Latent multinomial models for extended batch-mark data.

Batch marking is common and useful for many capture-recapture studies where individual marks cannot be applied due to various constraints such as timing, cost, or marking difficulty. When batch marks are used, observed data are not individual capture histories but a set of counts including the numbers of individuals first marked, marked individuals that are recaptured, and individuals captured but released without being marked (applicable to some studies) on each capture occasion. Fitting traditional capture-recapture models to such data requires one to identify all possible sets of capture-recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this paper, we propose a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in Central Madagascar.

Climate anomalies and competition reduce establishment success during island colonization.

Understanding the factors that facilitate or constrain establishment of populations in novel environments is crucial for conservation biology and the study of adaptive radiation. Important questions include: (1) Does the timing of colonization relative to stochastic events, such as climatic perturbations, impact the probability of successful establishment? (2) To what extent does community context (e.g., the presence of competitors) change the probability of establishment? (3) How do sources of intrapopulation variance, such as sex differences, affect success at an individual level during the process of establishment? Answers to these questions are rarely pursued in a field-experimental context or on the same time scales (months to years) as the processes of colonization and establishment. We introduced slender anole lizards (Anolis apletophallus) to eight islands in the Panama Canal and tracked them over multiple generations to investigate the factors that mediate establishment success. All islands were warmer than the mainland (ancestral) environment, and some islands had a native competitor. We transplanted half of these populations only 4 months before the onset of a severe regional drought and the other half 2 years (two generations) before the drought. We found that successful establishment depended on both the intensity of interspecific competition and the timing of colonization relative to the drought. The islands that were colonized shortly before the drought went functionally extinct by the second generation, and regardless of time before the drought, the populations on islands with interspecific competition declined continuously over the study period. Furthermore, the effect of the competitor interacted with sex, with males suffering, and females benefitting, from the presence of a native competitor. Our results reveal that community context and the timing of colonization relative to climactic events can combine to determine establishment success and that these factors can generate opposite effects on males and females.

Removal models accounting for temporary emigration.

Removal of protected species from sites scheduled for development is often a legal requirement in order to minimize the loss of biodiversity. The assumption of closure in the classic removal model will be violated if individuals become temporarily undetectable, a phenomenon commonly exhibited by reptiles and amphibians. Temporary emigration can be modeled using a multievent framework with a partial hidden process, where the underlying state process describes the movement pattern of animals between the survey area and an area outside of the study. We present a multievent removal model within a robust design framework which allows for individuals becoming temporarily unavailable for detection. We demonstrate how to investigate parameter redundancy in the model. Results suggest the use of the robust design and certain forms of constraints overcome issues of parameter redundancy. We show which combinations of parameters are estimable when the robust design reduces to a single secondary capture occasion within each primary sampling period. Additionally, we explore the benefit of the robust design on the precision of parameters using simulation. We demonstrate that the use of the robust design is highly recommended when sampling removal data. We apply our model to removal data of common lizards, Zootoca vivipara, and for this application precision of parameter estimates is further improved using an integrated model.

A Test of Positive Association for Detecting Heterogeneity in Capture for Capture-Recapture Data.

The Cormack-Jolly-Seber (CJS) model assumes that all marked animals have equal recapture probabilities at each sampling occasion, but heterogeneity in capture often occurs and should be taken into account to avoid biases in parameter estimates. Although diagnostic tests are generally used to detect trap-dependence or transience and assess the overall fit of the model, heterogeneity in capture is not routinely tested for. In order to detect and identify this phenomenon in a CJS framework, we propose a test of positive association between previous and future encounters using Goodman-Kruskal's gamma. This test is based solely on the raw capture histories and makes no assumption on model structure. The development of the test is motivated by a dataset of Sandwich terns (Thalasseus sandvicensis), and we use the test to formally show that they exhibit heterogeneity in capture. We use simulation to assess the performance of the test in the detection of heterogeneity in capture, compared to existing and corrected diagnostic goodness-of-fit tests, Leslie's test of equal catchability and Carothers' extension of the Leslie test. The test of positive association is easy to use and produces good results, demonstrating high power to detect heterogeneity in capture. We recommend using this new test prior to model fitting as the outcome will guide the model-building process and help draw more accurate biological conclusions. Supplementary materials accompanying this paper appear online. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary materials for this article are available at 10.1007/s13253-017-0315-4.

A novel application of mark-recapture to examine behaviour associated with the online trade in elephant ivory.

The illegal trade in elephant ivory is driving the unlawful killing of elephants such that populations are now suffering unsustainable reductions. The internet is increasingly being used as a platform to conduct illegal wildlife trade, including elephant ivory. As a globally accessible medium the internet is as highly attractive to those involved in the illegal trade as it is challenging to regulate. Characterising the online illegal wildlife (ivory) trade is complex, yet key to informing enforcement activities. We applied mark-recapture to investigate behaviour associated with the online trade in elephant ivory on eBay UK as a generalist online marketplace. Our results indicate that trade takes place via eBay UK, despite its policy prohibiting this, and that two distinct trading populations exist, characterised by the pattern of their ivory sales. We suggest these may represent a large number of occasional (or non-commercial) sellers and a smaller number of dedicated (or commercial) sellers. Directing resource towards reducing the volume of occasional sales, such as through education, would enable greater focus to be placed upon characterising the extent and value of the illegal, "commercial" online ivory trade. MRC has the potential to characterise the illegal trade in ivory and diverse wildlife commodities traded using various online platforms.

Parameter redundancy in discrete state-space and integrated models.

Discrete state-space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state-space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state-space models using discrete analogues of methods for continuous state-space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant.

Does your species have memory? Analyzing capture-recapture data with memory models.

We examine memory models for multisite capture-recapture data. This is an important topic, as animals may exhibit behavior that is more complex than simple first-order Markov movement between sites, when it is necessary to devise and fit appropriate models to data. We consider the Arnason-Schwarz model for multisite capture-recapture data, which incorporates just first-order Markov movement, and also two alternative models that allow for memory, the Brownie model and the Pradel model. We use simulation to compare two alternative tests which may be undertaken to determine whether models for multisite capture-recapture data need to incorporate memory. Increasing the complexity of models runs the risk of introducing parameters that cannot be estimated, irrespective of how much data are collected, a feature which is known as parameter redundancy. Rouan et al. (JABES, 2009, pp 338-355) suggest a constraint that may be applied to overcome parameter redundancy when it is present in multisite memory models. For this case, we apply symbolic methods to derive a simpler constraint, which allows more parameters to be estimated, and give general results not limited to a particular configuration. We also consider the effect sparse data can have on parameter redundancy and recommend minimum sample sizes. Memory models for multisite capture-recapture data can be highly complex and difficult to fit to data. We emphasize the importance of a structured approach to modeling such data, by considering a priori which parameters can be estimated, which constraints are needed in order for estimation to take place, and how much data need to be collected. We also give guidance on the amount of data needed to use two alternative families of tests for whether models for multisite capture-recapture data need to incorporate memory.

Multistate mark-recapture model selection using score tests.

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.