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Mathematical Biosciences and Engineering

2010, Volume 7, Issue 3: 719-728. doi: 10.3934/mbe.2010.7.719
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A model for phenotype change in a stochastic framework

  • 1.
    National Research Centre for Growth and Development & Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, Albany, Auckland
  • 2.
    National Research Centre for Growth and Development & AgResearch Limited, Ruakura Research Centre, Private Bag 3123, Hamilton
  • 3.
    National Research Centre for Growth and Development & Liggins Institute, University of Auckland, Private Bag 92019, Auckland
  • Received: 01 April 2009 Accepted: 29 June 2018 Published: 01 June 2010

  • MSC : Primary: 92D15, 60G15, 65K10; Secondary: 60G40, 60K40.

  • 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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  • 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.


  • This article has been cited by:

    1. Hamish G. Spencer, Anthony B. Pleasants, Peter D. Gluckman, Graeme C. Wake, A model of optimal timing for a predictive adaptive response, 2021, 2040-1744, 1, 10.1017/S2040174420001361
    2. Graeme Wake, 2015, Chapter 27, 978-3-319-22128-1, 155, 10.1007/978-3-319-22129-8_27
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  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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