Modeling Demographic Processes In Marked Populations

Mark recapture models have long been used for estimating wildlife population parameters. Typically, the data are summarized in terms of parameters that are interpreted in the context of an implicit demographic model for describing population dynamics. Usually, this demographic model plays little or no role in the mark-recapture model. Bayesian hierarchical models (BHM) offer a way to explicitly include demographic models in an analysis. We argue that such an approach should have wide appeal to ecologists as it allows inference to focus on ecological models of interest rather than obtaining a parsimonious depiction of the sampling process. We discuss the use of BHM’s for modeling mark-recapture data with a focus on models describing density-dependent growth.

The history of density dependence started in 1798 with Malthus’ sentence:

population, when unchecked, increases in a geometrical ratio

. The famous controversy between Lack, Andrewartha and Birch and others in the 1950s and 1960s remained largely unsolved: while the impossibility of long term exponential growth required density-dependence, density-independent environmental variation in vital rates was often dominant in empirical studies. Fifty years later, where are we left? I revisit first the representation of density-dependence in dynamical models, whether deterministic or stochastic, and I emphasize the lack of theory for the simultaneous occurrence of density-dependence and environmental variation. I then review approaches to detect and measure the intensity of density-dependence, in two steps: based on population size estimates and in demographic parameter analyses. I discuss then how the question of density-dependence could be efficiently revisited, taking advantage of progress in our understanding of spatio-temporal dynamics, statistical procedures, access to individual characteristics, and possibilities of experimental approaches.

A nonparametric approach has recently been proposed for estimating survival in capture-recapture models, which uses penalized splines to achieve flexibility in exploring the relationships with environmental covariates. However, this method is highly time-consuming because it is implemented through a fully Bayesian approach using Markov chain Monte Carlo simulations. To cope with this issue, we developed a two-step approach in which the existing method is used in conjunction with a multivariate normal approximation to the capture-recapture data likelihood. The ability of our approach to capture various nonlinearities in demographic parameters was validated by carrying out a simulation study. Two examples dealing with Snow petrel and Emperor penguin capture-recapture data sets were also considered to illustrate our procedure, including the relationship between survival rate, population size and climatic covariates.

We analyse 54 year long time series data on the numbers of common redstart (

Phoenicurus phoenicurus

), common whitethroat (

Sylvia communis

), garden warbler (

Sylvia borin

) and lesser whitethroat (

Sylvia curruca

) trapped in spring and autumn at Ottenby Bird Observatory, Sweden. The Ottenby time series could potentially serve as a reference on how much information on population change is available in count data on migrating birds. To investigate this, we combine spring and autumn data in a Bayesian state-space model trying to separate demographic signals and observation noise. The spring data are assumed to be a measure of the breeding population size, whereas the autumn data measure the population size after reproduction. At the demographic level we include seasonal density dependence and model winter dynamics as a function of precipitation in the Sahel region, south of the Sahara desert, where these species are known to spend the winter. Results show that the large fluctuations in the data restrict what conclusions can be drawn about the dynamics of the species. Annual catches are highly correlated between species and we show that a likely explanation for this is that trapping numbers are strongly dependent on local weather conditions. A comparative analysis of a related data set from the Courish Spit, Russia, gives rather different dynamics which may be caused by low information in the two data sets, but also by distinct populations passing Ottenby and the Courish Spit. This highlights the difficulty of validating results of the analyses when abundance indices derived by other methods or from other populations do not agree.

Capture-Mark-Recapture (CMR) modeling is one of the most commonly used estimation methods in population ecology of wild animals. Until recently, much of the emphasis of this method was on the estimation of abundance and survival probability. Despite common interest in estimation of such demographic parameters, evolutionary ecologists have often been more critical of CMR estimation methods than wildlife biologists, mostly because the available models did not allow investigators to address what is at the heart of evolutionary ecology. Evolutionary ecology aims at explaining biological diversity: studies in this area of research necessarily involve assessment of variation in traits among individuals, including fitness components. The main limitation of early CMR models was the inability to handle

states

among which individuals move in a stochastic manner throughout life (e.g., breeding activity and number of offspring raised, locations, physiological states, etc.). Several important advances have enhanced ecologists' ability to address evolutionary hypotheses using CMR data; namely multistate models and models with individual covariates.

Recently, methodological advances have allowed investigators to handle random effects models. This is bringing CMR models close to modern statistical models (Generalized linear mixed models) whose use is rapidly increasing in quantitative genetics. In quantitative genetics, the

animal model

aims at disentangling sources of phenotypic variation to draw inferences about heritability of any type of trait (morphological, demographic, behavioral, physiological traits). The

animal model

partitions variation in the trait of interest using variance components. Understanding evolution by natural selection and predicting its pace and direction requires understanding of the genetic and environmental influences on a trait. Phenotypic characteristics such as morphological or life-history traits (i.e. demographic parameters such as number of offspring raised and survival probability) are likely to be influenced by a large number of genes, the genetic basis of which can be quantified via statistical inferences based on similarities among relatives in a population. The extent of evolutionary responses in a quantitative trait is assumed to be proportional to the force of natural selection and heritability of a trait. Estimating the genetic basis of quantitative traits can be tricky for wild animal populations in natural environments: environmental variation often obscures the underlying evolutionary patterns. However, this genetic basis of traits is at the heart of natural selection, and recently there has been increased interest in applying the

animal model

to natural populations to understand their evolutionary dynamics. Such models have been applied to estimation of heritability in life history traits, either in the rare study populations where detection probability is close to 1, or without considering the probability of detecting animals that are alive and present in the study area (recapture or resighting probability). Applications of the

animal model

to demographic parameters (fitness components) such as survival, breeding probability or to lifetime reproductive success in wild animal populations where detection probability is < 1 require trans-disciplinary efforts; this is necessary to address evolutionary processes in such populations.

Capture–recapture (CR) is one of the most commonly used methods in quantitative ecology. Until recently, much of the emphasis of CR was on the estimation of abundance and vital rates, especially survival rates. Here, I discuss several important advances that have enhanced ecologists’ ability to address questions in evolutionary ecology. Generalizations of CR methodology to include group and covariate effects have allowed direct, empirical modeling of the influence of extrinsic and intrinsic factors on demographic rates. Advances in sampling design and software now allow CR modeling to address questions such as dispersal and natal fidelity, tradeoffs between reproductive effort and survival, senescence, and variability in demographic rates in relation to individual traits, among others. Furthermore, complex ecological and evolutionary questions seem to be especially amenable to a paradigm of multiple alternative (vs. single null) hypotheses, which is consistent both with information-theoretic and Bayesian approaches to inference.

Previous CR approaches have emphasized the estimation of averages of demographic parameters for individuals grouped into classes (age, sex, size or other attributes), but evolutionary questions tend to emphasize individual variability, with fitness “parameters” best characterized by frequency distributions. Bayesian approaches are particularly appropriate for modeling individual, temporal, spatial, and other components of variation via random effects models. Finally, Bayesian methods and conditional/hierarchical modeling allow for ready construction of complex models of life history from a variety of data sources. I present selected examples to illustrate each of these major points.

