Ecology, 91(11), 2010, pp. 3365–3375� 2010 by the Ecological Society of America

Studying dispersal at the landscape scale: efficient combinationof population surveys and capture–recapture data

GUILLAUME PERON,1,3 PIERRE-ANDRE CROCHET,1 PAUL F. DOHERTY, JR.,2 AND JEAN-DOMINIQUE LEBRETON1

1Centre d’Ecologie Fonctionnelle et Evolutive, CNRS, UMR 5175, 1919 Route de Mende, 34293 Montpellier, Cedex 5, 34293 France2Department of Fish, Wildlife, and Conservation Biology, Colorado State University, Fort Collins, Colorado 80523-1474 USA

Abstract. Researchers often rely on capture–mark–recapture (CMR) data to study animaldispersal in the wild. Yet their spatial coverage often does not encompass the entire dispersalrange of the study individuals, sometimes producing misleading results. Information containedin population surveys and variation in population spatial structure can be used to overcomethis issue. We build an integrated model in a multisite context in which CMR data are onlycollected at a subset of sites, but numbers of breeding pairs are counted at all sites. In a Black-headed Gull Chroicocephalus ridibundus population, the integrated-modeling approachinduces an increase in precision for the demographic parameters of interest (variances, onaverage, were decreased by 20%) and provides a more precise extrapolation of results from theCMR data to the whole population. Patterns of condition-dependent dispersal are thereforemade easier to detect, and we obtain evidence for colony-size dependence in recruitment,dispersal, and breeding success. These results suggest that first-time breeders disperse to smallcolonies in order to recruit earlier. The exchange of experienced breeders between coloniesappears as a main determinant of the observed variation in colony sizes.

Key words: Black-headed Gull; capture–recapture; central France; Chroicocephalus ridibundus;colony size; E-SURGE; Kalman filter; Larus spp.; Leslie matrix; metapopulation; spatially structuredpopulation.

INTRODUCTION

Dispersal is recognized as a key determinant of

population dynamics, and many changes in population

structure occur through movement (Pulliam 1988,

Gilpin and Hanski 1991). From an evolutionary

perspective, dispersal is believed to be a response to

spatiotemporal changes in habitat quality, in the

strength of intraspecific competition (density depen-

dence), or in the risk of inbreeding (Gandon and

Michakalis 2001). Yet evidence for a particular driving

force can be ambiguous because the costs and benefits of

dispersal can vary in intensity and direction when

dispersal distance increases (Lambin et al. 2001), while

at the same time the distance traveled by dispersing

individuals often exceeds the spatial coverage of

empirical studies. This well-known mismatch between

biological processes and data collection makes it difficult

to interpret observed dispersal patterns (Barrowclough

1978, Greenwood and Harvey 1982, Schaub et al. 2006)

and can bias the estimation of other key parameters

(e.g., Cilimburg et al. 2002).

Multistate capture–mark–recapture (CMR) statistical

models (Hestbeck et al. 1991) allow the simultaneous

modeling and analyzing of natal dispersal, recruitment,

and breeding dispersal among a finite set of sites

(Lebreton et al. 2003). However, including a large

fraction of the relevant sites in a CMR sampling scheme

can be difficult for logistical reasons. One solution is to

introduce a state ‘‘alive elsewhere’’ (AE), which repre-

sents non-monitored sites (Burnham 1993, Lebreton et

al. 1999, Schaub et al. 2004). The state AE is included as

an additional site in the multisite CMR design, with the

only difference being that the associated detection rate iszero. AE models have practical implementations; they

often use the recoveries of dead individuals (usually

outside the breeding season) to estimate the rate of

transition from the study sites to the state AE (e.g.,

Henaux et al. 2007). In the absence of dead recovery

data, temporary emigration models (Fujiwara and

Caswell 2002, Schaub et al. 2004) are needed. These

models allow Markovian (state-dependent) transitions

to and from the state AE. As is often pointed out, these

temporary emigration models do not separate perma-nent (as opposed to temporary) emigration from death.

In addition, this model structure can raise issues of

parameter identifiability and precision of the estimates

(Schaub et al. 2004), and can weaken the statistical

power of the tests of biological hypotheses.

In many long-term monitoring programs, numbers of

individuals (marked and unmarked) are counted in all

subpopulations, even those that are not searched for

marked individuals. Counting the numbers of individ-

uals is often less costly than CMR sampling and often

can be extended to cover a whole region. The most

Manuscript received 24 August 2009; revised 25 November2009; accepted 25 January 2010; final version received 8 April2010. Corresponding Editor: J. R. Sauer.

3 E-mail: peron_guillaume@yahoo.fr

3365

common use of such surveys is to produce an overall

estimate of population size (e.g., Kadlec and Drury

1968). Yet another use of these data is suggested by the

fact that, especially in long-lived species, a population

crash probably indicates a decrease in adult survival

(e.g., Weimerskirch et al. 1997) or a strong emigration

out of the study area. Similarly, in a multisite context,

simultaneous decreases in the size of some subpopula-

tions and increases in other subpopulations suggest

movements of individuals. Given the difficulty in

sampling marked individuals over a large fraction of

the sites occupied by a population, a method to combine

the dispersal information contained in the CMR data

and in the subpopulation surveys could become an

essential tool when studying dispersal at large spatial

scales.

