A mathematical model of social selection favoring reduced aggression

Abstract

Emergence of characteristically human traits, including extensive collaboration, prosociality, and cooperative communication, has presumably necessitated evolution toward lower aggression. While empirical studies have provided evidence for evolutionary reduction in human aggression, such as canine teeth reduction in hominins and craniofacial feminization in Homo sapiens, the underlying mechanisms for the reduction in human aggression are virtually unknown. A promising hypothesis is social selection by partner choice; that is, individuals’ choice of collaborative partners may have induced selection against exceedingly aggressive individuals. However, it is thus far unclear whether partner choice can give unaggressive individuals a fitness benefit that more than compensates for the lost advantage of being aggressive in interindividual conflict. This study explores the plausibility of the social selection hypothesis, using a game-theoretic model of coalition formation. Analysis of the game shows that partner choice can induce selection favoring reduced fighting ability if individuals are ecologically demanded to collaborate, they can be viewed as rational fitness maximizers, and they have communicative skills to bring a synergy in collaboration. The model also suggests a possible feedback loop between reduction of fighting ability and a correlated enhancement of communicative skills.

Significance statement

Domesticated animals often share a suite of morphological, physiological, and cognitive characteristics, called the domestication syndrome, that are distinct from their wild ancestors. Experimental studies have shown that the domestication syndrome can arise as a by-product of selection against aggressiveness. A similar process may occur in wild animals; in particular, it has been suggested that “self-domestication” through selection against aggression may have played a major role in human evolution. Despite the proposed role of reduced aggression, however, it is thus far unclear in what ecological context less aggressive individuals can be selectively favored over more aggressive ones. This study provides a theoretical foundation for the social selection hypothesis for the evolution of reduced aggression, using a game-theoretic model of coalition formation, and specifies the conditions under which individuals’ choice of collaborative partners can induce selection favoring reduced aggression.

Appendix. Further details of the three-player coalition game

We assume that the probabilities, h_S, h_T, and h_N, that the helper supports the starter, target, or none, respectively, are described by a logit model, namely,

$$ \left(\begin{array}{c}{h}_{\mathrm{S}}\\ {}{h}_{\mathrm{T}}\\ {}{h}_{\mathrm{H}}\end{array}\right)=\frac{1}{\varPhi}\left(\begin{array}{c}\exp \left[\alpha {w}_{\mathrm{H}\mid \mathrm{R}=\mathrm{S}}\right]\\ {}\exp \left[\alpha {w}_{\mathrm{H}\mid \mathrm{R}=\mathrm{T}}\right]\\ {}\exp \left[\alpha {w}_{\mathrm{H}\mid \mathrm{R}=\mathrm{N}}\right]\end{array}\right),\kern1em $$

(5)

where Φ = exp[αw_H|R=S] + exp[αw_H|R=T] + exp[αw_H|R=N]. In (5), w_H|R=ϕ denotes the helper’s winning probability given R = ϕ (Table 1), and α measures the extent to which the helper’s decision depends on the winning probabilities (α ≥ 0). When α = 0, the helper is equally likely to take each of the three choices, while when α → ∞, the helper always takes the option maximizing the prospect of winning.

The starter is assumed to have the access to the winning probability w_S, formally given by w_S(a_S, a_T, a_H) = h_Sw_S|R=S + h_Tw_S|R=T + h_Nw_S|R=N, as a function of a_S, a_T, and a_H. Consider the trio of individuals X, Y, and Z, with fighting abilities x, y, and z, respectively. To be specific, suppose that X is chosen to be the starter, so that a_S = x. The starter chooses a target on the basis of a comparison between w_S(x, y, z) and w_S(x, z, y), whereby determines the values for a_T and a_H. Let g_Y|S=X and g_Z|S=X denote the probabilities with which the starter X chooses Y or Z as the target, respectively. We assume that these probabilities follow the logit model given by

$$ \left(\begin{array}{c}{g}_{Y\mid \mathrm{S}=X}\\ {}{g}_{Z\mid \mathrm{S}=X}\end{array}\right)=\frac{1}{\Psi_X}\left(\begin{array}{c}\exp \left[\beta {w}_{\mathrm{S}}\left(x,y,z\right)\right]\\ {}\exp \left[\beta {w}_{\mathrm{S}}\left(x,z,y\right)\right]\end{array}\right),\kern1em $$

