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.     

Projecting the future burden of cancer: Bayesian age–period–cohort analysis with integrated nested Laplace approximations

The projection of age‐stratified cancer incidence and mortality rates is of great interest due to demographic changes, but also therapeutical and diagnostic developments. Bayesian age–period–cohort (APC) models are well suited for the analysis of such data, but are not yet used in routine practice of epidemiologists. Reasons may include that Bayesian APC models have been criticized to produce too wide prediction intervals. Furthermore, the fitting of Bayesian APC models is usually done using Markov chain Monte Carlo (MCMC), which introduces complex convergence concerns and may be subject to additional technical problems. In this paper we address both concerns, developing efficient MCMC‐free software for routine use in epidemiological applications. We apply Bayesian APC models to annual lung cancer data for females in five different countries, previously analyzed in the literature. To assess the predictive quality, we omit the observations from the last 10 years and compare the projections with the actual observed data based on the absolute error and the continuous ranked probability score. Further, we assess calibration of the one‐step‐ahead predictive distributions. In our application, the probabilistic forecasts obtained by the Bayesian APC model are well calibrated and not too wide. A comparison to projections obtained by a generalized Lee–Carter model is also given. The methodology is implemented in the user‐friendly R‐package BAPC using integrated nested Laplace approximations.     

Development of a standardized protein immunomarking protocol for insect mark–capture dispersal research

A field study was conducted to test the marking efficiency of broadcast spray applications of protein marks on stationary (represented by cadavers) and free‐roaming lady beetles Hippodamia convergens Guérin‐Méneville that were strategically placed in blooming alfalfa plots. The marks tested included three different concentrations of egg albumin from chicken egg white, casein from bovine milk and trypsin inhibitor from soy milk. The cadaver and free‐roaming beetle treatments served to measure the acquisition and retention of each protein treatment regime by direct contact with the spray solution and by residual contact with protein‐marked residue on alfalfa, respectively. In addition, the vertical distribution of marking efficacy was determined by sampling alfalfa plant tissue and beetle cadavers that were located on the upper and lower portion of the plant canopy. The data indicated that the backpack spray apparatus was very effective at uniformly administering the various protein marks, regardless of the concentration, throughout the entire plant canopy. Also, the free‐roaming beetles readily self‐marked by contact exposure to protein‐treated plants. We also identified concentrations of each protein type that will mark about 90% of the resident beetle population. Moreover, if a mark–capture‐type study only requires two unique protein marks, we determined that concentrations of 25% for egg white and 100% for bovine milk could be used to mark 98% of the population. Our results provide a significant step towards standardizing protein immunomarking protocols for insect mark–capture dispersal research. In addition, we identify several areas of research that are needed to further standardize the protein mark–capture procedure.     

Population size estimates based on the frequency of genetically assigned parent–offspring pairs within a subsample

Estimating population density as precise as possible is a key premise for managing wild animal species. This can be a challenging task if the species in question is elusive or, due to high quantities, hard to count. We present a new, mathematically derived estimator for population size, where the estimation is based solely on the frequency of genetically assigned parent–offspring pairs within a subsample of an ungulate population. By use of molecular markers like microsatellites, the number of these parent–offspring pairs can be determined. The study's aim was to clarify whether a classical capture–mark–recapture (CMR) method can be adapted or extended by this genetic element to a genetic‐based capture–mark–recapture (g‐CMR). We numerically validate the presented estimator (and corresponding variance estimates) and provide the R‐code for the computation of estimates of population size including confidence intervals. The presented method provides a new framework to precisely estimate population size based on the genetic analysis of a one‐time subsample. This is especially of value where traditional CMR methods or other DNA‐based (fecal or hair) capture–recapture methods fail or are too difficult to apply. The DNA source used is basically irrelevant, but in the present case the sampling of an annual hunting bag is to serve as data basis. In addition to the high quality of muscle tissue samples, hunting bags provide additional and essential information for wildlife management practices, such as age, weight, or sex. In cases where a g‐CMR method is ecologically and hunting‐wise appropriate, it enables a wide applicability, also through its species‐independent use.     

