Figure 1.

The Ecological Public Goods Game predicts a trade-off between cooperators' ability to face both ecological and evolutionary challenges. (a) Two different forces can compromise a cooperator allele's survival. On the one hand, freeloaders can emerge by mutation and take over, driving the cooperator allele to either go extinct or to survive at very low frequencies. Alternatively, the existence of a minimum critical population size may cause external stressors or environmental perturbation to drive an allele to extinction from purely ecological causes, even in the absence of evolutionary competition with freeloaders. (b) A diagram that depicts the measures used for determining the cooperator alleles' ability to face both evolutionary and ecological challenges. The cooperators' stability to a freeloader invasion is measured as the frequency of cooperators at equilibrium after introducing a small freeloader population into a pure cooperator population. Cooperators that survive with a larger relative frequency at the mixed equilibrium have a larger stability to freeloader invasion as their population density changes less when freeloaders invade. The ecological resilience of a pure population of cooperators (i.e. in the absence of evolutionary competition by freeloaders) is measured as the smallest perturbation to the population size that would cause population collapse. This is the distance between the stable (grey) and unstable (white) fixed points in a pure cooperating population. Precisely, it is the difference between the log positions of the equilibria. (c) The ecological resilience and stability to freeloader invasion were calculated, as described in (b), for 300 different randomly generated parameter sets for the EPGG. The parameters were randomly chosen from the ranges r/N ε [0, 1), N ε [3, 30), d ε [0.1, 5). All systems had the features in (b), with three fixed points in the pure cooperator population, one stable, interior fixed point for mixed populations initialized with a sufficient number of cooperators, and a line of stable fixed points at extinction. The ecological resilience and stability to freeloader invasion have a negative log–log correlation ρ = −0.67. (Online version in colour.)