The structure of genetic linkage data: from LIPED to 1M SNPs

There are three assumptions of independence or conditional independence that underlie linkage likelihood computations on sets of related individuals. The first is the independence of meioses, which gives rise to the conditional independence of haplotypes carried by offspring, given those of their parents. The second derives from the assumption of absence of genetic interference, which gives rise to the conditional independence of inheritance vectors, given the inheritance vector at an intermediate location. The third is the assumption of independence of allelic types, at the population level, both among haplotypes of unrelated individuals and also over the loci along a given haplotype. These three assumptions have been integral to likelihood computations since the first lod scores were computed, and remain key components in analysis of modern genetic data. In this paper we trace the role of these assumptions through the history of linkage likelihood computation, through to a new framework of genetic linkage analysis in the era of dense genomic marker data.