Non‐linear models of species' responses to environmental and spatial gradients

• Published in: Ecology letters Vol. 25; no. 12; pp. 2739 - 2752
• Main Authors: Anderson, Marti J., Walsh, Daniel C. I., Sweatman, Winston L., Punnett, Andrew J.
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 01.12.2022; John Wiley and Sons Inc
• Subjects: abundance; Animals; biomass; counts; cover; ecological statistics; Environment; Environment models; environmental variables; Error analysis; Fishes; gradient analysis; latitude; Mathematical models; Mean; Method; Methods; Nonlinear Dynamics; Spatial Analysis; Species; species distribution models; Spline functions; zero‐inflation; cover; biomass; ecological statistics; counts; species distribution models; abundance; latitude; environmental variables; gradient analysis; zero-inflation
• ISSN: 1461-023X; 1461-0248; 1461-0248
• DOI: 10.1111/ele.14121

Species' responses to broad‐scale environmental or spatial gradients are typically unimodal. Current models of species' responses along gradients tend to be overly simplistic (e.g., linear, quadratic or Gaussian GLMs), or are suitably flexible (e.g., splines, GAMs) but lack direct ecologically interpretable parameters. We describe a parametric framework for species‐environment non‐linear modelling (‘senlm’). The framework has two components: (i) a non‐linear parametric mathematical function to model the mean species response along a gradient that allows asymmetry, flattening/peakedness or bimodality; and (ii) a statistical error distribution tailored for ecological data types, allowing intrinsic mean–variance relationships and zero‐inflation. We demonstrate the utility of this model framework, highlighting the flexibility of a range of possible mean functions and a broad range of potential error distributions, in analyses of fish species' abundances along a depth gradient, and how they change over time and at different latitudes. We describe a new framework for non‐linear models of species to environmental or spatial gradients, along with an associated R package, 'senlm'. The framework has two essential components: (i) a non‐linear parametric mathematical function to model the mean species response curve along the gradient that allows for asymmetry, flattening/peakedness or bimodality; and (ii) a statistical error distribution tailored for ecological data types (counts, densities, biomass, cover, presence/absence, etc.), that allows for intrinsic mean‐variance relationships and zero‐inflation. The utility of the framework is demonstrated in analyses of fish abundances along a depth gradient, also showing how their responses can change over time and at different latitudes.