New Recurrent Series in Inbreeding Phenomena

Abstract

A NUMBER of recurrent series have been found in phenomena related to inbreeding. A new series is represented by the sequence of the values of ƒ′_m (the mean coefficient of inbreeding for sex-linked genes¹ in a strictly panmictic population model, as defined by Freire-Maia and Freire-Maia²), from sib matings through the subsequent simple full degrees of consanguinity (uncle–niece plus aunt–nephew, UN + AN; first cousin, 1C; first cousin once removed, 1½C; second cousin, 2C; etc.). This series is as follows: 1/4, 3/16, 5/64, 11/256, 21/1,024, 43/4,096, 85/16,384, … (Fig. 1) (cf. Freire-Maia and Freire-Maia² and unpublished work, and Freire-Maia and Marçallo³ for these terms). Knowing two consecutive values, the following value may be calculated by the formula: The general solution for this equation is: