Practical Evolution · ENTM 7230 · Individual-Based Models in Context

Same Sweep, Three Algorithms

One population, one directional selection pressure, one trait — represented three different ways. Watch where the predictions agree, and where one of them quietly stops being true.

Generation
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z̄ — individual-based
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z̄ — allele frequency
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z̄ — breeder's equation
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Mean phenotype over time — all three predictions

individual-based (dots = actual runs) allele-frequency recursion breeder's equation (Va fixed)

Locus fixed (or lost) in the individual-based run — compare where each model landed.

Individual-based

State: every individual's genotype and phenotype.

population = N individuals, allele ∈ {A, a} for generation: for each individual: z = genetic_value(allele) + N(0, Ve) w = exp(β·z) # selection population = resample N, chance ∝ w # haploid, clonal record p = freq(A), z̄ = mean(z)

Allele-frequency

State: one number — the frequency of allele A.

W_A, W_a = expected fitness of each allele (averaged over env. noise) p = p0 for generation: p = p·W_A / (p·W_A + (1−p)·W_a) record z̄ = α·p − α/2

Quantitative genetics

State: two numbers — the trait mean and its variance.

z̄ = z̄0 Va = Va0 # measured once, # then held fixed for generation: R = Va · β # breeder's equation z̄ = z̄ + R record z̄

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