The demographic benefits of belligerence and bravery: defeated group repopulation or victorious group size expansion?

Abstract

Intraspecific coalitional aggression between groups of individuals is a widespread trait in the animal world. It occurs in invertebrates and vertebrates, and is prevalent in humans. What are the conditions under which coalitional aggression evolves in natural populations? In this article, I develop a mathematical model delineating conditions where natural selection can favor the coevolution of belligerence and bravery between small-scale societies. Belligerence increases an actor's group probability of trying to conquer another group and bravery increase the actors's group probability of defeating an attacked group. The model takes into account two different types of demographic scenarios that may lead to the coevolution of belligerence and bravery. Under the first, the fitness benefits driving the coevolution of belligerence and bravery come through the repopulation of defeated groups by fission of victorious ones. Under the second demographic scenario, the fitness benefits come through a temporary increase in the local carrying capacity of victorious groups, after transfer of resources from defeated groups to victorious ones. The analysis of the model suggests that the selective pressures on belligerence and bravery are stronger when defeated groups can be repopulated by victorious ones. The analysis also suggests that, depending on the shape of the contest success function, costly bravery can evolve in groups of any size.

Figure 1. Demographic outcomes and events faced by the individuals in a focal group (the terms “outcomes” and “events” are used as defined in probability theory, e.g., p. 18, chapter 1 of [62]).

Each different connected series of edges starting at the root node (top of the figure) provides a demographic outcome. Different outcomes may lead to similar demographic events, which are denoted by and described in the text. The first series of edges, directly issued from the root node, represents the probabilities that the focal group fights or does not fight to conquer another group from the population. The second series of edges represent the probabilities that the focal group fights or does not fights locally. The third series of edges represent the winning probabilities of the various battles, which occur only if there is a fight. For instance, the left most series of connected edges represent the outcome where the focal group fights against another group upon attacking (probability ), it fights locally because it is attacked (probability ) and wins the two battles (probability ). In order to obtain the probabilities of occurrence of each demographic event describes in the text, one has to sum the probabilities of occurrence of outcomes where that event obtains, which gives , , , and .

Figure 2. Graph comparing the probability of identity in the DGR scenario to that obtained in the VGE scenario.

The quasi flat line is the the value of for the VGE scenario obtained without making any assumption on the value can take, while the downward bent line is the relatedness for the DGR scenario. The first set of two lines in the graph is for , while the second set of two lines is for , while the other parameter values are , , , and , where the value takes does not affect .

Figure 3. Selection gradient on belligerence for the DGR and VGE scenarios as a function of .

The functional relationships used are , given by eq. 4 with , and , and the resident trait value was set to . The parameter values are , , and the value takes does not affect the selection pressure on belligerence. Further, in the top right panel, in the top left panel, in the lower right panel, and in the lower left panel. The top line in each panel is eq. 21; that is, the selection gradient for the DGR scenario and denoted by . The second line in each panel is with eq. B-18 of Appendix S2 using and eq. B-20 of Appendix S2; the selection gradient for the VGE without making any assumption on the value can take, which is denoted by . The last line in each panel is eq. B-36 of Appendix S2; the selection gradient for the VGE assuming that is small and is denoted by . Three observations follow from this figure, which were also observed under a wider range of numerical exploration. First, for strong migration rates all three selective pressures agree. Second, for low migration rates the selective pressure is stronger under the DGR than under the VGE scenario for all values of . Third, the small approximation of the VGE scenario underestimates the strength of selection on belligerence when migration is low, but the approximation works quiet will for . Similar results were observed if the contest success function is of the difference form.