How environmental perturbations affect coexistence

Understanding the effects of environmental perturbations on coexistence is a key challenge in ecology, and models have played an important role in structuring our ideas and generating predictions, leading to quantitative hypotheses.In such models, environmental perturbations are often captured by changes in parameter values, such as the intrinsic growth rates of species (1-3).The question then becomes how much one can change these parameters without breaking coexistence and thus losing species (4).An intuitively appealing approach to address this question is to calculate a model's feasibility domain (5-7).Loosely defined, it is the fraction of parameter settings leading to the coexistence of all species.Mathematically speaking, it is a high-dimensional triangle, of which one can calculate the size, just as for plain two-dimensional triangles.