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

Abstract

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 zeroinflated 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 predatorprey 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. K E Y W O R D SBesag models, bio-physical habitats, hurdle models, integrated nested Laplace approximation, mobile marine species, spatial joint modeling, spatial niche selection, stochastic partial differential equations, zero-inflated models

Ecological costs of climate change on marine predator–prey population distributions by 2050

“…The common guillemot, black-legged kittiwake, and northern gannet density maps show seabird density across 25 years of data from at-sea surveys with data from all seasons (Kober et al, 2010). More details about the methods of modeling the different species can be found in Sadykova et al (2017). All the species data were given on a regular 7 × 7 km square grid.…”

“…We used Besag, York, and Mollie (BYM) (Besag, York, & Mollie, 1991) spatial hurdle and nonhurdle single and joint models following Sadykova et al (2017). BYM is an intrinsic autoregressive model, where the spatial effect of a particular area depends on the effects of the neighboring areas.…”

“…BYM is an intrinsic autoregressive model, where the spatial effect of a particular area depends on the effects of the neighboring areas. For the data without excess zeros, we assumed a model with gamma likelihood (Sadykova et al, 2017). Both spatial effect and heterogeneous effect are referred to as "random effects" in this paper.…”

“…The coupled species were assumed to share the same biophysical habitat variables (find more about single-species habitat selection in Sadykova et al, 2017). The coupled species were assumed to share the same biophysical habitat variables (find more about single-species habitat selection in Sadykova et al, 2017).…”

“…These outcomes can then be used in ecosystem models as predictors of the amount of future population change for a given stressor, that is, climate change or largescale renewable developments. This study uses spatial analytical tools (Sadykova et al, 2017) that can estimate the degree and strength of overlap (referred to as "common spatial trends") of spatial locations driven by important biological and physical variables by using a Bayesian hierarchical joint modeling approach with integrated nested Laplace approximation, INLA (Rue, Martino, & Chopin, 2009;Rue et al, 2017). Therefore, we know a lot about "where" seabirds and mammals and some of their main prey species may be located but we know far less about exactly "why" they are there, for example, what it is about these habitats that make them the (potentially limited) areas where mobile animals forage (Cox et al, 2018).…”