Multi-state mark-recapture models have seen increased use in recent years for studies of reproductive costs. When individuals in both breeding and non-breeding states can be observed, multi-state models can be used to directly estimate reproductive costs by comparing state-specific estimates of survival and breeding probabilities. The method assumes that each state that an animal occupies is observable, an assumption that is violated if some animals are absent for one or more breeding seasons and are thus, unobservable due to temporary emigration. Previous research on the case of a single observable state and a single unobservable state has shown that non-random (Markovian) temporary emigration can, if not accounted for, bias estimates of survival. Here, simulation is used to study effects of non-random (Markovian) temporary emigration on estimates of survival and breeding probabilities for the case of two observable states and one unobservable state. Results clearly show that temporary emigration can cause estimates of survival and breeding probability to be biased if the unobservable state is ignored. Bias was either positive or negative depending on circumstances, and was sometimes severe (percent relative bias was as high as 67% for estimates of breeding probability). Accordingly, the strengths and limitations of including an unobservable state in analyses are also considered. For some situations, simply including an unobservable state will be an adequate solution. But, for those studies particularly interested in temporal variation in costs of reproduction, it will be necessary to collect other information to avoid problems of parameter constraints. Additional information can consist of data from sub-sampling during primary sampling occasions, radio telemetry, or ring recoveries.

In many species, age or time of maturation and survival costs of reproduction may vary substantially within and among populations. We present a capture-mark-recapture model to estimate the latent individual trait distribution of time of maturation (or other irreversible transitions) as well as survival differences associated with the two states (representing costs of reproduction). Maturation can take place at any point in continuous time, and mortality hazard rates for each reproductive state may vary according to continuous functions over time. Although we explicitly model individual heterogeneity in age/time of maturation, we make the simplifying assumption that death hazard rates do not vary among individuals within groups of animals. However, the estimates of the maturation distribution are fairly robust against individual heterogeneity in survival as long as there is no individual level correlation between mortality hazards and latent time of maturation. We apply the model to biweekly capture–recapture data of overwintering field voles (

Microtus agrestis

) in cyclically fluctuating populations to estimate time of maturation and survival costs of reproduction. Results show that onset of seasonal reproduction is particularly late and survival costs of reproduction are particularly large in declining populations.

We summarize results of a November 2006 workshop dealing with recent research on the estimation of landbird abundance from count data. Our conceptual framework includes a decomposition of the probability of detecting a bird potentially exposed to sampling efforts into four separate probabilities. Primary inference methods are described and include distance sampling, multiple observers, time of detection, and repeated counts. The detection parameters estimated by these different approaches differ, leading to different interpretations of resulting estimates of density and abundance. Simultaneous use of combinations of these different inference approaches can not only lead to increased precision but also provides the ability to decompose components of the detection process. Recent efforts to test the efficacy of these different approaches using natural systems and a new bird radio test system provide sobering conclusions about the ability of observers to detect and localize birds in auditory surveys. Recent research is reported on efforts to deal with such potential sources of error as bird misclassification, measurement error, and density gradients. Methods for inference about spatial and temporal variation in avian abundance are outlined. Discussion topics include opinions about the need to estimate detection probability when drawing inference about avian abundance, methodological recommendations based on the current state of knowledge and suggestions for future research.

Avian point counts vary over space and time due to actual differences in abundance, differences in detection probabilities among counts, and differences associated with measurement and misclassification errors. However, despite the substantial time, effort, and money expended counting birds in ecological research and monitoring, the validity of common survey methods remains largely untested, and there is still considerable disagreement over the importance of estimating detection probabilities associated with individual counts. Most practitioners assume that current methods for estimating detection probability are accurate, and that observer training obviates the need to account for measurement and misclassification errors in point count data. Our approach combines empirical data from field studies with field experiments using a system for simulating avian census conditions when most birds are identified by sound. Our objectives are to: identify the factors that influence detection probability on auditory point counts, quantify the bias and precision of current sampling methods, and find new applications of sampling theory and methodologies that produce practical improvements in the quality of bird census data.

We have found that factors affecting detection probabilities on auditory counts, such as ambient noise, can cause substantial biases in count data. Distance sampling data are subject to substantial measurement error due to the difficulty of estimating the distance to a sound source when visual cues are lacking. Misclassification errors are also inherent in time of detection methods due to the difficulty of accurately identifying and localizing sounds during a count. Factors affecting detection probability, measurement errors, and misclassification errors are important but often ignored components of the uncertainty associated with point-count-based abundance estimates.

Population density is a key ecological variable, and it has recently been shown how captures on an array of traps over several closely-spaced time intervals may be modelled to provide estimates of population density (Borchers and Efford

2007

). Specifics of the model depend on the properties of the traps (more generally ‘detectors’). We provide a concise description of the newly developed likelihood-based methods and extend them to include ‘proximity detectors’ that do not restrict the movements of animals after detection. This class of detector includes passive DNA sampling and camera traps. The probability model for spatial detection histories comprises a submodel for the distribution of home-range centres (e.g. 2-D Poisson) and a detection submodel (e.g. halfnormal function of distance between a range centre and a trap). The model may be fitted by maximising either the full likelihood or the likelihood conditional on the number of animals observed. A wide variety of other effects on detection probability may be included in the likelihood using covariates or mixture models, and differences in density between sites or between times may also be modelled. We apply the method to data on stoats

Mustela erminea

in a New Zealand beech forest identified by microsatellite DNA from hair samples. The method assumes that multiple individuals may be recorded at a detector on one occasion. Formal extension to ‘single-catch’ traps is difficult, but in our simulations the ‘multi-catch’ model yielded nearly unbiased estimates of density for moderate levels of trap saturation (≤ 86% traps occupied), even when animals were clustered or the traps spanned a gradient in density.

In recent years, the mark-resight method for estimating abundance when the number of marked individuals is known has become increasingly popular. By using field-readable bands that may be resighted from a distance, these techniques can be applied to many species, and are particularly useful for relatively small, closed populations. However, due to the different assumptions and general rigidity of the available estimators, researchers must often commit to a particular model without rigorous quantitative justification for model selection based on the data. Here we introduce a nonlinear logit-normal mixed effects model addressing this need for a more generalized framework. Similar to models available for mark-recapture studies, the estimator allows a wide variety of sampling conditions to be parameterized efficiently under a robust sampling design. Resighting rates may be modeled simply or with more complexity by including fixed temporal and random individual heterogeneity effects. Using information theory, the model(s) best supported by the data may be selected from the candidate models proposed. Under this generalized framework, we hope the uncertainty associated with mark-resight model selection will be reduced substantially. We compare our model to other mark-resight abundance estimators when applied to mainland New Zealand robin (

Petroica australis

) data recently collected in Eglinton Valley, Fiordland National Park and summarize its performance in simulation experiments.

Data on linkage disequilibrium at unlinked loci provide an estimate of the inbreeding effective population size of the parental generation of the sampled cohort. The inbreeding effective population size,

N

e

, is the reciprocal of the probability that two gametes, selected at random without replacement from those that produced the sampled cohort, derive from the same parent. Effective population size is an important parameter for measuring the rate of inbreeding in a population. We detail the construction of the linkage disequilibrium estimator of

N

e

, and evaluate its performance by simulation. We simulate populations which are dioecious and non-selfing. We use the simulations to examine the effects of several types of deviation from ideal population conditions, and of sample size, genotyping errors, number of loci typed, and polymorphic loci. We find substantial bias in the

N

e

estimator when there have been recent fluctuations in census population size, when the index of breeding variability is greater than one, and when the ratio of sample size to effective population size differs substantially from one. Due to high variability, estimators that have low bias for the reciprocal of

N

e

can present substantial bias when used as estimators of

N

e

itself. We consider a recent small sample size bias correction proposed for the method, and find that it improves bias in the reciprocal, but at the expense of increased bias for

N

e

. The improvements in the bias of the reciprocal are usually small, but are substantial when sample size is much less than

N

e

, while the increase in bias for

N

e

is often substantial. We test the method on two exhaustively sampled rat populations, and find it performs as expected from simulation. For practitioners, we recommend that resources are spent first in ensuring that the sample size is likely to be greater than the effective population size, and only then that the number of loci is increased to improve the precision of the estimate.

