coalescent with epistasis
Fearnhead P 2003 Ancestral processes for non-neutral models of complex diseases. Theor Popul Biol 63:115-130.
- if we assume a multiplicative model of fitnesses at these loci (see Risch, 1990), then there is independence of the genealogies (and also the gene-frequencies) at different loci
- for linked, non-neutral loci, the genealogical history of these loci is described by a further Coalescent-type process, the ancestral influence graph (AIG) of Donnelly and Kurtz (1999)
- we consider an extension of the AIG, which we call the complex selection graph (CSG), which describes the genealogical processes at unlinked, non-neutral loci
- the derivation of the CSG is based on considering the limit as the recombination rate in the AIG tends to infinity, whilst keeping the selection rate fixed
- the proof that the CSG represents this limiting process is given in the appendix
- while the gene-interactions do not produce linkage disequilibrium, they can produce large dependencies between the allele frequencies at different loci
- an AIG (Donnelly and Kurtz, 1999) is a supragenealogy for a sample at linked non-neutral loci
- it can be viewed as an extension of the ASG (Krone and Neuhauser, 1997; Neuhauser and Krone, 1997) to include recombination
- or an extension of the ancestral recombination graph (Griffiths and Marjoram, 1996b) to include selection
- let nk(l) denote the number of chromosomes in the sample that have allele Ak at locus l
- let n(l) = (n1(l), ..., nK(l))
- the probability of all ordered samples consistent with (n(1), ..., n(L)) (that is with nk(l) chromosomes which have allele Ak at locus l, for l = 1, ..., L, and k = 1, ..., K) are identical
- one consequence of this is that there is linkage equilibrium across loci
- conditional on the allele frequencies (n(1), ..., n(L)), the alleles at different loci on the same chromosome are independent
- whilst selection can create linkage disequilibrium (Hartl and Clark, 1997), recombination, which acts at a much quicker rate, removes it
- this does not mean that the loci are independent
- there is dependence in the gene-frequencies at different loci