estimatesa (mean, 95% credible interval) related to survival and breeding state transitions of Whooping Cranes

(Grus americana) in the Eastern Migratory Population

Survival Model Parameters Mean (95% CI) Transition Model Parameters Mean (95% CI)

a 1ð Þ;age¼0b -1.00 (-2.17, -0.04) b 1;2ð Þ;age¼0

l -5.82 (-9.77, -1.71)

a 1ð Þ;age¼1 0.21 (-0.73, 1.04) b 1;2ð Þ;age¼1 1.05 (-0.22, 2.40)

a 1ð Þ;age¼2 -0.33 (-1.23, 0.49) b 1;2ð Þ;age¼2 2.08 (0.80, 3.39)

a 1ð Þ;age¼3 1.56 (-0.09, 4.51) b 1;2ð Þ;age¼3 2.48 (1.13, 3.89)

a 1ð Þ;age¼4þ -0.44 (-1.54, 0.70) b 1;2ð Þ;age¼4þ 0.21 (-2.36, 2.13)

a 1ð Þ;sexc -0.12 (-0.53, 0.27) b 1;2ð Þ;sex

m -0.20 (-0.56, 0.17)

a 2ð Þ;sex 1.26 (-0.93, 3.68) b 2;1ð Þ;sex 0.14 (-0.59, 0.89)

a 3ð Þ;sex -0.03 (-1.65, 1.62) b 2;3ð Þ;sex 0.01 (-0.64, 0.65)

a 1ð Þ;releasetyped 0.23 (-0.37, 0.78) b 3;1ð Þ;sex 3.83 (-0.45, 9.10)

r 1ð Þ;month (all months)e 0.62 (0.08, 1.38) b 3;2ð Þ;sex 0.15 (-6.37, 6.78)

r 2ð Þ;month (all months) 1.23 (0.09, 3.15) r 1;2ð Þ;month (all months)n 2.78 (1.60, 4.36)

r 3ð Þ;month (all months) 2.91 (0.88, 5.25) r 2;1ð Þ;month (all months) 2.67 (0.52, 5.58)

aI�ASf 0.02 (-0.36, 0.39) r 2;3ð Þ;month (April only) 2.38 (0.53, 7.55)

aI�QGg -0.15 (-0.51, 0.22) r 3;1ð Þ;month (April only) 4.41 (0.19, 9.74)

rdamh 0.54 (0.07, 1.39) r 3;2ð Þ;month (April only) 3.82 (0.12, 9.55)

rsirei 0.38 (0.01, 1.11)

rpairj 0.49 (0.05, 1.27)

aprodk 0.20 (-0.18, 0.60)

a With exception of the genetic effects, all estimated effects are from the Inbreeding-AS modelb Differential effects, from the mean, of each age class on unpaired survivalc Differential effects, from the mean, of being a male on unpaired (q = 1), paired (q = 2), and nester (q = 3) survivald Differential effect, from the mean, of being a direct autumn release bird on unpaired survivale Standard deviation of the random effect of time on unpaired (q = 1), paired (q = 2), and nester (q = 3) survivalf Blouin et al. (1996) inbreeding effect on survival, from Inbreeding-AS modelg Queller and Goodnight (1989) inbreeding effect on survival, from Inbreeding-QG modelh Standard deviation of the random effect of dam on survival, from Dam modeli Standard deviation of the random effect of sire on survival, from Sire modelj Standard deviation of the random effect of pair on survival, from Pair modelk The effect of dam productivity (number of a dam’s offspring) on survival, from Dam Productivity modell Differential effects, from the mean, of each age class on transitions from the unpaired to paired statem Differential effects, from the mean, of being a male on transitions from unpaired to paired (q = 1,2), paired to unpaired (q,r = 2,1), paired to

nester (q,r = 2,3), nester to unpaired (q,r = 3,1), and nester to paired (q,r = 3,2) statesn Standard deviation of the random effect of time on transitions from unpaired to paired (q = 1,2), paired to unpaired (q,r = 2,1), paired to

nester (q,r = 2,3), nester to unpaired (q,r = 3,1), and nester to paired (q,r = 3,2) states

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extinction.’’ We propose decision-analytic modeling (sensu

