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.     

Effects of neckbands on survival and fidelity of white-fronted and Canada geese captured as non-breeding adults

We conducted an experiment to examine the effect of neckbands, controlling for differences in sex, species and year of study (1991-1997), on probabilities of capture, survival, reporting, and fidelity in non-breeding small Canada ( Branta canadensis hutchinsi ) and white-fronted ( Anser albifrons frontalis ) geese. In Canada's central arctic, we systematically double-marked about half of the individuals from each species with neckbands and legbands, and we marked the other half only with legbands. We considered 48 a priori models that included combinations of sex, species, year, and neckband effects on the four population parameters produced by Burnham's (1993) model, using AIC for model selection. The four best approximating models each included a negative effect of neckbands on survival, and effect size varied among years. True survival probability of neckbanded birds annually ranged from 0.006 to 0.23 and 0.039 to 0.22 (Canada and white-fronted geese, respectively) lower than for conspecifics without neckbands. Changes in estimates of survival probability in neckbanded birds appeared to attenuate more recently, particularly in Canada Geese, a result that we suspect was related to lower retention rates of neckbands. We urge extreme caution in use of neckbands for estimation of certain population parameters, and discourage their use for estimation of unbiased survival probability in these two species.     

The use of auxiliary variables in capture-recapture modelling: An overview

I review the use of auxiliary variables in capture-recapture models for estimation of demographic parameters (e.g. capture probability, population size, survival probability, and recruitment, emigration and immigration numbers). I focus on what has been done in current research and what still needs to be done. Typically in the literature, covariate modelling has made capture and survival probabilities functions of covariates, but there are good reasons also to make other parameters functions of covariates as well. The types of covariates considered include environmental covariates that may vary by occasion but are constant over animals, and individual animal covariates that are usually assumed constant over time. I also discuss the difficulties of using time-dependent individual animal covariates and some possible solutions. Covariates are usually assumed to be measured without error, and that may not be realistic. For closed populations, one approach to modelling heterogeneity in capture probabilities uses observable individual covariates and is thus related to the primary purpose of this paper. The now standard Huggins-Alho approach conditions on the captured animals and then uses a generalized Horvitz-Thompson estimator to estimate population size. This approach has the advantage of simplicity in that one does not have to specify a distribution for the covariates, and the disadvantage is that it does not use the full likelihood to estimate population size. Alternately one could specify a distribution for the covariates and implement a full likelihood approach to inference to estimate the capture function, the covariate probability distribution, and the population size. The general Jolly-Seber open model enables one to estimate capture probability, population sizes, survival rates, and birth numbers. Much of the focus on modelling covariates in program MARK has been for survival and capture probability in the Cormack-Jolly-Seber model and its generalizations (including tag-return models). These models condition on the number of animals marked and released. A related, but distinct, topic is radio telemetry survival modelling that typically uses a modified Kaplan-Meier method and Cox proportional hazards model for auxiliary variables. Recently there has been an emphasis on integration of recruitment in the likelihood, and research on how to implement covariate modelling for recruitment and perhaps population size is needed. The combined open and closed 'robust' design model can also benefit from covariate modelling and some important options have already been implemented into MARK. Many models are usually fitted to one data set. This has necessitated development of model selection criteria based on the AIC (Akaike Information Criteria) and the alternative of averaging over reasonable models. The special problems of estimating over-dispersion when covariates are included in the model and then adjusting for over-dispersion in model selection could benefit from further research.     

