< Back to Article
The evolution of environmentally mediated social interactions and posthumous spite under isolation by distance
Fig 5
Selection favours altruism or spite depending on dispersal of the evolving species and the commons in a 2D lattice model.
Panels A-B: Regions of dispersal parameters leading to the evolution of altruism, Ω > 0 (in white), or of spite, Ω < 0 (in gray) for an example in a 2D lattice model (with D1 = D2 = 13 and N = 50) under a Wright-Fisher life-cycle with fecundity effects (with Ω computed from Eq 34). Panel A: Combination of dispersal probability of the evolving species m = 1 − m0 (x-axis) and of the commons d = 1 − d0 (y-axis) for different levels of environmental decay ϵ in different shades of gray (ϵ = 0.1, 0.5, 1) with expected dispersal distance fixed (
and 
). This shows that spite is favoured by high levels of dispersal and environmental decay. Panel B: Combination of expected dispersal distance of the evolving species 
(x-axis) and of the commons 
(y-axis) for different levels of environmental decay ϵ in different shades of gray (see panel A for the legend) with dispersal probability fixed (m = 0.98 and d = 1). This shows that spite is favoured by dispersal asymmetry between the evolving species and the commons. Panels C-D: Evolution of spite in individual-based simulations under a Wright-Fisher life-cycle with fecundity effects (with D1 = D2 = 13, N = 50, m = 0.3, 
, d = 1, 
, B = 2, αB = 1, C = 1, αC = 4, P(z) = Nz; for mutation, the trait mutates during reproduction with probability 10−4, in which case a normally distributed deviation with mean 0 and standard deviation 10−2 is added to the parental trait value). Panel C shows the average trait z in the population; panel D shows the average commons level or environmental variable n (with simulations in full lines—see S1 Code—and analytical prediction in dashed lines—from Eq 32 for z and 27 for n). See S1 Data for how to generate these figures using Mathematica.
doi: https://doi.org/10.1371/journal.pcbi.1012071.g005