Covariances between Arbitrary Relatives in Autotetraploids with Panmictic Disequilibrium.

In random mating autopolyploid populations which have not reached equilibrium, two alleles may be interdependent as a result of the phenomenon of gametic recombination, i.e. the maintenance through successive gamete generations of an association of two alleles from the same gamete in a source reference generation. Any two alleles are dependent by this relationship if they derive by descent from the same ancestral gamete in the source population. Applied with the classical notion of identity by descent, the concept thus defined identifies new coefficients of dependence between arbitrary relatives. Coefficients of dependence are probabilities attached to the drawing of genes from two zygotes such that there are certain relationships amongst them. Applying the concept to autotetraploids, consideration of the states of dependence between the genes of a zygote or of a pair of zygotes leads to the definition of new parameters bearing on population means, variances and covariances, for arbitrary inbreeding. The absence of epistasis is supposed. Some applications of interest in artificial selection are briefly envisaged, with simplifying restrictions on genetic effects. The particular case of diallelism is also considered.