The Effect of Inbreeding on the Variation Due to Recessive Genes.

N his classical treatment of inbreeding, WRIGHT (1921 ) developed the conI cept of the inbreeding. coefficient F, which he defined as the correlation between the genetic constitution of the gametes in the uniting egg and sperni. This is d.irectly related to the heterozygosity remaining. in the population which is equal to l F times the heterozygosity at the start of inbreeding. If a number of inbredelines are made without selection from a raildoni breeding population, the genetic variance due to genes which act additively increases between' lines as 2F and decreases within lines as 1 F. (If inbreeding is rapid, the value 1 F for the genetic variance within lines is not adequate, the correct expression being 1 + F 2F, where F is the inbreeding coefficient of the hypothetical progeny produced by randoni mating within lines in the present generation and 2 F is correct for the variance between lines.) For genes which do not act additively, there is not the same correspondence lietween heterozygosity and variance and the above relationships do not hold. A s we know little about the dominance relationships of the genes controlling continuous variation, it seemed desirable to investigate theoretically the effect of inbreeding on the variation due to genes which are conipletely recessive and to genes which show overdominance. Particular attention is given to the case in which the recessive (or quasi-recessive) is at low frequency as this is the most probable situation in natural populations. We shall deal first with continued full-sib mating in which the results can be worked out by simple, if rather laborious, arithmetic and where the process can be most easily visualised. The more general situation of slow inbreeding in lines of' constant breeding size requires more sophisticated niatheniatics and the details of the derivations are given in an appendix. The two methods are in good agreement.