title: Evolution of natal dispersal in spatially heterogenous environments.
abstract: Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal free distribution, is evolutionary stable in spatially varying but temporally constant environments. Many species, however, primarily disperse prior to reproduction (natal dispersal) and less commonly between reproductive events (breeding dispersal). These species include territorial species such as birds and reef fish, and sessile species such as plants, and mollusks. As demographic and dispersal terms combine in a multiplicative way for models of natal dispersal, rather than the additive way for the previously studied models, we develop new mathematical methods to study the evolution of natal dispersal for continuous-time and discrete-time models. A fundamental ecological dichotomy is identified for the non-trivial equilibrium of these models: (i) the per-capita growth rates for individuals in all patches are equal to zero, or (ii) individuals in some patches experience negative per-capita growth rates, while individuals in other patches experience positive per-capita growth rates. The first possibility corresponds to an ideal-free distribution, while the second possibility corresponds to a "source-sink" spatial structure. We prove that populations with a dispersal strategy leading to an ideal-free distribution displace populations with dispersal strategy leading to a source-sink spatial structure. When there are patches which cannot sustain a population, ideal-free strategies can be achieved by sedentary populations, and we show that these populations can displace populations with any irreducible dispersal strategy. Collectively, these results support that evolution selects for natal or breeding dispersal strategies which lead to ideal-free distributions in spatially heterogenous, but temporally homogenous, environments.
authors.affiliation: Department of Mathematics, University of Miami, Coral Gables, FL 33124, United States. Electronic address: rsc@math.miami.edu.
authors.forename: Robert Stephen
authors.initials: RS
authors.lastname: Cantrell
authors.affiliation: Department of Mathematics, University of Miami, Coral Gables, FL 33124, United States. Electronic address: gcc@math.miami.edu.
authors.forename: Chris
authors.initials: C
authors.lastname: Cosner
authors.affiliation: Institute for Mathematical Sciences, Renmin University of China, Beijing 100872, PRC, China; Department of Mathematics, Ohio State University, Columbus, OH 43210, United States. Electronic address: lou@math.ohio-state.edu.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Lou
authors.affiliation: Department of Evolution and Ecology, University of California at Davis, Davis, California 95616, United States. Electronic address: sschreiber@ucdavis.edu.
authors.forename: Sebastian J
authors.initials: SJ
authors.lastname: Schreiber
mesh_terms: D000818:Animals; D005075:Biological Evolution; D017753:Ecosystem; D008962:Models, Theoretical
keywords: Evolution of dispersal; Evolutionary stability; Ideal free distribution; Patchy environments; Source-sink populations