标题： 系统发生网络 显示英文标题

标题： Phylogenetic Networks

摘要： 系统发生学是研究生物之间进化关系的学科。 该领域的主要挑战之一是，根据一组生物的生物数据推断出一个进化树，这是一个表示这些关系的图。 开发用于推断系统发生树的实用且高效的方法，已在多个领域引发了许多有趣的数学问题。 然而，由于杂交和基因流动，系统发生网络可能更适合作为某些生物群体进化历史的表示。 在本章中，我们介绍系统发生学的一些基本概念，并展示与系统发生网络相关的本科研究项目，这些项目涉及图论和抽象代数的领域。 在第一部分中，我们描述了与系统发生网络组合学相关的几个开放研究问题。 在第二部分中，我们描述了与将系统发生统计模型理解为代数簇相关的问题。 显示英文摘要

摘要： Phylogenetics is the study of the evolutionary relationships between organisms. One of the main challenges in the field is to take biological data for a group of organisms and to infer an evolutionary tree, a graph that represents these relationships. Developing practical and efficient methods for inferring phylogenetic trees has lead to a number of interesting mathematical questions across a variety of fields. However, due to hybridization and gene flow, a phylogenetic network may be a better representation of the evolutionary history of some groups of organisms. In this chapter, we introduce some of the basic concepts in phylogenetics, and present related undergraduate research projects on phylogenetic networks that touch on areas of graph theory and abstract algebra. In the first section, we describe several open research questions related to the combinatorics of phylogenetic networks. In the second, we describe problems related to understanding phylogenetic statistical models as algebraic varieties.