In an influential paper, Kirkpatrick and Barton (Am Nat 150:1-23 1997) presented a system of diffusive partial differential equations modeling the joint evolution of population density and the mean of a quantitative trait when the trait optimum varies over a continuous spatial domain. We present a stability theorem for steady states of a simplified version of the system, originally studied in Kirkpatrick and Barton (Am Nat 150:1-23 1997). We also present a derivation of the system.
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