The use of auxiliary variables in capture-recapture modelling: an overview

I review the use of auxiliary variables in capture-recapture models for estimation of demographic parameters (e.g. capture probability, population size, survival probability, and recruitment, emigration and immigration numbers). I focus on what has been done in current research and what still needs to be done. Typically in the literature, covariate modelling has made capture and survival probabilities functions of covariates, but there are good reasons also to make other parameters functions of covariates as well. The types of covariates considered include environmental covariates that may vary by occasion but are constant over animals, and individual animal covariates that are usually assumed constant over time. I also discuss the difficulties of using time-dependent individual animal covariates and some possible solutions. Covariates are usually assumed to be measured without error, and that may not be realistic. For closed populations, one approach to modelling heterogeneity in capture probabilities uses observable individual covariates and is thus related to the primary purpose of this paper. The now standard Huggins-Alho approach conditions on the captured animals and then uses a generalized Horvitz-Thompson estimator to estimate population size. This approach has the advantage of simplicity in that one does not have to specify a distribution for the covariates, and the disadvantage is that it does not use the full likelihood to estimate population size. Alternately one could specify a distribution for the covariates and implement a full likelihood approach to inference to estimate the capture function, the covariate probability distribution, and the population size. The general Jolly-Seber open model enables one to estimate capture probability, population sizes, survival rates, and birth numbers. Much of the focus on modelling covariates in program MARK has been for survival and capture probability in the Cormack-Jolly-Seber model and its generalizations (including tag-return models). These models condition on the number of animals marked and released. A related, but distinct, topic is radio telemetry survival modelling that typically uses a modified Kaplan-Meier method and Cox proportional hazards model for auxiliary variables. Recently there has been an emphasis on integration of recruitment in the likelihood, and research on how to implement covariate modelling for recruitment and perhaps population size is needed. The combined open and closed 'robust' design model can also benefit from covariate modelling and some important options have already been implemented into MARK. Many models are usually fitted to one data set. This has necessitated development of model selection criteria based on the AIC (Akaike Information Criteria) and the alternative of averaging over reasonable models. The special problems of estimating over-dispersion when covariates are included in the model and then adjusting for over-dispersion in model selection could benefit from further research.     

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.     

Modelling postfledging survival and age-specific breeding probabilities in species with delayed maturity: A case study of Roseate Terns at Falkner Island,Connecticut

We modelled postfledging survival and age-specific breeding probabilities in endangered Roseate Terns ( Sterna dougallii ) at Falkner Island, Connecticut, USA using capture-recapture data from 1988-1998 of birds ringed as chicks and as adults. While no individuals bred as 2-year-olds during this period, about three-quarters of the young that survived and returned as 3-year-olds nested, and virtually all surviving birds had begun breeding by the time they reached 5 years of age. We found no evidence of temporal variation age of first breeding of birds from different cohorts. There was significant temporal variation in the annual survival of adults and the survival over the typical 3-year maturation period of prebreeding birds, with extremely low values for both groups from the 1991 breeding season. The estimated overwinter survival rate (0.62) for adults from 1991-1992 was about three-quarters the usual rate of about 0.83, but the low survival of fledglings from 1991 resulted in less than 25% of the otherwise expected number of young from that cohort returning as breeding birds; this suggests that fledglings suffered a greater proportional decrease in survival than did adults. The survival estimates of young from 1989 and 1990 show that these cohorts were not negatively influenced by the events that decimated the young from 1991, and the young from 1992 and 1993 had above-average survival estimates. The apparent decrease since 1996 in development of fidelity of new recruits to this site is suspected to be due mainly to nocturnal disturbance and predation of chicks causing low productivity.     

Survival rates of breeding common gulls in Estonia

The aim of the present paper was to estimate the survival rates of breeding common gulls, using mark-recapture data, gathered in 1968-1983 (16 sampling periods) in Estonia. We analyzed effects of age (breeding experience), year and sex on survival. Every year we observed more than 90% of the breeders and ringed about 95% of the nestlings. Two samples of gulls were used in the analyses. The first sample (347 individuals) consisted of birds thought to be first-time breeders when first observed in colony. The second sample (1269 individuals) may contain birds which have nested earlier. In the first sample, we did not detect any influence of age and sex on survival, but time dependence was significant and can be explained by winter severity. In cold winters the survival was lower (0.865) than in normal (0.896) and warm (0.929) winters. We suspect that the age effect on survival rate remained undetected owing to sparse data. In the second sample, we detected age- and time-dependent survival for both sexes. We also found differences between the sexes in recapture probability (in both samples). This was probably caused by lower site tenacity of females.     

Estimating nest site fidelity of adult female black brant with multi-state modeling and geographic information systems

Nest site fidelity of adult female black brant breeding at the Tutakoke River, Alaska was evaluated from 1987 to 1993 by recording nest locations of brant marked (approx. 1500) with individually coded tarsal tags. We used two approaches to study fidelity. First, we examined fidelity to four geographic strata within the Tutakoke River colony. For our second analysis approach, we used ARC/INFO to map and measure distances between successive nesting attempts and then estimated the probability of fidelity to within 200 m of the previous nest site. We used program MSSURVIV to estimate movement probabilities and to test hypotheses about fidelity. Both of our analysis approaches indicate that female black brant exhibit a high (>0.72) probability of fidelity to previous nest sites. Our estimates of fidelity were not biased by the confounding of detection, survival and movement probabilities that have plagued previous studies of fidelity.     

