Survival of bowhead whales,Balaena mysticetus,estimated from 1981-1998 photoidentification data

Annual survival probability of bowhead whales, Balaena mysticetus, was estimated using both Bayesian and maximum likelihood implementations of Cormack and Jolly-Seber (JS) models for capture-recapture estimation in open populations and reduced-parameter generalizations of these models. Aerial photographs of naturally marked bowheads collected between 1981 and 1998 provided the data. The marked whales first photographed in a particular year provided the initial 'capture' and 'release' of those marked whales and photographs in subsequent years the 'recaptures'. The Cormack model, often called the Cormack-Jolly-Seber (CJS) model, and the program MARK were used to identify the model with a single survival and time-varying capture probabilities as the most appropriate for these data. When survival was constrained to be one or less, the maximum likelihood estimate computed by MARK was one, invalidating confidence interval computations based on the asymptotic standard error or profile likelihood. A Bayesian Markov chain Monte Carlo (MCMC) implementation of the model was used to produce a posterior distribution for annual survival. The corresponding reduced-parameter JS model was also fit via MCMC because it is the more appropriate of the two models for these photoidentification data. Because the CJS model ignores much of the information on capture probabilities provided by the data, its results are less precise and more sensitive to the prior distributions used than results from the JS model. With priors for annual survival and capture probabilities uniform from 0 to 1, the posterior mean for bowhead survival rate from the JS model is 0.984, and 95% of the posterior probability lies between 0.948 and 1. This high estimated survival rate is consistent with other bowhead life history data.     

An extension of the Cormack-Jolly-Seber model for continuous covariates with application to Microtus pennsylvanicus

Recent developments in the Cormack-Jolly-Seber (CJS) model for analyzing capture-recapture data have focused on allowing the capture and survival rates to vary between individuals. Several methods have been developed in which capture and survival are functions of auxiliary variables that may be discrete, constant over time, or apply to the population as a whole, but the problem has not been solved for continuous covariates that vary with both time and individual. This article proposes a new method to handle such covariates by modeling changes over time via a diffusion process and using logistic functions to link the variable to the CJS capture and survival rates. Bayesian methods are used to estimate the model parameters. The method is applied to study the effect of body mass on the survival of the North American meadow vole, Microtus pennsylvanicus.     

Understanding the impact of correlation within pair‐bonds on Cormack–Jolly–Seber models

1. The Cormack–Jolly–Seber (CJS) model and its extensions have been widely applied to the study of animal survival rates in open populations. The model assumes that individuals within the population of interest have independent fates. It is, however, highly unlikely that a pair of animals which have formed a long‐term pairing have dissociated fates.
2. We examine a model extension which allows animals who have formed a pair‐bond to have correlated survival and recapture fates. Using the proposed extension to generate data, we conduct a simulation study exploring the impact that correlated fate data has on inference from the CJS model. We compute Monte Carlo estimates for the bias, range, and standard errors of the parameters of the CJS model for data with varying degrees of survival correlation between mates. Furthermore, we study the likelihood ratio test of sex effects within the CJS model by simulating densities of the deviance. Finally, we estimate the variance inflation factor c^ for CJS models that incorporate sex‐specific heterogeneity.
3. Our study shows that correlated fates between mated animals may result in underestimated standard errors for parsimonious models, significantly deflated likelihood ratio test statistics, and underestimated values of c^ for models taking sex‐specific effects into account.
4. Underestimated standard errors can result in lowered coverage of confidence intervals. Moreover, deflated test statistics will provide overly conservative test results. Finally, underestimated variance inflation factors can lead researchers to make incorrect conclusions about the level of extra‐binomial variation present in their data.

     

Cormack–Jolly–Seber model with environmental covariates: A P‐spline approach

In capture–recapture models, survival and capture probabilities can be modelled as functions of time‐varying covariates, such as temperature or rainfall. The Cormack–Jolly–Seber (CJS) model allows for flexible modelling of these covariates; however, the functional relationship may not be linear. We extend the CJS model by semi‐parametrically modelling capture and survival probabilities using a frequentist approach via P‐splines techniques. We investigate the performance of the estimators by conducting simulation studies. We also apply and compare these models with known semi‐parametric Bayesian approaches on simulated and real data sets.     

