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Optimization and phenotype allocation
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Jost, Jürgen and Wang, Ying (2014) Optimization and phenotype allocation. Bulletin of Mathematical Biology, Volume 76 (Number 1). pp. 184-200. doi:10.1007/s11538-013-9915-5 ISSN 0092-8240.
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Official URL: http://dx.doi.org/10.1007/s11538-013-9915-5
Abstract
We study the phenotype allocation problem for the stochastic evolution of a multitype population in a random environment. Our underlying model is a multitype Galton–Watson branching process in a random environment. In the multitype branching model, different types denote different phenotypes of offspring, and offspring distributions denote the allocation strategies. Two possible optimization targets are considered: the long-term growth rate of the population conditioned on nonextinction, and the extinction probability of the lineage. In a simple and biologically motivated case, we derive an explicit formula for the long-term growth rate using the random Perron–Frobenius theorem, and we give an approximation to the extinction probability by a method similar to that developed by Wilkinson. Then we obtain the optimal strategies that maximize the long-term growth rate or minimize the approximate extinction probability, respectively, in a numerical example. It turns out that different optimality criteria can lead to different strategies.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Research Centres > Warwick Systems Biology Centre | ||||
| Journal or Publication Title: | Bulletin of Mathematical Biology | ||||
| Publisher: | Springer New York LLC | ||||
| ISSN: | 0092-8240 | ||||
| Official Date: | 1 January 2014 | ||||
| Dates: |
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| Volume: | Volume 76 | ||||
| Number: | Number 1 | ||||
| Page Range: | pp. 184-200 | ||||
| DOI: | 10.1007/s11538-013-9915-5 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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