Spatial factor analysis: a new tool for estimating joint species distributions and correlations in species range

Abstract

Summary Predicting and explaining the distribution and density of species is one of the oldest concerns in ecology. Species distributions can be estimated using geostatistical methods, which estimate a latent spatial variable explaining observed variation in densities, but geostatistical methods may be imprecise for species with low densities or few observations. Additionally, simple geostatistical methods fail to account for correlations in distribution among species and generally estimate such cross‐correlations as a post hoc exercise. We therefore present spatial factor analysis ( SFA ), a spatial model for estimating a low‐rank approximation to multivariate data, and use it to jointly estimate the distribution of multiple species simultaneously. We also derive an analytic estimate of cross‐correlations among species from SFA parameters. As a first example, we show that distributions for 10 bird species in the breeding bird survey in 2012 can be parsimoniously represented using only five spatial factors. As a second case study, we show that forward prediction of catches for 20 rockfishes ( S ebastes spp.) off the U . S . W est C oast is more accurate using SFA than analysing each species individually. Finally, we show that single‐species models give a different picture of cross‐correlations than joint estimation using SFA . Spatial factor analysis complements a growing list of tools for jointly modelling the distribution of multiple species and provides a parsimonious summary of cross‐correlation without requiring explicit declaration of habitat variables. We conclude by proposing future research that would model species cross‐correlations using dissimilarity of species’ traits, and the development of spatial dynamic factor analysis for a low‐rank approximation to spatial time‐series data.