Clemen 1996) as a practical approach to examining this

interaction and making optimal decisions in the face of

both demographic and genetic considerations. By devel-

oping models that will project the impacts of various

breeding and release decisions through time on the ultimate

goals of endangered species recovery, generally framed as

long-term population viability, we can examine the weight

of evidence in favor of various decision rules (e.g., mini-

mize population mean kinship in releases, maximize the

number of individuals released, etc.). Such models must

Fig. 2 Predicted annual survival, with 95% credible intervals, of

unpaired released Whooping Cranes (Grus americana) as a function

of the individual’s inbreeding coefficient, based on Queller and

Goodnight’s (1989) measure of relatedness applied to microsatellite

analysis (Jones et al. 2002). Higher coefficients indicate greater

relatedness

Fig. 3 Predicted annual survival, with 95% credible intervals, of

unpaired released Whooping Cranes (Grus americana) as a function

of the individual’s dam. Dams are arranged in descending order of the

number of chicks they contributed to our dataset. Dams 1 and 2 were

removed from production in 2006 to maintain genotypic balance in

the Eastern Migratory Population

Fig. 4 Predicted annual survival, with 95% credible intervals, of

unpaired released Whooping Cranes (Grus americana) as a function

of the individual’s sire. Sires are arranged in descending order of the

number of chicks they contributed to our dataset. Sires 1 and 2 were

removed from production in 2006 to maintain genotypic balance in

the Eastern Migratory Population

Fig. 5 Predicted annual survival, with 95% credible intervals, of

unpaired released Whooping Cranes (Grus americana) as a function

of the captive breeding pair that produced the individual. Pairs are

arranged in descending order of the number of chicks they contributed

to our dataset. Pairs 1 and 2 were removed from production in 2006 to

maintain genotypic balance in the Eastern Migratory Population

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123

integrate both the effects of inbreeding and the effects of

individual quality on the future demographic performance

of Whooping Crane populations.

Our first step in developing decision-analytic models has

been estimation of the effects of factors such as inbreeding,

genotype, and genotype quality on demographic perfor-

mance. The next steps will involve developing basic indi-

vidual-based population projection models, and then

integrating the effects of inbreeding into those models. The

effect estimates we have reported here include substantial

uncertainty, and this uncertainty will be integrated directly

into the decision-analytic models, such that the projection

of the effect of inbreeding, for example, will be simulated

in the decision-analytic models from the posterior distri-

bution of the inbreeding effect parameter. As a first pro-

totype, we will then be able to examine tradeoffs between

demographic stochasticity and inbreeding in decisions

about whether to release more Whooping Cranes with

higher population mean kinship, or fewer cranes with lower

population mean kinship, by projecting inbreeding coeffi-

cients of birds in the population through time (e.g., by

assuming random mating). Future refinements will inte-

grate the impacts of genotype quality on these decisions.

Our results suggested a negative effect of inbreeding on

survival of offspring, at least based on the IQG measure.

Though the uncertainty around the effect estimate was

substantial, we note that 78% of the mass of the posterior

distribution for this effect estimate was \0. Analysis of

individual dam, sire, and pair effects did not indicate that

the particular dams, sires, or pairs that had been removed

from production had produced offspring with clearly higher

survival rates, due to the large sampling variance, though

we note that the survival point estimate for the offspring of

the most productive dam, most productive sire, and most

productive pair (right-most points in Figs. 3, 4, and 5,

respectively) were the second highest for any dam, sire, or

pair. There was also some indication that breeding females

that were more successful in captivity (based on produc-

tivity) had offspring that were more successful post-release

(based on survival). Though again, there was substantial

uncertainty around the effect estimate, 84% of the mass of

the posterior distribution was [0. We note that the corre-

lation between the number of chicks from a given dam

shipped to Wisconsin and the number of chicks from that

Fig. 6 Predicted annual survival, with 95% credible intervals, of

unpaired released Whooping Cranes (Grus americana) as a function

of the number of offspring of an individual’s dam that were released

to the Eastern Migratory Population

Table 2 Average annual survival probabilities and average monthly state transition probabilities for Whooping Cranes (Grus americana) in the

Eastern Migratory Populationa

State Annual survival probabilityb (95% CI) State transition Annual transition probabilityc (95% CI)

Unpaired 0.877 (0.791, 0.963) Unpaired to unpaired 0.993 (0.970, 0.999)

Unpaired to paired 0.007 (0.001, 0.030)

Paired 0.991 (0.940, 0.999) Paired to unpaired 0.044 (0.001, 0.179)

Paired to paired 0.459 (0.000, 0.916)

Paired to nester 0.498 (0.041, 0.958)

Nester 0.991 (0.939, 0.999) Nester to unpaired 0.030 (0.000, 0.347)

Nester to paired 0.016 (0.000, 0.143)

