## Definition An **Evolutionarily Stable Strategy (ESS)** is a behavioural strategy such that, if adopted by most members of a population, it cannot be invaded and replaced by any alternative ("mutant") strategy through natural selection. The concept was introduced by John Maynard Smith and George Price (1973) and brought to a wide audience by Dawkins in *The Selfish Gene*. An ESS is a Nash equilibrium under natural-selection dynamics: once the population is at an ESS, any individual deviating from it does worse, so selection drives deviants back. Dawkins's definition: > "An Evolutionarily Stable Strategy is defined as a strategy which, if most members of a population adopt it, cannot be bettered by an alternative strategy." ## The Hawk–Dove Model The archetypal ESS illustration uses two pure strategies competing for a resource of value $V$: - **Hawk:** always escalate; fight until injured or the opponent retreats. - **Dove:** display only; retreat if opponent escalates. Expected payoffs (assuming injury cost $C > V$): | Contest | Hawk payoff | Dove payoff | |---|---|---| | Hawk vs. Hawk | $\frac{V - C}{2}$ (negative if $C > V$) | 0 (retreat) | | Hawk vs. Dove | $V$ | 0 | | Dove vs. Dove | $\frac{V}{2}$ | $\frac{V}{2}$ | Neither pure Hawk nor pure Dove is an ESS when $C > V$: - In an all-Dove population a single Hawk mutant always wins $V$ and spreads. - In an all-Hawk population a single Dove mutant avoids costly fights and does better on average. The ESS is a **mixed equilibrium**: a stable frequency of Hawks $\hat{p} = V/C$ and Doves $1 - V/C$ in the population (or, equivalently, each individual plays Hawk with probability $V/C$). ## ESS and Group Benefit A crucial implication: the ESS is not necessarily what is best for the group. An all-Dove population would maximise collective welfare, but it is not evolutionarily stable. Natural selection optimises gene propagation, not population welfare — a recurring argument against group-selection theories. ## Tit-for-Tat as a Near-ESS Robert Axelrod's computer tournaments (reported in *The Evolution of Cooperation*, 1984) demonstrated that in iterated Prisoner's Dilemma games the strategy *Tit-for-Tat* — cooperate on the first move, then copy the opponent's last move — consistently outperformed all alternatives. Although technically it is not a strict ESS (it can be invaded by an unconditional cooperator in a Tit-for-Tat population), it illustrates how cooperation can be stable under repeated interaction, providing a game-theoretic underpinning for [[Kin Selection and Inclusive Fitness]] arguments about reciprocal altruism. ## Broader Significance ESS analysis applies far beyond aggression: sex ratios, parental investment levels, signalling honesty, immune evasion by parasites, and cooperative behaviour in humans all have been modelled as ESS problems. The concept bridges evolutionary biology and game theory and is a cornerstone of behavioural ecology. ## Related - [[Gene-Centred View of Evolution]] - [[The Selfish Gene]] - [[Kin Selection and Inclusive Fitness]] ## Sources - [[The Extended Selfish Gene (Dawkins 2016)]]