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THE SAMPLING DISTRIBUTION OF LINKAGE DISEQUILIBRIUM UNDER AN INFINITE ALLELE MODEL WITHOUT SELECTION
Richard R. Hudson 1
1 Biometry and Risk Assessment Program, National Institute of
Environmental Health Sciences, Research Triangle Park, North Carolina 27709
The sampling distributions of several statistics that measure
the association of alleles on gametes (linkage disequilibrium) are estimated
under a two-locus neutral infinite allele model using an efficient Monte Carlo
method. An often used approximation for the mean squared linkage disequilibrium
is shown to be inaccurate unless the proper statistical conditioning is used.
The joint distribution of linkage disequilibrium and the allele frequencies
in the sample is studied. This estimated joint distribution is sufficient
for obtaining an approximate maximum likelihood estimate of C = 4
Nc, where N is the population size and c is the recombination
rate. It has been suggested that observations of high linkage disequilibrium
might be a good basis for rejecting a neutral model in favor of a model in
which natural selection maintains genetic variation. It is found that a single
sample of chromosomes, examined at two loci cannot provide sufficient information
for such a test if C < 10, because with C this small,
very high levels of linkage disequilibrium are not unexpected under the neutral
model. In samples of size 50, it is found that, even when C is as
large as 50, the distribution of linkage disequilibrium conditional on the
allele frequencies is substantially different from the distribution when there
is no linkage between the loci. When conditioned on the number of alleles
at each locus in the sample, all of the sample statistics examined are nearly
independent of 
= 4Nµ, where µ is the neutral mutation
rate.
Accepted on November 16, 1984
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