On the use of secondary capture-recapture samples to estimate temporary emigration and breeding proportions

The use of the Cormack-Jolly-Seber model under a standard sampling scheme of one sample per time period, when the Jolly-Seber assumption that all emigration is permanent does not hold, leads to the confounding of temporary emigration probabilities with capture probabilities. This biases the estimates of capture probability when temporary emigration is a completely random process, and both capture and survival probabilities when there is a temporary trap response in temporary emigration, or it is Markovian. The use of secondary capture samples over a shorter interval within each period, during which the population is assumed to be closed (Pollock's robust design), provides a second source of information on capture probabilities. This solves the confounding problem, and thus temporary emigration probabilities can be estimated. This process can be accomplished in an ad hoc fashion for completely random temporary emigration and to some extent in the temporary trap response case, but modelling the complete sampling process provides more flexibility and permits direct estimation of variances. For the case of Markovian temporary emigration, a full likelihood is required.     

On the use of secondary capture-recapture samples to estimate temporary emigration and breeding proportions

The use of the Cormack-Jolly-Seber model under a standard sampling scheme of one sample per time period, when the Jolly-Seber assumption that all emigration is permanent does not hold, leads to the confounding of temporary emigration probabilities with capture probabilities. This biases the estimates of capture probability when temporary emigration is a completely random process, and both capture and survival probabilities when there is a temporary trap response in temporary emigration, or it is Markovian. The use of secondary capture samples over a shorter interval within each period, during which the population is assumed to be closed (Pollock's robust design), provides a second source of information on capture probabilities. This solves the confounding problem, and thus temporary emigration probabilities can be estimated. This process can be accomplished in an ad hoc fashion for completely random temporary emigration and to some extent in the temporary trap response case, but modelling the complete sampling process provides more flexibility and permits direct estimation of variances. For the case of Markovian temporary emigration, a full likelihood is required.     

Probability models on horse-race outcomes

SUMMARY A number of models have been examined for modelling probability based on rankings. Most prominent among these are the gamma and normal probability models. The accuracy of these models in predicting the outcomes of horse races is investigated in this paper. The parameters of these models are estimated by the maximum likelihood method, using the information on win pool fractions. These models are used to estimate the probabilities that race entrants finish second or third in a race. These probabilities are then compared with the corresponding objective probabilities estimated from actual race outcomes. The data are obtained from over 15 000 races. it is found that all the models tend to overestimate the probability of a horse finishing second or third when the horse has a high probability of such a result, but underestimate the probability of a horse finishing second or third when this probability is low.     

A Multiple State Model for Disability Using the Decomposition of Death Probabilities and Cross-Sectional Data

ABSTRACT

We split the components corresponding to the disability-free survival probability, and the disability survival probability. Our analysis is conducted for men and women separately, for age groups over 64 years. We discuss the estimation of a multiple state model under several scenarios when only a single survey of cross-sectional data is available. The conclusions are used to discuss the disability level of the Spanish elderly population and are helpful to develop welfare programs and insurance products.     

Regression Analysis for Multistate Models Based on a Pseudo-value Approach, with Applications to Bone Marrow Transplantation Studies

Abstract.  Typically, regression analysis for multistate models has been based on regression models for the transition intensities. These models lead to highly nonlinear and very complex models for the effects of covariates on state occupation probabilities. We present a technique that models the state occupation or transition probabilities in a multistate model directly. The method is based on the pseudo-values from a jackknife statistic constructed from non-parametric estimators for the probability in question. These pseudo-values are used as outcome variables in a generalized estimating equation to obtain estimates of model parameters. We examine this approach and its properties in detail for two special multistate model probabilities, the cumulative incidence function in competing risks and the current leukaemia-free survival used in bone marrow transplants. The latter is the probability a patient is alive and in either a first or second post-transplant remission. The techniques are illustrated on a dataset of leukaemia patients given a marrow transplant. We also discuss extensions of the model that are of current research interest.     