The design and analysis of multi-state studies when the states are discrete entities is now well understood with several robust software packages (e.g. M-Surge, MARK) available. However, recent technological advances in radio and archival tags will provide very rich datasets with very fine details on movement. Current methods for the analysis of such data often discretize the data to very coarse states. This paper will review the current state of the art on the analysis of such datasets and make some (bold) forecasts of future directions for the analysis of these data.

In stopover duration analysis for migratory birds, models with the probability of departure dependent upon time since arrival are useful if the birds are stopping over to replenish body fat. In capture–recapture studies, the exact time of arrival is not generally known, as a bird may not be captured soon after arrival, or it may not be captured at all. We present models which allow for the uncertain knowledge of arrival time, while providing estimates of the total number of birds stopping over, and the distribution and mean of true stopover times for the population.

Delayed recruitment (i.e. first reproduction) is a key feature of the demography of long-lived species such as seabirds. If physiological, behavioral, and environmental factors are thought to influence age at first breeding, knowledge of the fitness prospects corresponding to different recruitment tactics is needed to get insight into the evolution of delayed recruitment.

Because the age at which an individual recruits may depend on the location chosen to breed, we first investigated the relationship between habitat quality and age of first breeding in a long-lived seabird, the black-legged the Kittiwake (

Rissa tridactyla

). We used multi-state mark-recapture approaches to model the transition from non-breeding to breeding status as a function of age and habitat quality. We also investigated whether there was a relationship between age at recruitment and reproductive success in the year of recruitment. We assessed several non-exclusive hypotheses. (i) If experience plays a part in reproductive success

per se

(e.g. in the quality of parental care), or in acquisition of higher-quality breeding sites (i.e. increased competitive ability), then reproductive success should be lower for early recruits (i.e. age 3) than others. (ii) In the same vein, if delayed recruitment corresponds to a queuing tactic allowing access to higher-quality sites, then late recruits (age 6 or 7) should exhibit higher breeding success than others. Alternatively, delayed recruitment may reflect behavioral inability to access to higher-quality sites; in this case, late recruits should exhibit poorer breeding success than younger ones. (iii) Experience combined with social constraints may lead to an initial increase in breeding success with recruitment age, and a decrease in older recruits.

We found that recruitment probability was highest at intermediate ages (i.e. 5–6 years old), and that recruitment probability was maximal in habitat patches (i.e. ‘cliffs’) of medium quality. This may reflect harsh competition in the most productive cliffs, and avoidance of the least productive ones (i.e. where predation on eggs is high). In accordance with our predictions (i and iii), we found that the youngest recruits experienced poor breeding success at the beginning of their reproductive life, and that breeding success was higher for birds recruiting at intermediate age. In addition, recruitment probability was best predicted by apparent habitat quality the year preceding recruitment. The latter result suggests either that habitat selection takes place the year preceding settlement and first reproduction, or that the information available to individuals at the beginning of a season is temporally auto-correlated to past productivity.

Reproductive choices and/or the constraints met during the pre-reproductive stage of life may influence age at recruitment. Our results show that there is a relationship between age of first breeding and breeding success probability. However, age of first breeding may also have substantial effects on breeding success over life. Future study should examine if reproductive success improves, shows senescent decline, or remains the same over the life course of individuals recruiting at various ages.

Residence time, or stopover duration, is of considerable interest to biologists studying migratory populations. We present a method for estimating the distribution of residence time for a population of southern right whales (

Eubaleana australis

) in the subantarctic Auckland Islands, using photo-ID resightings data from the 1998 winter breeding season. We explain how we can estimate a smooth probability distribution for residence time, by formulating a likelihood penalized for roughness in the residence distribution. The estimated residence distribution is a cubic spline that maximizes the penalized likelihood. The non-parametric approach allows complete flexibility in the shape of the distribution for residence time, and can fit distribution shapes that would be difficult to obtain using a parametric mixture distribution. We show that cubic splines give a general solution to penalized likelihood problems, and fitting the spline is an optimization problem accessible to users of standard statistical software. The methodology is quite general in its potential for fitting smooth probability distributions to data.

In studies of migration, both between and within populations, it is not always feasible to use physical tags to track the movement of animals. Funding and time constraints may not allow for the trapping and tagging of a sufficiently large set of animals to expect that a reasonable number will be recaptured at a future time in another population. An alternative approach is to use genetic markers to estimate migration and population parameters of interest. This is a rapidly developing area of research, an advantage being that each captured subject has effectively been “tagged”. The choice of tag however is not at the discretion of the researcher, and is a realisation of a complex array of historical events and random fluctuations. It is therefore necessary to develop methods to interpret observed genetic characteristics in order to describe inter- and intra-population movements. We present research using simulated and real-world data which evaluates the performance of one recent genetic approach to handling these sorts of problems. The collected data is of an invasive species, where it is likely the populations from which the samples were taken were recently established and therefore did not meet the usual genetic equilibrium conditions.

Stochastic variation in survival rates is expected to decrease long-term population growth rates. This expectation influences both life-history theory and the conservation of species. From this expectation, Pfister (

1998

) developed the important life-history prediction that natural selection will have minimized variability in those elements of the annual life cycle (such as adult survival rate) with high sensitivity. This prediction has not been rigorously evaluated for bird populations, in part due to statistical difficulties related to variance estimation. I here overcome these difficulties, and in an analysis of 62 populations, I confirm her prediction by showing a negative relationship between the proportional sensitivity (elasticity) of adult survival and the proportional variance (CV) of adult survival. However, several species deviated significantly from this expectation, with more process variance in survival than predicted. For instance, projecting the magnitude of process variance in annual survival for American redstarts (

Setophaga ruticilla

) for 25 years resulted in a 44% decline in abundance without assuming any change in mean survival rate. For most of these species with high process variance, recent changes in harvest, habitats, or changes in climate patterns are the likely sources of environmental variability causing this variability in survival. Because of climate change, environmental variability is increasing on regional and global scales, which is expected to increase stochasticity in vital rates of species. Increased stochasticity in survival will depress population growth rates, and this result will magnify the conservation challenges we face.

We consider use of recoveries of marked birds harvested by hunters, in conjunction with continental harvest estimates, for drawing inferences about continental abundance of a select number of goose species. We review assumptions of this method, a version of the Lincoln–Petersen approach, and consider its utility as a tool for making decisions about harvest management in comparison to current sources of information. Finally, we compare such estimates with existing count data, photographic estimates, or other abundance estimates. In most cases, Lincoln estimates are far higher than abundances assumed or perhaps accepted by many waterfowl biologists and managers. Nevertheless, depending on the geographic scope of inference, we suggest that this approach for abundance estimation of arctic geese may have usefulness for retrospective purposes or to assist with harvest management decisions for some species. Lincoln’s estimates may be as close or closer to truth than count, index, or photo data, and can be used with marking efforts currently in place for estimation of survival and harvest rates. Although there are bias issues associated with estimates of both harvest and harvest rate, some of the latter can be addressed with proper allocation of marks to spatially structured populations if subpopulations show heterogeneity in harvest rates.