Combining capture–recapture data and known ages allows estimation of age‐dependent survival rates

In many animal populations, demographic parameters such as survival and recruitment vary markedly with age, as do parameters related to sampling, such as capture probability. Failing to account for such variation can result in biased estimates of population‐level rates. However, estimating age‐dependent survival rates can be challenging because ages of individuals are rarely known unless tagging is done at birth. For many species, it is possible to infer age based on size. In capture–recapture studies of such species, it is possible to use a growth model to infer the age at first capture of individuals. We show how to build estimates of age‐dependent survival into a capture–mark–recapture model based on data obtained in a capture–recapture study. We first show how estimates of age based on length increments closely match those based on definitive aging methods. In simulated analyses, we show that both individual ages and age‐dependent survival rates estimated from simulated data closely match true values. With our approach, we are able to estimate the age‐specific apparent survival rates of Murray and trout cod in the Murray River, Australia. Our model structure provides a flexible framework within which to investigate various aspects of how survival varies with age and will have extensions within a wide range of ecological studies of animals where age can be estimated based on size.     

Estimation of rates of births, deaths, and immigration from mark-recapture data

Summary .  The analysis of mark–recapture data is undergoing a period of development and expansion. Here we contribute to that by presenting a model which includes both births and immigration, as well as the usual deaths. Data come from a long-term study of the willow tit ( Parus montanus ), where we can assume that all births are recorded, and hence immigrants can also be identified as birds captured as adults for the first time. We model the rates of immigration, birth rate per parent, and death rates of juveniles and adults. Using a hierarchical model allows us to incorporate annual variation in these parameters. The model is fitted to the data using Markov chain Monte Carlo, as a Bayesian analysis. In addition to the model fitting, we also check several aspects of the model fit, in particular whether survival varies with age or immigrant status, and whether capture probability is affected by previous capture history. The latter check is important, as independence of capture histories is a key assumption that simplifies the model considerably. Here we find that the capture probability depends strongly on whether the individual was captured in the previous year.     

Open capture-recapture models with heterogeneity: I. Cormack-Jolly-Seber model

In open population capture-recapture studies, it is usually assumed that similar animals (e.g., of the same sex and age group) have similar survival rates and capture probabilities. These assumptions are generally perceived to be an oversimplification, and they can lead to incorrect model selection and biased parameter estimates. Allowing for individual variability in survival and capture probabilities among apparently similar animals is now becoming possible, due to advances in closed population models and improved computing power. This article presents a flexible framework of likelihood-based models which allow for individual heterogeneity in survival and capture rates. Heterogeneity is modeled using finite mixtures, which have enough flexibility of distribution shape to accommodate a wide variety of different patterns of individual variation. The models condition on the first capture of each animal, and include as a special case the Cormack-Jolly-Seber model. Model selection is done either using Akaike's information criterion or by likelihood ratio tests, making available checks of different influences on survival rates. Bias in parameter estimates is reduced by including individual heterogeneity. Model selection and bias reduction are important in population studies and for making informed management decisions.     

Effects of capture,shearing, and release on the ecology and behavior of wild vicuñas

The goals of sustainable use of wildlife include minimizing long term deleterious impacts of management. We evaluated the ethoecological and demographic responses of wild vicuñas (Vicugna vicugna) to capture, shearing, and release in northern Argentina, as well as effects on behavior, by comparing captured and shorn versus non-captured animals for 2 yr after capture events. We observed subtle and short-term changes in the movement behavior of individuals, likely due to thermal and behavioral stress following capture. We did not observe changes in survival and birth rates, social organization, or distribution of animals following capture. Therefore, we concluded that the capture techniques used resulted in low impacts on the wild vicuña population. © 2011 The Wildlife Society.     