Integrated population models (Besbeas et al. 2002,

2003) are employed to perform such a combination of

CMR and survey data. Since their introduction for

studying the population dynamics of terrestrial verte-

brates, they have been used in a number of single-site

settings (reviewed in Lebreton et al. 2009:158), where

they allow a more precise estimation of demographic

parameters, especially in small populations (e.g., Schaub

et al. 2007). Our aim here is to extend this methodology

to a multisite setting, as explored recently by Borysie-

wicz et al. (2009). They concluded that using simulated

data combining capture–recapture data with census data

considerably improves the overall precision, relative to

that based on the capture–recapture data alone. McCrea

et al. (R. S. McCrea and R. S. Borysiewicz are the same

person) reached the same conclusion in a combined

analysis of capture–recapture data on three colonies of

Great Cormorants (Phalacrocorax carbo) in Denmark

and of colony size censuses (R. S. McCrea, B. J. T.

Morgan, O. Gimenez, P. Besbeas, T. Bregnballe, V.

Henaux, and J.-D. Lebreton, unpublished manuscript).

However, these two papers consider only a subset of the

sites occupied by the study population: thus, permanent

emigration out of the study sites is confounded with

survival, and temporary emigration with probabilities of

capture. As a result, in particular, probabilities of

fidelity to the considered sites tend to be underestimated.

We develop here a state–space model at the regional

scale, encompassing all sites, by using a dummy state for

sites not submitted to recapture. Our approach makes it

possible for the first time to estimate dispersal in a

population at the regional scale in a non ad hoc fashion.

We expect integrated modeling to increase the precision

of estimates of parameters, particularly dispersal prob-

abilities, which are notoriously difficult to estimate when

a dummy state for non-monitored sites is taken in to

account (Henaux et al. 2007). We specifically tailor our

application to a data set from a multisite population of

the Black-headed Gull (Chroicocephalus ridibundus) in

central France that has been studied since 1977 (see

Plate 1). In colonial birds, the breeding habitat is

discrete (colonies). In many cases, dispersal occurs

mostly at the landscape or regional scale (i.e., 0–100

km; Brown and Bomberger Brown 1996, Grosbois and

Tavecchia 2003, Serrano et al. 2003, Henaux et al. 2007).

In our population, the largest colony (La Ronze, LR)

averaged more than 3000 pairs in recent years, while the

smaller colonies averaged 163 pairs (SD 171). Both the

total number of pairs in small colonies and the number

of small colonies decreased over the study period,

suggesting a net influx of birds from the small colonies

to the large colony. This system thus provides an

opportunity to investigate the interactions between

colony size and demographic parameters. Breeding in

large colonies brings advantages linked with group size,

including foraging enhancement (Clark and Mangel

1984) and predation risk reduction (Hamilton 1971,

Lazarus 1979), which supposedly enhances the attrac-

tiveness of large colonies, possibly only for the best

competitors. Indeed, from the hypothesis that site-

dependent population regulation occurs (Gill et al.

2001, Kokko et al. 2004), we further expect that

recruitment is delayed in large colonies (Crespin et al.

2006), potentially forcing dispersal of first-time breeders

(Grosbois et al. 2003, Henaux et al. 2007; see also Lena

et al. 1998, Le Galliard et al. 2005, Moore et al. 2006).

In this paper, our objective is thus twofold. First, we

want to introduce multisite integrated models as a novel

framework to combine CMR data and population

surveys at the regional scale. We will illustrate the

interest of these models for the study of dispersal in the

gull data set. Second, we want to discuss the ecological

implications of the results concerning dispersal in this

population. We are particularly interested in testing a

‘‘colony-size-dependent scenario.’’ We expect that: (1)

recruitment occurs later when settling in LR than in

small colonies, (2) fecundity is higher in LR than in

small colonies, (3) colony size influences adult site

fidelity positively and natal site fidelity negatively, (4)

the flow of natal dispersers from LR to small colonies

exceeds the flow from small colonies to LR, and

eventually (5) the flow of breeding dispersers from small

colonies to LR exceeds the flow from LR to small

colonies.

MATERIAL AND METHODS

‘‘Integrated modeling’’ (Besbeas et al. 2002, 2003)

aims to use multiple data sets in a single framework.

Briefly, assuming independence of the survey data and

CMR data, the likelihood of a population model is first

computed for the CMR data only, with CMR software

(e.g., E-SURGE; Choquet et al. 2009b), and second, is

computed for the survey data only, using Kalman

filtering (Harvey 1989). The two likelihoods are after-

ward combined as a product. The method is based on

the notion that the same demographic parameters drive

the realization of both the population survey data and

the CMR data. We will introduce the data, the CMR

GUILLAUME PERON ET AL.3366 Ecology, Vol. 91, No. 11

model, the state–space population model, and finally the

combined likelihood.