We investigated from 2003 to 2006 the population dynamics of Monk Parakeets (

Myiopsitta monachus

), an invasive, exotic, pest species inhabiting northeastern Spain. Our study focused on several colonies of parakeets in Barcelona. Starting in 2003, we trapped and marked birds at the main Barcelona colony in Ciutadella Park during 2 annual periods: winter (pre-nesting) and late summer (post-nesting), respectively. We marked 459 individuals, and subsequently reencountered marked birds at the colony via recapture, and additionally obtained resightings of parakeets throughout Barcelona (

n

= 381 recaptures and 570 resightings). We used a variation of the Robust Design in conjunction with reverse-time CR modelling to estimate survival and recruitment rates, and to determine the relative contribution of survival and recruitment to population growth rate. Due to high dispersal, apparent survival rates were low, so we used the combined recapture-resighting data to provide more realistic estimates of demographic survival. We then combined the projections with estimates of survival and recruitment elasticity from our statistical models in a decision model, in order to investigate alternative management scenarios for reducing damage from continued parakeet expansion. Given the logistical and social constraints under which managers operate, it appears that the most effective management strategy would be removal by trapping (in urban areas) or shooting (in rural areas) of birds during summer-winter period.

A challenge for integrated population methods is to examine the extent to which different surveys that measure different demographic features for a given species are compatible. Do the different pieces of the jigsaw fit together? One convenient way of proceeding is to generate a likelihood for census data using the Kalman filter, which is then suitably combined with other likelihoods that might arise from independent studies of mortality, fecundity, and so forth. The combined likelihood may then be used for inference. Typically the underlying model for the census data is a state-space model, and capture–recapture methods of various kinds are used to construct the additional likelihoods. In this paper we provide a brief review of the approach; we present a new way to start the Kalman filter, designed specifically for ecological processes; we investigate the effect of break-down of the independence assumption; we show how the Kalman filter may be used to incorporate density-dependence, and we consider the effect of introducing heterogeneity in the state-space model.

We investigated the utility of state-space models for determining the demographic causes of population declines, using the Song Thrush as an example. A series of integrated state-space models were fitted to census and ring-recovery data from the United Kingdom for the period 1968–2000. The models were fitted using Bayesian MCMC techniques with uniform priors and were ranked using the Deviance Information Criterion (DIC). Ring-reporting rates were modelled as a declining logit-linear function of year, with separate slopes for first-year birds and adults. The system process involved three demographic parameters, first-year survival, adult survival and productivity. Survival rates were modelled as year-specific, as specific to blocks with uniform population growth rates, or as logit-linear functions of weather or year. Productivity rates were modelled as random annual effects, as block-specific or as log-linear functions of year. We fitted 17 such models chosen on the basis of our prior knowledge of this system, given that it was not practical to fit all potential models. Six models within 10 points of the smallest DIC value were selected for inference. The posterior distributions from these preferred models suggest that population growth rates are best correlated with first year survival and that and that there is also a pattern of consistent but weaker correlations between population growth rate and adult survival. Correlations between population growth rates and productivity were more variable, and may have been influenced by errors in other parts of the model, as productivity is essentially measured by difference. Thus in this analysis the evidence for productivity having a substantial influence of population changes is equivocal. The interpretation of these results and the potential value of integrated state-space models for research into the population dynamics of declining populations are discussed.

We constructed a Bayesian hierarchical model for estimating the population size and associated probabilities of availability and conditional detection for Florida manatees aggregating during winter, based on a series of monitoring flights over 3 years, 2001–2003. Building upon the findings of Edwards et al. (

2007

), our approach combines four sources of monitoring data in a single integrated modeling framework to estimate all model parameters simultaneously. Population size was modeled as a function of availability and detection, which in turn were estimated with covariate models consisting of environmental predictor variables. Previous work estimating manatee abundance from aerial surveys have either serially combined parameters estimated in separate models (Edwards et al.

2007

), modeled availability and detection jointly (Craig and Reynolds

2004

) or ignored detection bias altogether. Time-specific estimates of availability were high, with some variation among flight series, while estimates of conditional detection were extremely variable from one survey to the next. We obtained improved precision in our estimates of population size relative to Edwards et al. (

2007

). Our results emphasize the consequences of ignoring detection bias when interpreting survey counts. We hope that this research will be influential in the design of a new state-wide aerial survey monitoring program for Florida manatees.

The statistical analysis of mark-recapture-recovery (MRR) data dates back to the 1960s, when the foundation was laid for stochastic models, fitted to data by the method of maximum likelihood. There have been a number of developments which have proved to be extremely influential. Two of these are: the extension of MRR data and modelling to multi-site inference, and the integrated modelling of single-site MRR and census data. The aim of this study is to unite these two independent research programs, in order to enable effective integrated analysis of multi-site MRR data and multi-site census data. Census data can be described by a state-space model, and the likelihood is formed using the Kalman filter. By making use of movement information provided by MRR data, it is possible to avoid flat likelihood surfaces, thus allowing estimation of site-dependent parameters. This increases the precision of dispersal parameters and allows estimation of parameters inestimable from MRR studies alone.

This paper extends research within the area of integrated population analysis by developing methods for analysing multi-site census data coupled with multi-site capture recapture data. The methodology is explored using a simulated data set, the structure of which is motivated by a dataset of Great cormorants (

Phalacrocorax carbo sinensis

).

Multimodel inference has two main themes: model selection, and model averaging. Model averaging is a means of making inference conditional on a model set, rather than on a selected model, allowing formal recognition of the uncertainty associated with model choice. The Bayesian paradigm provides a natural framework for model averaging, and provides a context for evaluation of the commonly used AIC weights. We review Bayesian multimodel inference, noting the importance of Bayes factors. Noting the sensitivity of Bayes factors to the choice of priors on parameters, we define and propose nonpreferential priors as offering a reasonable standard for objective multimodel inference.

We compared a method of moments approach using estimates from a maximum likelihood framework, ultrastructural models within a maximum likelihood framework, and hierarchical models estimated using Markov chain Monte Carlo within a Bayesian framework for estimating survival and recapture probabilities and their variance components for a large, complex 20 year data set consisting of both live recaptures and recoveries. Estimates of mean age-specific survival and recapture probabilities for four age classes (young, second-year, third-year and adult) were similar with all approaches, but the maximum likelihood approach with year-specific parameters estimated some recovery and recapture probabilities on boundaries, leading to overestimates of some individual adult survival probabilities and hence overestimates of adult variance components. All approaches estimated similar coefficients for the relationships between winter temperature and survival probabilities, but the maximum likelihood approaches appeared to exaggerate variation in relation to prey abundance. Annual estimates from the Bayesian hierarchical models were sensitive to the choice of the hierarchical structure; modelling the difference between second-year, third-year and adults in survival and recapture probabilities as random effects better estimated the patterns of annual variation than treating all age classes as independent. Our comparisons suggest that Bayesian hierarchical models may be more likely to produce reliable estimates than maximum likelihood methods, even for large data sets, especially if there are many parameters and considerable annual variation in sample sizes.