A spatial open-population capture-recapture model

A spatial open-population capture-recapture model is described that extends both the non-spatial open-population model of Schwarz and Arnason and the spatially explicit closed-population model of Borchers and Efford. The superpopulation of animals available for detection at some time during a study is conceived as a two-dimensional Poisson point process. Individual probabilities of birth and death follow the conventional open-population model. Movement between sampling times may be modeled with a dispersal kernel using a recursive Markovian algorithm. Observations arise from distance-dependent sampling at an array of detectors. As in the closed-population spatial model, the observed data likelihood relies on integration over the unknown animal locations; maximization of this likelihood yields estimates of the birth, death, movement, and detection parameters. The models were fitted to data from a live-trapping study of brushtail possums (Trichosurus vulpecula) in New Zealand. Simulations confirmed that spatial modeling can greatly reduce the bias of capture-recapture survival estimates and that there is a degree of robustness to misspecification of the dispersal kernel. An R package is available that includes various extensions.     

Demographic consequences of changing body size in a terrestrial salamander

Changes in climate can alter individual body size, and the resulting shifts in reproduction and survival are expected to impact population dynamics and viability. However, appropriate methods to account for size‐dependent demographic changes are needed, especially in understudied yet threatened groups such as amphibians. We investigated individual‐ and population‐level demographic effects of changes in body size for a terrestrial salamander using capture–mark–recapture data. For our analysis, we implemented an integral projection model parameterized with capture–recapture likelihood estimates from a Bayesian framework. Our study combines survival and growth data from a single dataset to quantify the influence of size on survival while including different sources of uncertainty around these parameters, demonstrating how selective forces can be studied in populations with limited data and incomplete recaptures. We found a strong dependency of the population growth rate on changes in individual size, mediated by potential changes in selection on mean body size and on maximum body size. Our approach of simultaneous parameter estimation can be extended across taxa to identify eco‐evolutionary mechanisms acting on size‐specific vital rates, and thus shaping population dynamics and viability.     

Movement patterns and study area boundaries: influences on survival estimation in capture–mark–recapture studies

The inability to account for the availability of individuals in the study area during capture–mark–recapture (CMR) studies and the resultant confounding of parameter estimates can make correct interpretation of CMR model parameter estimates difficult. Although important advances based on the Cormack–Jolly–Seber (CJS) model have resulted in estimators of true survival that work by unconfounding either death or recapture probability from availability for capture in the study area, these methods rely on the researcher's ability to select a method that is correctly matched to emigration patterns in the population. If incorrect assumptions regarding site fidelity (non‐movement) are made, it may be difficult or impossible as well as costly to change the study design once the incorrect assumption is discovered. Subtleties in characteristics of movement (e.g. life history‐dependent emigration, nomads vs territory holders) can lead to mixtures in the probability of being available for capture among members of the same population. The result of these mixtures may be only a partial unconfounding of emigration from other CMR model parameters. Biologically‐based differences in individual movement can combine with constraints on study design to further complicate the problem. Because of the intricacies of movement and its interaction with other parameters in CMR models, quantification of and solutions to these problems are needed. Based on our work with stream‐dwelling populations of Atlantic salmon Salmo salar, we used a simulation approach to evaluate existing CMR models under various mixtures of movement probabilities. The Barker joint data model provided unbiased estimates of true survival under all conditions tested. The CJS and robust design models provided similarly unbiased estimates of true survival but only when emigration information could be incorporated directly into individual encounter histories. For the robust design model, Markovian emigration (future availability for capture depends on an individual's current location) was a difficult emigration pattern to detect unless survival and especially recapture probability were high. Additionally, when local movement was high relative to study area boundaries and movement became more diffuse (e.g. a random walk), local movement and permanent emigration were difficult to distinguish and had consequences for correctly interpreting the survival parameter being estimated (apparent survival vs true survival).     

