Resolving social conflict among females without overt aggression

Abstract

Members of animal societies compete over resources and reproduction, but the extent to which such conflicts of interest are resolved peacefully (without recourse to costly or wasteful acts of aggression) varies widely. Here, we describe two theoretical mechanisms that can help to understand variation in the incidence of overt behavioural conflict: (i) destruction competition and (ii) the use of threats. The two mechanisms make different assumptions about the degree to which competitors are socially sensitive (responsive to real-time changes in the behaviour of their social partners). In each case, we discuss how the model assumptions relate to biological reality and highlight the genetic, ecological and informational factors that are likely to promote peaceful conflict resolution, drawing on empirical examples. We suggest that, relative to males, reproductive conflict among females may be more frequently resolved peacefully through threats of punishment, rather than overt acts of punishment, because (i) offspring are more costly to produce for females and (ii) reproduction is more difficult to conceal. The main need now is for empirical work to test whether the mechanisms described here can indeed explain how social conflict can be resolved without overt aggression.

Keywords: conflict resolution; evolution of cooperation; fighting; negotiation; reproductive skew; threats.

Figure 1.

Defining the battleground of evolutionary conflict over limited resources. (a) The direct fitness of players 1 and 2 (W₁ and W₂) as a function of player 2's share of a valuable resource, p₂. Player 1's share is 1 − p₂. In the figure, we assume some degree of diminishing returns in the net fitness benefits of increasing resource share. The particular diminishing returns function we use is W_i = V[(1−e^−qp_i)/(1−e^−q)], where the parameter q (0 < q < ∞) determines the ‘bowedness’ of the diminishing returns function (W_i approaches linearity as q approaches 0; and is highly ‘bowed’, where ). In the case shown q = 1. If the two players are non-relatives (as in (a)), the optimal division of resources from the perspective of player 1 is , and from the perspective of player 2 is . Thus, the zone of conflict or ‘battleground’ in the case of competition between non-relatives is simply all of the available resource. (b) The case where the two players are genetic relatives (specifically, in the plot we assume r = 0.5). IF₁ is the inclusive fitness payoff of player 1 (calculated as W₁ + r W₂). The optimum division of the resource for player 1 is the value of p₂ which maximizes IF₁, i.e. the value which solves the equation ∂IF₁/∂p₂ = 0. Given our chosen fitness functions, the solution for player 1's optimal allocation is ; and (since the players are symmetrical) for player 2 the optimal allocation is one minus this expression, i.e. 1/2 − (ln r)/2q. Thus, the battleground of conflict is 1/2 ± (ln r)/2q. Note that the value of the resource V has no effect on the width of the battleground. The lower and upper bounds of the battleground get closer together as r increases and as q increases. In other words, increasing relatedness and increasing ‘bowedness’ of the fitness function draw together the fitness optima of competitors, reducing the scope for evolutionary conflict.

Figure 2.

Contest success in a difference form model of evolutionary conflict. We plot the relative success of player 1 as a function of her effort invested in conflict x (using the difference form contest success function (3.2) in the text), for three values of the ‘decisiveness’ parameter d. Player 2 is assumed to invest y = 0.5. The effect of the decisiveness parameter is to change the marginal benefits of superior effort invested in conflict. Where decisiveness is high, a small advantage in conflict effort converts to a large advantage in relative success. For comparison, the dotted line shows the ratio form contest success function (x/(x + by)) used in Reeve et al.'s [41] tug-of-war model. In difference form models, unlike ratio form models, player 1 can still obtain some success even if she invests nothing in the conflict. Other parameter: b = 1.

Figure 3.

Peaceful and non-peaceful outcomes in a model of ‘destruction’ competition (adapted from [42]). The figures show the three types of ES outcome that can arise when we vary the two parameters of the contest success function (3.2), decisiveness d and relative strength or efficiency b. In the ‘mutual peace’ zone, the ES outcome is for both players to invest zero conflict effort. In the ‘one-sided peace’ zone, only the stronger player invests positive effort in conflict. In the ‘mutual conflict’ zone, the ES outcome features positive conflict effort by both players. (a) The case where players are non-relatives. In this case, the ES outcome is mutual peace below a threshold level of decisiveness equal to 2. (b) The case where the players are related by coefficient 0.5. In this case, mutual peace is the ES outcome below d = 2(1+r)/(1−r), i.e. d = 6. The ES outcomes are mutual peace in these zones because for these values of decisiveness and relative strength, investment in conflict effort is just not profitable.

Figure 4.

Fitness payoffs in a sequential or threat model of resource competition. In this model, player 2 makes a first move by claiming share p₂ of the resource. Player 1 observes player 2's behaviour and can respond by inflicting a punishment (for example, killing her offspring) if the claim exceeds a threshold level p_crit. The punishment costs player 1 u fitness units to carry out, and for simplicity is assumed to reduce player 2's fitness to zero when triggered. Bold lines represent stable outcomes where the threat of punishment is not exercised; thin lines represent the fitness consequences for both players when the threat is triggered. Dotted lines and dashed lines represent underlying fitness functions (dotted lines: the case where the resource is continuously divisible; dashed lines: the case where the resource is discretely divisible). If player 2 knows (or believes) with certainty the location of p_crit, her best strategy is to claim up to this threshold and no more. The threat of punishment by player 1 in the second step forces player 2 to exercise restraint in the first step. (a) The case where the resource is infinitely divisible and hence the fitness functions are smooth curves. (b) The case where player 2's claims come in discrete chunks or packages (such as individual offspring). Specifically, in (b) player 2 can only make claims of one-third of the resource at a time, resulting in a stepped fitness function for both players. In this situation, player 2's minimum claim is one-third, which exceeds the threat threshold p_crit, so player 1's threat is sufficient to enforce a monopoly on the resource. In general, the more ‘bulky’ the discrete packages of resource, the more player 2 should err on the side of caution, and the further below p_crit we can expect the resolved division of resource to lie.