Capture-recapture Experiments Research Articles

TheVGAMPackage for Capture-Recapture Data Using the Conditional Likelihood

It is well known that using individual covariate information (such as body weight or gender) to model heterogeneity in capture-recapture (CR) experiments can greatly enhance inferences on the size of a closed population. Since individual covariates are only observable for captured individuals, complex conditional likelihood methods are usually required and these do not constitute a standard generalized linear model (GLM) family. Modern statistical techniques such as generalized additive models (GAMs), which allow a relaxing of the linearity assumptions on the covariates, are readily available for many standard GLM families. Fortunately, a natural statistical framework for maximizing conditional likelihoods is available in the Vector GLM and Vector GAM classes of models. We present several new R functions (implemented within the VGAM package) specifically developed to allow the incorporation of individual covariates in the analysis of closed population CR data using a GLM/GAM-like approach and the conditional likelihood. As a result, a wide variety of practical tools are now readily available in the VGAM object oriented framework. We discuss and demonstrate their advantages, features and flexibility using the new VGAM CR functions on several examples.

Preliminary results on the biology of the European eel (Anguilla anguilla) in the European Southern tip

Event Abstract Back to Event Preliminary results on the biology of the European eel (Anguilla anguilla) in the European Southern tip Raquel Moreno-Valcárcel1*, Ramón J. De Miguel1, Mercedes Herrera1, Hayley S. Dean1 and Carlos Fernández-Delgado1 1 UNIVERSITY OF CÓRDOBA, ZOOLOGY, Spain In the context of the European Eel Recovery Plan, managers need confident biological information based on its own geographical areas. In the specific case of Andalusia (Southern Spain), we are developing a capture-recapture experiment based in the use of PIT-tags in order to obtain information that we lack for the species in the study area. In this communication, we focus on the biology of the species. Firstly, we carried out an ex-situ experiment to check the effect of the PIT-tag on the individuals of the eel. Once we ascertained there were no significant effects in the survival, length, and weight of the marked eels, we proceeded with the study in situ (Guadiaro river). Between October 2014 and July 2015 we captured 1011 eels (539 tagged; 252 recaptured). Approximately 90% of their lengths were between 16-40 cm (minimum 16.3 cm; maximum 67 cm). Eel’s length in March, April and May was significantly lower than those captured in the rest of months, probably because longer eels migrated before spring and only small eels remained in the population. More than 90% of the eels captured in all months were resident, and the higher proportions of migrants were detected in October 2014, November 2014 and July 2015. Mean lengths registered per maturation stage were notably lower than those found in other populations. The growth values showed in this population were higher in autumn (0.195 mm/day) than in winter (0.091 mm/day) and summer (0.096 mm/day), and residual condition factor showed normal values in comparison with other populations with minimum values in autumn. Acknowledgements This study have been supported by the Environmental Agency from Andalucía (Spain). Keywords: PIT-tag, Capture-recapture, condition index, Growth, maturation, Silvering Conference: XV European Congress of Ichthyology, Porto, Portugal, 7 Sep - 11 Sep, 2015. Presentation Type: Oral Presentation Topic: Life Cycles, Migration and Connectivity Citation: Moreno-Valcárcel R, De Miguel RJ, Herrera M, Dean HS and Fernández-Delgado C (2015). Preliminary results on the biology of the European eel (Anguilla anguilla) in the European Southern tip. Front. Mar. Sci. Conference Abstract: XV European Congress of Ichthyology. doi: 10.3389/conf.fmars.2015.03.00007 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 30 Oct 2015; Published Online: 04 Nov 2015. * Correspondence: Dr. Raquel Moreno-Valcárcel, UNIVERSITY OF CÓRDOBA, ZOOLOGY, CÓRDOBA, 14071, Spain, raquel.moreno@uco.es Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Raquel Moreno-Valcárcel Ramón J De Miguel Mercedes Herrera Hayley S Dean Carlos Fernández-Delgado Google Raquel Moreno-Valcárcel Ramón J De Miguel Mercedes Herrera Hayley S Dean Carlos Fernández-Delgado Google Scholar Raquel Moreno-Valcárcel Ramón J De Miguel Mercedes Herrera Hayley S Dean Carlos Fernández-Delgado PubMed Raquel Moreno-Valcárcel Ramón J De Miguel Mercedes Herrera Hayley S Dean Carlos Fernández-Delgado Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Estimation of capture probabilities using generalized estimating equations and mixed effects approaches.

