Equivalence by descent: pedigree analysis with inbreeding and gametic phase disequilibrium

In the presence of gametic phase disequilibrium and inbreeding, multiple lo cus genotype frequencies cannot be written solely in terms of identity by d escent (IBD) probabilities. Following Cockerham & Weir (1973) we introduce the concept of 'equivalence by descent' (EBD), an extension of the concept of IBD to include non-allelic genes. Two genes are said to be EBD if they d erive ultimately from the same founding gamete of a pedigree. Allelic genes that are EBD are also IBD. For two loci 11 EBD probabilities, the 'J-coeff icients' are required and for three loci 117 J-coefficients are required to write genotype probabilities. It is show how the 117 J-coefficients for th ree loci call be reduced to a basic set of 37. Computer programs, written i n the algebraic programming language, MAPLE (TM), are described which are c apable of calculating the two- and three-locus J-coefficients for any pedig ree, subject only to size limitations. The MAPLE (TM) packages are availabl e from the author upon request.