Assessing heterogeneity in transition propensity in multi-state capture-recapture data

Multi-state capture-recapture models are a useful tool to help understand the dynamics of movement within discrete capture-recapture data. The standard multi-state capture-recapture model however relies on assumptions of homogeneity within the population with respect to survival, capture and transition probabilities. There are many ways in which this model can be generalized so that some guidance as to what is really needed is highly desirable. Within this paper we derive a new test capable of detecting heterogeneity in transition propensity and show its good power using simulation and application to a Canada goose data set. We also demonstrate that existing tests which have traditionally been used to diagnose memory are in fact sensitive to other forms of transition heterogeneity and we propose modified tests which are able to distinguish between memory and other forms of transition heterogeneity

How ideas from ecological capture-recapture models may inform multiple systems estimation analyses

Abundance estimation, for both human and animal populations, informs policy decisions and population management. Capture-recapture and multiple sources data share a common structure; the population can be partially enumerated and individuals are identifiable. Consequently, the analytical methods were developed simultaneously. However, whilst ecological models have been developed to describe highly complex, biologically realistic scenarios, for example modeling population changes through time and combining different forms of data, multiple systems estimation has changed comparatively less so. In this paper we provide a brief description of the historical development of ecological and epidemiological capture-recapture and discuss the associated underlying differences that have led to model divergence. We identify three key areas where ecological modeling methods may inform and improve multiple systems estimation.Publisher PDFPeer reviewe

Integrated Population Models: Achieving their Potential

Precise and accurate estimates of abundance and demographic rates are primary quantities of interest within wildlife conservation and management. Such quantities provide insight into population trends over time and the associated underlying ecological drivers of the systems. This information is fundamental in managing ecosystems, assessing species conservation status and developing and implementing effective conservation policy. Observational monitoring data are typically collected on wildlife populations using an array of different survey protocols, dependent on the primary questions of interest. For each of these survey designs, a range of advanced statistical techniques have been developed which are typically well understood. However, often multiple types of data may exist for the same population under study. Analyzing each data set separately implicitly discards the common information contained in the other data sets. An alternative approach that aims to optimize the shared information contained within multiple data sets is to use a “model-based data integration” approach, or more commonly referred to as an “integrated model.” This integrated modeling approach simultaneously analyzes all the available data within a single, and robust, statistical framework. This paper provides a statistical overview of ecological integrated models, with a focus on integrated population models (IPMs) which include abundance and demographic rates as quantities of interest. Four main challenges within this area are discussed, namely model specification, computational aspects, model assessment and forecasting. This should encourage researchers to explore further and develop new practical tools to ensure that full utility can be made of IPMs for future studies

Discussion on “The central role of the identifying assumption in population size estimation” by Serge Aleshin-Guendel, Mauricio Sadinle, and Jon Wakefield

In this discussion response, we consider some practical implications of the authors’ consideration of the no-highest-order interaction (NHOI) model for multiple systems estimation, which permits the authors to derive the explicit (albeit untestable) identifying assumption related to the unobserved (or missing) individuals. In particular, we discuss several aspects, from the standard process of model selection to potential poor predictive performance due to over-fitting and the implications of data reduction. We discuss these aspects in relation to the case study presented by the authors relating to the number of civilian casualties within the Kosovo war, and conduct further preliminary simulations to investigate these issues further. The results suggest that the NHOI models considered, despite having a potentially useful theoretical result in relation to the underlying identifying assumption, may perform poorly in practice

Removal modelling in ecology: A systematic review

Removal models were proposed over 80 years ago as a tool to estimate unknown population size. More recently, they are used as an effective tool for management actions for the control of non desirable species, or for the evaluation of translocation management actions. Although the models have evolved over time, in essence, the protocol for data collection has remained similar: at each sampling occasion attempts are made to capture and remove individuals from the study area. Within this paper we review the literature of removal modelling and highlight the methodological developments for the analysis of removal data, in order to provide a unified resource for ecologists wishing to implement these approaches. Models for removal data have developed to better accommodate important features of the data and we discuss the shift in the required assumptions for the implementation of the models. The relative simplicity of this type of data and associated models mean that the method remains attractive and we discuss the potential future role of this technique

A Test for the Underlying State-Structure of Hidden Markov Models: Partially Observed Capture-Recapture Data

Hidden Markov models (HMMs) are being widely used in the field of ecological modeling, however determining the number of underlying states in an HMM remains a challenge. Here we examine a special case of capture-recapture models for open populations, where some animals are observed but it is not possible to ascertain their state (partial observations), whilst the other animals' states are assigned without error (complete observations). We propose a mixture test of the underlying state structure generating the partial observations, which assesses whether they are compatible with the set of states observed in the complete observations. We demonstrate the good performance of the test using simulation and through application to a data set of Canada Geese

Estimating Abundance from Multiple Sampling Capture-Recapture Data via a Multi-State Multi-Period Stopover Model

Capture-recapture studies often involve collecting data on numerous capture occasions over a relatively short period of time. For many study species, this process is repeated, for example annually, resulting in capture information spanning multiple sampling periods. To account for the different temporal scales, the robust design class of models have traditionally been applied providing a frame-work in which to analyse all of the available capture data in a single likelihood expression. However, these models typically require strong constraints, either the assumption of closure within a sampling period (the closed robust design) or conditioning on the number of individuals captured within a sampling period (the open robust design). For real datasets these assumptions may not be appropriate. We develop a general modelling structure that requires neither assumption by explicitly modelling the movement of individuals into the population both within and between the sampling periods, which in turn permits the estimation of abundance within a single consistent framework. The exibility of the novel model structure is further demonstrated by including the computationally challenging case of multi-state data where there is individual time-varying discrete covariate information. We derive an efficient likelihood expression for the new multi-state multi-period stopover model using the hidden Markov model framework. We demonstrate the significant improvement in parameter estimation using our new modelling approach in terms of both the multi-period and multi-state components through both a simulation study and a real dataset relating to the protected species of great crested newts, Triturus cristatus

Loss-based prior for the degrees of freedom of the Wishart distribution

Motivated by the proliferation of extensive macroeconomic and health datasets necessitating accurate forecasts, a novel approach is introduced to address Vector Autoregressive (VAR) models. This approach employs the global-local shrinkage-Wishart prior. Unlike conventional VAR models, where degrees of freedom are predetermined to be equivalent to the size of the variable plus one or equal to zero, the proposed method integrates a hyperprior for the degrees of freedom to account for the uncertainty in the parameter values. Specifically, a loss-based prior is derived to leverage information regarding the data-inherent degrees of freedom. The efficacy of the proposed prior is demonstrated in a multivariate setting both for forecasting macroeconomic data, and Dengue infection data

Open models for removal data

Individuals of protected species, such as amphibians and reptiles, often need to be removed from sites before development commences. Usually, the population is considered to be closed. All individuals are assumed to i) be present and available for detection at the start of the study period and ii) remain at the site until the end of the study, unless they are detected. However, the assumption of population closure is not always valid. We present new removal models which allow for population renewal through birth and/or immigration, and population depletion through sampling as well as through death/emigration. When appropriate, productivity may be estimated and a Bayesian approach allows the estimation of the probability of total population depletion. We demonstrate the performance of the models using data on common lizards, Zootoca vivipara, and great crested newts, Triturus cristatus