Moment Equations for the Evolution of Quantitative Traits in Space
The importance of genetic change, and in particular adaptive evolu-tion, during biological invasions is widely acknowledged, yet has to datereceived little attention from theoreticians. Here we present analysis of aset of models for the moments of a quantitative trait (i.e. a continuous ran-dom variable like body size) in a population that disperses in a continuousspatial habitat with a spatially varying trait optimum, building on workof Kirkpatrick and Barton (1997) and others. We focus on (discrete-time)integrodierence models incorporating \heavy-tailed" dispersal, which isknown to strongly inuence the speed of traveling wave solutions, represent-ing invasions, in purely ecological models without a genetic component. Weobtain both traveling wave speeds and, when maladaptation limits the ex-tend of an invasion, properties of the resulting localized (i.e. range-limited)population. These are contrasted with existing results (Kirkpatrick/Barton1997, Barton 2001, Garcia-Ramos/Rodriguez 2002) for partial dierentialequation models representing diusive movement. The results advance un-derstanding of how dispersal patterns interact with genetics and environ-mental conditions to determine the extent of a species' range.
Joint work with A. Castorena.
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