title: A model for phenotype change in a stochastic framework.
abstract: In some species, an inducible secondary phenotype will develop some time after the environmental change that evokes it. Nishimura (2006) [4] showed how an individual organism should optimize the time it takes to respond to an environmental change ("waiting time''). If the optimal waiting time is considered to act over the population, there are implications for the expected value of the mean fitness in that population. A stochastic predator-prey model is proposed in which the prey have a fixed initial energy budget. Fitness is the product of survival probability and the energy remaining for non-defensive purposes. The model is placed in the stochastic domain by assuming that the waiting time in the population is a normally distributed random variable because of biological variance inherent in mounting the response. It is found that the value of the mean waiting time that maximises fitness depends linearly on the variance of the waiting time.
authors.affiliation: National Research Centre for Growth and Development and Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, Albany, Auckland, New Zealand. g.c.wake@massey.ac.nz
authors.forename: Graeme
authors.initials: G
authors.lastname: Wake
authors.forename: Anthony
authors.initials: A
authors.lastname: Pleasants
authors.forename: Alan
authors.initials: A
authors.lastname: Beedle
authors.forename: Peter
authors.initials: P
authors.lastname: Gluckman
mesh_terms: D000222:Adaptation, Physiological / Q000502:physiology*; D000818:Animals; D008954:Models, Biological; D010641:Phenotype; D011235:Predatory Behavior / Q000502:physiology*; D013269:Stochastic Processes