Multistate Mark–Recapture Model Selection Using Score Tests

Summary Although multistate mark–recapture models are recognized as important, they lack a simple model‐selection procedure. This article proposes and evaluates a step‐up approach to select appropriate models for multistate mark–recapture data using score tests. Only models supported by the data require fitting, so that over‐complicated model structures with too many parameters do not need to be considered. Typically only a small number of models are fitted, and the procedure is also able to identify parameter‐redundant and near‐redundant models. The good performance of the technique is demonstrated using simulation, and the approach is illustrated on a three‐region Canada goose data set. In this case, it identifies a new model that is much simpler than the best model previously considered for this application.     

Applications of hidden hybrid Markov/semi‐Markov models: from stopover duration to breeding success dynamics

Usually in capture–recapture, a model parameter is time or time since first capture dependent. However, the case where the probability of staying in one state depends on the time spent in that particular state is not rare. Hidden Markov models are not appropriate to manage these situations. A more convenient approach would be to consider models that incorporate semi‐Markovian states which explicitly define the waiting time distribution and have been used in previous biologic studies as a convenient framework for modeling the time spent in a given physiological state. Here, we propose hidden Markovian models that combine several nonhomogeneous Markovian states with one semi‐Markovian state and which (i) are well adapted to imperfect and variable detection and (ii) allow us to consider time, time since first capture, and time spent in one state effects. Implementation details depending on the number of semi‐Markovian states are discussed. From a user's perspective, the present approach enhances the toolbox for analyzing capture–recapture data. We then show the potential of this framework by means of two ecological examples: (i) stopover duration and (ii) breeding success dynamics.     

Detection heterogeneity in underwater visual‐census data

This study shows how capture–mark–recapture (CMR) models can provide robust estimates of detection heterogeneity (sources of bias) in underwater visual‐census data. Detection biases among observers and fish family groups were consistent between fished and unfished reef sites in Kenya, even when the overall level of detection declined between locations. Species characteristics were the greatest source of detection heterogeneity and large, highly mobile species were found to have lower probabilities of detection than smaller, site‐attached species. Fish family and functional‐group detectability were also found to be lower at fished locations, probably due to differences in local abundance. Because robust CMR models deal explicitly with sampling where not all species are detected, their use is encouraged for studies addressing reef‐fish community dynamics.     

Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension

Summary Reversible jump Markov chain Monte Carlo (RJMCMC) methods are used to fit Bayesian capture–recapture models incorporating heterogeneity in individuals and samples. Heterogeneity in capture probabilities comes from finite mixtures and/or fixed sample effects allowing for interactions. Estimation by RJMCMC allows automatic model selection and/or model averaging. Priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models, in contrast to likelihood‐based methods. To demonstrate the approach we analyze the standard Snowshoe hare and Cottontail rabbit data sets from ecology, a reliability testing data set.     

Heterozygosity–fitness correlations in a wild mammal population: accounting for parental and environmental effects

HFCs (heterozygosity–fitness correlations) measure the direct relationship between an individual's genetic diversity and fitness. The effects of parental heterozygosity and the environment on HFCs are currently under‐researched. We investigated these in a high‐density U.K. population of European badgers (Meles meles), using a multimodel capture–mark–recapture framework and 35 microsatellite loci. We detected interannual variation in first‐year, but not adult, survival probability. Adult females had higher annual survival probabilities than adult males. Cubs with more heterozygous fathers had higher first‐year survival, but only in wetter summers; there was no relationship with individual or maternal heterozygosity. Moist soil conditions enhance badger food supply (earthworms), improving survival. In dryer years, higher indiscriminate mortality rates appear to mask differential heterozygosity‐related survival effects. This paternal interaction was significant in the most supported model; however, the model‐averaged estimate had a relative importance of 0.50 and overlapped zero slightly. First‐year survival probabilities were not correlated with the inbreeding coefficient (f); however, small sample sizes limited the power to detect inbreeding depression. Correlations between individual heterozygosity and inbreeding were weak, in line with published meta‐analyses showing that HFCs tend to be weak. We found support for general rather than local heterozygosity effects on first‐year survival probability, and g2 indicated that our markers had power to detect inbreeding. We emphasize the importance of assessing how environmental stressors can influence the magnitude and direction of HFCs and of considering how parental genetic diversity can affect fitness‐related traits, which could play an important role in the evolution of mate choice.     

