Disentangling the sources of variation in the survival of the European dipper

The population growth rate of the European dipper has been shown to decrease with winter temperature and population size. We examine here the demographic mechanism for this effect by analysing how these factors affect the survival rate. Using more than 20 years of capture-mark-recapture data (1974-1997) based on more than 4000 marked individuals, we perform analyses using open capture-mark-recapture models. This allowed us to estimate the annual apparent survival rates (probability of surviving and staying on the study site from one year to the next one) and the recapture probabilities. We partitioned the variance of the apparent survival rates into sampling variance and process variance using random effects models, and investigated which variables best accounted for temporal process variation. Adult males and females had similar apparent survival rates, with an average of 0.52 and a coefficient of variation of 40%. Chick apparent survival was lower, averaging 0.06 with a coefficient of variation of 42%. Eighty percent of the variance in apparent survival rates was explained by winter temperature and population size for adults and 48% by winter temperature for chicks. The process variance outweighed the sampling variance both for chick and adult survival rates, which explained that shrunk estimates obtained under random effects models were close to MLE estimates. A large proportion of the annual variation in the apparent survival rate of chicks appears to be explained by inter-year differences in dispersal rates.     

Disentangling the sources of variation in the survival of the European dipper

The population growth rate of the European dipper has been shown to decrease with winter temperature and population size. We examine here the demographic mechanism for this effect by analysing how these factors affect the survival rate. Using more than 20 years of capture-mark-recapture data (1974-1997) based on more than 4000 marked individuals, we perform analyses using open capture-mark-recapture models. This allowed us to estimate the annual apparent survival rates (probability of surviving and staying on the study site from one year to the next one) and the recapture probabilities. We partitioned the variance of the apparent survival rates into sampling variance and process variance using random effects models, and investigated which variables best accounted for temporal process variation. Adult males and females had similar apparent survival rates, with an average of 0.52 and a coefficient of variation of 40%. Chick apparent survival was lower, averaging 0.06 with a coefficient of variation of 42%. Eighty percent of the variance in apparent survival rates was explained by winter temperature and population size for adults and 48% by winter temperature for chicks. The process variance outweighed the sampling variance both for chick and adult survival rates, which explained that shrunk estimates obtained under random effects models were close to MLE estimates. A large proportion of the annual variation in the apparent survival rate of chicks appears to be explained by inter-year differences in dispersal rates.     

Estimation of long-term trends and variation in avian survival probabilities using random effects models

We obtained banding and recovery data from the Bird Banding Laboratory (operated by the Biological Resources Division of the US Geological Survey) for adults from 129 avian species that had been continuously banded for > 24 years. Data were partitioned by gender, banding period (winter versus summer), and by states/provinces. Data sets were initially screened for adequacy based on specific criteria (e.g. minimum sample sizes). Fifty-nine data sets (11 waterfowl species, the Mourning Dove and Common Grackle) met our criteria of adequacy for further analysis. We estimated annual survival probabilities using the Brownie et al. recovery model {St, ft} in program MARK. Trends in annual survival and temporal process variation were estimated using random effects models based on shrinkage estimators. Waterfowl species had relatively little variation in annual survival probabilities (mean CV = 8.7% and 10% for males and females, respectively). The limited data for other species suggested similar low temporal variation for males, but higher temporal variation for females (CV = 40%). Evidence for long-term trends varied by species, banding period and sex, with no obvious spatial patterns for either positive or negative trends in survival probabilities. An exception was Mourning Doves banded in Illinois/Missouri and Arizona/New Mexico where both males (slope = -0.0122, se = 0.0019 and females (slope = -0.0109 to -0.0128, se = 0.0018 -0.0032) exhibited declining trends in survival probabilities. We believe our approach has application for large-scale monitoring. However, meaningful banding and recovery data for species other than waterfowl is very limited in North America.     