Field methods and data collection

The study area is the Forez basin, central France (for

details, see Prevot-Julliard et al. 1998b). Each year, ;20

colonies of Black-headed Gulls occupy man-made ponds

in a farmland mosaic (Lebreton 1987). Pre-fledging

young birds have been banded at the colonies with metal

bands, and adult birds on some of the feeding sites, since

1977. Resighting effort was carried out at the largest

colony (La Ronze, LR) and in three other, small

colonies (Les Marquants, La Verchere and La Vallon-

#5, abbreviated as MA, VE, and V5, respectively). We

used a floating blind from which the codes of the metal

bands were read using a telescope (Lebreton 1987). We

restrict the data set to the period 1986–2005, to keep a

balance between data from LR and data from the small

colonies that were only searched for banded birds from

1994 onward. The CMR data consists of 32 033

individually banded birds, out of which 2476 individuals

were resighted as adults on at least one of the study

colonies. The data are coded as 0 (not observed), 1

(adult observed in LR), 2 (adult observed in MA), 3

(adult observed in V5), 4 (adult observed in VE), 5

(chick banded in LR), 6 (chick banded in MA), 7 (chick

banded in V5), 8 (chick banded in VE), 9 (chick banded

in another colony). The 10th state, adult Alive

Elsewhere (AE), is not observable, i.e., never appears

in the recapture data.

The surveys of colony sizes were conducted in May by

counting the number of individuals flying over the

colonies after having provoked a general alarm that put

all the gulls into flight. In small colonies, this number is

converted into a number of pairs using a simple ratio

calculation (Grosbois 2001). In the large LR colony, the

number of pairs could not be estimated from the ground

but instead was estimated with a sightability model

(Grosbois 2001). This model is based on additional data

(the ratio of banded/non-banded birds and the proba-

bility of reading the band of a bird when detected), and

on detection probabilities estimated from a CMR model

(Grosbois 2001). This nonindependence between CMR

and survey data is considered negligible.

CMR modeling in a multisite population

Here we describe how a population model is fitted to

the CMR data. We develop a population model similar

to the model of Lebreton et al. (2003). For each site we

define a pre-breeding state (individuals that did not yet

attempt to breed, denoted NX where X is the site) and a

breeding state (individuals after the first breeding

attempt, noted BX). When banded as a chick, individuals

enter the model in state NX, X being their colony of

birth. They then have the possibility to transit to state

NY, Y being their future colony of first breeding. At first

breeding they transit to state BY. They then have the

possibility to transit to state BZ, Z being a colony where

they disperse as breeders. More precisely, conditional on

the birds’ survival, three processes describe the popula-

tion dynamics.

1) Natal dispersal (dispersal from the site of birth to

the site of first reproduction) is modeled to occur during

the first year of life, following Lebreton et al. (2003). We

model a probability of transition from one site-specific

pre-breeding state to another site-specific pre-breeding

state. This representation focuses on the overall result of

any movement during the immature period, by consid-

ering only the birth site and the site of first reproduction,

in accordance with the operational definition of natal

dispersal by Greenwood and Harvey (1982).

2) Recruitment is modeled as the probability of

moving from the current site-specific pre-breeding state

into the corresponding breeding state. Chicks initially

enter the data set in the pre-breeding state. They

subsequently cannot be detected until they progressively

(starting at age two; Clobert et al. 1994) move into the

breeding states, where they can be detected on the

colonies. We assume that, once a bird starts breeding, it

at least attempts breeding each year for the rest of its

life. This assumption, common in recruitment models

(Clobert et al. 1994, Lebreton et al. 2003), implies that

recruitment consists of reaching adult breeding propen-

sity and that the detection probability incorporates the

potential effect of ‘‘reproduction skipping’’ (Aebischer

and Wanless 1992, Burnham 1993), of which the

occurrence in the species is, to our knowledge, not yet

documented.

3) Breeding dispersal (change of breeding site between

two reproduction events) is modeled as a probability of

transition from one site-specific breeding state to

another site-specific breeding state, between two con-

secutive breeding seasons. Breeding dispersal is divided

in two steps (Grosbois and Tavecchia 2003): first, the

decision to leave one’s current breeding location (site

fidelity probability) and second, the choice of the new

colony of settlement (settlement probabilities).

In some years, some of the small colonies were not

occupied. This information is directly incorporated into

the CMR model by constraining site fidelity and

settlement probabilities to zero in these colony-years.

Moreover in some years, some of the small colonies were

not searched for marked birds even if the colony was

active. This is accounted for by constraining the

detection probability in these colonies to zero in such

years. Further details on the CMR model are given in

Appendix A.

An approximate goodness-of-fit (GOF) test for the

CMR model is computed while assuming that the adult

part of the capture histories is the most important source

of potential lack of fit (see also Crespin et al. 2006).