Apparent survival and return rate of breeders in the southern temperate White‐rumped Swallow Tachycineta leucorrhoa

Life‐histories and demographic parameters of southern temperate bird species have been little studied. We estimated return rates between years and sexes, and adult apparent survival and recapture probabilities with mark–recapture data on White‐rumped Swallows and found a lower return rate of unsuccessful females. There was little support for influences of sex or year on survival rates. The estimates were equivalent to the lowest value reported for a northern congener, in contrast to the prediction of geographical variation under life‐history theory.     

Improved methods for estimating abundance and related demographic parameters from mark‐resight data

Over the past decade, there has been much methodological development for the estimation of abundance and related demographic parameters using mark‐resight data. Often viewed as a less‐invasive and less‐expensive alternative to conventional mark recapture, mark‐resight methods jointly model marked individual encounters and counts of unmarked individuals, and recent extensions accommodate common challenges associated with imperfect detection. When these challenges include both individual detection heterogeneity and an unknown marked sample size, we demonstrate several deficiencies associated with the most widely used mark‐resight models currently implemented in the popular capture‐recapture freeware Program MARK. We propose a composite likelihood solution based on a zero‐inflated Poisson log‐normal model and find the performance of this new estimator to be superior in terms of bias and confidence interval coverage. Under Pollock's robust design, we also extend the models to accommodate individual‐level random effects across sampling occasions as a potentially more realistic alternative to models that assume independence. As a motivating example, we revisit a previous analysis of mark‐resight data for the New Zealand Robin (Petroica australis) and compare inferences from the proposed estimators. For the all‐too‐common situation where encounter rates are low, individual detection heterogeneity is non‐negligible, and the number of marked individuals is unknown, we recommend practitioners use the zero‐inflated Poisson log‐normal mark‐resight estimator as now implemented in Program MARK.     

Combining capture–recapture data and pedigree information to assess heritability of demographic parameters in the wild

Quantitative genetic analyses have been increasingly used to estimate the genetic basis of life‐history traits in natural populations. Imperfect detection of individuals is inherent to studies that monitor populations in the wild, yet it is seldom accounted for by quantitative genetic studies, perhaps leading to flawed inference. To facilitate the inclusion of imperfect detection of individuals in such studies, we develop a method to estimate additive genetic variance and assess heritability for binary traits such as survival, using capture–recapture (CR) data. Our approach combines mixed‐effects CR models with a threshold model to incorporate discrete data in a standard ‘animal model’ approach. We employ Markov chain Monte Carlo sampling in a Bayesian framework to estimate model parameters. We illustrate our approach using data from a wild population of blue tits (Cyanistes caeruleus) and present the first estimate of heritability of adult survival in the wild. In agreement with the prediction that selection should deplete additive genetic variance in fitness, we found that survival had low heritability. Because the detection process is incorporated, capture–recapture animal models (CRAM) provide unbiased quantitative genetics analyses of longitudinal data collected in the wild.     

Decline in abundance and apparent survival rates of fin whales (Balaenoptera physalus) in the northern Gulf of St. Lawrence

Estimates of abundance and survivorship provide quantifiable measures to monitor populations and to define and understand their conservation status. This study investigated changes in abundance and survival rates of fin whales (Balaenoptera physalus) in the northern Gulf of St. Lawrence in the context of anthropogenic pressures and changing environmental conditions. A long‐term data set, consisting of 35 years of photo‐identification surveys and comprising more than 5,000 identifications of 507 individuals, formed the basis of this mark–recapture study. Based on model selection using corrected Akaike Information Criterion, the most parsimonious Cormack–Jolly–Seber model included a linear temporal trend in noncalf apparent survival rates with a sharp decline in the last 5 years of the study and a median survival rate of 0.946 (95% confidence interval (CI) 0.910–0.967). To account for capture heterogeneity due to divergent patterns of site fidelity, agglomerative hierarchical cluster analysis was employed to categorize individuals based on their annual and survey site fidelity indices. However, the negative trend in survivorship remained and was corroborated by a significant decline in the estimated super‐population size from 335 (95% CI 321–348) individuals in 2004–2010 to 291 (95% CI 270–312) individuals in 2010–2016. Concurrently, a negative trend was estimated in recruitment to the population, supported by a sharp decrease in the number of observed calves. Ship strikes and changes in prey availability are potential drivers of the observed decline in fin whale abundance. The combination of clustering methods with mark–recapture represents a flexible way to investigate the effects of site fidelity on demographic variables and is broadly applicable to other individual‐based studies.     

