Estimating genetic diversity parameters with traditional and novel metrics based on the metafounders methodology

During the last decade, the concept of metafounders has been developed to overcome the unrealistic assumption of unrelated base populations. Metafounders are used in genomic evaluations to estimate relationships within and across populations. However, so far, relationships based on gamma from the metafounders theory have not been compared to traditional genetic diversity parameters in real populations. Therefore, the objective of this study is to use gamma to estimate genetic diversity parameters and compare them with estimates based on traditional parameters. We will focus on different metrics used to estimate genetic distance, i.e., fixation index (Fst) and Nei’s minimum genetic distance (D), but also on population inbreeding coefficients based on homozygosity (Fhom), drift (Fdrift) or average heterozygosity (Fb), and apply them to a real population. To make the comparison between traditional and gamma estimated parameters, we will use the following formulas: for fixation index, Fst = 1–Hwithin/Hbetween and Fst = (γb/8+γb’/8–γbb’/4)/(1/2–γbb’/4); for Nei’s Minimum genetic distance, D = 1/n∑(pb–pb’)2 and D = γb/8+γb’/8+γbb’/4; for inbreeding coefficient based on homozygosity, Fhom = 1–1/n∑((2pb(t)qb(t))/(2pb(0)qb(0))) and Fhom = γb/2, for inbreeding coefficient based on drift, Fdrift = 1/n∑((pb(t)–pb(0))2/(pb(0)qb(0) )) and Fdrift = γb/2; for inbreeding coefficient based on average heterozygosity, Fb = 1–4/n∑(2pbqb) and Fb = γb–1, with Hwithin the within population heterozygosity, Hbetween the between population heterozygosity, γb and γb’ the within population gamma estimates, γbb’ the across-populations gamma estimate, n the number of SNP, pb and pb’ the allelic frequencies in the different populations, pb(t) and pb(0) the current and initial allelic frequencies (AF), respectively, and q = 1–p. The definition of equations based on gamma estimates supposes AF of base population of 0.5. Considering that initial heterozygosity in populations is probably lower than this, we might expect some differences in the traditionally and gamma computed genetic diversity parameters, except if they are more robust to changes in AF than expected.