First, the GOF of the full time- and site-dependent

multisite model where detection depends on both

departure and arrival sites (JMV [JollyMoVe] model;

Pradel et al. 2005) is tested using U-CARE (Choquet et

al. 2009a). The approximate GOF statistic for the

November 2010 3367INTEGRATED POPULATION MODELS: DISPERSAL

recruitment model then corresponds to the statistic for

the JMV model plus the statistic of the likelihood ratio

test between the JMV model and the time-dependent

multisite model where detection depends on the current

site only, the AS (Arnason-Schwartz) model (Hestbeck

et al. 1991, Pradel et al. 2005).

We then use AIC (Akaike’s information criterion;

Burnham and Anderson 2002) to compare the full time-

and site-dependent recruitment model to a simplified

model. Our candidate simplified model is based on

previous results (Prevot-Julliard et al. 1998a, Grosbois

and Tavecchia 2003, Grosbois et al. 2003) and includes

the following effects. (1) Detection probabilities depend

fully on time and site (i.e., one estimate per year and per

colony). (2) Site fidelity and settlement probabilities vary

between sites, but (3) are only partially time dependent.

As long as there is no change in the presence/absence of

the study colonies, the site fidelity and settlement

probabilities remain constant. (4) Survival probabilities

are not time- or site- dependent, but differ between first-

year and older birds. (5) Recruitment probabilities are

constant over time and age (after age 1), but different in

LR and small colonies.

State–space model for a multisite population

Here we describe how the same demographic model is

fitted to the population survey data. The state–space

population model is based on a state equation and an

observation equation (e.g., Gauthier et al. 2007). By

imposing a Gaussian assumption, it is possible to

calculate the likelihood of the survey data, based on

Kalman filtering (see Gauthier et al. 2007: Appendix

S1). The Kalman filter is a recursive procedure for

computing the optimal estimator of a state vector at

time t, xt, based on the information available at time t, yt(Harvey 1989). In our application yt is the colony sizes

counted at time t, and xt is the number of individuals in

each state, under the form:

xt ¼ ðNLRBLRNMABMANV5BV5NVEBVENABBABÞ>t :

The state equation (Eq. 1) describes how xt can be

predicted from xt�1:

xt ¼ Atðm;U;WÞxt�1 þ et: ð1Þ

At (presented in detail in Appendix B) is the Leslie

matrix (Caswell 2000) describing the deterministic

relationship between states at successive time steps. It

depends on the demographic parameters (fecundity

parameters m, survival probabilities U, and dispersal

probabilities W). The process noise et is considered to be

normally distributed with mean zero.

The observation equation describes how yt depends

on xt:

yt ¼ Htxt þ gt: ð2Þ

Ht is the observation matrix. In our case yt consists of

the breeding part of the population; thus the following

form for Ht:

Ht ¼

0 1 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 1

266664

377775: ð3Þ

The observation noise gt is considered to be normally

distributed with mean zero and variance matrix Rt. We

consider that the error on the colony counts is

proportional to the observed colony size (Eq. 4), which

is discussed in Veran and Lebreton (2008). Because

surveys were conducted differently in small colonies

(SC) and LR, we use two distinct parameters, r2LR and

r2SC, which represent the uncertainty on the colony

counts in LR and small colonies, respectively, and are

among the parameters to be estimated:

Rt ¼

r2LR 0 0 0 0

0 r2SC 0 0 0

0 0 r2SC 0 0

0 0 0 r2SC 0

0 0 0 0 r2SC

266664

377775

yt: ð4Þ

The population model is the same as in the CMR part

of the modeling exercise; it thus includes a reduced time-

dependent structure needed to describe the appearance

and disappearance of colonies. Parameters for fecundity,

which are not present in the CMR model, are considered

as time independent and as having a different value in

LR vs. the small colonies (as suggested by direct field

observation and unpublished analyses).

We denote H as the vector of parameters: H¼ (m, U,

W, r). At each time step, the Kalman filter is used to

derive the distribution of xtþ1 j y1, . . . , yt, H. Given that

all distributions are normal, the required distribution is

determined by the knowledge of atþ1¼E(xtþ1 j y1, . . . , yt,H) and Vtþ1 ¼ Var(xtþ1 j y1, . . . , yt, H). Recursively, we

eventually obtain the likelihood (L) of the realized

survey data as a function of H:

LðH jyÞ ¼ Pðy1; . . . ; y20 jHÞ

¼ Pðy1 jHÞY20

t¼2

Pðyt j y1; . . . ; yt�1;HÞ: ð5Þ

The Kalman filter is initialized by specifying values for

a1 and V1. We use the stable age distribution of the

population to produce these initial values.

Combined likelihood

To combine the two likelihoods, we first run the CMR

analysis. We obtain the likelihood of the CMR data set

as a function of the survival and dispersal probabilities,

but also on the detection probabilities (with vector P).

As proposed by Besbeas et al. (2003), we approximate

the CMR likelihood by its asymptotic multinormal

distribution function and obtain the function noted

LCMR.

