Non-equilibrium theory of the allele frequency spectrum ... - ICMS

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The forward equation without mutationThe frequency spectrum is obtained by taking a sum of pointmasses at the x i and moving it forwards with the 0-diffusionsemigroup.Set f o (y, t) := frequency spectrum, then∂∂t f o (y, t) = − ∂∂y [a(y)f o (y, t)] + 1 2with suitable boundary conditions.∂ 2∂y 2[b(y)f o (y, t)].
Introducing mutation from the ancestral typeIn the Markov chain model, new mutants arise at rate 2Nρµ = θ 2 ρper generation.The initial number of mutants at a locus is 1.Hence mutants appear at rate 2N θ 2ρ per unit of rescaled time,with the initial proportion of mutants at a locus being 12Nρ .
Page 1 and 2: Non-equilibrium theory of the allel
Page 3 and 4: Equilibria under stable conditionsI
Page 5 and 6: What if population size or selectio
Page 7 and 8: Discrete time finite population mod
Page 9 and 10: The diffusion limit for a single lo
Page 11: The diffusion frequency spectrum wi
Page 15 and 16: Introducing mutation from the ances
Page 17 and 18: Entrance boundary theory - continue
Page 19 and 20: Finding the boundary conditionSince
Page 21 and 22: Conclusion for the time-homogeneous
Page 23 and 24: Structured populationsThe same appr
Page 25 and 26: Example - continuedPut µ n (t) :=
Page 27 and 28: Recent human population growthAssum
Page 29 and 30: 10090f(x,0)f(x,0.3))8070f(x)6050403
Page 31 and 32: 43.5f i(n=20,t=0)f i(n=20,t=0.3))32
Page 33 and 34: 3f i(n=20,t=0)f i(n=20,t=0.3)2.52f
Page 35 and 36: *ReferencesBustamante, C. D., Wakel
Page 37 and 38: Nielsen, R., 2000. Estimation of po
Page 39: inference of selection and populati

Non-equilibrium theory of the allele frequency spectrum ... - ICMS

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