title: Moment equations in spatial evolutionary ecology.
abstract: How should we model evolution in spatially structured populations? Here, I review an evolutionary ecology approach based on the technique of spatial moment equations. I first provide a mathematical underpinning to the derivation of equations for the densities of various spatial configurations in network-based models. I then show how this spatial ecological framework can be coupled with an adaptive dynamics approach to compute the invasion fitness of a rare mutant in a resident population at equilibrium. Under the additional assumption that mutations have small phenotypic effects, I show that the selection gradient can be expressed as a function of neutral measures of genetic and demographic structure. I discuss the connections between this approach and inclusive fitness theory, as well as the applicability and limits of this technique. My main message is that spatial moment equations can be used as a means to obtain compact qualitative arguments about the evolution of life-history traits for a variety of life cycles.
authors.affiliation: Centre d׳Écologie Fonctionnelle et Évolutive (CEFE), UMR 5175 CNRS - Université de Montpellier - Université Paul-Valéry Montpellier - EPHE, 1919, route de Mende, 34293 Montpellier Cedex 5, France. Electronic address: sebastien.lion@cefe.cnrs.fr.
authors.forename: Sébastien
authors.initials: S
authors.lastname: Lion
mesh_terms: D005075:Biological Evolution; D004463:Ecology; D058865:Introduced Species; D008962:Models, Theoretical; D011157:Population Dynamics
keywords: Adaptive dynamics; Host–parasite interactions; Inclusive fitness; Pair approximation; Spatial models