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A phenomenological analysis of eco-evolutionary coupling under dilution. (English) Zbl 1394.92093

Summary: Evolutionary dynamics experienced by mixed microbial populations of cooperators and cheaters has been examined in experiments in the literature using a protocol of periodic dilution to investigate the properties of resilience and adaptability to environmental changes. Data depicted on an appropriate phase diagram indicate, among other features, a stable equilibrium point at which cooperators and cheaters coexist [A. Sanchez and J. Gore, “Feedback between population and evolutionary dynamics determines the fate of social microbial populations”, Plos Biol. 11, No. 4, e1001547 (2013; doi:10.1371/journal.pbio.1001547)]. We present here a phenomenological analysis of these data focusing on an eco-evolutionary-game perspective. To that end, we work on an extension of the model proposed in [Y. Tao and R. Cressman, Bull. Math. Biol. 69, No. 4, 1377–1399 (2007; Zbl 1298.91040)]. It’s original version takes into account changes of the total population density while the individuals experience a pairwise Prisoners Dilemma game. The extension devised here contains a dilution parameter to conform with the experimental procedure, in addition to a term accounting for Allee effects. In contrast to other descriptions proposed in similar contexts, however, the model here does not account for assortative encounters, group or kin selection. Nonetheless, it describes surprisingly well both qualitatively and quantitatively the features of the observed phase diagram. We discuss these results in terms of the behavior of an effective payoff matrix defined accordingly.

MSC:

92D15 Problems related to evolution
92D40 Ecology
92C99 Physiological, cellular and medical topics

Citations:

Zbl 1298.91040

References:

[1] Allen, B.; Nowak, M. A., Cooperation and the fate of microbial societies, PLoS Biol., 11, 4, e1001549 (2013)
[2] Bergstrom, T. C., The algebra of assortative encounters and the evolution of cooperation, Int. Game Theory Rev., 5, 03, 211-228 (2003) · Zbl 1051.91076
[3] Chen, A.; Sanchez, A.; Dai, L.; Gore, J., Dynamics of a producer-freeloader ecosystem on the brink of collapse, Nat. Commun., 5, 3713 (2014)
[4] Cremer, J.; Melbinger, A.; Frey, E., Evolutionary and population dynamics: a coupled approach, Phys. Rev. E, 84, 5, 051921 (2011)
[5] Dai, L.; Vorselen, D.; Korolev, K. S.; Gore, J., Generic indicators for loss of resilience before a tipping point leading to population collapse, Science, 336, 6085, 1175-1177 (2012)
[6] Hauert, C.; Wakano, J. Y.; Doebeli, M., Ecological public goods games: cooperation and bifurcation, Theor. Popul. Biol., 73, 2, 257-263 (2008) · Zbl 1208.92086
[7] Hirsch, M. W.; Smale, S.; Devaney, R. L., Differential Equations, Dynamical Systems, and an Introduction to Chaos (2004), Academic Press · Zbl 1135.37002
[8] Iooss, G.; Joseph, D. D., Elementary Stability and Bifurcation Theory (1989), Springer Science & Business Media
[9] Nowak, M. A., Evolutionary Dynamics (2006), Harvard University Press · Zbl 1098.92051
[10] Nowak, M. A.; Sigmund, K., Evolutionary dynamics of biological games, Science, 303, 5659, 793-799 (2004)
[11] Post, D. M.; Palkovacs, E. P., Eco-evolutionary feedbacks in community and ecosystem ecology: interactions between the ecological theatre and the evolutionary play, Philos. Trans. R. Soc. London B, 364, 1523, 1629-1640 (2009)
[12] Requejo, R. J.; Camacho, J., Coexistence of cooperators and defectors in well mixed populations mediated by limiting resources, Phys. Rev. Lett., 108, 3, 038701 (2012)
[13] Sanchez, A.; Gore, J., Feedback between population and evolutionary dynamics determines the fate of social microbial populations, PLoS Biol., 11, 4, e1001547 (2013)
[14] Stephens, P. A.; Sutherland, W. J., Consequences of the allee effect for behaviour, ecology and conservation, Trends Ecol. Evol., 14, 10, 401-405 (1999)
[15] Tao, Y.; Cressman, R., Stochastic fluctuations through intrinsic noise in evolutionary game dynamics, Bull. Math. Biol., 69, 4, 1377-1399 (2007) · Zbl 1298.91040
[16] Zhang, F.; Hui, C., Eco-evolutionary feedback and the invasion of cooperation in prisoner’s dilemma games, PLoS One, 6, 11, e27523 (2011)
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