A solution to the collective action problem in between-group conflict with within-group inequality

Abstract

Conflict with conspecifics from neighbouring groups over territory, mating opportunities and other resources is observed in many social organisms, including humans. Here we investigate the evolutionary origins of social instincts, as shaped by selection resulting from between-group conflict in the presence of a collective action problem. We focus on the effects of the differences between individuals on the evolutionary dynamics. Our theoretical models predict that high-rank individuals, who are able to usurp a disproportional share of resources in within-group interactions, will act seemingly altruistically in between-group conflict, expending more effort and often having lower reproductive success than their low-rank group-mates. Similar behaviour is expected for individuals with higher motivation, higher strengths or lower costs, or for individuals in a leadership position. Our theory also provides an evolutionary foundation for classical equity theory, and it has implications for the origin of coercive leadership and for reproductive skew theory.

Figure 1. Collective action in groups of size n=2 with benefit b=1.

Red lines show individual efforts x_i and blue lines show the shares of reproduction f_i/(f₁+f₂) for individuals 1 (solid lines) and 2 (broken lines). Both individuals contribute only if their valuations are larger than 0.25, otherwise the individual with the smaller valuation free rides.

Figure 2. Collective action in the basic model.

Results over 200,000 generations for a particular run with group size n=8 and within-group inequality δ=2. The values are averages over individuals of rank i in all groups in the population. Colours describe different ranks, from rank 1 (red) to rank 8 (dark green). (a) Individual efforts x_i for rank i; the average individual effort over all ranks is shown with the dashed line. (b) Relative fertilities for individuals of rank i.

Figure 3. Collective action in the basic model.

Summary results of the last 20,000 generations for a particular set of 10 runs with group size n=12 and within-group inequality δ=1, as a function of individual valuation v_i. For each run, the values are averages over individuals of rank i in all groups in the population. Values for individual runs are given by circles, the average over the 10 runs is given by a solid line. (a) Individual efforts x_i for rank i. (b) Relative fertilities for individuals of rank i.

Figure 4. Collective action in the basic model.

Summary results over all runs for one set of parameters, with group size n=4 (a,b) and n=8 (c,d) and cost c=0.5. For each set of runs, the values are averages over individuals of rank i in all groups in the population. Colours show the relevant amounts for individuals of different ranks, from the rank-1 individual at the bottom (red) to the rank-n individual at the top. Each set of bars corresponds to a specific value of benefit b. Each bar within a set corresponds to a specific value of within-group inequality δ, from the smallest on the left (δ=0.25; low inequality) to the largest on the right (δ=4; high inequality). (a) Individual efforts x_i for rank i with group size n=4; the height of the bar is the total group effort X*. (b) Share of reproduction for individuals of rank i with group size n=4. (c) Individual efforts x_i for rank i with group size n=8; the height of the bar is the total group effort X*. (d) Share of reproduction for individuals of rank i with group size n=8.

Figure 5. Collective action in the modified model with decisiveness β=2.

Group size n=8 and cost c=0.5. (a,b) Summary results of the last 20,000 generations for a particular set of 10 runs with within-group inequality δ=1, as a function of individual valuation v_i. For each set of runs, the values are averages over individuals of rank i in all groups in the population. Values for individual runs are given by circles, the average over the 10 runs is given by a solid line. (a) Individual efforts x_i for rank i. (b) Relative fertilities for individuals of rank i. (c,d) Summary results over all runs for one set of parameters. For each run, the values are averages over individuals of rank i in all groups in the population. Colours show the relevant amounts for individuals of different ranks, from the rank-1 individual at the bottom (red) to the rank-8 individual at the top (dark green). Each set of bars corresponds to a specific value of benefit b. Each bar within a set corresponds to a specific value of within-group inequality δ, from the smallest on the left (δ=0.25; low inequality) to the largest on the right (δ=4; high inequality). (c) Individual efforts x_i for rank i; the height of the bar is the total group effort X*. (d) Share of reproduction for individuals of rank i.

Figure 6. Collective action in the modified model with individual costs c_i increasing linearly with rank i.

Group size n=8 and egalitarian division of spoils (that is, the individual shares of the reward are v_i=1/n for all i). (a,b) Summary results of the last 20,000 generations for a particular set of five runs with within-group inequality d=0.2, as a function of individual cost c_i. For each run, the values are averages over individuals of rank i in all groups in the population. Values for individual runs are given by circles, the average over the five runs is given by a solid line. (a) Individual efforts x_i for rank i. (b) Relative fertilities for individuals of rank i. (c,d) Summary results over all runs for one set of parameters. For each set of runs, the values are averages over individuals of rank i in all groups in the population. Colours show the relevant amounts for individuals of different ranks, from the rank-1 individual at the bottom (red) to the rank-8 individual at the top (dark green). Each set of bars corresponds to a specific value of benefit b. Each bar within a set corresponds to a specific value of parameter d controlling differences in costs, from the smallest on the left (d=0.05; small difference in costs) to the largest on the right (d=0.8; high difference in costs). We used n equally spaced values of individual costs c_i from c × (1−d)/2 to c × (1+d)/2. (c) Individual efforts x_i for rank i; the height of the bar is the total group effort X*. (d) Share of reproduction for individuals of rank i.