Abstract
Fisher’s concepts of average effects and average excesses are at the core of the quantitative genetics theory. Their meaning and relationship have regularly been discussed and clarified. Here we develop a generalized set of one locus two-allele orthogonal contrasts for average excesses and average effects, based on the concept of the effective gene content of alleles. Our developments help understand the average excesses of alleles for the biallelic case. We dissect how average excesses relate to the average effects and to the decomposition of the genetic variance.
Highlights
Since Fisher (1918), partitioning of the genotypic values at a locus into additive and dominance effects has been used for conventional quantitative genetic analyses and recently for mapping quantitative trait loci (QTL; see, e.g., Lynch and Walsh, 1998)
Regardless of whether a population is in Hardy–Weinberg equilibrium (HWE) or Hardy–Weinberg disequilibrium (HWD), Fisher (1918) and others have shown that the additive and dominance genetic effects are the coefficient of a linear regression of the genotypic values on the gene content and the deviation from that regression, respectively
For the average effects formulation the predictions of the regression can be obtained by just summing up the appropriate average effects, this does not hold for the average-excess formulation [with c = 1/(1 + F )], i.e., α∗ij = α∗i + α∗j, unless the genotypic frequencies are under HWE
Summary
Since Fisher (1918), partitioning of the genotypic values at a locus into additive and dominance effects has been used for conventional quantitative genetic analyses and recently for mapping quantitative trait loci (QTL; see, e.g., Lynch and Walsh, 1998). Regardless of whether a population is in HWE or HWD, Fisher (1918) and others have shown that the additive and dominance genetic effects are the coefficient of a linear regression of the genotypic values on the gene content and the deviation from that regression, respectively.
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