The aim of this review is to present and analyze the probabilistic models of mathematical phylogenetics which have been intensively used in recent years in biology as the cornerstone of attempts to infer and reconstruct the ancestral relationships between species. We outline the development of theoretical phylogenetics, from the earliest studies based on morphological characters, through to the use of molecular data in a wide variety of forms. We bring the lens of mathematical physics to bear on the formulation of theoretical models, focussing on the applicability of many methods from the toolkit of that tradition -- techniques of groups and representations to guide model specification and to exploit the multilinear setting of the models in the presence of underlying symmetries; extensions to coalgebraic properties of the generators associated to rate matrices underlying the models, in relation to the graphical structures (trees and networks) which form the search space for inferring evolutionary trees. Aspects presented, include relating model classes to relevant matrix Lie algebras, as well as manipulations with group characters to enumerate various natural polynomial invariants, for identifying robust, low-parameter quantities for use in inference. Above all, we wish to emphasize the many features of multipartite entanglement which are shared between descriptions of quantum states on the physics side, and the multi-way tensor probability arrays arising in phylogenetics. In some instances, well-known objects such as the Cayley hyperdeterminant (the `tangle') can be directly imported into the formalism -- for models with binary character traits, and triplets of taxa. In other cases new objects appear, such as the remarkable quintic `squangle' invariants for quartet tree discrimination and DNA data, with their own unique interpretation in the phylogenetic modeling context.
TreeFlow: probabilistic modelling and automatic differentiation for phylogenetics
The University of Auckland（奥克兰大学）；University of Technology Sydney（悉尼科技大学）；Tulane University（杜兰大学）；Fred Hutchinson Cancer Research Center（弗雷德·哈钦森癌症研究中心）；University of California, Los Angeles（加州大学洛杉矶分校）；University of Washington（华盛顿大学）
Microclimatic variation in tropical canopies: A glimpse into the processes of community assembly in epiphytic bryophyte communities
Xishuangbanna Tropical Botanical Garden, Chinese Academy of Sciences（中国科学院西双版纳热带植物园）；University of Liège（列日大学）；University of Lausanne（洛桑大学）；Aba Academy of Ecological Protection and Development（阿坝生态保护与发展研究院）；Institute of Geochemistry, Chinese Academy of Sciences（中国科学院地球化学研究所）；Consejo Superior de Investigaciones Científicas (CSIC)（西班牙国家研究委员会）；University of La Laguna（拉各拉大学）；INRAE AgroParisTech, Université Paris-Saclay（法国国家农业食品环境研究院巴黎理工学院，萨克雷大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）；Kunming Institute of Botany, Chinese Academy of Sciences（中国科学院昆明植物研究所）；East China Normal University（华东师范大学）；Guangxi Institute of Botany, Guangxi Zhuang Autonomous Region and Chinese Academy of Sciences（广西植物研究所）；Hainan University（海南大学）；Chinese Academy of Sciences（中国科学院）
A Class of Unrooted Phylogenetic Networks Inspired by the Properties of Rooted Tree-Child Networks
Delft Institute of Applied Mathematics, Delft University of Technology（代尔夫特理工大学应用数学研究所）；Department of Computer Science, Middlesex University（中伦敦大学计算机科学系）；School of Computer Science, University of Auckland（奥克兰大学计算机科学学院）；Faculty of Computer Science, Dalhousie University（达尔豪斯大学计算机科学学院）
Tree Thinking in the Genomic Era: Unifying Models Across Cells, Populations, and Species
Stanford University（斯坦福大学）；University of Oxford（牛津大学）；University of California, Berkeley（加州大学伯克利分校）；Peking University（北京大学）；Guangzhou Laboratory（广州实验室）；Guangzhou Medical University（广州医科大学）