Selection among open population capture-recapture models when capture probabilities are heterogeneous

Selection of a parsimonious model as a basis for statistical inference from capture-recapture data is critical, especially when using open models in the analysis of multiple, interrelated data sets (e.g. males and females, with two to three age classes, over three to five areas and 10-15 years). The global (i.e. most general) model for such data sets might contain hundreds of survival and recapture parameters. Here, we focus on a series of nested models of the Cormack-Jolly-Seber type wherein the likelihood arises from products of multinomial distributions whose cell probabilities are reparameterized in terms of survival ( phi ) and mean capture ( p ) probabilities. This paper presents numerical results on two information-theoretic methods for model selection when the capture probabilities are heterogeneous over individual animals: Akaike's Information Criterion (AIC) and a dimension-consistent criterion (CAIC), derived from a Bayesian viewpoint. Quality of model selection was evaluated based on the relative Euclidian distance between standardized theta and theta (parameter theta is vector-valued and contains the survival ( phi ) and mean capture ( p ) probabilities); this quantity (RSS = sigma{(theta i - theta i )/ theta i } 2 ) is a sum of squared bias and variance. Thus, the quality of inference (RSS) was judged by comparing the performance of the two information criteria and the use of the true model (used to generate the data), in relation to the model that provided the smallest RSS. We found that heterogeneity in the capture probabilities had a negligible effect on model selection using AIC or CAIC. Model size increased as sample size increased with both AIC- and CAIC-selected models.     

MATLAB: An environment for analyzing ring-recovery and recapture data

The programming environment provided by MATLAB makes it easy to write code for the interactive analysis of data from ring-recovery and recapture studies. In particular, it is simple to write down a log-likelihood for any given model, to maximize this log-likelihood to estimate the parameters of the model and calculate their standard errors, to perform likelihood ratio and score test comparisons of models, and to compute goodness-of-fit statistics and examine residuals. Eagle is a package of simple MATLAB programs that provides an interactive environment for the analysis of ring-recovery data. Eagle will cope with any model of the Freeman-Morgan kind, where the survival and recovery probabilities may be specified as constant, time- or age-dependent, or as depending on one or more external covariates. This will be extended to handle data from recapture studies and from combined recovery and recapture studies. The package may also be used to analyze arbitrary models, at the expense of a small amount of extra MATLAB programming. A demonstration is given of use of Eagle to analyze data from a ring-recovery study on grey herons ( Ardea cinera ), with and without covariates. The use of the MATLAB programming environment is illustrated by fitting a simple model to some recapture data on herring gulls ( Larus argentatus ).     

Return rates in studies of life history evolution: Are biases large?

Studies of life history evolution in passerine birds often depend on examination of annual survival probability of adult birds. Most studies rely on return rates (proportion of marked individuals released in one year that are recaptured in the next year) to estimate annual survival probability. Yet, return rate includes both the probability of survival and the probability of recapturing or resighting the bird in the next time interval. We use numerical estimation to illustrate the increasing bias in return rate as an estimator of annual survival probability as recapture/resighting probability decreases. Recapture/resighting probability is normally assumed to be high and relatively invariant for recapture/resighting studies of color-banded territorial birds. We tested this assumption through examination of 11 color-banding studies of passerines. These studies showed that recapture/resighting probabilities vary strongly and cannot be generalized as high. In short, return rates generally are poor estimators of annual survival probabilities and use of return rates may strongly bias relationships explored in comparative studies or bias results of experiments to test survival costs of reproduction. Recapture/resighting probabilities should be estimated in all studies that attempt to estimate annual survival probabilities.     

On the integrated maximum likelihood estimators for a closed population capture–recapture model with unequal capture probabilities

Nuisance parameter elimination is a central problem in capture–recapture modelling. In this paper, we consider a closed population capture–recapture model which assumes the capture probabilities varies only with the sampling occasions. In this model, the capture probabilities are regarded as nuisance parameters and the unknown number of individuals is the parameter of interest. In order to eliminate the nuisance parameters, the likelihood function is integrated with respect to a weight function (uniform and Jeffrey's) of the nuisance parameters resulting in an integrated likelihood function depending only on the population size. For these integrated likelihood functions, analytical expressions for the maximum likelihood estimates are obtained and it is proved that they are always finite and unique. Variance estimates of the proposed estimators are obtained via a parametric bootstrap resampling procedure. The proposed methods are illustrated on a real data set and their frequentist properties are assessed by means of a simulation study.     

