A model for phenotype change in a stochastic framework - Graeme Wake; Anthony Pleasants; Alan Beedle; Peter Gluckman (Mathematical Biosciences and Engineering)
In some species, an inducible secondary phenotype will develop sometime after the environmental change that evokes it. Nishimura (2006)[4] showed how an individual organism should optimizethe time it takes to respond to an environmental change ('waitingtime''). If the optimal waiting time is considered to act over thepopulation, there are implications for the expected value of themean fitness in that population. A stochastic predator-prey model isproposed in which the prey have a fixed initial energy budget.Fitness is the product of survival probability and the energyremaining for non-defensive purposes. The model is placed in thestochastic domain by assuming that the waiting time in thepopulation is a normally distributed random variable because ofbiological variance inherent in mounting the response. It is foundthat the value of the mean waiting time that maximises fitnessdepends linearly on the variance of the waiting time.