Algebraic Invariants for Phylogenetic Network Inference

系统发育网络推理的代数不变量

基本信息

批准号：
EP/W007134/1
负责人：
Richard Leggett
金额：
$ 8.16万
依托单位：
Earlham Institute
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2022
资助国家：
英国
起止时间：
2022 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FW007134%2F1
关键词：
Algebraic Invariants Phylogenetic Network Inference

项目摘要

The key goal in phylogenetics is to be able to infer the evolutionary histories of species from DNA sequence data of their living relatives. This has applications in many fields, such as tracing the mutations of viral outbreaks, understanding speciation events to aid conservation, and even tracing the histories of ancient manuscripts that were copied by hand through generations.Most evolutionary histories can be described with a phylogenetic tree, where the "leaves" of the tree represent species that are alive today, and the vertices higher up the tree represent common ancestor species. However, for many biological problems, a tree cannot properly represent the evolutionary history of the species involved. Such problems are said to have seen "horizontal evolution". One example occurs in microbiomes, where different microbial species are able to share portions of their DNA in a process called horizontal gene transfer. This is one mechanism by which antibiotic resistance can spread between bacteria, and so being able to describe when such events have occurred has important implications for human health. To describe horizontal evolution, biologists use what's called a phylogenetic network. Here, one can use a tree structure as a backbone, onto which further edges are drawn to represent horizontal evolution events.The problem of inferring the evolutionary histories of species where horizontal evolution has occurred is particularly challenging, and is the focus of much of the research in phylogenetics today. One method of phylogenetic inference is to use algebraic invariants. These have seen significant development for inferring evolution along a tree, and in some cases have been shown to outperform other methods. For phylogenetic networks however, very little research on algebraic invariants has been done. This project will develop and test the method of using algebraic invariants for phylogenetic network inference.For a particular phylogenetic network, the process of evolution along it can be modelled using a type of probabilistic model called a Markov model. Under this model, one can calculate the probability of observing particular patterns of DNA at the leaves of the network, and these probabilities can be expressed as polynomials in the numerical parameters of the model. By allowing the numerical parameters to vary freely (i.e. treating them as variables) we can represent the network as the set of solutions to the equations describing the probabilities. Such a set of solutions forms an object that algebraists call an algebraic variety. Using this model gives us the advantage of being able to use the powerful machinery of algebraic geometry in determining whether observed DNA sequence data is a good fit for the network. In particular, we can describe the variety corresponding to a network by using expressions called algebraic invariants. To determine whether a particular network is a good fit for observed DNA sequence data, the idea is to calculate the frequencies of patterns in the data, and then apply the network's algebraic invariants to these frequencies. The resulting quantities will determine how closely the data matches the network.This project will examine how effective this method is to infer phylogenetic networks from DNA sequence data. To do this, we will utilize the most recent developments in the field to calculate the invariants for a small class of phylogenetic networks. Next, we will develop a computational tool that will infer the network that best describes the evolutionary history coming from a set of DNA sequence data, by using the invariants we have calculated. We will then test our tool on both simulated DNA sequence data and real DNA sequence data, and compare the results to state of the art methods.

系统发育学的关键目标是能够从其生物亲戚的DNA序列数据中推断物种的进化史。 This has applications in many fields, such as tracing the mutations of viral outbreaks, understanding speciation events to aid conservation, and even tracing the histories of ancient manuscripts that were copied by hand through generations.Most evolutionary histories can be described with a phylogenetic tree, where the "leaves" of the tree represent species that are alive today, and the vertices higher up the tree represent common ancestor species.但是，对于许多生物学问题，一棵树不能正确地代表所涉及的物种的进化史。据说这些问题已经看到了“水平进化”。一个例子发生在微生物中，其中不同的微生物物种能够在称为水平基因转移的过程中共享其DNA的一部分。这是一种机制，抗生素耐药性可以在细菌之间传播，因此能够描述何时发生此类事件对人类健康具有重要意义。为了描述水平进化，生物学家使用所谓的系统发育网络。在这里，人们可以将树结构用作骨干，在该骨干上绘制进一步的边缘来代表水平进化事件。推断出进行水平进化的物种进化历史的问题特别具有挑战性，并且是当今系统发育学研究中许多研究的重点。一种系统发育推断的一种方法是使用代数不变性。这些已经看到了沿树推断进化的重大发展，在某些情况下已显示出优于其他方法。但是，对于系统发育网络，对代数不变的研究很少。该项目将开发并测试使用代数不变性进行系统发育网络推理的方法。对于特定的系统发育网络，可以使用称为Markov模型的概率模型对其进行进化过程进行建模。在此模型下，可以计算观察网络叶片上DNA的特定模式的概率，并且这些概率可以在模型的数值参数中表示为多项式。通过允许数值参数自由变化（即将它们视为变量），我们可以将网络表示为描述概率的方程的解决方案集。这样的解决方案构成了代数主义者称为代数品种的对象。使用此模型使我们能够在确定观察到的DNA序列数据是否适合网络时能够使用强大的代数几何形状机械。特别是，我们可以使用称为代数不变的表达式来描述与网络相对应的变体。为了确定特定网络是否适合观察到的DNA序列数据，其想法是计算数据中模式的频率，然后将网络的代数不变性应用于这些频率。最终的数量将决定数据与网络匹配的距离。该项目将检查此方法从DNA序列数据中推断系统发育网络的有效性。为此，我们将利用该领域的最新发展来计算一小类系统发育网络的不变性。接下来，我们将开发一种计算工具，该工具将通过使用我们计算的不变性来推断最能描述来自一组DNA序列数据的进化历史的网络。然后，我们将在模拟的DNA序列数据和实际DNA序列数据上测试我们的工具，并将结果与最先进的方法进行比较。