Species richness is the most widely used biodiversity measure. Virtually always, it cannot be observed but needs to be estimated because some species may be present but remain undetected. This fact is commonly ignored in ecology and management, although it will bias estimates of species richness and related parameters such as occupancy, turnover or extinction rates. We describe a species community modeling strategy based on species-specific models of occurrence, from which estimates of important summaries of community structure, e.g., species richness, occupancy, or measures of similarity among species or sites, are derived by aggregating indicators of occurrence for all species observed in the sample, and for the estimated complement of unobserved species. We use data augmentation for an efficient Bayesian approach to estimation and prediction under this model based on MCMC in WinBUGS. For illustration, we use the Swiss breeding bird survey (MHB) that conducts 2–3 territory-mapping surveys in a systematic sample of 267 1 km

2

units on quadrat-specific routes averaging 5.1 km to obtain species-specific estimates of occupancy, and estimates of species richness of all diurnal species free of distorting effects of imperfect detectability. We introduce into our model species-specific covariates relevant to occupancy (elevation, forest cover, route length) and sampling (season, effort). From 1995 to 2004, 185 diurnal breeding bird species were known in Switzerland, and an additional 13 bred 1–3 times since 1900. 134 species were observed during MHB surveys in 254 quadrats surveyed in 2001, and our estimate of 169.9 (95% CI 151–195) therefore appeared sensible. The observed number of species ranged from 4 to 58 (mean 32.8), but with an estimated 0.7–11.2 (mean 2.6) further, unobserved species, the estimated proportion of detected species was 0.48–0.98 (mean 0.91). As is well known, species richness declined at higher elevation and fell above the timberline, and most species showed some preferred elevation. Route length had clear effects on occupancy, suggesting it is a proxy for the size of the effectively sampled area. Detection probability of most species showed clear seasonal patterns and increased with greater survey effort; these are important results for the planning of focused surveys. The main benefit of our model, and its implementation in WinBUGS for which we provide code, is its conceptual simplicity. Species richness is naturally expressed as the sum of occurrences of individual species. Information about species is combined across sites, which yields greater efficiency or may even enable estimation for sites with very few observed species in the first place. At the same time, species detections are clearly segregated into a true state process (occupancy) and an observation process (detection, given occupancy), and covariates can be readily introduced, which provides for efficient introduction of such additional information as well as sharp testing of such relationships.

Advances in capture–recapture methodology have allowed the inclusion of continuous, time-dependent individual-covariates as predictors of survival and capture probabilities. The problem posed by these covariates is that they are only observed for an individual when that individual is captured. One solution is to assume a model of the covariate which defines the distribution of unobserved values, conditional on the observed values, and apply Bayesian methods to compute parameter estimates and to test the covariate’s effect.

Previous applications of this approach have modeled the survival probability as a linear function of the covariate on some scale (e.g. identity or logistic). In some applications a linear function may not adequately describe the true relationship. Here we incorporate semi-parametric regression to allow for more flexibility in the relationship between the covariate and the survival probabilities of the Cormack–Jolly–Seber model. A fully Bayesian, adaptive algorithm is used to model the relationship with splines, in which the complexity of the relationship is governed by the number and location of the knots in the spline. A reversible jump Markov chain Monte Carlo algorithm is implemented to explore splines with different knot configurations, and model averaging is used to compute the final estimates of the survival probabilities.

The method is applied to a simulated data set and to data collected through the Dutch Constant Effort Sites ringing project to study the survival of reed warblers (

Acrocephalus scirpaceus

) as a function of condition.

The idea behind the mother-of-all-models is to have the likelihoods for commonly used capture–recapture models factorized into conditional likelihoods that can be called and combined on request to give a user specified model. Barker and White (

2004

) mapped out a conceptual plan for the mother-of-all-models that included the robust design model and joint recapture, live re-sighting models. However they were unable to obtain a factorization that could easily include the multi-state model. Including any missing data directly into the model using data augmentation allows us to write the model in terms of the complete data likelihood (CDL). The CDL is a more natural representation of the model that factors into separate components that can be combined to give many different capture–recapture models, including the multi-state model. Overcoming the obstacles in the factorization brings the mother-of-all-models one step closer with the development of software the next step.

Many biological systems include a portion of the target population that is unobservable during certain life history stages. Transition to and from an unobservable state may be of primary interest in many ecological studies and such movements are easily incorporated into multi-state models. Several authors have investigated properties of open-population multi-state mark-recapture models with unobservable states, and determined the scope and constraints under which parameters are identifiable (or, conversely, are redundant), but only in the context of a single observable and a single unobservable state (Schmidt et al.

2002

; Kendall and Nichols

2002

; Schaub et al.

2004

; Kendall

2004

). Some of these constraints can be relaxed if data are collected under a version of the robust design (Kendall and Bjorkland

2001

; Kendall and Nichols

2002

; Kendall

2004

; Bailey et al.

2004

), which entails >1 capture period per primary period of interest (e.g., 2 sampling periods within a breeding season). The critical assumption shared by all versions of the robust design is that the state of the individual (e.g. observable or unobservable) remains static for the duration of the primary period (Kendall

2004

). In this paper, we extend previous work by relaxing this assumption to allow movement among observable states within primary periods while maintaining static observable or unobservable states. Stated otherwise, both demographic and geographic closure assumptions are relaxed, but all individuals are either observable or unobservable within primary periods. Within these primary periods transitions are possible among multiple observable states, but transitions are not allowed among the corresponding unobservable states.

Our motivation for this work is exploring potential differences in population parameters for pond-breeding amphibians, where the quality of habitat surrounding the pond is not spatially uniform. The scenario is an example of a more general case where individuals move between habitats both during the breeding season (within primary periods; transitions among observable states only) and during the non-breeding season (between primary periods; transitions between observable and unobservable states). Presumably, habitat quality affects demographic parameters (e.g. survival and breeding probabilities). Using this model we are able to test this prediction for amphibians and determine if individuals move to more favorable habitats to increase survival and breeding probabilities.

For many species, non-invasive sampling of feathers, hair, feces or other tissue has the potential to be very useful and in some cases is already widely used to answer ecological questions. These samples are genotyped and the genotypes are used to identify individuals. There is some level of uncertainty when identifying individuals from genotyping results. We present an extension to the robust design capture–recapture model that allows for the estimation of genotyping error rate and properly estimates population size, survival, temporary emigration, and capture probability in the face of genotyping error. The model uses information contained in the secondary encounter occasions to estimate genotyping error which would otherwise be impossible for an open-population model with a robust design component. We further extend the model to allow estimation of the probability of correctly genotyping a sample from laboratory data. We demonstrate that with an additional data source for genotyping error, parameters are more precisely estimated by allowing some genotyping error and a larger sample size than by culling samples to eliminate the potential for errors in genotypes and reducing model complexity. We use noninvasive and hunter collected data from black bears in Michigan as an example.

