COS 220-5 - Quantifying effects of climate change using non-linear models of species-environment relationships

Abstract: The non-linear (typically unimodal) response of species to environmental and spatial gradients is a cornerstone of macro-ecology. By estimating the modal position (optimum) and spread (tolerance) of non-zero species abundance values along key gradients, such as temperature, latitude, elevation, moisture, nutrients, etc., researchers can characterize a realized niche from broad-scale studies. Non-linear models are therefore essential to accurately track and predict global shifts in species’ distributions caused by rapid climate change.

Here, we showcase a new mathematical mean function, called ‘modskurt’, to be used within our recently described species-environment non-linear modelling (‘senlm’) framework. Our approach is specifically designed to handle known statistical properties of broad-scale ecological field data, including species’ counts, biomass, cover, presence/absence, etc. The modskurt function flexibly accommodates complexities of species-environment relationships like asymmetry, flatness and/or peakedness in the modal mean response of a species, and its placement within the senlm framework simultaneously allows for overdispersion, inherent mean-variance relationships and zero-inflation in statistical error structures. The senlm models generally outperform classical approaches (such as Gaussian or quadratic GLMs or GAMs), which can produce biased results in the face of asymmetry and/or zero-inflation. Furthermore, we propose a new hierarchical Bayesian implementation for the entire senlm framework (called ‘senlm-B’), that can integrate and track changes in key parameters of ecological interest (such as the peak modal position and/or range of a species along the gradient) through time, through space or across different species or levels of another factor. Careful use of informative prior probabilities in senlm-B can provide a principled way to incorporate ecological knowledge, prevent illogical outcomes, and improve the accuracy and reliability of predictions and uncertainties.

We demonstrate our approach in analyses of long-term datasets for North American birds and for groundfish in the Northeast Pacific. For example, our models show that a culturally important and threatened fish species, Eulachon, has shifted its optimum position along the depth gradient to occupy deeper, cooler waters over the past 15 years. In another example, we found that approximately one-third of the birds in North America have shown significant shifts in their latitudinal optima over the past 55 years, with the majority shifting northward (at an overall average rate of ~1.4 km per year) in response to a warming climate. Our models rigorously quantify key ecological parameters (such as species’ optima) for gradient analyses at any scale, enhancing our understanding of species’ distributions and supporting management objectives to sustain biodiversity.