Phylogenetic networks provide a mathematical model to represent the evolution of a set of species where, apart from speciation, reticulate evolutionary events have to be taken into account. Among these events, lateral gene transfers need special consideration due to the asymmetry in the roles of the species involved in such an event. To take into account this asymmetry, LGT networks were introduced. Contrarily to the case of phylogenetic trees, the combinatorial structure of phylogenetic networks is much less known and difficult to describe. One of the approaches in the literature is to classify them according to their level and find generators of the given level that can be used to recursively generate all networks. In this paper, we adapt the concept of generators to the case of LGT networks. We show how these generators, classified by their level, give rise to simple LGT networks of the specified level, and how any LGT network can be obtained from these simple networks, that act as building blocks of the generic structure. The stochastic models of evolution of phylogenetic networks are also much less studied than those for phylogenetic trees. In this setting, we introduce a novel two-parameter model that generates LGT networks. Finally, we present some computer simulations using this model in order to investigate the complexity of the generated networks, depending on the parameters of the model.

中文翻译：

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级别k LGT网络的生成。

系统发育网络提供了代表一组物种进化的数学模型，除物种形成外，还必须考虑网状进化事件。在这些事件中，由于涉及此类事件的物种的角色不对称，因此需要特别考虑横向基因转移。考虑到这种不对称性，引入了LGT网络。与系统发育树相反，系统发育网络的组合结构鲜为人知，难以描述。文献中的方法之一是根据它们的级别对它们进行分类，并找到可用于递归生成所有网络的给定级别的生成器。在本文中，我们将生成器的概念适应LGT网络的情况。我们展示这些发电机如何 按照其级别进行分类，可以生成指定级别的简单LGT网络，以及如何从这些简单网络中获取任何LGT网络，这些网络充当通用结构的构建块。与系统树的随机模型相比，系统树的网络演化的随机模型的研究也少得多。在这种情况下，我们介绍了一个生成LGT网络的新颖的两参数模型。最后，我们提出了一些使用此模型的计算机模拟，以便根据模型的参数调查生成的网络的复杂性。与系统进化树相比，系统进化网络的随机模型研究也少得多。在这种情况下，我们介绍了一个生成LGT网络的新颖的两参数模型。最后，我们提出了一些使用此模型的计算机模拟，以便根据模型的参数调查生成的网络的复杂性。与系统树的随机模型相比，系统树的网络演化的随机模型的研究也少得多。在这种情况下，我们介绍了一个生成LGT网络的新颖的两参数模型。最后，我们提出了一些使用此模型的计算机模拟，以便根据模型的参数调查生成的网络的复杂性。