Evolutionary dynamics of prey-predator systems with Holling type II functional response - Jian Zu; Wendi Wang; Bo Zu (Mathematical Biosciences and Engineering)
This paper considers the coevolution of phenotypes in a communitycomprising the populations of predators and prey. The evolutionarydynamics is constructed from a stochastic process of mutation andselection. We investigate the ecological and evolutionary conditionsthat allow for continuously stable strategy and evolutionarybranching. It is shown that branching in the prey can inducesecondary branching in the predators. Furthermore, it is shown thatthe evolutionary dynamics admits a stable limit cycle. Theevolutionary cycle is a likely outcome of the process, whichrequires higher evolutionary speed of prey than of predators. Itis also found that different evolutionary rates and conversionefficiencies can influence the lengths of evolutionary cycles.