GUILLAUME PERON ET AL.3368 Ecology, Vol. 91, No. 11

Second we run the Kalman filter (KF) algorithm on

the colony size data. We obtain the likelihood of the

survey data LKF as a function of the survival and

dispersal probabilities, as well as the fecundity and count

precision parameters.

The combined likelihood LC is the product of the

likelihood of the CMR data and of the survey data

(Besbeas et al. 2002):

LCðm;U;W;P; rÞ ¼ LCMRðU;W;PÞ3 LKFðm;U;W; rÞ:ð6Þ

Practical issues

The initial values of the survival, dispersal, and

detection probabilities in the optimization procedure

are the estimates obtained when using CMR data alone,

plus a random deviation of SE ¼ 0.1. The initial

variance–covariance matrix of the survival, dispersal,

and detection probabilities is that of the CMR analysis,

modified so that none of the eigenvalues falls below

10�6, in order to avoid giving too much weight to

E-SURGE boundary estimates. Boundary estimates

correspond to parameters that are estimated to 0 or 1.

For example, the probability of movement between two

sites during a given time interval can be estimated

at the boundary 0, if that peculiar transition is by

chance never recorded in the data. The initial values

for the parameters that are absent from the CMR

model (fecundities and count precision) were arbitrarily

chosen.

Local minima proved to be a problem when

maximizing the combined likelihood. This issue may

well be common to all multisite designs (Lebreton et al.

2009) and was addressed using the following three

methods. (1) The algorithm was launched 25 times

starting from different initial conditions, and the lowest

deviance solution was selected. (2) We constrained

fecundity to be above 0.6 offspring per pair to discard

solutions where fecundity was lower than expected from

previous fecundity estimates in the same population

(Prevot-Julliard 1996). (3) Considering that the estima-

tion of the size of small colonies in the field is precise to

the nearest 10% (as indicated by previous results; see

Appendix C), we added to the log-likelihood a term

saying that the uncertainty on the surveys of small

colonies (rSC) follows a normal distribution of mean ¼0.1 and SE ¼ 0.01. This was intended to discard

solutions where colony sizes were too far from the

survey values, and was similar to considering that the

normal density term for rSC had arisen as the likelihood

of an independent set of observations designed to

estimate this parameter. The sensitivity of the results

to the prior distribution parameters is extensively

examined in Appendix C and summarized in the results

section. Following earlier works, we did not use any link

function.

RESULTS

CMR model including a site ‘‘alive elsewhere’’

Here we used CMR data only. The approximate GOF

test was statistically nonsignificant [(1) GOF for the

JMV model: df¼163, v2¼197.00; (2) difference between

the AS and JMV models: df ¼ 58, DAIC ¼ 26.70; (3)

resulting approximate GOF test for the recruitment

model: df ¼ 221, v2 ¼ 223.70, P ¼ 0.44]. This result

indicated that the time-dependent model adequately

fitted the data. Under the assumption that survival

probability was independent of site, and the return rate

from ‘‘site’’ AE was constant over several capture

sessions, we did not detect any problems of identifi-

ability of parameters using E-SURGE (Rouan et al.

2009: Appendix A).

The model with reduced time dependence was more

parsimonious than the complete time-dependent model

(DAIC ¼ 139.03). We thus used this model in the

integrated approach. Values of the parameters estimated

using CMR data only (Table 1, first column) indicated

that the ‘‘colony-size-dependent scenario’’ (see Introduc-

tion) was likely.

Using survey data in addition to CMR data

Here we used survey data in addition to CMR data.

We gained precision for several parameters (Table 1,

columns 4 vs. 2). The sum of parameter variance

(covariance matrix trace) was 20% lower in the

integrated-modeling approach than when using CMR

data only. Reduced standard errors were observed for

parameters concerning the immature period, which are

usually hard to estimate from recapture data from adults

only, and for parameters concerning dispersal, which are

generally rendered imprecise by the incorporation of the

dummy state AE (Fig. 1).

In Appendix C, we show that the parameter estimates

and their estimated standard errors are moderately

sensitive to the prior distribution of the parameter for

uncertainty on small colony counts (rSC). In particular,

the parameter variance is not affected by using such a

prior distribution and by the particular choice of its

parameter values (Appendix C: Fig. C1a). The integrat-

ed-modeling approach provided an estimate of fecundity

that fell within the range of previous estimates for the

species (see Discussion: Population growth rate) and

matched our expectation that breeding success was

higher in the large colony LR than in the smaller

colonies. Furthermore, moderate changes occurred in

the values of the estimates when moving from CMR to

integrated-modeling estimates (Table 1). Most notably,

in the integrated model, adults appeared more faithful to

the LR colony than in the CMR model (see Discussion).

Accession to reproduction (a) was also slower in the

integrated model than in the CMR model, especially in

LR.

