  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, J. Gore, PLOs
Biology, 11 (4), e1001547 (2013)]. 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 by Tao and Cressman Y. Tao, R.
Cressman, Bull. Math. Biol. 69, 1377 - 1399 (2007). It's original version takes
into account changes of the total population density while the individuals
experience pairwise Prisoner's Dilemma game. The extension devised here
contains a dilution factor to be conform with the experimental procedure, in
addition of a term accounting for Allee effects. Differently from 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.