A temporally stratified extension of space-for-time Cormack–Jolly–Seber for migratory animals

Understanding drivers of temporal variation in demographic parameters is a central goal of mark-recapture analysis. To estimate the survival of migrating animal populations in migration corridors, space-for-time mark–recapture models employ discrete sampling locations in space to monitor marked populations as they move past monitoring sites, rather than the standard practice of using fixed sampling points in time. Because these models focus on estimating survival over discrete spatial segments, model parameters are implicitly integrated over the temporal dimension. Furthermore, modeling the effect of time-varying covariates on model parameters is complicated by unknown passage times for individuals that are not detected at monitoring sites. To overcome these limitations, we extended the Cormack–Jolly–Seber (CJS) framework to estimate temporally stratified survival and capture probabilities by including a discretized arrival time process in a Bayesian framework. We allow for flexibility in the model form by including temporally stratified covariates and hierarchical structures. In addition, we provide tools for assessing model fit and comparing among alternative structural models for the parameters. We demonstrate our framework by fitting three competing models to estimate daily survival, capture, and arrival probabilities at four hydroelectric dams for over 200 000 individually tagged migratory juvenile salmon released into the Snake River, USA.     

Effect of Net-Gun Capture on Survival of Mule Deer

Capture techniques to deploy radio-collars often risk mortality and injury to the animal. Capture-induced mortality can affect population sizes but also introduces bias in survival estimates based on data from captured animals. In recent years, a large-scale research and monitoring project in Utah, USA, has involved capturing and radio-collaring hundreds of mule deer (Odocoileus hemionus), a species of great interest in large parts of North America. Our objective was to investigate how the survival rates of these mule deer were affected by capture and handling. During winters of 2014–2018, an experienced capture crew net-gunned and fitted 1,805 animals with global positioning system (GPS)-collars. We estimated survival rates during the first 6 weeks after capture using Cox proportional hazard regression, and compared the survival rates of animals that were captured in a particular year to those of animals that were not captured but fitted with a GPS-collar in a previous year. We used a model selection framework to evaluate how long survival rates of captured animals were different from those of animals that were not captured. Our results indicated that weekly survival rates of captured animals were 0.985 ± 0.003 (SE), 0.988 ± 0.002, and 0.990 ± 0.001 in weeks 1, 2 and 3, respectively. Weekly survival rates of captured deer during weeks 4–6 were 0.993 ± 0.001, the same as those of deer that were not captured at the same time. Furthermore, post-capture survival rates were positively influenced by body size and negatively influenced by age. We conclude that the mortality resulting from helicopter capture was low but recommend comparing newly captured and previously captured individuals to examine what proportion of observed mortality is likely capture-related. © 2020 The Wildlife Society.     

Using dynamic N‐mixture models to test cavity limitation on northern flying squirrel demographic parameters using experimental nest box supplementation

Dynamic N‐mixture models have been recently developed to estimate demographic parameters of unmarked individuals while accounting for imperfect detection. We propose an application of the Dail and Madsen ( 2011 : Biometrics, 67 , 577–587) dynamic N‐mixture model in a manipulative experiment using a before‐after control‐impact design (BACI). Specifically, we tested the hypothesis of cavity limitation of a cavity specialist species, the northern flying squirrel, using nest box supplementation on half of 56 trapping sites. Our main purpose was to evaluate the impact of an increase in cavity availability on flying squirrel population dynamics in deciduous stands in northwestern Québec with the dynamic N‐mixture model. We compared abundance estimates from this recent approach with those from classic capture–mark–recapture models and generalized linear models. We compared apparent survival estimates with those from Cormack–Jolly–Seber (CJS) models. Average recruitment rate was 6 individuals per site after 4 years. Nevertheless, we found no effect of cavity supplementation on apparent survival and recruitment rates of flying squirrels. Contrary to our expectations, initial abundance was not affected by conifer basal area (food availability) and was negatively affected by snag basal area (cavity availability). Northern flying squirrel population dynamics are not influenced by cavity availability at our deciduous sites. Consequently, we suggest that this species should not be considered an indicator of old forest attributes in our study area, especially in view of apparent wide population fluctuations across years. Abundance estimates from N‐mixture models were similar to those from capture–mark–recapture models, although the latter had greater precision. Generalized linear mixed models produced lower abundance estimates, but revealed the same relationship between abundance and snag basal area. Apparent survival estimates from N‐mixture models were higher and less precise than those from CJS models. However, N‐mixture models can be particularly useful to evaluate management effects on animal populations, especially for species that are difficult to detect in situations where individuals cannot be uniquely identified. They also allow investigating the effects of covariates at the site level, when low recapture rates would require restricting classic CMR analyses to a subset of sites with the most captures.     

