Non-local models for eco-evolutionary processes
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Every eco-evolutionary process requires thoughful consideration of the scales of the population and of the individual. Evolution takes place on the population scale while many ecological processes occur on the individual scale. Classically, the way to treat these processes is through the mean-field approximation, which treats the two scales as if they are identical, or through the PDE approximation, which treats the two scales as if they are incomparable. In between these two ends of the spectrum exist the non-local models which are gaining popularity in ecology and evolution. These models make it possible to formulate spatially structured models rigorously when the PDE formulation cannot be justified. Moreover, when the scale of the individual and the population is comparable and the PDE model is inapproraite. Non-local models can serve as a highly flexible and tractable method for modeling these processes.