Modeling individual heterogeneity in capture probabilities has been one of the most challenging tasks in capture–recapture studies. Heterogeneity in capture probabilities can be modeled as a function of individual covariates, but correlation structure among capture occasions should be taking into account. A proposed generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) approaches can be used to estimate capture probabilities and population size for capture–recapture closed population models. An example is used for an illustrative application and for comparison with currently used methodology. A simulation study is also conducted to show the performance of the estimation procedures. Our simulation results show that the proposed quasi-likelihood based on GEE approach provides lower SE than partial likelihood based on either generalized linear models (GLM) or GLMM approaches for estimating population size in a closed capture–recapture experiment. Estimator performance is good if a large proportion of individuals are captured. For cases where only a small proportion of individuals are captured, the estimates become unstable, but the GEE approach outperforms the other methods.

Limited-Information Modeling of Loggerhead Turtle Population Size

We attempt to estimate the size of a population of female loggerhead turtles. In traditional capture-recapture experiments to estimate the size of an animal population, individual animals are tagged and the information about which individuals are captured repeatedly is crucial. For these loggerhead turtle data, information about individual turtles is not available. Rather, we observe only the counts of successful and failed nestings at a location over a series of days (in our case, three). We view the turtles’ nesting behavior as an alternating renewal process, model it using parametric distributions, and then derive probability distributions that describe the behavior of the turtles during the three days via a 3-way contingency table. We adopt a Bayesian approach, formulating our model in terms of parameters about which strong prior information is available. We use a Gibbs sampling algorithm to sample from the posterior distribution of our random quantities, the most crucial of which is the number of turtles remaining offshore during the entire sampling period. We illustrate the method using data sets from loggerhead turtle sites along the South Carolina coast. We provide a simulation study which illustrates the quality and robustness of the method and investigates sensitivity to prior parameter specification.

On Population Size Estimators in the Poisson Mixture Model

Estimating population sizes via capture-recapture experiments has enormous applications. The Poisson mixture model can be adopted for those applications with a single list in which individuals appear one or more times. We compare several nonparametric estimators, including the Chao estimator, the Zelterman estimator, two jackknife estimators and the bootstrap estimator. The target parameter of the Chao estimator is a lower bound of the population size. Those of the other four estimators are not lower bounds, and they may produce lower confidence limits for the population size with poor coverage probabilities. A simulation study is reported and two examples are investigated.

Accounting for matching uncertainty in two stage capture–recapture experiments using photographic measurements of natural marks

We propose a Bayesian hierarchical modeling approach for estimating the size of a closed population from data obtained by identifying individuals through photographs of natural markings. We assume that noisy measurements of a set of distinctive features are available for each individual present in a photographic catalogue. To estimate the population size from two catalogues obtained during two different sampling occasions, we embed the standard two-stage \(M_t\) capture–recapture model for closed population into a multivariate normal data matching model that identifies the common individuals across the catalogues. In addition to estimating the population size while accounting for the matching process uncertainty, this hierarchical modelling approach allows to identify the common individuals by using the information provided by the capture–recapture model. This way, our model also represents a novel and reliable tool able to reduce the amount of effort researchers have to expend in matching individuals. We illustrate and motivate the proposed approach via a real data set of photo-identification of narwhals. Moreover, we compare our method with a set of possible alternative approaches by using both the empirical data set and a simulation study.

Information dynamics and optimal sampling in capture-recapture

SUMMARY The build up of information in a continued capture-recapture experiment of simple random sampling of an open population is studied by predicting the conditional approximate Fisher information for abundance in data from one survey given the previous data. By neglecting the stochasticity in survival, a simple approximate likelihood is obtained. Optimal temporal allocation of a given total effort is found by numerical optimization for various objective functions based on the approximate Fisher information. For aerial photographic surveys of bowhead whales, the performance of estimates of abundance and of demographic parameters is compared between constant yearly survey effort and nominally optimal sampling by simulating a realistic model over 50 years.

Integrodifference model for blowfly invasion

We propose a stage-structured integrodifference model for blowflies’ growth and dispersion taking into account the density dependence of fertility and survival rates and the non-overlap of generations. We assume a discrete-time, stage-structured, model. The spatial dynamics is introduced by means of a redistribution kernel. We treat one and two dimensional cases, the latter on the semi-plane, with a reflexive boundary. We analytically show that the upper bound for the invasion front speed is the same as in the one-dimensional case. Using laboratory data for fertility and survival parameters and dispersal data of a single generation from a capture-recapture experiment in South Africa, we obtain an estimate for the velocity of invasion of blowflies of the species Chrysomya albiceps. This model predicts a speed of invasion which was compared to actual observational data for the invasion of the focal species in the Neotropics. Good agreement was found between model and observations.

