Population counts along elliptical habitat contours: hierarchical modelling using Poisson-lognormal mixtures with nonstationary spatial structure

TL;DR

This paper develops hierarchical Poisson-lognormal models with nonstationary spatial structures to analyze population counts along elliptical habitats, accounting for environmental and unobserved ecological effects.

Contribution

It introduces flexible spatial modeling approaches, including nonstationary Gaussian processes, for ecological count data along irregular spatial domains.

Findings

Models effectively capture spatial variation in fish populations.

Nonstationary models outperform stationary counterparts in fit.

Approaches are applicable to other irregular spatial domains.

Abstract

Ecologists often interpret variation in the spatial distribution of populations in terms of responses to environmental features, but disentangling the effects of individual variables can be difficult if latent effects and spatial and temporal correlations are not accounted for properly. Here, we use hierarchical models based on a Poisson log-normal mixture to understand the spatial variation in relative abundance (counts per standardized unit of effort) of yellow perch, Perca flavescens, the most abundant fish species in Lake Saint Pierre, Quebec, Canada. The mixture incorporates spatially varying environmental covariates that represent local habitat characteristics, and random temporal and spatial effects that capture the effects of unobserved ecological processes. The sampling design covers the margins but not the central region of the lake. We fit spatial generalized linear mixed models based on three different prior covariance structures for the local latent effects: a single Gaussian process (GP) over the lake, a GP over a circle, and independent GP for each shore. The models allow for independence, isotropy, or nonstationary spatial effects. Nonstationarity is dealt with using two different approaches, geometric anisotropy, and the inclusion of covariates in the correlation structure of the latent spatial process. The proposed approaches for specification of spatial domain and choice of Gaussian process priors may prove useful in other applications that involve spatial correlation along an irregular contour or in discontinous spatial domains.