Refinements to the partitioning of the inbred genotypic variance

Natural gene flow is often localised because of gamete dispersal limitations, and the quantity and structure of the genotypic variance in such populations is a key to predicting the advance from selection, in both evolution and artificial breeding programmes. Earlier derivations of this variance have shown that the total dominance variance may increase with inbreeding despite the fact that heterozygosity is decreasing. This anomaly has been corrected following the de novo biometrical derivation presented in this paper. The whole population also subdivides into descendant lineages that differ in allele frequencies and means because of the dispersion caused by genetic drift and continuing localisation of gamodemes. The paper defines for the first time the among-line and within-line partitions of the dominance variance; and corrects anomalies in the total genic (additive genetic) variance, and its underlying inbred average alle-substitution effect. The revisions also clarify the connections between the Fisher-Falconer, Mather-Hayman, and Wright approaches to defining the inbred genotypic variance. Relationships are discussed between the population dispersion structure and genetic efficiency in selection.