Phylogenetic trees provide a fundamental representation of evolutionary relationships, yet the combinatorial explosion of possible tree topologies renders inference computationally challenging. Classical approaches to characterizing tree space, such as the Billera-Holmes-Vogtmann (BHV) space, offer elegant geometric structure but suffer from statistical and computational limitations. An alternative perspective arises from tropical geometry, the tropical Grassmannian tropGr(2,n), introduced by Speyer and Sturmfels, which coincides with phylogenetic tree space. In this paper, we review the structure of the tropical Grassmannian and present algorithmic methods for its computational study, including procedures for sampling from the tropical Grassmannian. Our aim is to make these concepts accessible to evolutionary biologists and computational scientists, and to motivate new research directions at the interface of algebraic geometry and phylogenetic inference.

翻译：系统发育树为进化关系提供了基础表示，然而可能树拓扑的组合爆炸使得推断在计算上具有挑战性。描述树空间的经典方法，如Billera-Holmes-Vogtmann（BHV）空间，提供了优雅的几何结构，但存在统计和计算上的局限性。热带几何学提供了一个替代视角，由Speyer和Sturmfels引入的热带格拉斯曼流形tropGr(2,n)与系统发育树空间相吻合。本文回顾了热带格拉斯曼流形的结构，并提出了其计算研究的算法方法，包括从热带格拉斯曼流形采样的程序。我们的目标是使这些概念对进化生物学家和计算科学家易于理解，并激发代数几何与系统发育推断交叉领域的新研究方向。