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The evolution of environmentally mediated social interactions and posthumous spite under isolation by distance
Fig 6
Isolation by distance allows for the evolution of a wider range of social behaviours than the island model under environmental feedback.
Panel A: Singular trait value z* from Eq 32 for m = 0.75 (in black) and m = 0.2 (in gray). Other parameters: D1 = D2 = 13, so that D = 169, N = 50, 
, d = 0.99, B = 2, αB = 1, C = 1, αC = 4, P(z) = Nz. Dashed lines show the singular trait value with the same parameters but under the island model of dispersal for both the species and the commons (from Eq 32 with Ω given by eq. (A-126 in S1 Text) derived in Appendix G.3). Panel B: Observed vs. predicted equilibrium trait value in individual-based simulations running for 20 000 generations under different expected dispersal distance of the commons 
leading to altruism (z > 0) and spite (z < 0). Other parameters: same as in Fig 5C and 5D. The prediction is shown as a dashed line (from Eq 32) with grey region around for twice the standard deviation obtained from the stationary phenotypic distribution (from eq. A-136 in S1 Text). Observed values of the trait average in the population are shown as black dots for the average from generation 5 000 to 20 000, with error bars for standard deviation over the same 15 000 generations. Simulations were initialised at the predicted convergence stable trait value. S1 Code for simulation code and S2 Data for simulation results.
doi: https://doi.org/10.1371/journal.pcbi.1012071.g006