Nester to nester 0.955 (0.448, 1.000)

a All estimates in table are based on the Inbreeding-AS model; mean estimates varied little from model to modelb Survival was estimated on a monthly time step and then annualized (uannual = umonthly

12 )c Transition probabilities were calculated on a monthly time step, except for transitions into and out of the nester state, which were only allowed

to occur in April, and so in effect were estimated naturally on an annual scale. Transitions between the unpaired and paired states were

annualized as: cannual = 12 9 cmonthly 9 (1 - cmonthly)11, i.e., as the probability of making a transition exactly once during the year. The

probabilities of remaining in a given state were calculated by subtraction from the relevant annual probabilities, as described in the text

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dam that were actually released was 0.97, suggesting that

our finding was not due to having all but the phenotypically

strongest of a dam’s chicks die prior to release.

There are future improvements to be made in this

analysis. Most notably is that, with additional data, it will

be feasible to examine impacts of inbreeding, genotype,

and genotype quality on reproductive behavior (e.g., pair-

ing and nesting probabilities). Through May of 2008, there

were relatively few breeders in the population, but with

continued data collection, closer analysis of breeding state

transitions may reveal important patterns. First, it may be

that breeding behavior is a more important indicator of

population success than survival, as survival in the EMP

has been fairly good to date (based on comparisons with

survival in the AWBP; Link et al. 2003) while breeding has

not been very successful (only 1 individual fledged from 24

nests through May of 2008); thus reproduction appears to

be the limiting factor in establishment of the EMP. In

addition, given that our measure of genotype quality was

dam productivity, there is a stronger argument for an

expectation of correlation between a dam’s productivity in

captivity and her offspring’s productivity in the wild (an

analysis that will be possible in the near future), rather than

with her offspring’s survival in the wild. Related to this

point, we are interested in developing better measures of

genotype success from captive birds, especially for male

birds, though this will be challenging. Given how closely

birds’ breeding contributions are managed in captivity, a

genotype has limited ability to express its quality, though

we note that, given the health care that birds receive, this

point would be likely even more true if we had used captive

survival as a metric of individual quality for captive birds.

Finally, a stronger genetic description of the captive flock

will be beneficial in examining the effects of inbreeding.

This may be accomplished in the future either by analysis

of additional microsatellites, or, more promising still,

mapping of the Whooping Crane genome (K.L. Jones,

University of Georgia, personal communication).

On a more technical level, further development is needed

on goodness-of-fit procedures for Bayesian multi-state

models. Currently, technology does not exist for assessing fit

of these models. While, with binary data, investigators have

used posterior predictive assessment to evaluate fit (e.g.,

Green et al. 2009), the appropriate fit statistics have not been

developed for data of the type we analyze here. However, we

note that, while we did not conduct goodness-of-fit, a lack of

fit would only serve to increase the already large 95%

credible intervals around the genetic effect coefficients, and

would not substantially change our inference.

While the success of the EMP is in doubt, largely

because of mass nest failures, apparently due to nest

abandonment, the survival and state transition probabilities

that we estimated provide some hope. First, we note that

survival has been higher in the EMP than in the Florida

Non-Migratory Population and on a par with birds in the

AWBP (Link et al. 2003; Moore et al. 2008; Moore et al.

2011). Second, while transitions from the unpaired into the

paired state were low, this was likely due to the young

age of the birds; in May 2008, 24% of the birds were in age

class 0, 5% in age class 1, 23% in age class 2, 13% in age

class 3, and 36% in age class 4?. And third, state transi-

tions from the paired and nester states were heartening—

once birds became paired, they were more likely to nest

than they were to become unpaired, and once birds nested,

they were unlikely to stop nesting in subsequent years.

Finally, we did find evidence that release type had an effect

on post-release survival, but if DAR birds prove to be more

successful breeders than their ULR counterparts (because

releases of DAR birds began only in 2005, these individ-

uals were as yet too young to have entered breeding states

by the end of our study period), there will be a strong

argument in favor of continuing this release method.

Acknowledgments We thank Ken Jones who provided the

inbreeding coefficients. We thank the field and breeding center staff

who were involved in collecting and providing data, especially J.

Chandler, A. Fasoli, B. Hartup, M. Wellington, and S. Zimorski. We

extend our appreciation to the Whooping Crane Eastern Partnership

for facilitating our collaboration and to the National Fish and Wildlife

Foundation for funding this work. D. Diefenbach, K. Jones, E. Zipkin,

and one anonymous reviewer provided helpful reviews of the draft

manuscript. Use of trade, product, or firm names does not imply

endorsement by the U.S. Government.

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