In an idealized model, evolutionary adaptation speed peaks at intermediate selection pressure due to a phase transition where random effects overtake genetic fitness, illustrating a biological Goodhart's law.
Either ≍ 1/ log(N) when γ < γ c, or log(log(χ(µ, γ)/ log(N))) when γ > γ c
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Selection of the fittest or selection of the luckiest: the emergence of Goodhart's law in evolution
In an idealized model, evolutionary adaptation speed peaks at intermediate selection pressure due to a phase transition where random effects overtake genetic fitness, illustrating a biological Goodhart's law.