The Kalman filter provided smoothed estimates of

colony sizes (Fig. 2), with the uncertainty on these

November 2010 3369INTEGRATED POPULATION MODELS: DISPERSAL

estimates (r parameters) estimated at 0.17 (SE ¼ 0.02)

and 0.16 (SE ¼ 0.005) in LR and small colonies,

respectively. These smoothed colony size estimates

indicated that the decrease in population size was not

restricted to small colonies, but also occurred in LR

(black bold line in Fig. 2).

Colony size effects on demographic parameters

Accession to reproduction was significantly faster in

small colonies than in LR (Table 1, parameters aSC vs.

aLR), a finding that CMR data alone could hardly have

supported because of their insufficient precision. Breed-

TABLE 1. Comparison of parameter estimates and standard errors from the CMR-only and integrated-modeling approaches forBlack-headed Gulls Chroicocephalus ridibundus in central France.

Notation DefinitionCMR

estimates CMR SEIntegratedestimates

IntegratedSE

mLR Number of fledgings per pair in LR (i.e., fecundity) 1.732 0.074mSC Number of fledgings per pair in small colonies 0.605 0.127sB Survival of adults 0.828 0.021 0.860 0.010sY Survival during the first year 0.273 0.021 0.213 0.034fB,LR Breeding fidelity in LR 0.830 0.026 1.000 0.000fB,MA Breeding fidelity in MA 0.662 0.053 0.626 0.034fB,V5 Breeding fidelity in V5 0.537 0.078 0.373 0.055fB,VE Breeding fidelity in VE 0.803 0.053 0.469 0.038fB,AE Breeding fidelity in AE 0.954 0.008 0.938 0.008fY,LR Natal fidelity in LR 0.320 0.076 0.392 0.088fY,MA Natal fidelity in MA 0.429 0.045 0.454 0.038fY,V5 Natal fidelity in V5 0.713 0.074 0.784 0.058fY,VE Natal fidelity in VE 0.695 0.137 0.722 0.140fY,AE Natal fidelity in AE 0.591 0.101 0.301 0.089aLR Rate of accession to reproduction in LR 0.716 0.068 0.619 0.058aSC Rate of accession to reproduction in small colonies 0.827 0.092 0.846 0.096

Notes: CMR is capture–mark–recapture; AE is the dummy state ‘‘alive elsewhere,’’ representing non-monitored colonies.Monitoring was conducted at one large colony, La Ronze (LR), and at three small colonies (SC): Les Marquants (MA), LaVerchere (VE), and La Vallon#5 (V5). Subscript B denotes a breeder; subscript Y denotes a pre-breeder. For blank cells, no valueis possible.

FIG. 1. Standard errors for settlement probabilities ofBlack-headed Gulls (Chroicocephalus ridibundus) at colonies incentral France: from CMR data alone vs. from the integrated-monitoring approach. Data points correspond to modelestimates. On average, variance is 1.21 greater in the CMR-only analysis than in the integrated-modeling approach.

FIG. 2. Black-headed Gull colony size, 1986–2005, from (a)survey data and (b) smoothed estimates of colony size. Colonysize is the number of breeding pairs per colony. Colonyabbreviations are: LR, La Ronze; MA, Les Marquants; VE, LaVerchere; and V5, La Vallon #5.

GUILLAUME PERON ET AL.3370 Ecology, Vol. 91, No. 11

ing success was higher in LR than in smaller colonies

(Table 1, parameters mLR vs. mSC). The probabilities of

breeding site fidelity appeared to be strongly linked to

the average colony sizes over the study period (Fig. 3),

something that was not apparent in the estimates from

the CMR model. Strikingly, breeders in LR appeared to

be extremely site faithful (site fidelity estimated at upper

boundary). However, the effect of colony size on the

probability of natal site fidelity was not statistically

significant. There was also no statistically significant

correlation between colony-specific natal and breeding

site fidelities, although the tendency was for a negative

correlation (P . 0.25 when weighing the correlation

using SEs). Nevertheless when considering small colo-

nies as a single entity, the exchange of first-time breeders

appeared completely unbalanced, with an estimated

0.052 6 0.006 natal dispersal rate from small colonies to

LR and 0.608 6 0.088 from LR to small colonies (mean

6 SE).

An average flow of 1905 6 227 first-time breeders

dispersed from LR toward small colonies each year,

whereas the flux of birds born in small colonies and

settling in LR was 167 6 62 per year (mean 6 SD over

time, computed using parameter estimates from Table 1

and smoothed estimates of colony sizes). The opposite

pattern for breeding adults was detected, with an

estimated 29 6 3 adults dispersing from LR toward

small colonies (note: given that site fidelity in LR was

estimated at boundary, we arbitrarily set this parameter

at 0.99 here) and 142 6 67 from small colonies toward

LR each year (mean 6 SD). The maintenance of small

colonies therefore largely depended on the flow of LR-

born natal dispersers.

