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

Dinara Sadykova,Beth E Scott,Judith Wolf,Sarah L Wakelin,Alexander Sadykov,Michela De Dominicis

doi:10.1002/ece3.3081

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 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.

Highlights

The marine environment is changing rapidly due to climate change (Burrows et al, 2011) and increasing anthropogenic activities (Wakelin, Artioli, Butenschön, Allen, & Holt, 2015) including large- scale energy extraction
To deal with the above issues and investigate whether there are common spatial trends between competing and predator–prey species, we considered a Bayesian hierarchical joint modeling approach with integrated nested Laplace approximation (INLA) that substantially reduce the computational cost of fitting complex spatial models (Rue, Martino, & Chopin, 2009) and applied the methodology to the single-species and joint-species spatial and spatiotemporal hurdle and zero-inflated models
We considered all possible combinations of covariates excluding the combinations with highly (>0.6) correlated variables

Summary

| INTRODUCTION

The marine environment is changing rapidly due to climate change (Burrows et al, 2011) and increasing anthropogenic activities (Wakelin, Artioli, Butenschön, Allen, & Holt, 2015) including large- scale energy extraction (tidal, wave, and wind; Shields & Payne, 2014). Due to the high number of zeros in the observational data, we used seabird density maps (×102) (Fig. S3 in Appendix S1, left panel) which were based on the bird observation data using Poisson kriging and represent predicted density of common guillemot, black-legged kittiwake, and northern gannet in each 6 × 6 km grid cells across the 28-year data (1979–2006). In a similar way to the seabird data, we constructed an effort variable that determines how many times each grid cell was visited (with the grid size of 300 × 300 m) Due to such high number of zeros in the observational data, we created sandeel density maps (×102) (Fig. S4 in Appendix S1, left panel) in 7 × 7 km grid mesh across the 16-year data (1989–2005) using Poisson kriging, which takes into account unequal survey efforts and is suitable to the observation data that are heterogeneously distributed (Kober et al, 2010). For the observation data and the abundance/density/usage maps with finer resolution grids, we used predictive joint modeling with misalignment (Krainski, Lindgren, Simpson, & Rue, 2015) to predict bio/physical variables on the species locations (see the Joint Modeling with Misalignment section)

| METHODS

| DISCUSSION

| CONCLUSION