Descent Graph Methods

Abstract

Mapping disease and marker loci from pedigree phenotypes is one of the most computationally onerous tasks in modern biology. Even tightly optimized software can be quickly overwhelmed by the synergistic obstructions of missing data, multiple marker loci, multiple alleles per marker locus, and inbreeding. This unhappy situation has prompted mathematical and statistical geneticists to formulate alternatives to the Elston-Stewart algorithm. The most productive alternatives use elementary graph theory. The Lander-Green-Kruglyak algorithm alluded to in Chapter 7 exploits gene flow graphs and works well on small pedigrees. For large pedigrees, it is helpful to combine the graph theory perspective with stochastic methods of numerical integration [12, 23, 24, 32, 39, 40, 42].KeywordsMarkov ChainTransition RuleAcceptance ProbabilityLocation ScoreEpisodic AtaxiaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.