Can a simple algebraic analysis predict markers-genome heterozygosity correlations?

A current algebraic analysis on genome-wide heterozygosity estimates suggests that correlations between molecular markers and genome-wide heterozygosity, rho, depend on the ratio between the number of markers used, r, and the number of genome loci, n; that is: rho approximately square root r/n. Hence, it is unfeasible to obtain reliable estimates of genome-wide heterozygosity in species of large genome using a few markers. We cast some doubts about this analysis as it assumed that the probability that an individual was heterozygous at a locus is equal to the average heterozygosity of this locus in the population. However, we believe that individual heterozygosity at a given locus depends on individual pedigree. Because the pedigree is common for all loci of an individual, their probabilities of heterozygosity are not independent within the genome. We first performed simulations generating random genomes for 100 individuals. Among these individuals, markers and genome-wide heterozygosities correlated as expected from the above equation. However, when we simulated random mating among these individuals and in successive generations including their descendents, as occur in real populations, the correlations between markers and genome-wide heterozygosity were much higher than those predicted from algebraic analyses, and estimates of genome-wide heterozygosity improved slightly with the increment of the number of loci in the genome.