Kinetic equations in spatial quantitative genetics

Judith Miller (October 25, 2011)

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We derive kinetic differential or integrodifference equations for the mean and variance or of a quantitative trait as a function of space and time, in some cases recovering known equations and in some cases obtaining new ones that capture effects, such as nonmonotonicity of traveling waves, that can be seen in stochastic simulations. We then reanalyze kinetic equations due to Kirkpatrick and Barton for population range limits, showing that they exhibit bistability and hysteresis. This suggests a possible mechanism for lag times between establishment and subsequent explosive growth and range expansion in the absence of an Allee effect.