For many animal populations, one or more life stages are not accessible to sampling, and therefore an unobservable state is created. For colonially-breeding populations, this unobservable state could represent the subset of adult breeders that have foregone breeding in a given year. This situation applies to many seabird populations, notably albatrosses, where skipped breeders are either absent from the colony, or are present but difficult to capture or correctly assign to breeding state. Kendall et al. (in press) have proposed design strategies for investigations of seabird demography where such temporary emigration occurs, suggesting the use of the robust design to permit the estimation of time-dependent parameters and to increase the precision of estimates from multi-state models. A traditional robust design, where animals are subject to capture multiple times in a sampling season, is feasible in many cases. However, due to concerns that multiple captures per season could cause undue disturbance to animals, Kendall et al. (in press) developed a less-invasive robust design (LIRD), where initial captures are followed by an assessment of the ratio of marked-to-unmarked birds in the population or sampled plot. This approach has recently been applied in the Northwestern Hawaiian Islands to populations of Laysan (

Phoebastria immutabilis

) and black-footed (

P. nigripes

) albatrosses. In this paper, we outline the LIRD and its application to seabird population studies. We then describe an approach to determining optimal allocation of sampling effort in which we consider a non-robust design option (nRD), and variations of both the traditional robust design (RD), and the LIRD. Variations we considered included the number of secondary sampling occasions for the RD and the amount of total effort allocated to the marked-to-unmarked ratio assessment for the LIRD. We used simulations, informed by early data from the Hawaiian study, to address optimal study design for our example cases. We found that the LIRD performed as well or nearly as well as certain variations of the RD in terms of root mean square error, especially when relatively little of the total effort was allocated to the assessment of the marked-to-unmarked ratio versus to initial captures. For the RD, we found no clear benefit of using 2, 4, or 6 secondary sampling occasions per year, though this result will depend on the relative effort costs of captures versus recaptures and on the length of the study. We also found that field-readable bands, which may be affixed to birds in addition to standard metal bands, will be beneficial in longer-term studies of albatrosses in the Northwestern Hawaiian Islands. Field-readable bands reduce the effort cost of recapturing individuals, and in the long-term this cost reduction can offset the additional effort expended in affixing the bands. Finally, our approach to determining optimal study design can be generally applied by researchers, with little seed data, to design their studies at the outset.

Deviations from model assumptions in the application of capture–recapture models to real life situations can introduce unknown bias. Understanding the type and magnitude of bias under these conditions is important to interpreting model results. In a robust design analysis of long-term photo-documented sighting histories of the endangered Florida manatee, I found high survival rates, high rates of non-random temporary emigration, significant time-dependence, and a diversity of factors affecting temporary emigration that made it difficult to model emigration in any meaningful fashion. Examination of the time-dependent survival estimates indicated a suspicious drop in survival rates near the end of the time series that persisted when the original capture histories were truncated and reanalyzed under a shorter time frame. Given the wide swings in manatee emigration estimates from year to year, a likely source of bias in survival was the convention to resolve confounding of the last survival probability in a time-dependent model with the last emigration probabilities by setting the last unmeasurable emigration probability equal to the previous year’s probability when the equality was actually false. Results of a series of simulations demonstrated that if the unmeasurable temporary emigration probabilities in the last time period were not accurately modeled, an estimation model with significant annual variation in survival probabilities and emigration probabilities produced bias in survival estimates at the end of the study or time series being explored. Furthermore, the bias propagated back in time beyond the last two time periods and the number of years affected varied positively with survival and emigration probabilities. Truncating the data to a shorter time frame and reanalyzing demonstrated that with additional years of data surviving temporary emigrants eventually return and are detected, thus in subsequent analysis unbiased estimates are eventually realized.

Knowing the extent and magnitude of the potential bias can help in making decisions as to what time frame provides the best estimates or the most reliable opportunity to model and test hypotheses about factors affecting survival probability. To assess bias, truncating the capture histories to shorter time frames and reanalyzing the data to compare time-specific estimates may help identify spurious effects. Running simulations that mimic the parameter values and movement conditions in the real situation can provide estimates of standardized bias that can be used to identify those annual estimates that are biased to the point where the 95% confidence intervals are inadequate in describing the uncertainty of the estimates.

Multistate capture–recapture models continue to be employed with greater frequency to test hypotheses about metapopulation dynamics and life history, and more recently disease dynamics. In recent years efforts have begun to adjust these models for cases where there is uncertainty about an animal’s state upon capture. These efforts can be categorized into models that permit misclassification between two states to occur in either direction or one direction, where state is certain for a subset of individuals or is always uncertain, and where estimation is based on one sampling occasion per period of interest or multiple sampling occasions per period. State uncertainty also arises in modeling patch occupancy dynamics. I consider several case studies involving bird and marine mammal studies that illustrate how misclassified states can arise, and outline model structures for properly utilizing the data that are produced. In each case misclassification occurs in only one direction (thus there is a subset of individuals or patches where state is known with certainty), and there are multiple sampling occasions per period of interest. For the cases involving capture–recapture data I allude to a general model structure that could include each example as a special case. However, this collection of cases also illustrates how difficult it is to develop a model structure that can be directly useful for answering every ecological question of interest and account for every type of data from the field.

The development of the use of CR multistate models is a major feature of the last 5 years. However, concerns have rightfully appeared about uncertainty in state assignment. I examine situations where uncertainties seem to be intrinsic such as with breeding status. But I also argue that uncertainty is not just a liability, it can be an opportunity – for instance, to exploit more fully the data at hand and limit disturbance. Then I examine the methodological answers that have been proposed. They mainly concern the models conditional on first release and are of a more or less general applicability. I advocate a general approach that can be adapted to each particular case and be used to expand extant specialized approaches. I will also consider how uncertainty could be incorporated into non-conditional models such as models of stopover duration. I conclude that, with the advent of genetic sampling, the new challenges for CR models will be uncertainty in individual identity and dependence among individuals.

Unobservable stages are common in many life cycles. Estimates of the vital rates, such as survival and breeding probabilities, of these stages are essential for demographic analysis but difficult to obtain. Explicit modeling of these states in multi-state mark-recapture methods can provide such estimates. However, models can be rank-deficient, meaning that not all parameters can be estimated. Determining whether a model is full rank is essential for interpretation of model selection and estimation results. Full rank models can be obtained by imposing biologically reasonable constraints on parameters. Developing such models requires an efficient way to assess model rank and determine which parameters, if any, are redundant. We introduce the use of automatic differentiation (AD) for this purpose. It generates the Jacobian matrix of the likelihood function in a way that is numerically stable, can accommodate large complicated models, and produces rank estimates accurate to machine precision. It reveals whether a model is full rank or rank-deficient (either intrinsically or for a particular data set), how many parameters or parameter combinations can be estimated, and which parameters are confounded. We use the method to explore three examples relevant to seabirds: a model with multiple breeding sites, a model distinguishing successful and failed breeders, and a model for pre-breeder survival and recruitment. We find a surprisingly large number of time-invariant and time-varying models to be of full rank, thus allowing estimation of all parameters, despite the unobservable states. We present a biological example for the Wandering Albatross (

Diomedea exulans

). Reliable assessment of model rank for multi-state mark-recapture models with unobservable stages will make it possible to use these methods in demographic applications.

Wildlife managers and ecologists are often interested in estimating abundance of animals belonging to a certain fixed group (e.g. sex), but in some cases group membership cannot always be ascertained. Group assignment uncertainties can occur either through the inability to assign group membership because of a lack of group-specific characteristics (e.g. males and females look alike), lack of training (e.g. volunteers), or through errors in assignment. Recently, methodological advances in closed population capture-recapture models have allowed for the inclusion of classification uncertainties in parameter estimates. We build on this work by addressing identification uncertainty in abundance estimation (open population models), providing a general method for dealing with multiple groups/states when the true underlying group/state can be considered fixed for the duration of the experiment. We then apply this methodology to estimate the sex-specific abundances of walleyes (

Stizostedion vitreum

) in Mille Lacs, Minnesota.

Multievent models (Pradel

2005

,

2008

) handle state uncertainty, and they therefore cover a range of situations like hidden capture heterogeneity and sex determination from behaviour which cannot be treated in the multistate paradigm. We introduce a new software application called

e-surge

, built upon the concepts developed in program

m-surge

(Choquet et al.

