THE EXACT TEST FOR CYTONUCLEAR DISEQUILIBRIA

We extend the analysis of the statistical properties of cytonuclear di sequilibria in two major ways. First, we develop the asymptotic sampli ng theory for the nonrandom associations between the alleles at a hapl oid cytoplasmic locus and the alleles and genotypes at a diploid nucle ar locus, when there are an arbitrary number of alleles at each marker . This includes the derivation of the maximum likelihood estimators an d their sampling variances for each disequilibrium measure, together w ith simple tests of the null hypothesis of no disequilibrium. In addit ion to these new asymptotic tests, we provide the first implementation of Fisher's exact test for the genotypic cytonuclear disequilibria an d some approximations of the exact test. We also outline an exact test for allelic cytonuclear disequilibria in multiallelic systems. An exa ct test should be used for data sets when either the marginal frequenc ies are extreme or the sample size is small. The utility of this new s ampling theory is illustrated through applications to recent nuclear-m tDNA and nuclear-cpDNA data sets. The results also apply to population surveys of nuclear loci in conjunction with markers in cytoplasmicall y inherited microorganisms.