Comparison of photo‐matching algorithms commonly used for photographic capture–recapture studies

Photographic capture–recapture is a valuable tool for obtaining demographic information on wildlife populations due to its noninvasive nature and cost‐effectiveness. Recently, several computer‐aided photo‐matching algorithms have been developed to more efficiently match images of unique individuals in databases with thousands of images. However, the identification accuracy of these algorithms can severely bias estimates of vital rates and population size. Therefore, it is important to understand the performance and limitations of state‐of‐the‐art photo‐matching algorithms prior to implementation in capture–recapture studies involving possibly thousands of images. Here, we compared the performance of four photo‐matching algorithms; Wild‐ID, I3S Pattern+, APHIS, and AmphIdent using multiple amphibian databases of varying image quality. We measured the performance of each algorithm and evaluated the performance in relation to database size and the number of matching images in the database. We found that algorithm performance differed greatly by algorithm and image database, with recognition rates ranging from 100% to 22.6% when limiting the review to the 10 highest ranking images. We found that recognition rate degraded marginally with increased database size and could be improved considerably with a higher number of matching images in the database. In our study, the pixel‐based algorithm of AmphIdent exhibited superior recognition rates compared to the other approaches. We recommend carefully evaluating algorithm performance prior to using it to match a complete database. By choosing a suitable matching algorithm, databases of sizes that are unfeasible to match “by eye” can be easily translated to accurate individual capture histories necessary for robust demographic estimates.     

Capwire: a R package for estimating population census size from non‐invasive genetic sampling

Non‐invasive genetic sampling is an increasingly popular approach for investigating the demographics of natural populations. This has also become a useful tool for managers and conservation biologists, especially for those species for which traditional mark–recapture studies are not practical. However, the consequence of collecting DNA indirectly is that an individual may be sampled multiple times per sampling session. This requires alternative statistical approaches to those used in traditional mark–recapture studies. Here we present the R package capwire , an implementation of the population size estimators of Miller et al. (Molecular Ecology 2005; 14 : 1991), which were designed to deal specifically with this type of sampling. The aim of this project is to enable users across platforms to easily manipulate their data and interact with existing R packages. We have also provided functions to simulate data under a variety of scenarios to allow for rigorous testing of the robustness of the method and to facilitate further development of this approach.     

Attraction of wild‐like and colony‐reared Bactrocera cucurbitae (Diptera:Tephritidae) to cuelure in the field

The attraction of wild tephritids to semiochemical‐based lures is the ideal basis for trap network design in detection programmes, but in practice, mass‐reared colony insects are usually used to determine trap efficiency. For Bactrocera cucurbitae Coquillett, a lower response by wild males compared with colony‐derived individuals, usually used to estimate attraction parameters, could mean that the sensitivity of detection networks targeting this pest is reduced. We describe the results of mark–release–recapture experiments with wild‐ and colony‐derived B. cucurbitae males in a grid of cuelure‐baited traps within a macadamia nut orchard in Hawaii Island designed to quantify the attraction of cuelure to each fly type. For colony males, we estimate a 65% probability of capture at 27 m, intermediate with previous estimates on the attraction of methyl eugenol to Bactrocera dorsalis Hendel (36 m) and trimedlure to Ceratitis capitata Wiedemann (14 m) at the same site. Results suggest similar response over distance by wild‐derived B. cucurbitae compared with colony in the field, but there may be qualitative differences in response between wild and colony based on very low response of wild males in a standard bioassay of attraction. For both fly types, the estimates of attraction in the smaller of two grid sizes tested were lower than for the larger spacing, suggesting trap competition was a factor at an intertrap distance of 75 m. Dispersal patterns within the grid were generally to the south for the colony‐derived males and more variable for the wild‐derived males. In neither case was the direction of recapture correlated with the prevailing direction of the wind.     

