Format

Send to

Choose Destination
See comment in PubMed Commons below
Theor Popul Biol. 2007 Feb;71(1):109-19. Epub 2006 Jun 23.

Non-equilibrium theory of the allele frequency spectrum.

Author information

1
Department of Statistics #3860, University of California at Berkeley, 367 Evans Hall, Berkeley, CA 94720-3860, USA. evans@stat.Berkeley.edu

Abstract

A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection and varying population size, the boundary condition is lim(x downward arrow0)xf(x,t)=thetarho(t), where f(.,t) is the frequency spectrum of derived alleles at independent loci at time t and rho(t) is the relative population size at time t. When population size and selection intensity are independent of time, the forward equation is equivalent to the backwards diffusion usually used to derive the frequency spectrum, but this approach allows computation of the time dependence of the spectrum both before an equilibrium is attained and when population size and selection intensity vary with time. From the diffusion equation, a set of ordinary differential equations for the moments of f(.,t) is derived and the expected spectrum of a finite sample is expressed in terms of those moments. The use of the forward equation is illustrated by considering neutral and selected alleles in a highly simplified model of human history. For example, it is shown that approximately 30% of the expected total heterozygosity of neutral loci is attributable to mutations that arose since the onset of population growth in roughly the last 150,000 years.

PMID:
16887160
DOI:
10.1016/j.tpb.2006.06.005
[Indexed for MEDLINE]
PubMed Commons home

PubMed Commons

0 comments
How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for Elsevier Science
    Loading ...
    Support Center