Non-equilibrium theory of the allele frequency spectrum ... - ICMS
Non-equilibrium theory of the allele frequency spectrum ... - ICMS
Non-equilibrium theory of the allele frequency spectrum ... - ICMS
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Conclusion for <strong>the</strong> time-inhomogeneous caseSuppose that everything is allowed to depend on time.Write f(x, t) for <strong>the</strong> <strong>frequency</strong> <strong>spectrum</strong>.Allowing a, b, θ and ρ to be piecewise constant, using <strong>the</strong> aboveanalysis, and <strong>the</strong>n taking limits gives∂∂f(y, t) = −∂t ∂y [a(y, t)f(y, t)] + 1 2∂y2[b(y, t)f(y, t)]with lim y↓0 yf(y, t) = θ(t) limx x↓0 b(x,t) and lim y↑1 f(y, t) finite.∂ 2
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