Identifiability and inferential issues in capture-recapture experiments with heterogeneous detection probabilities

We focus on a capture-recapture model in which capture probabilities arise from an unspecified distribution $F$. We show that model parameters are identifiable based on the unconditional likelihood. This is not true with the conditional likelihood. We also clarify that consistency and asymptotic equivalence of maximum likelihood estimators based on conditional and unconditional likelihood do not hold. We show that estimates of the undetected fraction of population based on the unconditional likelihood converge to the so-called estimable sharpest lower bound and we derive a new asymptotic equivalence result. We finally provide theoretical and simulation arguments in favor of the use of the unconditional likelihood rather than the conditional likelihood especially when one is willing to infer on the sharpest lower bound.

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

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

Studies on the bionomics of male Anopheles gambiae Giles and male Anopheles funestus Giles from southern Mozambique

Little is known about the fitness of wild male mosquitoes, the females of which are vectors of malaria. The problem of studying male biology has been exacerbated by difficulties associated with catching them. In southern Mozambique, however, almost the entire adult population of An. funestus and An. gambiae s.l. rest inside houses. They leave in a dusk exodus, which makes them easy to collect. In 8,348 exit collections from a village from 2003 to 2009, 567,195 male An. funestus and 34,591 male An. gambiae s.l. were collected. During the study, numbers of An. funestus increased but numbers of An. gambiae s.l. declined to the point of extinction. Overall numbers of An. gambiae s.l. were positively correlated with temperature, whilst the relationship between temperature and numbers of An. funestus changed from an initially positive one in the first three years of the study to a negative one in the last three years. Marked males were recaptured up to 300 m from the release site, with most recaptures occurring within 150 m. Estimated mean daily survival of male An. funestus was 0.86 (95% C.I. 0.869-0.850). For the years 2003-2007, estimated mean daily survival of male An gambiae s.l. was 0.660 (95% C.I. 0.682-0.638). For either species, there was no relationship between mean weekly temperature and estimated daily survival. These results imply that males of An. funestus live as long as females but have a relatively short flight range. They are discussed in the light of possible release strategies of sterile or genetically modified mosquitoes.

A Review of the Use of Conditional Likelihood in Capture-Recapture Experiments

Resume Nous presentons une perspective moderne de l'approche par vraisemblances conditionnelles de l'analyse des experiences de capture-recapture. Nous montrons que ces vraisemblances conditionnelles relevent d'un modele lineaire generalise, ce qui permet l'application des nombreuses methodes elaborees dans ce cadre. Pour replacer ces applications dans leur contexte, nous passons en revue quelques-unes des approches existantes dans les modeles de capture-recapture avec probabilites de capture heterogenes au sein de populations fermees. Nous decrivons, en particulier, l'utilisation de modeles de melange parametriques et non parametriques, et examinons de facon plus detaillee le cas ou les probabilites de capture sont fonction de covariables. Summary We present a modern perspective of the conditional likelihood approach to the analysis of capture-recapture experiments, which shows the conditional likelihood to be a member of generalized linear model (GLM). Hence, there is the potential to apply the full range of GLM methodologies. To put this method in context, we first review some approaches to capture-recapture experiments with heterogeneous capture probabilities in closed populations, covering parametric and non-parametric mixture models and the use of covariates. We then review in more detail the analysis of capture-recapture experiments when the capture probabilities depend on a covariate.

A robust P-spline approach to closed population capture–recapture models with time dependence and heterogeneity

We extend the conditional likelihood approach to the analysis of capture–recapture experiments for closed populations by nonparametrically modeling the relationship between capture probabilities and individual covariates using P-splines. The model allows nonparametric functions of multivariate continuous covariates as well as categorical covariates and time effects, greatly enhancing the techniques available to an analyst. To implement this approach in practice, we found it necessary to develop a robust modification of the Horvitz–Thompson estimator. The method is illustrated on several data sets and a small simulation study is conducted.

Heterogeneous Capture-Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations

In practice, when analyzing data from a capture-recapture experiment it is tempting to apply modern advanced statistical methods to the observed capture histories. However, unless the analysis takes into account that the data have only been collected from individuals who have been captured at least once, the results may be biased. Without the development of new software packages, methods such as generalized additive models, generalized linear mixed models, and simulation-extrapolation cannot be readily implemented. In contrast, the partial likelihood approach allows the analysis of a capture-recapture experiment to be conducted using commonly available software. Here we examine the efficiency of this approach and apply it to several data sets.

