Integrated data analysis in the presence of emigration and mark loss

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.

Multiple Systems Estimation (or Capture-Recapture Estimation) to Inform Public Policy

Estimating population sizes has long been of interest, from the estimation of the human or ecological population size within regions or countries to the hidden number of civilian casualties in a war. Total enumeration of the population, for example, via a census, is often infeasible or simply impractical. However, a series of partial enumerations or observations of the population is often possible. This has led to the ideas of capture-recapture methods, which have been extensively used within ecology to estimate the size of wildlife populations, with an associated measure of uncertainty, and are most effectively applied when there are multiple capture occasions. Capture-recapture ideology can be more widely applied to multiple data-sources, by the linkage of individuals across the multiple lists. This is often referred to as Multiple Systems Estimation (MSE). The MSE approach has been preferred when estimating "capture-shy" or hard-to-reach populations, including those caught up in the criminal justice system; or homeless; or trafficked; or civilian casualties of war. Motivated by a range of public policy applications of MSE, each briefly introduced, we discuss practical problems with potentially substantial methodological implications. They include: "period" definition; "case" definition; when an observed count is not a true count of the population of interest but an upper bound due to mismatched definitions; exact or probabilistic matching of "cases" across different lists; demographic or other information about the "case" which may influence capture-propensities; required permissions to access extant-lists; list-creation by research-teams or interested parties; referrals (if presence on list A results - almost surely - in presence on list B); different mathematical models leading to widely different estimated population sizes; uncertainty in estimation; computational efficiency; external validation; hypothesis-generation; and additional independent external information. Returning to our motivational applications, we focus on whether the uncertainty which qualified their estimates was sufficiently narrow to orient public policy; and, if not, what options were available and/or taken to reduce the uncertainty or to seek external validation. We also consider whether MSE was hypothesis-generating: in the sense of having spawned new lines of inquiry.

Investigating the effects of age-related spatial structuring on the transmission of a tick-borne virus in a colonially breeding host

Higher pathogen and parasite transmission is considered a universal cost of colonial breeding due to the physical proximity of colony members. However, this has rarely been tested in natural colonies, which are structured entities, whose members interact with a subset of individuals and differ in their infection histories. We use a population of common guillemots, Uria aalge, infected by a tick-borne virus, Great Island virus, to explore how age-related spatial structuring can influence the infection costs borne by different members of a breeding colony. Previous work has shown that the per-susceptible risk of infection (force of infection) is different for prebreeding (immature) and breeding (adult) guillemots which occupy different areas of the colony. We developed a mathematical model which showed that this difference in infection risk can only be maintained if mixing between these age groups is low. To estimate mixing between age groups, we recorded the movements of 63 individually recognizable, prebreeding guillemots in four different parts of a major colony in the North Sea during the breeding season. Prebreeding guillemots infrequently entered breeding areas (in only 26% of watches), though with marked differences in frequency of entry among individuals and more entries toward the end of the breeding season. Once entered, the proportion of time spent in breeding areas by prebreeding guillemots also varied between different parts of the colony. Our data and model predictions indicate low levels of age-group mixing, limiting exposure of breeding guillemots to infection. However, they also suggest that prebreeding guillemots have the potential to play an important role in driving infection dynamics. This highlights the sensitivity of breeding colonies to changes in the behavior of their members-a subject of particular importance in the context of global environmental change.

Bayesian joint models with INLA exploring marine mobile predator-prey and competitor species habitat overlap

Understanding spatial physical habitat selection driven by competition and/or predator–prey interactions of mobile marine species is a fundamental goal of spatial ecology. However, spatial counts or density data for highly mobile animals often (1) include excess zeros, (2) have spatial correlation, and (3) have highly nonlinear relationships with physical habitat variables, which results in the need for complex joint spatial models. In this paper, we test the use of Bayesian hierarchical hurdle and zero‐inflated joint models with integrated nested Laplace approximation (INLA), to fit complex joint models to spatial patterns of eight mobile marine species (grey seal, harbor seal, harbor porpoise, common guillemot, black‐legged kittiwake, northern gannet, herring, and sandeels). For each joint model, we specified nonlinear smoothed effect of physical habitat covariates and selected either competing species or predator–prey interactions. Out of a range of six ecologically important physical and biologic variables that are predicted to change with climate change and large‐scale energy extraction, we identified the most important habitat variables for each species and present the relationships between these bio/physical variables and species distributions. In particular, we found that net primary production played a significant role in determining habitat preferences of all the selected mobile marine species. We have shown that the INLA method is well‐suited for modeling spatially correlated data with excessive zeros and is an efficient approach to fit complex joint spatial models with nonlinear effects of covariates. Our approach has demonstrated its ability to define joint habitat selection for both competing and prey–predator species that can be relevant to numerous issues in the management and conservation of mobile marine species.

Bringing It All Together: Multi-species Integrated Population Modelling of a Breeding Community

Integrated population models (IPMs) combine data on different aspects of demography with time-series of population abundance. IPMs are becoming increasingly popular in the study of wildlife populations, but their application has largely been restricted to the analysis of single species. However, species exist within communities: sympatric species are exposed to the same abiotic environment, which may generate synchrony in the fluctuations of their demographic parameters over time. Given that in many environments conditions are changing rapidly, assessing whether species show similar demographic and population responses is fundamental to quantifying interspecific differences in environmental sensitivity and highlighting ecological interactions at risk of disruption. In this paper, we combine statistical approaches to study populations, integrating data along two different dimensions: across species (using a recently proposed framework to quantify multi-species synchrony in demography) and within each species (using IPMs with demographic and abundance data). We analyse data from three seabird species breeding at a nationally important long-term monitoring site. We combine demographic datasets with island-wide population counts to construct the first multi-species Integrated Population Model to consider synchrony. Our extension of the IPM concept allows the simultaneous estimation of demographic parameters, adult abundance and multi-species synchrony in survival and productivity, within a robust statistical framework. The approach is readily applicable to other taxa and habitats. Supplementary materials accompanying this paper appear on-line.

Electronic Supplementary Material

Supplementary materials for this article are available at 10.1007/s13253-017-0279-4.

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.