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Scaffold S8 — Selection coefficient from Δp

Five rounds. You are given a starting allele frequency p0, a later frequency pt, the number of generations elapsed t, and the effective population size Ne. Predict the selection coefficient s that best explains the change. The reveal shows the likelihood profile for s and the 95% confidence interval — sometimes tight, sometimes spanning zero. All calculations use the haploid-selection approximation (Δ ln(p/(1−p)) ≈ s · t); for diploid additive selection multiply s by 2.

Locked — answer the pretest above first.

Running tally — estimated s and 95% CI across rounds

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Every round reduced to the same calculation: Δψ = ln(pt/(1−pt)) − ln(p0/(1−p0)), and ŝ = Δψ / t. The point estimate only depends on p0, pt, and t. The confidence depends on Ne·t·p̄(1−p̄), because the drift variance of Δψ is 1/(2Ne·p̄(1−p̄)) per generation.

Rounds 1 and 2 had identical endpoints but different t — so the same observed change implied very different s. Round 3 used the same change in a small population: the CI spanned zero, so selection was not distinguishable from drift. Round 4 (LTEE-like) had a huge product of Ne·t and gave a razor-tight CI. Round 5 (FSJ-like) had a small product and gave a CI that spanned zero — the observed Δp is consistent with pure drift.

Estimating s requires all three: Δp, t, and Ne. Give up any one and the answer is either unidentified or has no CI. In your own work, when you want to report "how strong is selection here?", you must report all three alongside.