2004

) to encompass this new class of capture–recapture models. It also improves on

m-surge

by allowing the decomposition of transitions into several steps. We present the new concepts involved, notably the event and the multistep process, and how they are implemented in

e-surge

. We then illustrate the use of

e-surge

with three examples. One example deals with breeding propensity where the breeding state cannot always be ascertained; a further deals with emigration which is considered as a two-step process (Grosbois and Tavecchia

2003

) and the last one with a version of a memory model where survival can be handled directly.

The Lifetime Reproductive Success (LRS) of an individual i.e. the number of young raised during its lifespan is an indicator of its contribution to future generations and thus a measure of fitness. Nevertheless, the LRS is hard to estimate because of the difficulty to keep track of the outcome of each breeding attempt (successful or failed and, if successful, number of young raised). We propose two new methods to estimating the LRS that takes into account the uncertainty about the reproductive status when the individuals are not detected or when the reproductive status cannot be assessed. We illustrate these two methods using roe deer reproductive histories and discuss their advantages and disadvantages.

The computer package WinBUGS is introduced. We first give a brief introduction to Bayesian theory and its implementation using Markov chain Monte Carlo (MCMC) algorithms. We then present three case studies showing how WinBUGS can be used when classical theory is difficult to implement. The first example uses data on white storks from Baden Württemberg, Germany, to demonstrate the use of mark-recapture models to estimate survival, and also how to cope with unexplained variance through random effects. Recent advances in methodology and also the WinBUGS software allow us to introduce (i) a flexible way of incorporating covariates using spline smoothing and (ii) a method to deal with missing values in covariates. The second example shows how to estimate population density while accounting for detectability, using distance sampling methods applied to a test dataset collected on a known population of wooden stakes. Finally, the third case study involves the use of state-space models of wildlife population dynamics to make inferences about density dependence in a North American duck species. Reversible Jump MCMC is used to calculate the probability of various candidate models. For all examples, data and WinBUGS code are provided.

Mark-recapture studies are one of the most common methods used to obtain demographic parameters for wildlife populations. Time specific estimates of parameters representing population processes contain both temporal variability in the process (process error) and error in estimating the parameters (observation error). Therefore, to estimate the temporal variation in the population process, it is important to separate these two errors. Traditional random effect models can be used to separate the two errors. However, it is difficult to implement the required simultaneous maximization and integration for dynamic nonlinear non-Gaussian models. An alternative hierarchical Bayesian approach using MCMC integration is easier to apply, but requires priors for all model parameters.

AD Model Builder (ADMB) is a general software environment for fitting parameter rich nonlinear models to data. It uses automatic differentiation to provide a more efficient and stable parameter estimation framework. ADMB has both random effects using Laplace approximation and importance sampling, and MCMC to implement Bayesian analysis.

To demonstrate ADMB and investigate methods to analyze mark-recapture data, we implement fixed effect, random effect, and hierarchical Bayes estimators in ADMB and apply them to three mark-recapture data sets. Our results showed that unrestricted time-effects, random effects, and hierarchical Bayes methods often give similar results, but not in all cases or for all parameters.

Producing accurate, reliable indices of abundance, enabling the status of breeding bird populations to be monitored is of interest to government, conservation groups and other bodies. Indices for Sedge Warblers

Acrocephalus schoenobaenus

from 1983 to 2002 were produced using catch data from the British Trust for Ornithology’s (BTO) Constant Effort Scheme (CES). This is a ringing programme based on standardised mist-netting across up to 12 annual visits to each of a large number of sites. A feature of these data is that some yearly site counts are “censored” due to visits missed within certain years. Peach et al. (

1998

) developed an intuitive, non-parametric method for correcting for missed visits, prior to model-fitting in the form of a Poisson regression model with an additive offset. In this paper a novel Bayesian approach is introduced, which produces annual indices of abundance whose uncertainty also incorporates a component due to the correction for missed visits. We describe the method in detail, applied to the Sedge Warbler data and to simulated data, and compare the results with those from the current method of Peach et al. (

1998

).

The age structure of harvests has long been an important source of information in fisheries stock assessments, especially when augmented with data from catch-effort or research vessel surveys. Age-at-harvest data are also collected for many terrestrial species, a fact which has recently prompted several authors to propose models for analyzing wildlife age-at-harvest data, with the object of estimating abundance, survival, harvest parameters, and recruitment. Since analysis with age-at-harvest data alone often leads to problems with parameter identification, these authors suggested that data from studies of marked animals could be used to inform the estimation of survival and recovery rates. However, little work has been done to examine estimator performance, particularly when model assumptions are violated, as when aging errors occur or when mark-recovery and age-at-harvest data are non-independent. Similarly, we know of no studies that have investigated the efficacy of posterior simulation when Bayesian estimation methods are used for such problems. In this paper, we employ a suite of simulation modules to quantify estimator performance under a number of hypothetical biological scenarios. When all assumptions are satisfied, we show that bias is typically of small magnitude, coefficient of variation is small, and that credible interval coverage is satisfactory. Estimators were robust to errors in age determination but precision had the potential to be severely overestimated when data from marked animals were also included in age-at-harvest summaries. Nevertheless, joint analysis of age-at-harvest and mark-recovery data may represent a viable monitoring strategy for many terrestrial species.

Spatial heterogeneity in survival and capture probabilities is a critical issue to consider in tagging experiments. If a non-trivial level of spatial heterogeneity exists and is not accounted for, it can lead to unreliable estimates of mortality rates and abundance, and of the uncertainty in these estimates. Here we present a spatial model for analysing multiyear tag-recovery and fishery catch data that allows for mortality rates and abundance to differ among discrete regions and for fish to move among these regions at discrete time intervals. For a given cohort of fish tagged in consecutive years in all regions, this model can provide year- and region-specific estimates of both natural mortality and fishing mortality, region-specific estimates of abundance at the time of initial tagging, as well as year-specific movement probabilities between regions. The precision of parameter estimates can be poor with such a full model, but can be improved with more restricted model parameterizations. Tagging in some regions may be logistically difficult and/or very expensive. We show that if tagging is conducted in all regions in the first year of the experiment, but only in one region thereafter, accurate and precise parameter estimates can sometimes still be achieved. It is not always the regional estimates of mortality rates and abundance that are of primary interest, but rather the population-wide estimates (over all regions). Such population-wide estimates can be obtained by applying a non-spatial model to the data pooled across regions; however, simulation results suggest that there are many situations for which large biases are incurred by using a non-spatial model. Simulations also suggest that there is almost no loss in precision from using the spatial model to obtain population-wide estimates even when the non-spatial model would suffice.

The Hierarchical Predictive Model (HPM) is a semiparametric mixed model where the fixed effects are fit with a user-specified non-parametric component. This approach extends current spline-based semiparametric mixed model formulations, allowing for more flexible nonparametric estimation. Greater adaptability simplifies model specification making it easier to analyze data sets with large numbers of predictors. Greater automation also extends the scope of exploratory analyses that may be performed with mixed models. Using a HPM, the analyst may select the predictive model to best suit their needs, exploiting the strengths of currently available predictive methods. A simulation study is used to demonstrate the advantages of accounting for known hierarchical structure in predictive models and to illustrate the adaptability of current decision-tree based predictive models. A HPM of the relative abundance of the North American House Finch (

Carpodacus mexicanus

) is used to demonstrate exploratory analysis with a real data set.

