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When parents have the same surname this is often due to common ancestry and therefore parental isonymy is an indication of increased homozygosity in the chil­dren. For a large class of relationships the inbreeding coefficient of the children is 1/4 the proportion of isonymy in their parents. The average inbreeding coefficient in a population at time t, Ft, can be divided into random, Ft, and nonrandom, Fnt, components: Ft = Frt + Fnt — FrtFnt. Fn, Fr, and F correspond to Wright’s FIS, FST, and FIT. Two methods for computing these quantities from isonymy data are given. Method A is preferred if the population has a short history so that most of the inbreeding is from matings between second or third cousins and closer relatives. Method B is preferred if the population is older so that cumulative effects of inbreeding become important, as is usually the case.In deriving this information the pedigree F is used and it is shown that the average inbreeding coefficient in generation t is given by Ft = FrT + Fpt - FrTFptwhere F t is the inbreeding coefficient at time t, Fpt is the pedigree F defined as the inbreeding coefficient based solely on information in the pedigree of the individuals in generation t, and Frτ is the random component of the inbreeding coefficient at time r. Time t is taken such that the complete pedigrees are known back to generation t — 1.