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.

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Code availability

C code for simulation is available upon request.

Funding

This work was supported by the Japanese Society for the Promotion of Science KAKENHI (Grant Number JP17H06381).

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YI designed the research, did the analyses, and wrote the paper.

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Correspondence to Yasuo Ihara.

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Appendix. Further details of the three-player coalition game

Appendix. Further details of the three-player coalition game

We assume that the probabilities, hS, hT, and hN, 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[αwH|R=S] + exp[αwH|R=T] + exp[αwH|R=N]. In (5), wH|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 wS, formally given by wS(aS, aT, aH) = hSwS|R=S + hTwS|R=T + hNwS|R=N, as a function of aS, aT, and aH. 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 aS = x. The starter chooses a target on the basis of a comparison between wS(x, y, z) and wS(x, z, y), whereby determines the values for aT and aH. Let gY|S=X and gZ|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 ΨX = exp[βwS(x, y, z)] + exp[βwS(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 gY|S=X = gZ|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 gX|S=Y, gZ|S=Y, gX|S=Z, and gY|S=Z are defined in a manner analogous to (6), wT(aS, aT, aH) = hSwT|R=S + hTwT|R=T + hNwT|R=N, and wH(aS, aT, aH) = hSwH|R=S + hTwH|R=T + hNwH|R=N.

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Ihara, Y. A mathematical model of social selection favoring reduced aggression. Behav Ecol Sociobiol 74, 91 (2020). https://doi.org/10.1007/s00265-020-02875-4

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Keywords

  • Bonobo
  • Coalition formation
  • Evolution
  • Human
  • Self-domestication
  • Tyrant problem