A Bayesian estimate of harbour seal survival using sparse photo-identification data

Survival rates have rarely been estimated for pinniped populations due to the constraints of obtaining unbiased sample data. In this paper, we present an approach for estimating survival probabilities from individual recognition data in the form of photographic documentation of pelage patterns. This method was applied to estimate adult (age 2+) survival for harbour seals in the Moray Firth, NE Scotland. An astronomical telescope was used to obtain digital images of individual seals, and high-quality images were used to document the annual presence or absence of individuals at a single haul-out site over a 4-year period. A total of 95 females, 10 males and 57 individuals of unknown sex were photographically documented during the study period. Survival and recapture probabilities were estimated using Jolly–Seber mark–recapture models in a Bayesian statistical framework. Computer-intensive Markov Chain Monte Carlo methods were used to estimate the probability distributions for the survival and recapture probabilities, conveying the full extent of the uncertainty resulting from unavoidably sparse observational data. The deviance information criterion was used to identify a best-fitting model that accounted for variation in the probability of capture between sexes, with constant survival. The model estimated adult survival as 0.98 (95% probability interval of 0.94–1.00) using our photo-identification data alone, and 0.97 (0.92–0.99) with the use of an informative prior distribution based on previously published estimates of harbour seal survival. This paper represents the first survival estimate for harbour seals in the UK, and the first survival estimate using photo-identification data in any species of pinniped.     

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.     

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.     

Capture–recapture models with heterogeneity to study survival senescence in the wild

Detecting senescence in wild populations and estimating its strength raise three challenges. First, in the presence of individual heterogeneity in survival probability, the proportion of high‐survival individuals increases with age. This increase can mask a senescence‐related decrease in survival probability when the probability is estimated at the population level. To accommodate individual heterogeneity we use a mixture model structure (discrete classes of individuals). Second, the study individuals can elude the observers in the field, and their detection rate can be heterogeneous. To account for detectability issues we use capture–mark–recapture (CMR) methodology, mixture models and data that provide information on individuals’ detectability. Last, emigration to non‐monitored sites can bias survival estimates, because it can occur at the end of the individuals’ histories and mimic earlier death. To model emigration we use Markovian transitions to and from an unobservable state. These different model structures are merged together using hidden Markov chain CMR models, or multievent models. Simulation studies illustrate that reliable evidence for survival senescence can be obtained using highly heterogeneous data from non site‐faithful individuals. We then design a tailored application for a dataset from a colony of black‐headed gull Chroicocephalus ridibundus. Survival probabilities do not appear individually variable, but evidence for survival senescence becomes significant only when accounting for other sources of heterogeneity. This result suggests that not accounting for heterogeneity leads to flawed inference and/or that emigration heterogeneity mimics survival heterogeneity and biases senescence estimates.     

Capture-recapture when time and behavioral response affect capture probabilities

We consider a capture-recapture model in which capture probabilities vary with time and with behavioral response. Two inference procedures are developed under the assumption that recapture probabilities bear a constant relationship to initial capture probabilities. These two procedures are the maximum likelihood method (both unconditional and conditional types are discussed) and an approach based on optimal estimating functions. The population size estimators derived from the two procedures are shown to be asymptotically equivalent when population size is large enough. The performance and relative merits of various population size estimators for finite cases are discussed. The bootstrap method is suggested for constructing a variance estimator and confidence interval. An example of the deer mouse analyzed in Otis et al. (1978, Wildlife Monographs 62, 93) is given for illustration.     

Survival and aging in the wild via residual demography

Information about the age distribution and survival of wild populations is of much interest in ecology and biodemography, but is hard to obtain. Established schemes such as capture-recapture often are not feasible. In the proposed residual demography paradigm, individuals are randomly sampled from the wild population at unknown ages and the resulting captive cohort is reared out in the laboratory until death. Under some basic assumptions one obtains a demographic convolution equation that involves the unknown age distribution of the wild population, the observed survival function of the captive cohort, and the observed survival function of a reference cohort that is independently raised in the laboratory from birth. We adopt a statistical penalized least squares method for the deconvolution of this equation, aiming at extracting the age distribution of the wild population under suitable constraints. Under stationarity of the population, the age density is proportional to the survival function of the wild population and can thus be inferred. Several extensions are discussed. Residual demography is demonstrated for data on fruit flies Bactrocera oleae.     

