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

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Introducing mutation from the ancestral type – continuedPass to the diffusion limit for the allele frequencies, but for nowstill work with a finite N for the description of the appearanceof new mutants.The evolving point process has new points added at location 12Nρat rate θ 2 2Nρ.The points then evolve as independent copies of the diffusion.
Introducing mutation from the ancestral type – continuedSet P t (x, dy) := 0-diffusion semigroup.Contribution to the frequency spectrum at y ∈ (0, 1) from mutationsthat appear after time 0 =2N θ ∫ ( )t 12 ρ P t−s0 2Nρ , dy ds.
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 and 12: The diffusion frequency spectrum wi
Page 13: 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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