Additive genetic variation and the distribution of QTN effects among sites

Early quantitative genetic theories emphasize the distribution of gene effects at individual loci or the distribution of mutant effects in maintaining quantitative genetic variation, but infrequently stress the distribution of gene effects among loci. In this study, we analyse the effects of the distribution of quantitative trait nucleotides (QTN) effects among sites under artificial and stabilizing selection. Wright's formula is applied to describing the density distribution of allele frequencies of multiple diallelic QTN at the equilibrium of mutation-drift-selection. Our results demonstrate that the distribution of QTN effects among sites can affect additive genetic variation in terms of total additive variance, average gene diversity, per-class contribution of QTN effects and per-QTN contribution. When the distribution of QTN effects among sites is changed from L-shaped to bell-shaped or to be a flatter, both the total additive variance and the average gene diversity are changed. Per-class and per-QTN contributions exhibit different distribution patterns. The L-shaped distribution indicates the predominant role of the aggregative effects from the QTN of small finite effects. The bell-shaped or flatter distributions indicate the predominance of the QTN of intermediate and large effects. These predictions highlight the significance of the distribution of QTN effects among sites in interpreting the maintenance of quantitative genetic variation at the fine genome scale.