(6)

where Ψ_X = exp[βw_S(x, y, z)] + exp[βw_S(x, z, y)]. Here, β is a measure of the extent to which the starter’s decision depends on the winning probabilities (β ≥ 0). When β = 0, then g_Y|S=X = g_Z|S=X = 1/2, whereas when β → ∞, the starter always takes the option leading to the highest winning probability.

Considering that each individual is chosen to be the starter with probability 1/3, the unconditional winning probabilities for X, Y, and Z are given by

$$ {w}_X=\frac{1}{3}\left[{g}_{Y\mid \mathrm{S}=X}{w}_{\mathrm{S}}\left(x,y,z\right)+{g}_{Z\mid \mathrm{S}=X}{w}_{\mathrm{S}}\left(x,z,y\right)\right]+\frac{1}{3}\left[{g}_{X\mid \mathrm{S}=Y}{w}_{\mathrm{T}}\left(y,x,z\right)+{g}_{Z\mid \mathrm{S}=Y}{w}_{\mathrm{H}}\left(y,z,x\right)\right]+\frac{1}{3}\left[{g}_{X\mid \mathrm{S}=Z}{w}_{\mathrm{T}}\left(z,x,y\right)+{g}_{Y\mid \mathrm{S}=Z}{w}_{\mathrm{H}}\left(z,y,x\right)\right],\kern1em $$

(7a)

$$ {w}_Y=\frac{1}{3}\left[{g}_{Y\mid \mathrm{S}=X}{w}_{\mathrm{T}}\left(x,y,z\right)+{g}_{Z\mid \mathrm{S}=X}{w}_{\mathrm{H}}\left(x,z,y\right)\right]+\frac{1}{3}\left[{g}_{X\mid \mathrm{S}=Y}{w}_{\mathrm{S}}\left(y,x,z\right)+{g}_{Z\mid \mathrm{S}=Y}{w}_{\mathrm{S}}\left(y,z,x\right)\right]+\frac{1}{3}\left[{g}_{X\mid \mathrm{S}=Z}{w}_{\mathrm{H}}\left(z,x,y\right)+{g}_{Y\mid \mathrm{S}=Z}{w}_{\mathrm{T}}\left(z,y,x\right)\right],\kern1em $$

(7b)

$$ {w}_Z=\frac{1}{3}\left[{g}_{Y\mid \mathrm{S}=X}{w}_{\mathrm{H}}\left(x,y,z\right)+{g}_{Z\mid \mathrm{S}=X}{w}_{\mathrm{T}}\left(x,z,y\right)\right]+\frac{1}{3}\left[{g}_{X\mid \mathrm{S}=Y}{w}_{\mathrm{H}}\left(y,x,z\right)+{g}_{Z\mid \mathrm{S}=Y}{w}_{\mathrm{T}}\left(y,z,x\right)\right]+\frac{1}{3}\left[{g}_{X\mid \mathrm{S}=Z}{w}_{\mathrm{S}}\left(z,x,y\right)+{g}_{Y\mid \mathrm{S}=Z}{w}_{\mathrm{S}}\left(z,y,x\right)\right],\kern1em $$

(7c)

where g_X|S=Y, g_Z|S=Y, g_X|S=Z, and g_Y|S=Z are defined in a manner analogous to (6), w_T(a_S, a_T, a_H) = h_Sw_T|R=S + h_Tw_T|R=T + h_Nw_T|R=N, and w_H(a_S, a_T, a_H) = h_Sw_H|R=S + h_Tw_H|R=T + h_Nw_H|R=N.