A framework for analyzing ecological trait-based models in multi-dimensional niche spaces

Abstract: We develop an theoretical approach for predicting biodiversity in multi-dimensional niche spaces, arising due to ecological drivers such as competitive exclusion. The novelty of our approach relies on the fact that ecological niches are described by sequences of strings, which allows us to describe multiple traits. We define the mathematical framework for analyzing pattern forming instabilities in these models, showing surprisingly that the analytic linear theory predicts the asymptotically long time population distributions of niches in the model. We propose a test for identifying ecological drivers in biodiversity distributions, based on representing ecosystem data by means of a certain transform introduced in the theory.