Emergent multilevel selection in a simple spatial model of the evolution of altruism
Fig 3
The origins of altruism and colony formation in the one-dimensional habitat.
(A) Dynamics of a representative simulation run (see S4 Fig) with default parameters (Table 1). A small domain of space-time is visualized. The left-hand part of the figure shows the local population density; the striped pattern indicates that regularly spaced colonies develop. The right-hand side plots the center of mass of each colony; color indicates mean level of altruism. The two representations overlap in the middle of the figure to demonstrate their consistency. Black squares mark the deaths of colonies; orange circles indicate reproduction of colonies by binary fission. (B) Prediction from linear stability analysis. (See also section Materials and methods and S2 Fig.) Colonies are expected to emerge in the yellow part of the phase diagram where the scale of competition is clearly larger than the scale of altruism (σa = 1 by definition) and the scale of motility is small. The red cross marks the default parameters used in panel A. (C) Simulation results testing the prediction of panel B. As predicted, colonies emerge only in the region to the right of the red line, which is copied from panel B: the variance of the local population density increases precipitously when the line is crossed. (D) Mean level of altruism at the end of evolutionary simulations. Altruism evolves only in the regime where colonies can form. Each data point plotted represents the mean of three independent replicate simulations. (E) Same as panel D, but as a function of mutation probability μ. Two independent replicates are plotted in gray; colored circles represent their mean value.