 This can be written as the convolution
Using a moment-generating-function transformation
it has been shown that the critical wave speed

Other types of equations used to model population dynamics through space include reaction-diffusion equations and metapopulation equations.However, diffusion equations do not as easily allow for the inclusion of explicit dispersal patterns and are only biologically accurate for populations with overlapping generations.Metapopulation equations are different from integrodifference equations in the fact that they break the population down into discrete patches rather than a continuous landscape.