Who are we sampling? Apparent survival differs between methods in a secretive species

Survival is a fundamental parameter in population dynamics with increasing importance in the management and conservation strategies of wildlife populations. Survival probability in vertebrates is usually estimated by live‐encounter data obtained by means of physical mark–capture–recapture protocols. Non‐invasive acoustic marking relying on individual‐specific features of signals has been alternatively applied as a marking technique, especially in secretive species. Nevertheless, to date no research has compared survival rate estimates obtained by acoustic and physical marking. We estimated half‐yearly and annual survival and recapture rates of a secretive and threatened passerine, the Dupont's lark Chersophilus duponti, using two separate live‐encounter data sets of males collected simultaneously by physical and acoustic marking in the same study area. The separate analysis of both methods led to different model structures, since transient individuals had to be accounted for in the acoustic marking but not in the physical marking data set. Furthermore, while reencounter probabilities did not differ between methods, survival estimates employing physical marking were lower than those obtained acoustically, especially between the postbreeding and the breeding period when the apparent survival of colour‐banded birds was twice as low as for acoustic marking. The combination of marking methods suggested the existence of different subsets of individuals differentially sampled within the population: whereas colour‐banded males seemed to represent the territorial fraction of the population, both resident and floater individuals were probably detected by acoustic marking. Using traditional mark–recapture methods exclusively could have misled our estimates of survival rates, potentially affecting prospective predictions of population dynamics. Acoustic marking has been poorly applied in mark–recapture studies, but might be a powerful complement to obtain accurate estimates of fundamental demographic parameters such as survival and dispersal.     

Effect of Tooth Removal on Recaptures of Raccoons

Abstract: Researchers have extensively used mark—recapture techniques to obtain information on demographic parameters of wildlife populations. However, researchers have recognized that a number of factors can influence capture probabilities of wildlife species, which in turn can bias mark—recapture estimates of demographic parameters. Tooth extraction, which is a commonly used technique in studies of mesopredator species to obtain precise age estimates and to monitor the use of vaccine baits, is an aspect of animal handling that clearly might affect the recapture probability of individuals. However, the effect that tooth removal has on the individual recapture probabilities of wildlife species is unknown. During 2005, we trapped and marked 91 raccoons (Procyon lotor) in northern Indiana, USA, as part of a mark—recapture study designed specifically to determine if tooth extractions have an effect on recapture probabilities of individuals. We performed tooth extractions on 50% of the raccoons at the time of capture, and we attempted to balance tooth extractions with respect to sex and age of raccoons. We used logistic regression to model the effects of sex, age, and tooth removal on recapture probabilities, and we used Mann—Whitney U-tests to examine the effect of tooth removal on the number of times we recaptured individuals. The probability of recapture differed between sexes but did not differ as a function of tooth removal or among age classes. In addition, we failed to detect any difference in the mean number of times that we recaptured raccoons between the tooth removed and non—tooth-removed groups. Our results suggest that managers can use tooth extractions as an effective management tool without biasing population estimates or compromising other management objectives.     

Strange bayes indeed: uniform topological priors imply non-uniform clade priors

While Bayesian analysis has become common in phylogenetics, the effects of topological prior probabilities on tree inference have not been investigated. In Bayesian analyses, the prior probability of topologies is almost always considered equal for all possible trees, and clade support is calculated from the majority rule consensus of the approximated posterior distribution of topologies. These uniform priors on tree topologies imply non-uniform prior probabilities of clades, which are dependent on the number of taxa in a clade as well as the number of taxa in the analysis. As such, uniform topological priors do not model ignorance with respect to clades. Here, we demonstrate that Bayesian clade support, bootstrap support, and jackknife support from 17 empirical studies are significantly and positively correlated with non-uniform clade priors resulting from uniform topological priors. Further, we demonstrate that this effect disappears for bootstrap and jackknife when data sets are free from character conflict, but remains pronounced for Bayesian clade supports, regardless of tree shape. Finally, we propose the use of a Bayes factor to account for the fact that uniform topological priors do not model ignorance with respect to clade probability.     

Erratum to: Using multistate capture–mark–recapture models to quantify effects of predation on age-specific survival and population growth in black-tailed deer

Effective species management and conservation relies on accurate estimates of vital rates and an understanding of their link to environmental variables. We used multistate capture–mark–recapture models to directly quantify effects of predation on age-specific survival of black-tailed deer Odocoileus hemionus columbianus in California, USA. Survival probabilities were derived from individual encounter histories of 136 fawns and 57 adults monitored over 4 years. Based on results from our survival analysis we parameterized a Lefkovitch matrix and used elasticity analyses to investigate contributions of mortality due to predation to changes in population growth. We found strong evidence for age-specific survival including senescence. Survival of females >1 year old was consistently low (0.56 ± 0.18 for yearlings, 0.77 ± 0.13 for prime-aged females, and 0.55 ± 0.08 for senescent individuals), primarily due to high puma Puma concolor predation during summer. Predation from black bears Ursus americanus and coyotes Canis latrans was the primary cause for low annual survival of fawns (0.24 ± 0.16). Resulting estimates of population growth rates were indicative of a strongly declining population (λ = 0.82 ± 0.13). Despite high sensitivity to changes in adult survival, results from a lower-level elasticity analysis suggested that predation on fawns was the most significant individual mortality component affecting population decline. Our results provide a rare, direct link between predation, age-specific survival and the predicted population decline of a common ungulate species. The magnitude of predation was unexpected and suggests that ungulates in multi-predator systems struggle to cope with simultaneous reductions in survival probabilities from predators targeting different age classes.     

