A model for phenotype change in a stochastic framework
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1.
National Research Centre for Growth and Development & Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, Albany, Auckland
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2.
National Research Centre for Growth and Development & AgResearch Limited, Ruakura Research Centre, Private Bag 3123, Hamilton
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3.
National Research Centre for Growth and Development & Liggins Institute, University of Auckland, Private Bag 92019, Auckland
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Received:
01 April 2009
Accepted:
29 June 2018
Published:
01 June 2010
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MSC :
Primary: 92D15, 60G15, 65K10; Secondary: 60G40, 60K40.
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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.
Citation: Graeme Wake, Anthony Pleasants, Alan Beedle, Peter Gluckman. A model for phenotype change in a stochastic framework[J]. Mathematical Biosciences and Engineering, 2010, 7(3): 719-728. doi: 10.3934/mbe.2010.7.719
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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.
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