Adult survival probability is a key parameter in any population model for a long-lived species. For many species, information on adult survival comes from a capture–recapture study involving individuals for whom age is unknown. If the species experiences senescence, the estimate of overall adult survival probability will be negatively biased. The purpose of this paper is to assess the extent to which the estimate is biased and the implications for population modelling. We show that the amount of bias depends on the capture probability and the strength of senescence. If the capture probability is greater than 0.5, the expected bias is at most 1%, unless senescence is strong and begins early in adulthood. Individual heterogeneity in capture probability can also lead to negative bias in estimates of survival probability, meaning that moderate effects from senescence and heterogeneity may combine to produce a non-negligible amount of bias. Capture–recapture methods for survival are also used to estimate the time that migrating animals spend at intermediate “stop-over” sites. In this context, an increase in departure probability with time since arrival is analogous to senescence, leading to a negative bias in estimated stop-over duration. This bias will often be large because capture probabilities in such studies are generally very low and departure probability may increase abruptly once animals have rested and re-fueled.

The percentage overlap between prior and posterior distributions is obtained easily from the output of MCMC samplers. A 35% guideline for overlap between univariate marginal prior and posterior distributions has been suggested as an indicator of weak identifiability of a parameter. As long as uniform prior distributions are adopted for all of the model parameters, then the suggested guideline has been found to work well for a range of models of mark-recapture-recovery data, where all the parameters are probabilities. Its use is illustrated on models for ring-recovery data on male mallards, and the Cormack-Jolly-Seber model for capture-recapture data on dippers.

We evaluate the performance of a new mixture model for heterogeneity in capture probability when estimating the size of a closed population of wild animals. The new model expresses the capture probability as a mixture of a binomial distribution and a beta-binomial distribution. For real data sets, it is shown how the new model can provide a suitable framework for model discrimination. When there is no best model from within the family of models represented by the new mixture, we recommend adopting a conservative approach to estimating population size.

Knowledge about proportions of specific mortality causes is important for the design of efficient conservation measures or the determination of harvest regulations. Unfortunately, these proportions are difficult to estimate. We (Schaub and Pradel 2004a) have recently introduced a multistate capture-recapture model that allows one to estimate proportions of specific mortality causes from recoveries of dead animals with known cause of death. However, parameter estimation was found to be difficult, because the likelihood surface of the model relative to most parameters has a flat ridge, unless the proportions of mortality causes vary with time and the cause-specific recovery rates are constant. These conditions are likely to be violated in most empirical situations. For the application of this model, it is therefore important to study the sensitivity of parameter estimates to violations of these assumptions. I use a Bayesian implementation of the model to evaluate bias, precision and accuracy of parameter estimates under variable means and temporal variation of mortality cause proportions and recovery rates. Survival rate estimates were unbiased in all scenarios. Bias and precision of the proportion of mortality causes and of the cause-specific recovery probabilities decreased with increasing temporal variance of the proportion of mortality causes while their accuracy increased. The bias of these estimates also decreased with decreasing difference between cause-specific recovery probabilities and with decreasing temporal variation of them. Moreover, informative priors affected the posterior distribution of the parameters when temporal variation in the proportion of mortality causes was low. Temporal variance of the proportion of mortality causes could be estimated reliably regardless of bias. This result is important, since it allows one to assess whether accuracy of the estimates of mortality proportions is acceptable for the objectives of a study. The bias of the naïve estimator (quotient of the number of animals reported dying from a particular cause to the total number reported altogether) was usually much larger than the bias of the corresponding estimator from the multistate model. In conclusion, a careful application of the multistate capture-recapture model can give useful information about the proportion of mortality causes that is otherwise hard to obtain.

The development of statistical methods for the analysis of demographic processes in marked animal populations has brought with it the challenges of communication between the disciplines of statistics, ecology, evolutionary biology and computer science. In order to aid communication and comprehension, we sought to root out a number of cases of ambiguity, redundancy and inaccuracy in notation and terminology that have developed in the literature. We invited all working in this field to submit topics for resolution and to express their own views. In the ensuing discussion forum it was then possible to establish a series of general principles which were, almost without exception, unanimously accepted. Here we set out the background to the areas of confusion, how these were debated and the conclusions which were reached in each case. We hope that the resulting guidelines will be widely adopted as standard terminology in publications and in software for the analysis of demographic processes in marked animal populations

The true distribution of migrant species is rarely immediately apparent from the distribution of ring recoveries due to a heavy bias in regional recovery probabilities. For western Palearctic species, the recovery probability is especially low in Africa, but also varies within Europe. However, little work has been done to derive actual estimates of these recovery probabilities needed to infer the “true” underlying distribution. Here, we investigate the potential of using ringing data to estimate the seasonal distribution densities of migrant species. Using likelihoods based on a two point mixture distribution, the proportions of individuals wintering south of the Sahara are estimated using differences in recovery distributions among species in species groups where the location-specific probability of a ring recovery can be assumed to be essentially the same among species. We consider two such approaches. In the first, survival associated with a wintering area must be set constant across species. In the second, we assume the time series is long enough that a single binary response (recovered/not recovered) may be modeled independently of survival parameters. Under the first approach, we estimated the proportion of sub-Saharan migrants, together with 95% profile likelihood confidence intervals, for redstart as 0.84 [0.70,0.93], thrush nightingale 1.00 [0.49,1.00], garden warbler 0.95 [0.85;0.99], blackcap 0.60 [0.32;0.78], reed warbler 0.87 [0.72,0.95], and pied flycatcher 0.90 [0.76;0.97] using recovery data for birds ringed in Denmark and assuming that all robins winter north of Sahara. In the second approach, estimated proportions of sub-Saharan migrants were similar, but the confidence intervals were somewhat narrower. Although further work is required to examine the underlying assumptions, the models and analyses presented here provide a framework for making better use of existing ring recovery datasets to understand the “true” seasonal distribution patterns of European birds.

Monte Carlo simulation was used to evaluate properties of a simple Bayesian MCMC analysis of the random effects model for single group Cormack-Jolly-Seber capture-recapture data. The MCMC method is applied to the model via a logit link, so parameters

$p,\ S$

are on a logit scale, where

$\mathrm{logit}(S)$

is assumed to have, and is generated from, a normal distribution with mean

$\upmu$

and variance

$\upsigma^{2}$

. Marginal prior distributions on

$\mathrm{logit}(p)$

and

$\upmu$

were independent normal with mean zero and standard deviation 1.75 for

$\mathrm{logit}(p)$

and 100 for

$\upmu$

; hence minimally informative. Marginal prior distribution on

$\upsigma^{2}$

was placed on

$\uptau^{2}=1/\upsigma^{2}$

as a gamma distribution with

$\upalpha=\upbeta=0.001$

. The study design has 432 points spread over 5 factors: occasions

$(t)$

, new releases per occasion

$(u),\ p,\ \upmu$

, and

$\upsigma$

. At each design point 100 independent trials were completed (hence 43,200 trials in total), each with sample size

$n=10,000$

from the parameter posterior distribution. At 128 of these design points comparisons are made to previously reported results from a method of moments procedure. We looked at properties of point and interval inference on

$\upmu$

, and

$\upsigma$

based on the posterior mean, median, and mode and equal-tailed 95% credibility interval. Bayesian inference did very well for the parameter

$\upmu$

, but under the conditions used here, MCMC inference performance for

$\upsigma$

was mixed: poor for sparse data (i.e., only 7 occasions) or

$\upsigma=0$

, but good when there were sufficient data and not small

$\upsigma$

.