Location: Fields Institute , 222 College Street, Toronto
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July 9, 2008 - 3:30 p.m.
Graeme Wake
Centre for Mathematics in Industry, Massey University @ Auckland,
New Zealand

A model for phenotype change in a stochastic framework
In some species, an inducible secondary phenotype will develop some time after the environmental change that evokes it. Nishimura (EER 8:553) showed how an individual organism should optimize the time it takes to respond to such an environmental change.
Question: If the optimal response time is considered to act over the population, what are the implications for the expected value of the mean fitness in that population?
Model: A stochastic predator-prey model in which the prey have a fixed initial energy budget. Prey individuals trade off reduction in the probability of predation against increase in the energy required to maintain a phenotype with improved defense. Fitness is assessed as the product of survival probability and the energy that remains for non-defensive purposes.
Key assumption: The response time in the population is a normally distributed random variable because of biological variance inherent in mounting the response.
Conclusions: No unique values for mean response time and variance in response time maximize fitness. Rather, maximum fitness is described by pairs of these values lying on a straight line in the plane of mean time and variance. Populations with equal mean fitness will show different frequency distributions of response times, which may allow different populations to explore different environments. If a significant proportion of the population delays an inducible response, the population may suffer no loss of fitness from either its predation level or the energy expenditures it requires to maintain plasticity.
This work is in conjunction with the Liggins Institute (Professor Peter Gluckman) and AgResearch (Tony Pleasants).