Questions: Evolutionary Stable Strategy (ESS)

Question 1

In a population where every individual plays pure Dove (always yield in conflicts), a single Hawk mutant appears. What happens?

• A. The Hawk is eliminated because the population's collective yielding behavior provides no payoff advantage to aggression
• B. The Hawk spreads because it wins every conflict at no cost, demonstrating that pure Dove is not an ESS
• C. Nothing changes — rare mutants are always eliminated by drift before selection can act
• D. The Hawk reaches a stable low frequency immediately, limited by frequency-dependent costs

Answer: (B)

An ESS requires that no rare mutant can invade — that invaders do worse than the resident strategy. A Hawk in an all-Dove population wins every conflict without fighting (Doves always yield), gaining maximum payoff at zero injury cost. The Hawk's fitness far exceeds the Dove's, so it spreads. Pure Dove fails the ESS invasion criterion. This is not about consciousness or calculation — natural selection simply increases the frequency of whatever strategy yields more offspring.

Question 2

The ESS in the Hawk-Dove game is a mixed strategy rather than pure Hawk or pure Dove. In evolutionary terms, this means:

• A. Each individual consciously calculates and chooses how aggressively to behave in each encounter
• B. At equilibrium, each individual plays Hawk with some probability and Dove with the rest, such that the expected payoffs from each pure strategy are equal and no alternative can invade
• C. The population is split evenly between genetically pure Hawks and genetically pure Doves, with natural selection maintaining the 50/50 ratio
• D. Selection eliminated both Hawk and Dove phenotypes, producing a new intermediate 'neither' strategy

Answer: (B)

The mixed-strategy ESS in Hawk-Dove means individuals probabilistically vary their behavior — playing Hawk with probability p* and Dove with probability (1 − p*) — calibrated so the expected fitness gain from each pure strategy is identical. At this equilibrium, no mutant playing a different probability does better. Note that the same equilibrium can also manifest as a polymorphism (a stable population mix of pure Hawk and pure Dove individuals), but in both cases the mechanism is fitness equalization, not conscious choice or a compromise phenotype.

Question 3

An evolutionarily stable strategy (ESS) is expected to generally be a single pure strategy; mixed or probabilistic strategies can seldom be evolutionarily stable because selection favors definite behaviors.

• T. True
• F. False

Answer: False

This is a common misconception. An ESS can be a mixed strategy (where each individual plays each pure strategy with some probability), a pure strategy (if one strategy outperforms all others when common), or a polymorphism (a stable population mix of pure types maintained by frequency-dependent selection). The Hawk-Dove ESS is typically a mixed strategy or polymorphism. The defining criterion is the invasion test — not the strategy type.

Question 4

The ESS invasion criterion states that a strategy is evolutionarily stable if it does better against itself than any rare mutant alternative does against it.

• T. True
• F. False

Answer: True

This is the formal definition. Strategy I is an ESS if, when the population plays I, any rare mutant J satisfies: payoff(I vs I) > payoff(J vs I). If payoff(I vs I) = payoff(J vs I), the secondary condition payoff(I vs J) > payoff(J vs J) must also hold. Together these conditions ensure that the ESS cannot be invaded and displaced by any alternative strategy, making it a self-correcting evolutionary equilibrium.

Question 5

Why does the ESS concept apply to organisms that cannot consciously choose strategies, such as plants or bacteria?

Model answer: ESS is a property of the fitness consequences of behaviors, not of the cognitive processes producing them. Natural selection acts as the optimizer: heritable strategies that yield higher fitness spread; those yielding lower fitness decline. Over generations, the population converges toward the ESS through differential reproduction, regardless of whether organisms 'know' what they are doing. The ESS invasion criterion asks only whether a mutant strategy yields higher fitness against the resident population — a question answered by ecology and genetics, not cognition. This is why the ESS framework applies to microbial cooperation, plant resource allocation, and sex ratio evolution, not just animal behavior.

Fisher's principle — that equal investment in sons and daughters is an ESS for sex ratios — is the classic example. No organism calculates its optimal sex ratio; selection eliminates genotypes that deviate from the ESS proportion by imposing fitness penalties on overproduced sexes. The ESS emerges from selection, not strategy.