Why a time effect often has a limited impact on capture‐recapture estimates in closed populations

The author is concerned with log‐linear estimators of the size N of a population in a capture‐recapture experiment featuring heterogeneity in the individual capture probabilities and a time effect. He also considers models where the first capture influences the probability of subsequent captures. He derives several results from a new inequality associated with a dispersive ordering for discrete random variables. He shows that in a log‐linear model with inter‐individual heterogeneity, the estimator N is an increasing function of the heterogeneity parameter. He also shows that the inclusion of a time effect in the capture probabilities decreases N in models without heterogeneity. He further argues that a model featuring heterogeneity can accommodate a time effect through a small change in the heterogeneity parameter. He demonstrates these results using an inequality for the estimators of the heterogeneity parameters and illustrates them in a Monte Carlo experiment     

Costs of reproduction in common eiders ( Somateria mollissima ): an assessment of relationships between reproductive effort and future survival and reproduction based on observational and experimental studies

The two traditional approaches to the study of costs of reproduction, correlational and experimental, have been used in parallel in a breeding colony of common eiders ( Somateria mollissima ) and were compared in this paper. The analysis of the observational data was based on a two-strata capture-recapture model, the strata being defined on the basis of the clutch size laid by individual females in a given year. The best model according to AIC C indicated substantial variation in survival, recapture and transition rates, but overall a pattern emerged: females laying large clutches have a somewhat higher survival and much higher capture rate than females laying small clutches, and transition from large to small clutch size occurs much more frequently than the reverse transition. The analysis of the experimental data (adding/removing one egg) showed that no clear effect was found on either survival or transition rates. We conclude by suggesting (1) that condition should be included in multi-strata models in addition to reproductive effort; (2) that a specific study design for estimating the proportion of non-breeding females should be implemented, and (3) that non-breeding (a non-observable state in this study) may be influenced by previous reproduction events.     

A SEMIPARAMETRIC MODEL FOR A FUNCTIONAL BEHAVIOURAL RESPONSE TO CAPTURE IN CAPTURE–RECAPTURE EXPERIMENTS

Capture–recapture experiments are commonly used to estimate the size of a closed population. However, the associated estimators of the population size are well known to be highly sensitive to misspecification of the capture probabilities. To address this, we present a general semiparametric framework for the analysis of capture–recapture experiments when the capture probability depends on individual characteristics, time effects and behavioural response. This generalizes well‐known general parametric capture–recapture models and extends previous semiparametric models in which there is no time dependence or behavioural response. The method is evaluated in simulations and applied to two real data sets.     

Costs of reproduction in common eiders ( Somateria mollissima ): An assessment of relationships between reproductive effort and future survival and reproduction based on observational and experimental studies

The two traditional approaches to the study of costs of reproduction, correlational and experimental, have been used in parallel in a breeding colony of common eiders ( Somateria mollissima ) and were compared in this paper. The analysis of the observational data was based on a two-strata capture-recapture model, the strata being defined on the basis of the clutch size laid by individual females in a given year. The best model according to AIC C indicated substantial variation in survival, recapture and transition rates, but overall a pattern emerged: females laying large clutches have a somewhat higher survival and much higher capture rate than females laying small clutches, and transition from large to small clutch size occurs much more frequently than the reverse transition. The analysis of the experimental data (adding/removing one egg) showed that no clear effect was found on either survival or transition rates. We conclude by suggesting (1) that condition should be included in multi-strata models in addition to reproductive effort; (2) that a specific study design for estimating the proportion of non-breeding females should be implemented, and (3) that non-breeding (a non-observable state in this study) may be influenced by previous reproduction events.     

