Co-evolutionary Dynamics of Collective Action with Signaling for a Quorum
Fig 1
Evolutionary robustness and Prevalence of signaling strategy (10|01).
The top contour plots indicate the regions of model parameters in which the signaling strategy (10|01) is Evolutionary Robust (ERS) (bright areas). To this end we vary the selection pressure γ and the cost of signaling cS (left panel); the cost of cooperation c and cS (center panel) and the probability that Nature chooses α (λ) and cS. The bottom panels show, for the same parameter space, the prevalence of the population in a configuration in which all individuals adopt the signaling strategy (10|01). The remaining parameters (and also those plotted whenever not varied) are Z = 100, N = 9, M = 5, c = 0.5, γ = 5, F = 10, λ = 0.5. A signaling system emerges for a wide range of values of the model parameters. Comparison of top and bottom panels shows the existence of parameter regions in which (10|01) is an ERS and yet the population almost never adopts this strategy and, conversely, there are regions in which (10|01) is not an ERS and yet the population spends approximately 30% of its time in configuration comprising only this strategy (see main text for details). Note, in particular, that signaling systems emerge more robustly under strong selection, a scenario that is very likely to occur in many cases under α conditions (those that entail a public good). Moreover, for some species the enhancement factor F = 10 possibly constitutes an underestimate given that, under α, survival may be at stake (as is the case in, e.g., many bacterial species), and successful cooperation likely leads to higher benefits. Nonetheless, a signaling system emerges for a wide range of values of λ, provided that cS < c/2.