Figure 3
From: Competitive environments sustain costly altruism with negligible assortment of interactions
Threshold relatedness r above which the ESS supports altruism.
An altruist incurs a payoff S < 0 to itself in giving benefit b = 0.4 to another, here showing alternative S = −0.1, −0.2 … −1.3 (lines left to right in each colour). For any given S, the graph shows that the threshold r declines with higher competition cost d of mutual defection, whether competition expresses displacement (dashed orange lines, condition (3)) or retreat (solid blue lines, condition (4)); open circles mark the point on each line beyond which altruism gives way to parasitism, by virtue of S > P. Green region sustains altruism with displacement or retreat competition, blue region sustains altruism with retreat only. (a) Retreat d = 0.15 sustains acts of altruism with S = −0.2 (i.e., net personal cost of c = 0.2 for a conferred benefit, or c = 0.6 for a public good) amongst relatives with r > 0.125; (b) retreat d = 0.3 sustains altruism with S = −0.4 (i.e., conferred c = 0.4, or public good c = 0.8) amongst relatives with r > 0.25.