Estimation of sex‐specific survival with uncertainty in sex assessment

In monomorphic species, determination of sex from behavior is prone to errors. The authors develop capture‐recapture survival models that account for uncertainty in the assessment of sex. They examine parameter redundancy for four basic models with constant or time‐dependent survival and encounter probabilities. They further develop a more refined and more appropriate model for an Audouin's gull data set where four distinct behavioral clues have been used. They examine how useful it is to incorporate the least reliable of the clues and the genetic determination of sex available for only a handful of individuals. They finally discuss the implications of their findings for the design of field studies.     

APPLICATION OF SEMIPARAMETRIC REGRESSION MODELS IN THE ANALYSIS OF CAPTURE-RECAPTURE EXPERIMENTS

If the capture probabilities in a capture‐recapture experiment depend on covariates, parametric models may be fitted and the population size may then be estimated. Here a semiparametric model for the capture probabilities that allows both continuous and categorical covariates is developed. Kernel smoothing and profile estimating equations are used to estimate the nonparametric and parametric components. Analytic forms of the standard errors are derived, which allows an empirical bias bandwidth selection procedure to be used to estimate the bandwidth. The method is evaluated in simulations and is applied to a real data set concerning captures of Prinia flaviventris, which is a common bird species in Southeast Asia.     

From distance sampling to spatial capture–recapture

Distance sampling and capture–recapture are the two most widely used wildlife abundance estimation methods. capture–recapture methods have only recently incorporated models for spatial distribution and there is an increasing tendency for distance sampling methods to incorporated spatial models rather than to rely on partly design-based spatial inference. In this overview we show how spatial models are central to modern distance sampling and that spatial capture–recapture models arise as an extension of distance sampling methods. Depending on the type of data recorded, they can be viewed as particular kinds of hierarchical binary regression, Poisson regression, survival or time-to-event models, with individuals’ locations as latent variables and a spatial model as the latent variable distribution. Incorporation of spatial models in these two methods provides new opportunities for drawing explicitly spatial inferences. Areas of likely future development include more sophisticated spatial and spatio-temporal modelling of individuals’ locations and movements, new methods for integrating spatial capture–recapture and other kinds of ecological survey data, and methods for dealing with the recapture uncertainty that often arise when “capture” consists of detection by a remote device like a camera trap or microphone.     

Transformed Logit Confidence Intervals for Small Populations in Single Capture–Recapture Estimation

The good performance of logit confidence intervals for the odds ratio with small samples is well known. This is true unless the actual odds ratio is very large. In single capture–recapture estimation the odds ratio is equal to 1 because of the assumption of independence of the samples. Consequently, a transformation of the logit confidence intervals for the odds ratio is proposed in order to estimate the size of a closed population under single capture–recapture estimation. It is found that the transformed logit interval, after adding .5 to each observed count before computation, has actual coverage probabilities near to the nominal level even for small populations and even for capture probabilities near to 0 or 1, which is not guaranteed for the other capture–recapture confidence intervals proposed in statistical literature. Thus, given that the .5 transformed logit interval is very simple to compute and has a good performance, it is appropriate to be implemented by most users of the single capture–recapture method.     

Transient animals in a resident population of snow geese: Local emigration or heterogeneity?

The estimation of survival rates from analysis of recapture of individually marked animals assumes that all individuals are equally likely to be re-encountered. This assumption is frequently violated in natural populations due to movements to and from the sampling area. We evaluated potential sources of heterogeneity using data from recaptures of 36000 individually marked female lesser snow geese, Anser c. caerulescens , from an expanding population in northern Manitoba, Canada. By stratifying individuals according to marking age and origin (hatched at the colony or not), we assessed the degree to which variation in apparent survival reflected permanent or temporary differences in emigration and effects of handling. In general, for birds ringed as adults, estimated apparent survival rates were significantly lower during the first year after ringing than in subsequent years. By comparing birds ringed as adults (classified by origin) with those ringed as goslings, we were able to demonstrate that these differences are not due to permanent emigration from the colony by transient individuals or heterogeneity of individual capture probability, but more likely reflect differences among individuals in their response to initial marking. Approximately 25% of birds permanently emigrate from the sampling area following marking.     

