CSS, NIS and dynamic stability for two-species behavioral models with continuous trait spaces.
Static continuously stable strategy (CSS) and neighborhood invader strategy (NIS) conditions are developed for two-species models of frequency-dependent behavioral evolution when individuals have traits in continuous strategy spaces. These are intuitive stability conditions that predict the eventual outcome of evolution from a dynamic perspective. It is shown how the CSS is related to convergence stability for the canonical equation of adaptive dynamics and the NIS to convergence to a monomorphism for the replicator equation of evolutionary game theory. The CSS and NIS are also shown to be special cases of neighborhood p(*)- superiority for p(*) equal to one half and zero, respectively. The theory is illustrated when each species has a one-dimensional trait space.
Cressman
Ross
R
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada. rcressma@wlu.ca
D000220:Adaptation, Biological / Q000502:physiology; D025041:Animal Migration / Q000502:physiology*; D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior / Q000502:physiology; D003710:Demography; D004291:Dominance-Subordination; D017753:Ecosystem; D005716:Game Theory; D008962:Models, Theoretical; D011157:Population Dynamics; D013037:Spatial Behavior / Q000502:physiology*; D013045:Species Specificity