  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.
