New and efficient approaches to Markov chain Monte Carlo sampling of gene genealogies conditional on observed genetic data

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This research program will use the DNA of individuals sampled from natural populations to gain insight into how their DNA sequences are related, genetically. The pairs of DNA variants that individuals carry at certain DNA locations, or loci, are the data. These data, referred to as genotypes, can help narrow down the possible relationships among sequences. For example, two individuals with identical genotypes at a large number of DNA loci are more likely to be related than two with different genotypes. Just as we trace surnames in genealogy, we trace relationships for the DNA variants at a particular DNA locus in terms of descent from the same ancestral copy. At any given locus, the relationships among the sampled variants can be summarized by a binary ancestral tree. From mathematical population genetics, we have a stochastic or random model for this tree called the coalescent, and a model for the suite of trees at the set of genotyped loci called the ancestral recombination graph. These stochastic models provide us with expectations about what sorts of relationships are reasonable, without any genotype data. However, once we collect the genotype data, these prior expectations need to be modified because the data give clues that some DNA variants are more related than others. These modifications in light of the genotype data give the "posterior distribution" of the ancestral trees. The way to think about this distribution is that there is no single, known ancestral tree relating the variants at a given locus, but rather an extremely large number of possible trees that have different probability weightings. The genotype data help narrow down the possibilities a great deal but, even so, the number of trees is still unmanageably large. This research proposes new statistical methods to explore the vast number of relationship possibilities efficiently, and to assign these possibilities accurate probability weights. The methods will enable more reliable statistical inference pertaining to ancestral relationships to be extracted from DNA data. Reliable inference from DNA data is important because the concept of ancestral relationships underlies many key research problems in genetics and allied fields such as virology, ecology, zoology and human genetics.