On the feasibility of applying capture–recapture experiments for web evolution estimations

This paper proposes a novel application for estimating the size and evolution of web page populations, based on the capture–recapture methodology, which is mainly used in wildlife biological studies. Firstly, we present the necessary modifications and amendments needed for the web capture–recapture paradigm, and then we discuss the limitations confronted. The paper provides the implementation details of the proposed web capture recapture model along with its initial assessment. The anticipated outcome was to examine whether we can conduct capture–recapture experiments on the web (or a web sub-universe such as an Internet search engine directory), in order to further estimate evolution rates in web page populations.

Statistical analysis of an endemic disease from a capture-recapture experiment

There are a number of statistical techniques for analysing epidemic outbreaks. However, many diseases are endemic within populations and the analysis of such diseases are complicated by changing population demography. Motivated by the spread of cowpox among rodent populations, a combined mathematical model for population and disease dynamics is introduced. An MCMC algorithm is then constructed to make statistical inference for the model based on data being obtained from a capture–recapture experiment. The statistical analysis is used to identify the key elements in the spread of the cowpox virus.

Using capture-recapture data and hybrid Monte Carlo sampling to estimate an animal population affected by an environmental catastrophe

We propose a dynamic model for the evolution of an open animal population that is subject to an environmental catastrophe. The model incorporates a capture-recapture experiment often conducted for studying wildlife population, and enables inferences on the population size and possible effect of the catastrophe. A Bayesian approach is used to model unobserved quantities in the problem as latent variables and Markov chain Monte Carlo (MCMC) is used for posterior computation. Because the particular interrelationship between observed and latent variables negates the feasibility of standard MCMC methods, we propose a hybrid Monte Carlo approach that integrates a Gibbs sampler with the strategies of sequential importance sampling (SIS) and acceptance-rejection (AR) sampling for model estimation. We develop results on how to construct effective proposal densities for the SIS scheme. The approach is illustrated through a simulation study, and is applied to data from a mountain pygmy possum ( Burramys Parvus) population that was affected by a bushfire.

Estimating evolution of freshness in Internet cache directories under the capture–recapture methodology

In this paper, we describe a new web sampling scheme for measuring the evolution of freshness in search engines. The methodology used is the capture-recapture, which is mainly applied for estimating evolution rates in wildlife biological studies. After modifications and amendments, necessary for web paradigm application, we conducted three capture-recapture experiments of different duration over the caches of Google and MSN. In parallel, we used a typical sampling scheme, similar to many other web sampling approaches used in the literature, to evaluate the robustness of our proposal. The paper provides the implementation details of a web-based capture-recapture model along with its assessment. The results show that through the capture-recapture methodology we are able not only to measure the freshness of the tested search services but also to monitor its evolution over time, with a substantially lower amount of required sampling instances. It was not our intention to compare the performance of Google and MSN. However, through our experiments, we observed that although one sometimes presents better refresh rates than the other, in general both search services have virtually equal capabilities in refreshing their directories and providing new and up-to-date results to their users.

Reference Bayesian methods for recapture models with heterogeneity

In the context of capture–recapture experiments heterogeneous capture probabilities are often perceived as one of the most challenging features to be incorporated in statistical models. In this paper we propose within a Bayesian framework a new modeling strategy for inference on the unknown population size in the presence of heterogeneity of subject characteristics. Our approach is attractive in that parameters are easily interpretable. Moreover, no parametric distributional assumptions are imposed on the latent distribution of individual heterogeneous propensities to be captured. Bayesian inference based on marginal likelihood by-passes some common identifiability issues, and a formal default prior distribution can be derived. Alternative default prior choices are considered and compared. Performance of our formal default approach is favorably evaluated with two real data sets and with a small simulation study.

A Comparison of Population Size Estimators under the Truncated Count Model With and Without Allowance for Contaminations

The purpose of the study is to estimate the population size under a homogeneous truncated count model and under model contaminations via the Horvitz-Thompson approach on the basis of a count capture-recapture experiment. The proposed estimator is based on a mixture of zero-truncated Poisson distributions. The benefit of using the proposed model is statistical inference of the long-tailed or skewed distributions and the concavity of the likelihood function with strong results available on the nonparametric maximum likelihood estimator (NPMLE). The results of comparisons, for finding the appropriate estimator among McKendrick's, Mantel-Haenszel's, Zelterman's, Chao's, the maximum likelihood, and the proposed methods in a simulation study, reveal that under model contaminations the proposed estimator provides the best choice according to its smallest bias and smallest mean square error for a situation of sufficiently large population sizes and the further results show that the proposed estimator performs well even for a homogeneous situation. The empirical examples, containing the cholera epidemic in India based on homogeneity and the heroin user data in Bangkok 2002 based on heterogeneity, are fitted with an excellent goodness-of-fit of the models and the confidence interval estimations may also be of considerable interest.