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

这项研究计划将使用从自然种群中采样的个体的DNA来深入了解他们的DNA序列是如何在遗传上相关的。个体在特定DNA位置或基因座携带的DNA变异体对就是数据。这些数据被称为基因类型，可以帮助缩小序列之间可能的关系。例如，两个在大量DNA基因座上有相同基因的个体比两个基因不同的个体更有可能是相关的。就像我们在系谱中追踪姓氏一样，我们根据同一祖先副本的血统来追踪特定DNA基因座上的DNA变体的关系。在任何给定的位置，样本变异体之间的关系可以用二叉祖先树来概括。从数学种群遗传学中，我们有一个关于这种树的随机或随机模型，称为聚合体，以及一个关于在一组基因分型座位上的树的模型，称为祖先重组图。这些随机模型为我们提供了关于哪种关系是合理的预期，而没有任何基因数据。然而，一旦我们收集了基因数据，这些先前的预期就需要改变，因为这些数据给出了一些DNA变异比其他DNA变异更相关的线索。根据基因数据进行的这些修改给出了祖先树的“后验分布”。考虑这种分布的方式是，没有单一的已知祖先树将给定基因座上的变异联系在一起，而是有非常大量的可能树具有不同的概率权重。基因数据有助于极大地缩小可能性，但即便如此，树木的数量仍然难以管理。这项研究提出了新的统计方法，以有效地探索大量的关系可能性，并为这些可能性分配准确的概率权重。这些方法将使从DNA数据中提取与祖先关系有关的更可靠的统计推断成为可能。从DNA数据进行可靠的推断很重要，因为祖先关系的概念是遗传学及其相关领域的许多关键研究问题的基础，如病毒学、生态学、动物学和人类遗传学。

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.