DISCUSSION

Costs and benefits of group size

The delayed recruitment in LR compared to small

colonies suggests that the offspring from this colony face

increased competition if they want to recruit in LR (see

Potts et al. 1980, Kokko et al. 2004). Among the many

likely proximal mechanisms, one might first consider

competition for the best nest sites. A direct clue to such a

competition is provided by an increase in the nest height

with age, from age 2 to 5 years (Lebreton and Landry

1979, Grosbois et al. 2003), the younger breeders

apparently being confined to sites where they can only

build a low nest, more vulnerable to water level changes

and waves. Alternatively, colony size might influence the

daily distance to foraging areas and the time individuals

spend foraging (Brandl and Gorke 1988, Lewis et al.

2006), which might prevent inexperienced breeders from

settling in large colonies if their time budget is more

constrained. The lack of correlation between breeding

and natal site fidelity, as opposed to what was found, for

example, in Sterna dougallii (Lebreton et al. 2009),

possibly indicates that in our system first-time and

experienced breeders respond differently to the same

constraints. This might be interpreted as an increase in

competitive ability with age.

Fecundity was lower in small colonies than in LR.

Moreover, the monitoring of the colonies’ average

breeding success shows that complete breeding failures

are common among the smallest colonies, particularly

those numbering only a few dozen pairs (Peron et al.

2010b). Small colonies therefore seem to correspond to

low-quality breeding habitat, intrinsically or because

they have a higher proportion of inexperienced individ-

uals than large colonies. Once recruited there, individ-

uals would probably gain much from returning to a

larger colony such as LR. This is congruent with our

estimates of the probabilities of breeding site fidelity:

colony size is a good predictor of site fidelity (Fig. 3).

Strong attraction for the largest colony (possibly social

attraction; Veene 1977) is further apparent in the

settlement probabilities. We suggest that young birds

are faced with intense competition with more experi-

enced individuals, and hence temporarily settle on a

small colony instead of delaying their first reproduction

if trying to integrate LR first. Overall, the pattern looks

similar to a ‘‘buffer effect’’ (Brown 1969, Gill et al. 2001,

Gunnarsson et al. 2005). At high population size (at the

beginning of the study; Fig. 2), the use of low-quality

sites (small colonies) constitutes an alternative to

suffering from the adverse consequences of density. This

strategy bears demographic costs (low breeding success),

but allows an earlier onset of reproductive life. At low

population size (end of the study period; Fig. 2) most of

the population concentrates in the best habitat (large

colony). The fact that the large LR colony resisted the

overall decline in population size better than the small

colonies is in line with these considerations.

FIG. 3. Breeding site fidelity of Black-headed Gulls (with95% confidence intervals) in relation to average colony size asestimated in the integrated model. Colony size is the number ofpairs per colony.

November 2010 3371INTEGRATED POPULATION MODELS: DISPERSAL

Population growth rate

Overall the population seems to have decreased in size

during the study period (as indicated by the smoothed

estimates in Fig. 2). The pattern is particularly obvious

in the non-monitored colonies (site AE), which crashed

from an estimated 3000 to 1100 pairs, with a parallel

decline in the number of colonies (result not shown).

Given the estimated demographic parameters, we were

able to conclude that this decline in the AE compart-

ment was mostly the consequence of a transfer ofbreeders from the smallest colonies toward LR. This

transfer occurred in conjunction with, and probably as a

consequence of, a lower breeding success in small

colonies than in LR. During the last part of the study

period, LR also apparently experienced a decline (Fig.

3). The influx of adult breeders into LR was thus not

sufficient and the whole regional gull population seems

to be in a phase of slow decline.

Life history theory predicts that, in a long-lived

species such as the Black-headed Gull, the demography

should be more sensitive to variation in adult survival

rate than in fecundity or immature survival rate (Stearns

1992). Our estimate of the annual adult survival

probability is higher than most values reported for the

species: 0.860 6 0.010 (mean 6 SE), vs. 0.72 to 0.85

(Coulson fide Patterson 1965, Flegg and Cox 1975,

Lebreton and Isenmann 1976, Majoor et al. 2005).

Therefore the observed population decline cannot be

explained by a low adult survival rate. Similarly, the

values of fecundity obtained in this study, compared to

previous results, seem compatible with the maintenance

of the population size at its original level: 1.732 6 0.074

in LR and 0.605 6 0.127 in small colonies (mean 6 SE),

vs. 0.31 to 0.9 in declining populations (Patterson 1965,

van Dijk et al. 2009), and 0.96 to 2.11 in growing

populations (Greenhalgh 1975, Lebreton and Isenmann

1976, Viksne 1980). In contrast, our estimate of

immature survival probability is lower than previously

reported: 0.184 6 0.011 in our study (the product of sYand sB), vs. 0.32 to 0.38 in previous ones (Lack fide

Patterson 1965, Patterson 1965, Lebreton and Isenmann

1976). Our estimate of immature survival corresponds,

as is the case in all similar study designs, to local survival

probability after banding, i.e., the overall probability of

both surviving from mean age at banding to the age at

maturity and returning to the study area. Consequently,

we speculate that the decline of the Forez Black-headed

Gull population might originate from either a high

death rate during the immature period and/or a high

rate of permanent emigration of young birds out of the

Forez. Further analyses using band recoveries and the

search for banded birds in colonies out of the Forez

regional populations are needed to confirm this inter-

pretation.