The one‐inflated positive Poisson mixture model for use in population size estimation

The one‐inflated positive Poisson mixture model (OIPPMM) is presented, for use as the truncated count model in Horvitz–Thompson estimation of an unknown population size. The OIPPMM offers a way to address two important features of some capture–recapture data: one‐inflation and unobserved heterogeneity. The OIPPMM provides markedly different results than some other popular estimators, and these other estimators can appear to be quite biased, or utterly fail due to the boundary problem, when the OIPPMM is the true data‐generating process. In addition, the OIPPMM provides a solution to the boundary problem, by labelling any mixture components on the boundary instead as one‐inflation.     

Estimating age‐dependent survival when juveniles resemble females: Invasive ring‐necked parakeets as an example

Many species only show sexual dimorphism at the age of maturity, such that juveniles typically resemble females. Under these circumstances, estimating accurate age‐specific demographic parameters is challenging. Here, we propose a multievent model parameterization able to estimate age‐dependent survival using capture–recapture data with uncertainty in age and sex assignment of individuals. We illustrate this modeling approach with capture–recapture data from the ring‐necked parakeet Psittacula krameri. We analyzed capture, recapture, and resighting data (439 recaptures/resightings) of 156 ring‐necked parakeets tagged with neck collars in Barcelona city from 2003 to 2016 to estimate the juvenile and adult survival rate. Our models successfully estimated the survival probabilities of the different age classes considered. Survival probability was similar between adults (0.83, 95% CI = 0.77–0.87) and juveniles during their second (0.79, 95% CI = 0.58–0.87) and third winter (0.83, 95% CI = 0.65–0.88). The youngest juveniles (1st winter) showed a slightly lower survival (0.57, 95% CI = 0.37–0.79). Among adults, females showed a slightly higher survival than males (0.87, 95% CI = 0.78–0.93; and 0.80, 95% CI = 0.73–0.86, respectively). These high survival figures predict high population persistence in this species and urge management policies. The analysis also stresses the usefulness of multievent models to estimate juvenile survival when age cannot be fully ascertained.     

The Petersen–Lincoln Estimator and its Extension to Estimate the Size of a Shared Population

The Petersen–Lincoln estimator has been used to estimate the size of a population in a single mark release experiment. However, the estimator is not valid when the capture sample and recapture sample are not independent. We provide an intuitive interpretation for “independence” between samples based on 2 × 2 categorical data formed by capture/non‐capture in each of the two samples. From the interpretation, we review a general measure of “dependence” and quantify the correlation bias of the Petersen–Lincoln estimator when two types of dependences (local list dependence and heterogeneity of capture probability) exist. An important implication in the census undercount problem is that instead of using a post enumeration sample to assess the undercount of a census, one should conduct a prior enumeration sample to avoid correlation bias. We extend the Petersen–Lincoln method to the case of two populations. This new estimator of the size of the shared population is proposed and its variance is derived. We discuss a special case where the correlation bias of the proposed estimator due to dependence between samples vanishes. The proposed method is applied to a study of the relapse rate of illicit drug use in Taiwan. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Density‐dependent survival and recruitment in a long‐distance Palaearctic migrant,the Sand Martin Riparia riparia

Long‐term studies can provide powerful insights into the relative importance of different demographic and environmental factors determining avian population dynamics. Here we use 23 years of capture–mark–recapture data (1981–2003) to estimate recruitment and survival rates for a Sand Martin Riparia riparia population in Cheshire, NW England. Inter‐annual variation in recruitment and adult survival was positively related to rainfall in the sub‐Saharan wintering grounds, but unrelated to weather conditions on the breeding grounds. After allowing for the effects of African rainfall, both demographic rates were negatively density‐dependent: adult survival was related to the size of the western European Sand Martin population (probably reflecting competition for resources in the shared wintering grounds) while recruitment was related to the size of the local study population in Cheshire (potentially reflecting competition for nesting sites or food). Local population size was more sensitive to variation in adult survival than to variation in recruitment, and an increase in population size after 1995 was driven mainly by the impact of more favourable conditions in the African wintering grounds on survival rates of adults. Overwinter survival in this long‐distance Palaearctic migrant is determined partly by the amount of suitable wetland foraging habitat in the sub‐Saharan wintering grounds (which is limited by the extent of summer rainfall) and partly by the number of birds exploiting that habitat.