Evolutionarily_stable_strategy

# Evolutionarily stable strategy ## Microsim (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Evolutionarily_stable_strategy.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin"></iframe> </div> *Where [[Decision_theory]] meets natural selection: this GENOMICS microsim watches a population of aggressive "Hawks" and cautious "Doves" settle into a stable mix — the same frequency-dependent logic that shapes [[Kin_selection]] and Reciprocal altruism across behavioural [[Ecology]].* > An evolutionarily stable strategy (ESS) is a heritable behaviour that, once common in a population, cannot be displaced by any rare alternative. In the Hawk-Dove game, animals contest a resource: Hawks escalate and risk injury, while Doves display and yield. Because each strategy's success depends on how many others already use it, selection settles the population into a stable balance rather than a single winner. By sliding the resource value and the injury cost, you can watch the fraction of Hawks climb or fall toward that balance — and see why unrestrained aggression rarely takes over. ## About this microsim The microsim runs the Hawk-Dove contest under replicator dynamics using four sliders and three buttons. **Resource value V** (1-10) sets the fitness payoff of winning a contest; **Injury cost C** (1-20) sets the penalty a Hawk pays when it loses a fight; **Initial hawk fraction p₀** (0-1) sets the starting proportion of Hawks; and **Evolution speed** (0.1-3x) scales how fast selection updates the population each step. Press **▶ Play** to animate the trajectory, **Step +Δt** to advance one increment at a time, and **Reset** to return to the starting fraction. ## Related microsims - [[Kin_selection]] — another evolutionary-game route to social behaviour, where relatedness rather than injury cost tips the payoff toward restraint. - Reciprocal altruism — the cooperative counterpart, showing how repeated encounters make yielding pay off over time. - [[Decision_theory]] — the payoff-and-equilibrium machinery that game-theoretic biology borrows and reinterprets as fitness. - [[Population_growth]] — the population-dynamics backdrop; replicator dynamics track strategy frequencies the way growth models track numbers. - [[Ecology]] — the behavioural-ecology setting where contests over real resources shape animal aggression. ## Links (Wikipedia order)  `Abiogenesis` · `Accident-proneness` · `Acquired_characteristic` · [[Adaptation]] · `Adaptationism` · `Adaptive_radiation` · `Adaptive_unconscious` · 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`Visual_perception` · `Vitalism` · `Volunteer's_dilemma` · `W._D._Hamilton` · `War_of_attrition_(game)` · `Wason_selection_task` · [[Wayback_Machine]] · `Weak_evolutionarily_stable_strategy` · `Westermarck_effect` · `William_Vickrey` · `Winning_Ways_for_Your_Mathematical_Plays` · `Win–stay,_lose–switch` · `Win–win_game` · `Zermelo's_theorem_(game_theory)` · `Zero-sum_game` · `Zugzwang` ## Overview The ESS concept was introduced by John Maynard Smith and George Price in 1973 to import game theory into evolutionary biology. It is the biological refinement of the Nash equilibrium: instead of assuming rational players, it asks which heritable strategy, if fixed in a population, resists invasion by rare mutants. Because a strategy's payoff depends on how common it is — **frequency-dependent selection** — the best behaviour is relative to the crowd, not fixed. The Hawk-Dove game is its canonical illustration, explaining why animal contests are so often ritualized displays rather than fights to the death. ## The mechanism Two individuals compete for a resource worth $V$. A Hawk always escalates; a Dove displays and retreats if attacked. The payoff matrix (fitness to the row player) is: | | vs Hawk | vs Dove | |---|---|---| | **Hawk** | $(V-C)/2$ | $V$ | | **Dove** | $0$ | $V/2$ | When two Hawks meet, each wins half the time and pays the injury cost $C$ half the time. Two Doves share the resource. - If $V > C$, injury is cheap, Hawk dominates, and **all-Hawk** is the ESS. - If $C > V$, neither pure strategy is stable. The population settles at a **mixed ESS** with a Hawk fraction of $p^* = \frac{V}{C}.$ With the defaults $V=6$, $C=10$, this predicts $p^*=0.6$: starting from $p_0=0.30$, selection pushes the Hawk fraction up to 60%, where Hawks and Doves earn equal average fitness. This equilibrium reads either as a stable polymorphism (60% Hawks, 40% Doves) or as every individual playing Hawk 60% of the time. ## Controls -> what each maps to | Control | Maps to | Range / values | Meaning | |---|---|---|---| | Resource value V | Payoff for winning ($V$) | 1-10 | Fitness gained from the contested resource | | Injury cost C | Loser's penalty ($C$) | 1-20 | Fitness lost when a Hawk loses a fight | | Initial hawk fraction p₀ | Starting state | 0-1 | Proportion of Hawks before selection acts | | Evolution speed | Time-step scale | 0.1-3x | How fast replicator dynamics update the mix | | ▶ Play / Step +Δt / Reset | Playback | buttons | Run, single-step, or restart the trajectory | ## Learning objective Understand how frequency-dependent selection drives a population to an evolutionarily stable mix of behaviours, and predict that mix as $p^* = V/C$ whenever injury cost exceeds resource value. ## Limits and connections The model assumes an infinite, well-mixed population of asexual clones with contests decided pairwise at random — no kinship, memory, spatial structure, or ownership (the "Bourgeois" strategy relaxes that last one). Real disputes layer these back in, but the core insight — that the cost of conflict caps the spread of aggression — carries directly into models of cooperation and social evolution. ## Poster & source <div class="microsim-fallback">  <p><em>Live microsim · <a href="https://wikitube-3d-microsims.netlify.app/Evolutionarily_stable_strategy.html">open full</a> · source: Microsims for Dissemination/GENOMICS_ThreeJS_Microsims/Evolutionarily_stable_strategy.html</em></p> </div>  *Built to the [[WT!Three_js_Microsim_Master_Class|three.js Master Class]].*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Evolutionarily_stable_strategy) : [Wikitube](https://en.wikitube.io/wiki/Evolutionarily_stable_strategy) ## Previous hub tags Tree parent: [[Game_theory]]. Legacy hubs: `GENOMICS`. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*