Estimating survival in the Apennine brown bear accounting for uncertainty in age classification

For most rare and elusive species, estimating age-specific survival is a challenging task, although it is an important requirement to understand the drivers of population dynamics, and to inform conservation actions. Apennine brown bears Ursus arctos marsicanus are a small, isolated population under a severe risk of extinction, for which the main demographic mechanisms underlying population dynamics are still unknown, and population trends have not been formally assessed. We present a 12-year analysis of their survival rates using non-invasive genetic sampling data collected through four different sampling techniques. By using multi-event capture–recapture models, we estimated survival probabilities for two broadly defined age classes (cubs and older individuals), even though the age of the majority of sampled bears was unknown. We also applied the Pradel model to provide a preliminary assessment of population trend during the study period. Survival was different between cubs [ϕ = 0.51, 95% CI (0.22, 0.79)], adult males [ϕ = 0.85, 95% CI (0.76, 0.91)] and adult females [ϕ = 0.92, 95% CI (0.87, 0.95)], no temporal variation in survival emerged, suggesting that bear survival remained substantially stable throughout the study period. The Pradel analysis of population trend yielded an estimate of λ = 1.009 [SE = 0.018; 95% CI (0.974, 1.046)]. Our results indicate that, despite the status of full legal protection, the basically stable demography of this relict population is compatible with the observed lack of range expansion, and that a relatively high cub mortality could be among the main factors depressing recruitment and hence population growth.     

Continuous Covariates in Mark‐Recapture‐Recovery Analysis: A Comparison of Methods

Summary Time varying, individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured. We examine three methods to incorporate time varying, individual covariates of the survival probabilities into the analysis of data from mark‐recapture‐recovery experiments: deterministic imputation, a Bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history, and a conditional approach considering only the events for which the associated covariate data are completely observed (the trinomial model). After describing the three methods, we compare results from their application to the analysis of the effect of body mass on the survival of Soay sheep (Ovis aries) on the Isle of Hirta, Scotland. Simulations based on these results are then used to make further comparisons. We conclude that both the trinomial model and Bayesian imputation method perform best in different situations. If the capture and recovery probabilities are all high, then the trinomial model produces precise, unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate. In contrast, the Bayesian imputation method performs substantially better when capture and recovery probabilities are low, provided that the specified model of the covariate is a good approximation to the true data‐generating mechanism.     

Analyzing complex capture-recapture data in the presence of individual and temporal covariates and model uncertainty

SUMMARY: We consider the issue of analyzing complex ecological data in the presence of covariate information and model uncertainty. Several issues can arise when analyzing such data, not least the need to take into account where there are missing covariate values. This is most acutely observed in the presence of time-varying covariates. We consider mark-recapture-recovery data, where the corresponding recapture probabilities are less than unity, so that individuals are not always observed at each capture event. This often leads to a large amount of missing time-varying individual covariate information, because the covariate cannot usually be recorded if an individual is not observed. In addition, we address the problem of model selection over these covariates with missing data. We consider a Bayesian approach, where we are able to deal with large amounts of missing data, by essentially treating the missing values as auxiliary variables. This approach also allows a quantitative comparison of different models via posterior model probabilities, obtained via the reversible jump Markov chain Monte Carlo algorithm. To demonstrate this approach we analyze data relating to Soay sheep, which pose several statistical challenges in fully describing the intricacies of the system.     

Spatial variation in age-specific probabilities of first reproduction for Weddell seals

Spatial variation in vital rates can affect the dynamics and persistence of a population. We evaluated the prediction that age-specific probabilities of survival and first reproduction for Weddell seals would vary as a function of birth location in Erebus Bay, Antarctica. We used multi-state mark–resight models and 25 years of data to estimate demographic rates for female seals. We predicted that probabilities of survival and first reproduction would be higher for seals born at near-shore colonies or more southerly-located colonies with consistent ice conditions. Contrary to predictions, results revealed higher age-specific probabilities of first reproduction at offshore colonies relative to near-shore colonies and no spatial variation in survival rates. For 7-year old females (average age at 1st reproduction=7.6 years old) born at offshore colonies to mothers aged 10.8 years (average maternal age), probability of first reproduction was 0.43 (SE=0.07), whereas probability of first reproduction for females born at near-shore colonies was 0.30 (SE=0.05) based on estimates from our top-ranked model. Breeding probabilities following first reproduction were also higher at offshore colonies. Thus, our results (1) provide evidence of spatial variation in breeding probabilities, (2) reveal the importance of birth location on a female's vital rates, and (3) suggest that the effect persisted for many years. Birth-colony effects may be attributed to spatial variation in prey availability, or to heterogeneity in female quality in this population. If females who are superior competitors consistently chose offshore colonies for pupping, pups born at these locations may have inherited those superior qualities and displayed higher probabilities of first reproduction, relative to seals born at other colonies. Further research into physical or food-related differences among colonies may offer insight into spatial variation in breeding probabilities documented in this paper.     

