An evolutionary tolerance model explaining spatial patterns in species richness under environmental gradients and geometric constraints

In this study, we developed a simulation model based on the ecological and evolutionary dynamics of geographical ranges, to understand the role of species' environmental tolerances and the strength of the environmental gradient in determining spatial patterns in species richness. Using an one-dimensional space, we present the model and dissect its parameters. Also, we test the ability of the model to simulate richness in complex two-dimensional domains and to fit real patterns in species richness, using South American Tyrannidae as an example. We found that a mid-spatial peak in species richness arises spontaneously under conditions of high environmental tolerances and/or a weak environmental gradient, since this condition causes wide species' geographic ranges, which are constrained by domain's boundary and tend to overlap in the middle. Our model was also a good predictor of real patterns in species richness, especially under conditions of high environmental strength and small species' tolerance. We conclude that this kind of spatial simulation models based on species' physiological tolerance may be an important tool to understand the evolutionary dynamics of species' geographic ranges and in spatial patterns of species richness.