Inverse inbreeding coefficient problems with an application to linkage analysis of recessive diseases in inbred populations

Medical geneticists connect relatives having the same disease into a family structure called a pedigree. Genetic linkage analysis uses pedigrees to fi nd the approximate chromosomal locations of disease-causing genes. The prob lem of choosing a pedigree is particularly interesting for diseases inherit ed in an autosomal recessive pattern in inbred populations because there ar e many possible paths of inheritance to choose from. A variety of shortcuts are taken to produce plausible pedigrees from inbred populations. We lay t he mathematical foundations for a shortcut that was recently used in a pedi gree-disease study of an inbred Mennonite population. Recessive disease gen es can be localized using the shortcut of homozygosity mapping by finding r egions of the genome where affected persons are homozygous. An important qu antity in homozygosity mapping is the inbreeding coefficient of a person, w hich is the prior probability that the person inherited the same piece of D NA on both copies of the chromosome from a single ancestor. Software packag es are ill-suited to handle large pedigrees with many inbreeding loops. The refore, we consider the problem of generating small pedigrees that match th e inbreeding coefficient of one or more affected persons in the larger pedi gree. We call such a problem an inverse inbreeding coefficient problem, We focus on the case where there is one sibship with one or more affected pers ons, and consider the problem of constructing a pedigree so that it is "sim pler" and gives the sibship a specified inbreeding coefficient. First, we g ive a construction that yields small pedigrees for any inbreeding coefficie nt. Second, we add the constraint that ancestor-descendant matings are not allowed, and we give another more complicated construction to match any inb reeding coefficient. Third, we show some examples of how to use the one-sib ship construction to do pedigree replacement on real pedigrees with multipl e affected sibships. Fourth, we give a different construction to match the inbreeding coefficient of one sibship, while attempting to minimize a measu re of the inbreeding loop complexity. (C) 2000 Elsevier Science B.V. All ri ghts reserved.