Estimating Realized Heritability in Panmictic Populations

Abstract

Narrow sense heritability [Formula: see text] is a key concept in quantitative genetics, as it expresses the proportion of the observed phenotypic variation that is transmissible from parents to offspring. [Formula: see text] determines the resemblance among relatives, and the rate of response to artificial and natural selection. Classical methods for estimating [Formula: see text] use random samples of individuals with known relatedness, as well as response to artificial selection, when it is called realized heritability. Here, we present a method for estimating realized [Formula: see text] based on a simple assessment of a random-mating population with no artificial manipulation of the population structure, and derive SE of the estimates. This method can be applied to arbitrary phenotypic segments of the population (for example, the top-ranking parents and offspring), rather than random samples. It can thus be applied to nonpedigreed random mating populations, where relatedness is determined from molecular markers in the selected parents and offspring, thus substantially saving on genotyping costs. Further, we assessed the method by stochastic simulations, and, as expected from the mathematical derivation, it provides unbiased estimates of [Formula: see text] We compared our approach to the regression and maximum-likelihood approaches utilizing Galton's dataset on human heights, and all three methods provided identical results.

Towards an information theory of quantitative genetics

“…If Ω 123 is the multi-information for three variables, then Ω 123 ≥ 13 + 23 , Ω 123 ≥ 12 + 23 , Ω 123 ≥ 13 + 12 (13) This result is intuitive and elementary, but still not entirely obvious. For completeness we provide a proof in Appendix A.…”

“…Genomic heritability is the fraction of the genetic variance that can be explained by regression on the markers, and will only be quantitatively accurate when all causal variants are genotyped. See [23] for a nice discussion of heritability for panmictic populations.…”

“…Contrast this with Fisher's heritability, in the broad sense, which is the ratio of the variances of phenotype to genotype in the population. Narrow sense heritability is more important in the sense that it quantitates the proportion of the phenotypic variation that is transmitted from parents to offspring [23]. The argument for this interpretation that ignores epistatic effects, which are frequently disrupted by segregation, is plausible, but incomplete.…”

“…and23 , and the total dependence is Ω 123 , the three-way dependence is given by their difference, Δ 3 . The fractional dependencies are then simply the ratios…”

Toward an Information Theory of Quantitative Genetics

“…Many modern authors have argued and provided evidence that gene/gene interactions are rather common (Gilbert-Diamond and Moore, 2011 ). The most common way to deal with these interactions quantitatively, however, has been to use regression methods (Lstiburek et al, 2018 ), and more recently, other machine learning tools. In all these cases, however, the starting loci are most often those identified by GWAS or some pairwise method, which will then miss those loci that are invisible to pairwise methods.…”