Working life expectancies: the case of Finland 1980–2006

Summary.  Working life expectancy is the future time that a person is expected to spend in employment. The paper is concerned with its estimation jointly with the expected times spent in the related states of 'on disability pension' and 'other alive'. The method, which is novel in this field, first estimates year- and age-dependent probabilities of being in the states of interest by large sample multivariate logistic regression. Estimates of probabilities, and subsequently expectancies, are given for the case of Finnish women and men aged 16–64 years for selected years in the period 1980–2001, together with projections for 2006. Since 1996 the decline in the employment of males has largely been due to the increasing popularity of early retirement. It was not due to an increase in disability. There has been no such decline for women, and the working life expectancy for males has been predicted to decline to or to fall below the initially lower figure for females by 2006. Considering that the Finnish population is aging rapidly, these trends could entail serious social and economic consequences for society in the coming years because of a looming shortage in the labour force that could undermine the sustainability of a welfare state.     

Transient animals in a resident population of snow geese: local emigration or heterogeneity?

The estimation of survival rates from analysis of recapture of individually marked animals assumes that all individuals are equally likely to be re-encountered. This assumption is frequently violated in natural populations due to movements to and from the sampling area. We evaluated potential sources of heterogeneity using data from recaptures of 36000 individually marked female lesser snow geese, Anser c. caerulescens , from an expanding population in northern Manitoba, Canada. By stratifying individuals according to marking age and origin (hatched at the colony or not), we assessed the degree to which variation in apparent survival reflected permanent or temporary differences in emigration and effects of handling. In general, for birds ringed as adults, estimated apparent survival rates were significantly lower during the first year after ringing than in subsequent years. By comparing birds ringed as adults (classified by origin) with those ringed as goslings, we were able to demonstrate that these differences are not due to permanent emigration from the colony by transient individuals or heterogeneity of individual capture probability, but more likely reflect differences among individuals in their response to initial marking. Approximately 25% of birds permanently emigrate from the sampling area following marking.     

The use of multi-state capture-recapture models to address questions in evolutionary ecology

Multi-state capture-recapture models can be used to estimate survival rates in populations that are stratified by location or by state variables associated with individual animals. In populations stratified by location, movement probabilities can be estimated and used to test hypotheses relevant to population genetics and evolutionary ecology. When the interest is in state variables, these models permit estimation and testing of hypotheses about state-specific survival probabilities. If the state variable of interest is reproductive activity or success, then the multi-state modeling approach can be used to test hypotheses about life history trade-offs and a possible cost of reproduction.     

Costs of reproduction: Assessing responses to brood size manipulation on life-history and behavioural traits using multi-state capture-recapture models

Costs of reproduction are fundamental trade-offs shaping the evolution of life histories. There has been much interest, discussion and controversy about the nature and type of reproductive costs. The manipulation of reproductive effort (e.g. brood size manipulation) may alter not only life-history traits such as future adult survival rate and future reproductive effort, but also behavioural decisions affecting recapture/resighting and dispersal probabilities. We argue that many previous studies of the costs of reproduction may have erroneously concluded the existence or non-existence of such costs because of their use of local return rates to assess survival. In this paper, we take advantage of the modern multistate capture-recapture methods to highlight how the accurate assessment of the costs of reproduction requires incorporating not only recapture probability, but also behavioural 'state' variables, for example dispersal status and current reproductive investment. The inclusion of state-dependent decisions can radically alter the conclusions drawn regarding the costs of reproduction on future survival or reproductive investment. We illustrate this point by re-analysing data collected to address the question of the costs of reproduction in the collared flycatcher and the great tit. We discuss in some detail the methodological issues and implications of the analytical techniques.