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Pareto-optimal trade-off for phenotypic switching of populations in a stochastic environment

View ORCID ProfileL. Dinis, J. Unterberger, View ORCID ProfileD. Lacoste
doi: https://doi.org/10.1101/2022.01.18.476793
L. Dinis
1GISC - Grupo Interdisciplinar de Sistemas Complejos and Dpto. de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid, 28040 Spain
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J. Unterberger
2Institut Elie Cartan, UMR CNRS 7502, Université de Lorraine, BP 239 F-54506 Vandoeuvre-lès-Nancy Cedex, France
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D. Lacoste
3Gulliver Laboratory, UMR CNRS 7083, PSL Research University, ESPCI, 10 rue Vauquelin, F-75231 Paris Cedex 05, France
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  • For correspondence: david.lacoste@gmail.com
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Abstract

Finding optimal survival strategies of living systems embedded in fluctuating environments generally involves a balance between phenotypic diversification and sensing. If we neglect sensing mechanisms, it is known that slow, resp. fast, environmental transitions favor a regime of heterogeneous, resp. homogeneous, phenotypic response.

We focus here on the simplest non-trivial case, i.e. two randomly switching phenotypes subjected to two stochastically switching environments. The optimal asymptotic (long term) growth rate of this model was studied elsewhere; we further expand these results by discussing finite time growth rate fluctuations. An exact asymptotic expression for the variance, alongside with approximations valid in different regimes, are tested numerically in details. Our simulations of the dynamics suggest a close connection between this variance and the extinction probability, understood as risk for the population. Motivated by an earlier trade-off analysis between average capital growth rate and risk in Kelly’s gambling model, we study the trade-off between the average growth rate and the variance in the present model. Despite considerable differences between the two models, we find similar optimal trade-off curves (Pareto fronts), suggesting that our conclusions are robust, and broadly applicable in various fields ranging from biology/ecology to economics.

Competing Interest Statement

The authors have declared no competing interest.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-ND 4.0 International license.
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Posted January 21, 2022.
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Pareto-optimal trade-off for phenotypic switching of populations in a stochastic environment
L. Dinis, J. Unterberger, D. Lacoste
bioRxiv 2022.01.18.476793; doi: https://doi.org/10.1101/2022.01.18.476793
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Pareto-optimal trade-off for phenotypic switching of populations in a stochastic environment
L. Dinis, J. Unterberger, D. Lacoste
bioRxiv 2022.01.18.476793; doi: https://doi.org/10.1101/2022.01.18.476793

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