General applicability of the integrated-modeling method

The single-site formulation of integrated population

models has already been applied to a variety of taxa and

situations (reviewed in Lebreton et al. 2009), from

country-level counts of common bird species (Besbeas et

al. 2002) to site-specific study of an endangered bat

(Schaub et al. 2007). The basic requirement is that it

PLATE 1. A black-headed Gull Chroicocephalus ridibundus, with a numbered metal ring. Repeated resightings of suchindividuals over several study sites provide individual histories, from which, using appropriate statistical models, demographicparameters characterizing survival, dispersal, and accession to reproduction can be estimated. Photo credit: J.-D. Lebreton.

GUILLAUME PERON ET AL.3372 Ecology, Vol. 91, No. 11

must be possible to count the individuals, or at least to

obtain some estimate of population size that is

independent from the capture–recapture data. When

extending the method to the multisite setting, an

additional requirement appears: the definition of sub-

populations must be straightforward. Colonial birds and

their very discrete breeding habitat constitute ideal study

systems from that point of view. In more diffusely

distributed populations, potential applications include

the study of the effects of habitat fragmentation and the

estimation of dispersal between study plots within a

continuous habitat.

On the other hand, the method raises several practical

issues. First, local minima can be a problem when

maximizing the combined likelihood. We discussed in

Methods three ways to overcome the issue, and vigilance

is clearly required in any future application. Second, we

did not use any link function in our estimation

framework (model parameters were thereby allowed to

vary between �‘ and þ‘). When designing more

complex models than ours, we recommend the use of a

link function. Third, we did not specifically address

potential problems raised by the quality of the survey

data. It seems obvious that the less precise the data, the

less informative they are. The r parameters (uncertainty

on population counts), however, are specifically de-

signed to accommodate survey data imperfection. These

parameters allow the use of relatively complex survey

data and take the associated uncertainty into account

(e.g., via separate parameters associated with each

source of data, as we did here). The almost inevitable

inequality in survey precision between small and large

populations is also included in our model (Eq. 4). Our

study indicates that even imprecise population counts

(17% CV) can be useful. Actually, the variation over

time and space in the population size data appears more

informative than their point value. Another potential

source of bias is the violation of the normality

assumption that underlies the Kalman filter, but that is

beyond the scope of this study.

Costs and benefits of the

integrated-modeling methodology

In our study area, one day per season is sufficient to

survey most colonies for the number of breeding pairs,

whereas the same day devoted to CMR data collection

would increase the data set by only a few percentage

points. If using CMR data only, precision of the

estimates is expectedly proportional to the CMR sample

size. Thereby, use of integrated modeling renders the

time spent counting population size much more efficient

than CMR data sampling.

A second difference between the CMR-only and the

integrated-modeling approach appears when examining

the estimates for breeding site fidelity. In the integrated

model, breeders in LR are almost always faithful

(probability of breeding dispersal is almost zero). In

the CMR model, site fidelity is not markedly different in

LR and in small colonies. This result most likely

originates from biases due to at least two well-identified

phenomena. First, the detection probability in LR is

individually variable (Peron et al. 2010a). This individ-

ual heterogeneity is not accounted for in our CMR

model. It possibly created an artificially high rate of

transition between LR and AE. AE in this case modeled

not only non-monitored colonies, but also the least

accessible parts of LR. Prevot-Julliard et al. (1998a)

provide a more detailed discussion of individual

heterogeneity in LR. Second, if skipping reproduction

and early failures (or any mechanism producing birds

that do not frequent any colony during one or several of

the fieldwork sessions) were not occurring at random

but rather fitted a Markovian transition process (Burn-

ham 1993), the involved individuals would have been

modeled as temporarily moving to state AE. AE in this

case modeled not only non-monitored colonies, but also

early-failed and reproduction-skipping individuals.

In short, using survey data in addition to CMR data

increases the precision of the estimates, controls for bias

in the estimation of site fidelity, and produces an

estimate of fecundity. Our results overall are promising

for the future use of integrated models in long-term

monitoring programs of multisite populations when

CMR data exist for only a part of the study population.

ACKNOWLEDGMENTS

Thanks are due to all volunteers, students and researcherswho contributed to the fieldwork. We are grateful to land-owners who gave access to their properties. We thank inparticular J. Arquillere, Manager of La Ronze for continuoussupport and help throughout this study. R. Choquet providedhelpful advice for the optimization procedure. We thankVictoria Dreitz and one anonymous reviewer for their insights.

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APPENDIX A

Multisite CMR recruitment model with a nonobservable state: matrix description (Ecological Archives E091-238-A1).

APPENDIX B

Leslie Matrix (Ecological Archives E091-238-A2).

APPENDIX C

Sensitivity of the results of the integrated model to changes in the prior distribution of the survey error parameter (EcologicalArchives E091-238-A3).

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