Little Peacemakers: Microbes Can Promote Nonviolent Conflict Resolution by Their Hosts

Abstract

Conflicts between individuals of the same species are common in nature and are mostly resolved with limited aggression. Several theoretical studies, such as the Hawk-Dove (HD) game model, investigate the evolution of limited aggression expressed during conflicts between individuals. These studies mainly focus on the individuals involved in the conflict and their genes. Recently accumulating evidence indicates that microbes are associated with diverse functions of their host and can affect host behavior. Here we extend the classic HD game model to include both the hosts and their microbes, examining how natural selection acts on the microbes. We find that nonaggressive host behavior is more likely to evolve and spread in a population when induced by the microbes residing in the host, compared to nonaggressive behavior induced by host genes. Horizontal transmission allows microbes to colonize new hosts, making their success dependent on the fitness of both the host and its opponent. Therefore, selection on the microbes favors reduced host aggressiveness under wider conditions compared to selection acting on genes alone. Our results suggest that microbes may help explain the ubiquity of nonviolent conflict resolution. Consequently, factors that alter the microbial composition within hosts may affect the aggressiveness level in host populations.

Keywords: Hawk‐Dove game; aggressiveness; conflict resolution; host‐microbes interactions; mathematical model; microbiome.

FIGURE 1

Payoff matrix and illustration of microbes‐dependent Hawk–Dove (mHD) game. Individuals interact randomly in pairs with a Hawk–Dove (HD) game payoff. During host interaction, microbes can be transmitted between the interacting hosts. The fitness benefit to the host from obtaining a resource is denoted by $b$, the fitness cost due to injury during aggressive interaction is denoted by $c$, and $T_{\mathit{ij}}$ stand for the probability of transmission and establishment of microbe $i$ during its host interaction with a host carrying microbe of type $j$.

FIGURE 2

Horizontal transmission rates affect the stable equilibria of the Hawk–Dove game. The expected equilibrium proportion of hosts carrying microbe $H$ in population, for different $b/c$ ratio (y‐axis) and different values of horizontal transmission probability (x‐axis), plotted for (a) $T_{\mathrm{DH}}/T_{\mathrm{HD}}=1$, (b) $T_{\mathrm{DH}}/T_{\mathrm{HD}}=1.05$, (c) $T_{\mathrm{DH}}/T_{\mathrm{HD}}=0.9$, and (d) $T_{\mathrm{DH}}/T_{\mathrm{HD}}=0.95$. $c=0.1$. The black dotted area represents the parameter range where microbe $H$ takes over the population, the colored area represents the parameter range where microbe $H$ and microbe $D$ reach stable polymorphism, and the white area represents the parameter range where microbe $D$ takes over the population. Note that (a) presents the symmetrical transmission case, (b) and (d) biased transmission to similar levels at different directions. The stars refer to the dynamics shown in Figure 3. For derivation see Section 4.1, 4.2.

FIGURE 3

Vertical transmission and mean fitness in the mHD game model. (a) The estimated frequency of microbe $H$ in the population as function of generations number, plotted for different values of vertical transmission probability of the microbes ($\mathrm{VT}$). Solid lines represent perfect vertical transmission $\mathrm{VT}=1$, dashed lines $\mathrm{VT}=0.5$, and the dotted lines $\mathrm{VT}=0.1$. The blue line refers to the genetic case ($T_{\mathrm{HD}}=T_{\mathrm{DH}}=0$, $\mathrm{VT}=1$), and the colors of the other lines correspond to the stars shown in Figure 2, with different ratios of $T_{\mathrm{DH}}$ and $T_{\mathrm{HD}}$, and $c=0.1,b=0.06,T_{\mathrm{HD}}=0.3$. See Sections 4.1, 4.3. (b) The mean fitness differences between the mHD game and the genetic HD game (y‐axis) evaluated in the stable equilibrium state ($\Delta \overline{\omega }={\overline{\omega }}_{mHD game}-{\overline{\omega }}_{\text{genetic}HD game}$), as function of horizontal transmission probability of microbe $H$ (x‐axis), plotted for $c=0.1$, and different $T_{\mathrm{DH}}/T_{\mathrm{HD}}$ ratios. The black area represents the mean fitness differences range for different $b$ values and for $T_{\mathrm{DH}}/T_{\mathrm{HD}}=1$, the reddish area $T_{\mathrm{DH}}/T_{\mathrm{HD}}=0.95$, the orange $T_{\mathrm{DH}}/T_{\mathrm{HD}}=1$, and the gray $T_{\mathrm{DH}}/T_{\mathrm{HD}}=1.05$.

FIGURE 4

Equilibrium stable states of the population when there is a competition between the genes mixed strategy and an alternative mixed strategy induced by a microbe. (a and b) The expected proportion of hosts carrying microbe $A$ in population, based on equilibrium and stability analysis of the mixed strategies model of microbes Hawk–Dove game, for different Hawk‐strategy frequencies induced by microbe $A$ (y‐axis) and different values of horizontal transmission probability (x‐axis), plotted for (a) $P_{\mathrm{B}}\left(H\right)=b/c=0.7$ and (b) $P_{\mathrm{B}}\left(H\right)=b/c=0.9$. The blue dotted area represents the range of parameters in which microbe $A$ cannot evolve, the colored area represents a range of parameters in which microbe $A$ and microbe $B$ reach stable polymorphism, and the white area represents the range of parameters in which microbe $A$ takes over the population. The aggression threshold $\frac{b}{c}\left(1-2T\right)$ is shown as well. When $P_{\mathrm{A}}\left(H\right)<P_{\mathrm{B}}\left(H\right)=\frac{b}{c}$, the threshold determines whether microbe $A$ fixates in the population ($P_{\mathrm{B}}\left(H\right)>P_{\mathrm{A}}\left(H\right)>\frac{b}{c}\left(1-2T\right)$) or reaches stable polymorphism with microbe $B$ ($P_{\mathrm{A}}\left(H\right)<\frac{b}{c}\left(1-2T\right)<P_{\mathrm{B}}\left(H\right)$). For derivation see Sections 4.5, 4.6. (c and d) The expected proportion of Hawk‐like behavior in the population in the equilibrium stable state. (c) Corresponds to (a), and (d) corresponds to (b), plotted for $P_{\mathrm{B}}\left(H\right)=b/c=0.7$ and $P_{\mathrm{B}}\left(H\right)=b/c=0.9$, respectively.