Inferences about population dynamics from count data using multistate models: a comparison to capture–recapture approaches

Wildlife populations consist of individuals that contribute disproportionately to growth and viability. Understanding a population's spatial and temporal dynamics requires estimates of abundance and demographic rates that account for this heterogeneity. Estimating these quantities can be difficult, requiring years of intensive data collection. Often, this is accomplished through the capture and recapture of individual animals, which is generally only feasible at a limited number of locations. In contrast, N‐mixture models allow for the estimation of abundance, and spatial variation in abundance, from count data alone. We extend recently developed multistate, open population N‐mixture models, which can additionally estimate demographic rates based on an organism's life history characteristics. In our extension, we develop an approach to account for the case where not all individuals can be assigned to a state during sampling. Using only state‐specific count data, we show how our model can be used to estimate local population abundance, as well as density‐dependent recruitment rates and state‐specific survival. We apply our model to a population of black‐throated blue warblers (Setophaga caerulescens) that have been surveyed for 25 years on their breeding grounds at the Hubbard Brook Experimental Forest in New Hampshire, USA. The intensive data collection efforts allow us to compare our estimates to estimates derived from capture–recapture data. Our model performed well in estimating population abundance and density‐dependent rates of annual recruitment/immigration. Estimates of local carrying capacity and per capita recruitment of yearlings were consistent with those published in other studies. However, our model moderately underestimated annual survival probability of yearling and adult females and severely underestimates survival probabilities for both of these male stages. The most accurate and precise estimates will necessarily require some amount of intensive data collection efforts (such as capture–recapture). Integrated population models that combine data from both intensive and extensive sources are likely to be the most efficient approach for estimating demographic rates at large spatial and temporal scales.     

Survival analysis of mortality in pre-weaning kids of Sirohi goat

Pre-weaning animals exit a flock through death induced by various reasons, causing significant economic losses to the goat producers. In this study, we investigated the survival from birth to weaning of Sirohi goat kids within framework of the survival analysis. Kid records were accessed from 1997 to 2017, with the information on 4417 pre-weaning animals of farmed Sirohi goat native to the Rajasthan State of India. A multivariable Cox regression was fitted to the data after checking the assumptions of regression. The explanatory variables were sex, type of birth, season of birth, birthweight, doe weight at kidding and year of birth. Model selection eliminated doe weight from the model, and sex, type of birth, season of birth, birthweight and year of birth were retained in the model. With model calibration also, these five covariates were retained in the model. The mortality on the first day after birth was 0.3%, constituting 3.5% of all pre-weaning mortality. The mortality until the end of weaning period was 7.8%. Regression analysis revealed that the higher birthweight at kidding was associated with reduced hazard of death among the kids. Male kids had higher hazards of death compared with female kids. The single-born kids had lower risks of death compared with twin-born kids after accounting for heterogeneity. The winter season had a very high adverse effect on the survival of the kids. With each passing year, risks of death decreased. The results of this study indicate that better survival of kids can be achieved by controlling both environmental and animal-related factors.     

