ANOVA for estimating Nei’s diversity and related parameters in a fixed set of populations with an application in genetic resources conservation

Genetic diversity parameters are used by plant breeders to develop efficient genetic resources sampling and conservation strategies. Extending previous developments on the use of ANOVA on allele frequencies in a fixed set of populations, we show that this approach allows unbiased estimation of diversity parameters, including Nei’s diversity parameters, HS, the within-population diversity; DST, the between-population differentiation; HT, the total gene diversity; and other related parameters well suited for guiding conservation decisions. We consider two cases: selfing plants and outcrossing plants. For outcrossing plants, this approach also allows the estimation of the average frequency of heterozygotes (H0) and average departure of populations from a random mating equilibrium. These unbiased ANOVA estimators correspond to those derived by Nei and Chesser (Ann Hum Genet 47:253–259, 1983) by using properties related to the multinomial sampling of genotypes. With an equal number of individuals sampled per population, we first developed analyses of variation for each allele at one locus. Then, considering the whole set of alleles, we show the correspondence between the sum of the variances in allele frequencies over the alleles and Nei’s within- and between-population diversities. Considering large populations leads to Nei’s relationship, HT = HS + DST, which is a decomposition of the total variance in allele frequencies into within- and between-population variance components, variance meaning the sum of the variances of each allele over the whole set of alleles. Finally, we use theoretical results of the ANOVA approach to consider a genetic resources conservation design with only one individual per population, which allows Nei’s total gene diversity to be maintained.