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

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Contemporary traces of past human population growth?It is suggested in Reich and Lander (2001) and Williamson et al.(2005) that the effective size of the modern human populationwas stable at around 10 4 until 1.5 × 10 5 years ago.The current effective size is 1.6 × 10 9 .If the population grew according to a given schedule over thisperiod (e.g. exponential growth at a constant rate), how wouldthis manifest itself in the genetic composition of contemporaryhumans?
Equilibria under stable conditionsIf mutations are not reversible at a polymorphic locus, then oneallele will eventually fix there (i.e. no other alleles will be presentin the population).However, the distribution of allele frequencies across polymorphicloci (the frequency spectrum) reaches a non-trivial equilibrium ifboth population size and selection intensities are constant.The theory for the equilibrium frequency spectrum under irreversiblemutation was developed in Fisher (1930), Wright(1938), Kimura (1964). Kimura (1969), Sawyer and Hartl(1992), Bustamante et al. (2001), Williamson et al. (2004),...
Page 1: Non-equilibrium theory of the allel
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 and 14: Introducing mutation from the ances
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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