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DETECTION OF NONRANDOM ASSOCIATION OF ALLELES FROM THE DISTRIBUTION OF THE NUMBER OF HETEROZYGOUS LOCI IN A SAMPLE
Ranajit Chakraborty 1
1 Center for Demographic and Population Genetics, University
of Texas Graduate School of Biomedical Sciences, Houston, Texas 77225
The distribution of the number of heterozygous loci in two randomly
chosen gametes or in a random diploid zygote provides information regarding
the nonrandom association of alleles among different genetic loci. Two alternative
statistics may be employed for detection of nonrandom association of genes
of different loci when observations are made on these distributions: observed
variance of the number of heterozygous loci (s2
k) and a goodness-of-fit criterion (X2) to
contrast the observed distribution with that expected under the hypothesis
of random association of genes. It is shown, by simulation, that s
2k is statistically more efficient than X
2 to detect a given extent of nonrandom association. Asymptotic normality
of s2k is justified, and X
2 is shown to follow a chi-square (
2) distribution with
partial loss of degrees of freedom arising because of estimation of parameters
from the marginal gene frequency data. Whenever direct evaluations of linkage
disequilibrium values are possible, tests based on maximum likelihood estimators
of linkage disequilibria require a smaller sample size (number of zygotes
or gametes) to detect a given level of nonrandom association in comparison
with that required if such tests are conducted on the basis of s
2k. Summarization of multilocus genotype (or haplotype)
data, into the different number of heterozygous loci classes, thus, amounts
to appreciable loss of information.
Accepted on June 6, 1984
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