Motivation: The abundance of gene flow in the Tree of Life challenges the notion that evolution can be represented with a fully bifurcating process, as this process cannot capture important biological realities like hybridization, introgression, or horizontal gene transfer. Coalescent-based network methods are increasingly popular, yet not scalable for big data, because they need to perform a heuristic search in the space of networks as well as numerical optimization that can be NP-hard. Results: Here, we introduce a novel method to reconstruct phylogenetic networks based on algebraic invariants. While there is a long tradition of using algebraic invariants in phylogenetics, our work is the first to define phylogenetic invariants on concordance factors (frequencies of 4-taxon splits in the input gene trees) to identify level-1 phylogenetic networks under the multispecies coalescent model. Our novel inference methodology is optimization-free as it only requires the evaluation of polynomial equations, and as such, it bypasses the traversal of network space, yielding a computational speed at least 10 times faster than the fastest-to-date network methods. We illustrate the accuracy and speed of our new method on a variety of simulated scenarios as well as in the estimation of a phylogenetic network for the genus Canis. Availability and Implementation: We implement our novel theory on an open-source publicly available Julia package PhyloDiamond.jl available at https://github.com/solislemuslab/PhyloDiamond.jl with broad applicability within the evolutionary biology community. Contact: [email protected]

翻译：动机：生命树中基因流的普遍性挑战了进化可用完全二分过程表示的观点，因为该过程无法捕捉杂交、渐渗或水平基因转移等重要生物学现实。基于溯祖的网络方法日益流行，但难以扩展至大数据，因为它们需要在网络空间中进行启发式搜索以及可能为NP-hard的数值优化。结果：本文提出了一种基于代数不变量重建系统发育网络的新方法。尽管在系统发育学中使用代数不变量已有悠久传统，但我们的工作首次在一致性因子（输入基因树中4分类群分裂的频率）上定义系统发育不变量，以识别多物种溯祖模型下的1级系统发育网络。我们的新推理方法无需优化，仅需评估多项式方程，因此绕过了网络空间的遍历，计算速度比目前最快的网络方法至少快10倍。我们在多种模拟场景以及犬属系统发育网络估计中展示了新方法的准确性和速度。可用性与实现：我们将新理论实现为开源公开的Julia包PhyloDiamond.jl，可通过https://github.com/solislemuslab/PhyloDiamond.jl获取，在进化生物学领域具有广泛适用性。联系方式：[email protected]