Accounting for tagging‐to‐harvest mortality in a Brownie tag‐recovery model by incorporating radio‐telemetry data

The Brownie tag‐recovery model is useful for estimating harvest rates but assumes all tagged individuals survive to the first hunting season; otherwise, mortality between time of tagging and the hunting season will cause the Brownie estimator to be negatively biased. Alternatively, fitting animals with radio transmitters can be used to accurately estimate harvest rate but may be more costly. We developed a joint model to estimate harvest and annual survival rates that combines known‐fate data from animals fitted with transmitters to estimate the probability of surviving the period from capture to the first hunting season, and data from reward‐tagged animals in a Brownie tag‐recovery model. We evaluated bias and precision of the joint estimator, and how to optimally allocate effort between animals fitted with radio transmitters and inexpensive ear tags or leg bands. Tagging‐to‐harvest survival rates from >20 individuals with radio transmitters combined with 50–100 reward tags resulted in an unbiased and precise estimator of harvest rates. In addition, the joint model can test whether transmitters affect an individual's probability of being harvested. We illustrate application of the model using data from wild turkey, Meleagris gallapavo, to estimate harvest rates, and data from white‐tailed deer, Odocoileus virginianus, to evaluate whether the presence of a visible radio transmitter is related to the probability of a deer being harvested. The joint known‐fate tag‐recovery model eliminates the requirement to capture and mark animals immediately prior to the hunting season to obtain accurate and precise estimates of harvest rate. In addition, the joint model can assess whether marking animals with radio transmitters affects the individual's probability of being harvested, caused by hunter selectivity or changes in a marked animal's behavior.     

Stopover of migrating birds: simultaneous analysis of different marking methods enhances the power of capture–recapture analyses

Analyses of stopover parameters of migrating birds with Cormack–Jolly–Seber (CJS) capture–recapture models often suffer from low precision due to sparse data sets. Low recapture rates result in low power to detect violations of the underlying assumptions and factors influencing stopover behaviour. We studied stopover behaviour of Palearctic migrant passerines in an oasis in Mauritania, West Africa. Using capture–recapture data and systematic observations of colour-ringed birds, we analysed the effect of increased sample size on probability of stay and recapture probability and the influence of a possible trap response on these parameters. We analysed capture–recapture data with the conventional CJS model and compared the results with those from a multistate model using in addition resighting data. The analyses including resighting data resulted in a higher precision of the estimates of the probabilities of stay compared to analyses using only capture–recapture data of the same individuals. Moreover, the power to detect transients was substantially enhanced. Capture had no effect on the estimates of probability to stay and recapture probability; birds did not leave the stopover site or avoid nets as a reaction to capture. The estimates of probability of stay were up to 15.7% higher when resighting data were included, probably due to the higher power to detect transients and the elimination of the bias induced by non-random temporary emigration when both data types are considered. As a consequence, stopover duration would have been underestimated when only the capture–recapture data were available. We conclude that additional resightings of colour ringed birds can produce more accurate results needed for enhancing our understanding of stopover ecology of migrants. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users. From the Swiss Ornithological Institute project on bird migration across the Sahara.     

SURVIVORSHIP PATTERNS IN THREE SPECIES OF CAPTIVE CETACEANS

Survival rates for three species of captive cetaceans are reported, based on records of dates of capture, birth, and death of individual animals. The annual survival rate was 0.93 for bottlenose dolphins and killer whales and 0.94 for white whales. Confidence limits of these estimates are discussed. Differences in survival rates between institutions were significant for bottlenose dolphins only. Calf survival for bottlenose dolphins was lower than non-calf survival. Survivorship of male killer whales was significantly less than survivorship of female killer whales; sex-specific survival rates were similar for the other two species. Estimates of average or maximum longevity alone were not useful in comparing rates of survival. Because survival in the first year of captivity may be lower than subsequent years, estimates of the expected lifespan, based on data from the first few years of captivity, may be biased.     

Constant-parameter capture-recapture models

Jolly (1982, Biometrics 38, 301-321) presented modifications of the Jolly-Seber model for capture-recapture data, which assume constant survival and/or capture rates. Where appropriate, because of the reduced number of parameters, these models lead to more efficient estimators than the Jolly-Seber model. The tests to compare models given by Jolly do not make complete use of the data, and we present here the appropriate modifications, and also indicate how to carry out goodness-of-fit tests which utilize individual capture history information. We also describe analogous models for the case where young and adult animals are tagged. The availability of computer programs to perform the analysis is noted, and examples are given using output from these programs.