8.1 Specifying inheritance

For MORGAN programs, genetic relationships between individuals in a data set are specified in the pedigree file. Individuals at the top of a pedigree (family), whose parents are unspecified, are the founders of the pedigree; other individuals are non-founders. By definition, founders are unrelated to one another. Descent through the pedigree of genes at marker and trait loci is tracked by meiosis indicators, also called inheritance indicators. At each locus, non-founders are assigned two 0/1 meiosis indicators, representing genes inherited from the individual's father and mother. The first indicator is coded as `0' if the non-founder inherited the gene carried by her father's mother and `1' if she inherited the gene carried by her father's father, i.e. her paternal grandmother and grandfather, respectively. The second indicator is coded as `0' if the non-founder inherited the gene carried by her mother's mother and `1' if she inherited the gene carried by her mother's father, i.e., her maternal grandmother and grandfather, respectively. We use the term gene to refer to a segment of DNA that is copied from parents to offspring, the concept captured by Mendel's term factor. The set of all inheritance indicators is notated as S = ( Sij ) where

Sij =	0 if DNA involved in meiosis i at locus j is the gamete's parent's maternal DNA
	1 if DNA involved in meiosis i at locus j is the gamete's parent's paternal DNA

S.j is referred to as the inheritance vector at locus j. It is the list of the inheritance indicators for all meioses in the sample at a single locus (locus j). The elements of S.j are independent of one another, as they represent the grandmaternal or grandpaternal inheritance for each gamete at the locus and meiosis events are independent of one another. Si. is the list of the inheritance indicators at all loci for a single meiosis (i.e., within a single gamete). The elements of Si. have first--order Markov dependence. That is, the probability of a `0' or `1' at locus j + 1 is a function of the the value at locus j and the recombination fraction between the loci. In other words, the value at locus j + 1 is conditionally independent of all other loci, given the value at locus j. If inheritance indicators are known, identity by descent (ibd) is also known. If probabilities can be assigned to patterns of inheritance indicators in a pedigree, the probability that any two gametes in the pedigree are ibd can be computed.