Modeling and simulation study of the stoichiometric niche space and niche overlap based on the copula method

Abstract

To qualify niche space and niche overlap, the current methods are based on a strict assumption of the normal distribution and restrict dependence to the linear structure between resource axes. In this study, we propose a new method for measuring the stoichiometric niche space and niche overlap based on copula theory. Our method does not require the resource axes to obey the multivariate normal distribution and only assumes that each dimension of resource availability follows a one-dimensional normal distribution. Based on the dependence structure presented by the three resource axes, an appropriate copula is selected to couple the normal assumptions and thus determine a joint distribution that fits the carbon, nitrogen and phosphorus concentration data. Additional simulation studies were conducted to calculate niche space and niche overlap. We applied our method to qualify the stoichiometric niche space and niche overlap between seven grassland plants in Inner Mongolia, North China. Our results demonstrate that, except for a positive correlation, symmetrical tail correlations existed between nitrogen and phosphorus concentrations, which had a significant influence on the shape of the niche space. The new method presented in our work extends types of joint distribution fitting resource axes from a multivariate normal distribution to an arbitrary joint distribution determined by copulas and normal margins, and it has the advantage of describing the complex dependence between resource axes.