Analysing drug abuse with British Crime Survey data: modelling and questionnaire design issues

We use the British Crime Survey (BCS) to analyse the demand for illicit drugs and the implications of drug use for the probability of subsequent unemployment. We demonstrate that the BCS questionnaire has a serious design flaw for this purpose, and we propose some simple modifications. We also develop a modelling technique that is suitable for existing BCS data and apply it to the 1994 and 1996 samples. We find evidence that soft drug use is associated with a greatly increased probability of later hard drug use and that past drug use is associated with increased probabilities of unemployment.     

A marginalized diffusion model for estimating age at first lower endoscopy use from current status data

Summary.  We propose an approach for estimating the age at first lower endoscopy examination from current status data that were collected via two series of cross-sectional surveys. To model the national probability of ever having a lower endoscopy examination, we incorporate birth cohort effects into a mixed influence diffusion model. We link a state-specific model to the national level diffusion model by using a marginalized modelling approach. In future research, results from our model will be used as microsimulation model inputs to estimate the contribution of endoscopy examinations to observed changes in colorectal cancer incidence and mortality.     

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.     

Influence of behavioural tactics on recruitment and reproductive trajectory in the kittiwake

Many studies have provided evidence that, in birds, inexperienced breeders have a lower probability of breeding successfully. This is often explained by lack of skills and knowledge, and sometimes late laying dates in the first breeding attempt. There is growing evidence that in many species with deferred reproduction, some prebreeders attend breeding places, acquire territories and form pairs. Several behavioural tactics assumed to be associated with territory acquisition have been described in different species. These tactics may influence the probability of recruiting in the breeding segment of the population, age of first breeding, and reproductive success in the first breeding attempt. Here we addressed the influence of behaviour ('squatting') during the prebreeding period on demographic parameters (survival and recruitment probability) in a long-lived colonial seabird species: the kittiwake. We also investigated the influence of behaviour on reproductive trajectory. Squatters have a higher survival and recruitment probability, and a higher probability of breeding successfully in the first breeding attempt in all age-classes where this category is represented. The influence of behaviour is mainly expressed in the first reproduction. However, there is a relationship between breeding success in the first occasion and subsequent occasions. The influence of breeding success in the first breeding attempt on the rest of the trajectory may indirectly reflect the influence of behaviour on breeding success in the first occasion. The shape of the reproductive trajectory is influenced by behaviour and age of first breeding. There is substantial individual variation from the mean reproductive trajectory, which is accounted for by heterogeneity in performance among individuals in the first attempt, but there is no evidence of individual heterogeneity in the rate of change over time in performance in subsequent breeding occasions     

Influence of behavioural tactics on recruitment and reproductive trajectory in the kittiwake

Many studies have provided evidence that, in birds, inexperienced breeders have a lower probability of breeding successfully. This is often explained by lack of skills and knowledge, and sometimes late laying dates in the first breeding attempt. There is growing evidence that in many species with deferred reproduction, some prebreeders attend breeding places, acquire territories and form pairs. Several behavioural tactics assumed to be associated with territory acquisition have been described in different species. These tactics may influence the probability of recruiting in the breeding segment of the population, age of first breeding, and reproductive success in the first breeding attempt. Here we addressed the influence of behaviour ('squatting') during the prebreeding period on demographic parameters (survival and recruitment probability) in a long-lived colonial seabird species: the kittiwake. We also investigated the influence of behaviour on reproductive trajectory. Squatters have a higher survival and recruitment probability, and a higher probability of breeding successfully in the first breeding attempt in all age-classes where this category is represented. The influence of behaviour is mainly expressed in the first reproduction. However, there is a relationship between breeding success in the first occasion and subsequent occasions. The influence of breeding success in the first breeding attempt on the rest of the trajectory may indirectly reflect the influence of behaviour on breeding success in the first occasion. The shape of the reproductive trajectory is influenced by behaviour and age of first breeding. There is substantial individual variation from the mean reproductive trajectory, which is accounted for by heterogeneity in performance among individuals in the first attempt, but there is no evidence of individual heterogeneity in the rate of change over time in performance in subsequent breeding occasions     

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.     

A New lifetime model for multivariate survival data with a surviving fraction

In this paper we propose a new lifetime model for multivariate survival data with a surviving fraction. We develop this model assuming that there are m types of unobservable competing risks, where each risk is related to a time of the occurrence of an event of interest. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis for the proposed model. We also perform a simulation study in order to analyse the frequentist coverage probabilities of credible interval derived from posteriors. Our modelling is illustrated through a real data set.