论文标题
系统发育空间和曲线模量空间的比较定理
Comparison Theorems of Phylogenetic Spaces and the Moduli Spaces of Curves
论文作者
论文摘要
遗传学和生物学方面的快速发展导致系统发育方法成为癌症和病毒进化研究的重要方向。 Although our understanding of gene biology and biochemistry has increased and is increasing at a remarkable rate, the theoretical models of genetic evolution still use the phylogenetic tree model that was introduced by Darwin in 1859 and the generalization to phylogenetic networks introduced by Grant in 1971. Darwin's model uses phylogenetic trees to capture the evolutionary relationships of reproducing individuals [6];格兰特对系统发育网络的概括旨在解释水平基因转移的现象[14]。因此，重要的是要对这些模型进行准确的数学描述，并了解它们与其他数学领域的联系。在本文中，我们关注系统发育和网络的图理论方面及其与稳定曲线的联系。 We introduce the building blocks of evolutionary moduli spaces, the dual intersection complex of the moduli spaces of stable curves, and the categorical relationship between the phylogenetic spaces and stable curves in $\overline{\mathfrak{M}}_{0,n}(\mathbb{C})$ and $ \ OVERLINE {\ MATHFRAK {M}} _ {0，N}（\ Mathbb {r}）$。我们还表明，网络拓扑的空间将其映射到$ \ overline {\ mathfrak {m}}} _ {g，n}（\ mathbb {c}）$的边界。
Rapid developments in genetics and biology have led to phylogenetic methods becoming an important direction in the study of cancer and viral evolution. Although our understanding of gene biology and biochemistry has increased and is increasing at a remarkable rate, the theoretical models of genetic evolution still use the phylogenetic tree model that was introduced by Darwin in 1859 and the generalization to phylogenetic networks introduced by Grant in 1971. Darwin's model uses phylogenetic trees to capture the evolutionary relationships of reproducing individuals [6]; Grant's generalization to phylogenetic networks is meant to account for the phenomena of horizontal gene transfer [14]. Therefore, it is important to provide an accurate mathematical description of these models and to understand their connection with other fields of mathematics. In this article, we focus on the graph theoretical aspects of phylogenetic trees and networks and their connection to stable curves. We introduce the building blocks of evolutionary moduli spaces, the dual intersection complex of the moduli spaces of stable curves, and the categorical relationship between the phylogenetic spaces and stable curves in $\overline{\mathfrak{M}}_{0,n}(\mathbb{C})$ and $\overline{\mathfrak{M}}_{0,n}(\mathbb{R})$. We also show that the space of network topologies maps injectively into the boundary of $\overline{\mathfrak{M}}_{g,n}(\mathbb{C})$.
