Solving the freeloaders paradox: Genetic associations and frequency-dependent selection in the evolution of cooperation among nonrelatives

Abstract

One of the enduring problems in the study of social evolution has been to understand how cooperation can be maintained in the presence of freeloaders, individuals that take advantage of the more cooperative members of groups they are eager to join. The freeloader problem has been particularly troublesome when groups consist of nonrelatives, and no inclusive fitness benefits accrue to individuals that contribute more heavily to communal activities. These theoretical difficulties, however, are not mirrored by the numerous examples of cooperative or even altruistic behaviors exhibited by groups of nonrelatives in nature (e.g., many human groups, communally nesting bees, multiple queen-founding ants, cellular slime molds, and social bacteria). Using a model in which cooperation and grouping tendencies are modeled as coevolving dynamical variables, I show that the freeloader problem can be addressed when group-size effects on fitness are considered explicitly. I show that freeloaders, whose presence is reflected in the development of linkage disequilibrium between grouping and cooperation, increase in frequency when rare, but are selected against when common due to the reduced productivity of the groups they overburden with their presence. Freeloader frequencies thus periodically rise and fall around an equilibrium shown here to be dynamic. These results highlight the importance of group-level effects in the origin and maintenance of sociality, illustrate the dynamic nature of equilibria when multiple levels of selection are involved, and provide a solution to the freeloaders paradox.

Fig 1.

Equilibrium levels of cooperation (A), the average group size (B), grouping tendencies (C), and the between-group/total genetic variance (D) as a function of the relative fitness costs of cooperation (β = 0.0, 0.2, 0.4, or 0.6) and group carrying-capacity (1/c = 10, 17, or 50) parameters. The simulations were run for a maximum of 200 groups (limited nesting sites model; ref. 13) and an intrinsic rate of growth of r = 2.0. Nearly identical results were obtained for r = 0.5, 1.0, and 1.5 (13). The equilibrium values shown are averages over the last 500 generations of simulations run for 2,500 generations. Curves are cubic spline fits (λ = 0.0001 for cooperation and 0.001 for the others) across four replicates of each combination of parameter values.

Fig 2.

A potential solution to the freeloaders paradox. (A) Relative fitness within groups for freeloaders (dark dots and line) and other group members [light dots and line; F(1,3439) = 304.9, P < 0.0001; whole-model R² = 0.21, with freeloader, group size, and group size-freeloader interaction in the model]. (B) Difference in the per capita group productivity of groups with greater than average freeloader frequencies, termed “loaded” (dark dots and line) vs. other groups in the population (light dots and line) [F(1, 494) = 72.7, P < 0.0006; whole-model R² = 0.42, with “loaded,” group size, squared group size, and the interactions of the latter two with “loaded” in the model]. (C) Absolute fitness of freeloaders and other group members after within- and between-group level effects are accounted for (ordinal logistic Wald χ² = 0.92, P = 0.34; whole-model R² = 0.04, with freeloader, group size, squared group size, and their interactions with freeloader in the model). Data obtained are from a simulation run for β = 0.2, r = 0.5, c = 0.1 and 500 groups. Curves are cubic spline fits of the data, with λ = 1,000 (A) or 100 (B and C).

Fig 3.

An example of the periodic change in the sign of the association between cooperative and grouping tendencies for a case with complete outcrossing and full linkage. Each dot represents the average cooperative tendencies of a group as a function of its grouping tendencies. (A) When freeloaders were common, the relationship between the two variables was negative [slope (±standard error) = −0.44 ± 0.08, F(1,498) = 27.8, P < 0.0001]. (B) Because freeloaders were being purged from the population, the relationship disappeared [slope = 0.006 ± 0.08, F(1,498) = 0.006, P = 0.94]. (C) Because freeloaders became rarer, the relationship became positive [slope = 0.38 ± 0.07, F(1,498) = 24.9, P < 0.0001]. Data shown correspond to generations 2,189 (A), 2,221 (B), and 2,268 (C) of the simulation shown in Fig. 4. As discussed in the text, the group-level associations shown reflect linkage disequilibrium at the level of individual genomes.

Fig 4.

Time series showing oscillations in the proportion of freeloaders, cooperative and grouping tendencies, and the average group size in a simulation run for β = 0.6, r = 2.0, c = 0.1 and 500 groups. The lines shown are cubic spline fits, with flexibility parameter λ = 10,000, of the original data. Fourier analyses show that the oscillations had intrinsic periodicity and were not the result of white noise [Fisher's κ was 100.0, P ≪ 0.00001 (A), 618.0, P ≪ 0.00001 (B), 254.3, P ≪ 0.00001 (C), and 182.4, P ≪ 0.00001 (D)].