Demographic window to aging in the wild: constructing life tables and estimating survival functions from marked individuals of unknown age

Summary We address the problem of establishing a survival schedule for wild populations. A demographic key identity is established, leading to a method whereby age-specific survival and mortality can be deduced from a marked cohort life table established for individuals that are randomly sampled at unknown age and marked, with subsequent recording of time-to-death. This identity permits the construction of life tables from data where the birth date of subjects is unknown. An analogous key identity is established for the continuous case in which the survival schedule of the wild population is related to the density of the survival distribution in the marked cohort. These identities are explored for both life tables and continuous lifetime data. For the continuous case, they are implemented with statistical methods using non-parametric density estimation methods to obtain flexible estimates for the unknown survival distribution of the wild population. The analytical model provided here serves as a starting point to develop more complex models for residual demography, i.e. models for estimating survival of wild populations in which age-at-entry is unknown and using remaining information in randomly encountered individuals. This is a first step towards a broad new concept of 'expressed demographic information content of marked or captured individuals'.     

Logistic regression in capture-recapture models

The effect of population heterogeneity in capture-recapture, or dual registration, models is discussed. An estimator of the unknown population size based on a logistic regression model is introduced. The model allows different capture probabilities across individuals and across capture times. The probabilities are estimated from the observed data using conditional maximum likelihood. The resulting population estimator is shown to be consistent and asymptotically normal. A variance estimator under population heterogeneity is derived. The finite-sample properties of the estimators are studied via simulation. An application to Finnish occupational disease registration data is presented.     

Disappearances of individuals from social groups have implications for understanding natal dispersal in monogamous owl monkeys (Aotus azarai)

The socially monogamous owl monkeys (Aotus spp.) live in small groups of two to five individuals. We used monthly demographic data collected from 16 social groups between 1997-2001 to estimate the age of disappearance from their natal groups and the timing of those disappearances in a population of owl monkeys (Aotus azarai azarai) in Formosa, Argentina. We applied survival analysis techniques to 48 months of observations of 47 individuals to construct age-specific probabilities of disappearance. Two-thirds of the individuals (eight of 12), for which disappearance could be well timed, disappeared at around 2 years of age. The average age at disappearance for these individuals was 29 months (+/-8), whereas the mean age of disappearance obtained from the survival analysis of censored and uncensored data was almost 3 years (mean+/-SD, 35+/-3 months). Ninety-two percent of all disappearances of adult size individuals (11 of 12) occurred around the birth season. Our data suggest that at least some individuals disperse soon after sexual maturation while others remain for up to 4 years in their natal groups.     

ESTIMATION OF AGE-SPECIFIC PROBABILITIES OF FIRST RETURN AND ANNUAL SURVIVAL RATES FOR THE MALE GRAY SEAL (HALICHOERUS GRYPUS) ON SABLE ISLAND FROM CAPTURE-RECAPTURE DATA

We used a longitudinal capture-recapture study to estimate the age-specific probabilities of first return to the breeding colony and annual survival rates for male gray seals ( Halichoerus grypus ), based on resightings of seals branded as young on Sable Island. We estimated that the average age of first returns for seals born in 1969–1970 to be 9.1 (SE 0.4) yr; for seals born in 1973–1974 it is estimated to be 9.8 (SE 0.2) yr. The estimated annual survival rate of these males was estimated to be 0.976 (SE 0.003).     

Local survival in Semipalmated Sandpipers Calidris pusilla breeding at La Pérouse Bay, Canada

A hierarchical modelling approach was used to examine adult and age-specific survival in an 8-year study of breeding Semipalmated Sandpipers Calidris pusilla at La Pérouse Bay, Canada. The survival of adult sandpipers was best described by a model with time dependence in local survival rate and probability of recapture. Annual variation in the local survival rate of adults was not correlated with nest success, timing of breeding or "return rates" and was not biased by an effect of first capture. Local survival rate of adult females (0.56, 95% c.l. = 0.51-0.61) was consistently lower than that of adult males (0.61, 95% c.l. = 0.56-0.66); these estimates were comparable with data from other shorebirds. The survival of returning young was best fitted by a model with both age and time dependence in local survival rate and probability of recapture. We evaluated our estimates of local survival rate with reference to patterns of breeding fidelity and philopatry in Semipalmated Sandpipers and other shorebirds.     

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.