On population abundance and niche structure

Recent published evidence indicates a negative correlation between density of populations and the distance of their environments to a suitably defined 'niche centroid'. This empirical observation lacks theoretical grounds. We provide a theoretical underpinning for the empirical relationship between population density and position in niche space, and use this framework to understand the circumstances under which the relationship will fail. We propose a metapopulation model for the area of distribution, as a system of ordinary differential equations coupled with a dispersal kernel. We present an analytical approximation to the solution of the system as well as R code to solve the full model numerically. We use this tool to analyze various scenarios and assumptions. General and realistic demographic assumptions imply a good correlation between position in niche space and population abundance. Factors that modify this correlation are: transitory states, a heterogeneous spatial structure of suitability, and Allee effects. We also explain why the raw output of the niche modeling algorithm MaxEnt is not a good predictor of environmental suitability. Our results elucidate the empirical results for spatial patterns of population size in niche terms, and provide a theoretical basis for a structured theory of the niche.