Probabilistic Techniques in Mathematical Phylogenetics

提出从概率的角度研究系统发育重建问题。推断一组生物的物种形成历史是进化生物学中的一个基本问题。这段历史是由一个历史性的，即，一种有根的树，其叶子对应于当前物种，分支表明物种形成事件。在这样一个随机演化上的分子序列的随机演化是树上的马尔可夫模型的一个实例。在这个项目中，PI将进一步发展吉布斯测度理论与系统发育重建问题之间的联系。一个特别强调的是，将给予插入和缺失的模型，提供一个多序列比对问题的概率分析的目标。与信息论问题的联系也将被考虑。组装生命之树是生物学中的一个基本问题，它为进化，适应和物种形成的研究提供了见解。许多关于过去进化事件的信息可以从现有物种收集的DNA序列数据分析中推断出来。分子序列进化的一个显著特征是随机性所起的重要作用。近年来，概率论，随机性的数学研究，提供了关键的新的见解，在评估统计方法的力量，以重建大规模遗传学的进化过程。本项目的主题是进一步研究这些联系。特别是，将考虑更现实的进化模型。将开发和实施新的系统发育分析技术。

It is proposed to investigate the phylogenetic reconstruction problem from a probabilistic perspective. Inferring the speciation history of a group of organisms is a fundamental problem in evolutionary biology. This history is represented by a phylogeny, i.e., a rooted tree where the leaves correspond to current species and branchings indicate speciation events. The stochastic evolution of molecular sequences on such a phylogeny is an instance of a Markov model on a tree. In this project, the PI will further develop connections between the theory of Gibbs measures on trees and the phylogenetic reconstruction problem. A particular emphasis will be given to models of insertions and deletions with the objective of providing a probabilistic analysis of the multiple sequence alignment problem. Connections to information theory problems will also be considered.Assembling the Tree of Life is a fundamental problem in biology which provides insights in the study of evolution, adaptation, and speciation. Much information about past evolutionary events can be inferred from the analysis of DNA sequence data collected from existing species. A notable feature of the evolution of molecular sequences is the significant role played by randomness. In recent years, probability theory, the mathematical study of randomness, has provided key new insights in assessing the power of statistical methods to reconstruct evolutionary processes in large-scale phylogenetics. The main theme of this project is to further investigate these connections. In particular, more realistic models of evolution will be considered. New phylogenetic analysis techniques will be developed and implemented.