title: On evolution under symmetric and asymmetric competitions.
abstract: This paper considers the coevolution of phenotypic traits in a community comprising two competitive species subject to strong Allee effects. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy under symmetric competition. Secondly, we find that evolutionary suicide is impossible when the two species undergo symmetric competition, however, evolutionary suicide can occur in an asymmetric competition model with strong Allee effects. Thirdly, it is found that evolutionary bistability is a likely outcome of the process under both symmetric and asymmetric competitions, which depends on the properties of symmetric and asymmetric competitions. Fourthly, under asymmetric competition, we find that evolutionary cycle is a likely outcome of the process, which depends on the properties of both intraspecific and interspecific competition. When interspecific and intraspecific asymmetries vary continuously, we also find that the evolutionary dynamics may admit a stable equilibrium and two limit cycles or two stable equilibria separated by an unstable limit cycle or a stable equilibrium and a stable limit cycle.
authors.affiliation: School of Sciences, Southwest Petroleum University, Sichuan Province 610500, PR China. zujian122281@yahoo.com.cn
authors.forename: Jian
authors.initials: J
authors.lastname: Zu
authors.forename: Wendi
authors.initials: W
authors.lastname: Wang
authors.forename: Yasuhiro
authors.initials: Y
authors.lastname: Takeuchi
authors.forename: Bo
authors.initials: B
authors.lastname: Zu
authors.forename: Kaifa
authors.initials: K
authors.lastname: Wang
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior; D003198:Computer Simulation; D017753:Ecosystem; D053476:Extinction, Biological; D005716:Game Theory; D049810:Genetic Speciation; D008954:Models, Biological