Quote:
. Being a PhD, do you have anything less entry level? Any human attraction studies that would blow my mind?
sure.
In order for a strategy to be evolutionarily stable, it must have the property that if almost every member of the population follows it, no mutant (that is, an individual who adopts a novel strategy) can successfully invade. This idea can be given a precise characterization as follows: Let ΔF(s1,s2) denote the change in fitness for an individual following strategy s1 against an opponent following strategy s2, and let F(s) denote the total fitness of an individual following strategy s; furthermore, suppose that each individual in the population has an initial fitness of F0. If σ is an evolutionarily stable strategy and μ a mutant attempting to invade the population, then
F(σ) = F0 + (1−p)ΔF(σ,σ) + pΔF(σ,μ)
F(μ) = F0 + (1−p)ΔF(μ,σ) + pΔF(μ,μ)
where p is the proportion of the population following the mutant strategy μ.
Since σ is evolutionarily stable, the fitness of an individual following σ must be greater than the fitness of an individual following μ (otherwise the mutant following μ would be able to invade), and so F(σ) > F(μ). Now, as p is very close to 0, this requires that either that
ΔF(σ,σ) > ΔF(μ,σ)
or that
ΔF(σ,σ) = ΔF(μ,σ) and ΔF(σ,μ) > ΔF(μ,μ)
(This is the definition of an ESS that Maynard Smith and Price give.) In other words, what this means is that a strategy σ is an ESS if one of two conditions holds: (1) σ does better playing against σ than any mutant does playing against σ, or (2) some mutant does just as well playing against σ as σ, but σ does better playing against the mutant than the mutant does.
follow?