Generation of Level-k LGT Networks

Abstract

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.

Comparing the topology of phylogenetic network generators

“…For our comparison, we select the LGT network generator [43] and the ZODS network generator [53] as representations of network generators based on the Yule model (i.e., beta-splitting model with β = 0). We compare these network generators to a new network generator which is an extension of Heath's tree generator [24].…”

“…The LGT network generator is a network generator designed to model the lateral gene transfer (LGT) events. The generator is introduced in [43], and, from its description, the speciation events are designed as in the Yule model, that is, a leaf node at the current state is chosen uniformly at random for branching. The LGT network generator uses n-type reticulations and has two parameters governing the introduction of reticulation events: a parameter α ∈ [0, 1] controls the probability of the next event being a reticulation event instead of a speciation event, and a parameter γ ≥ 0 regulates the probability of a reticulation event being within an existing blob, where smaller γ corresponds to higher probability of a local reticulation event.…”

“…There are a few approaches that existing network generators usually take to constructing random networks. One approach is to alter a tree generator and add hybrid edges, for example, network generators [29,43] that are based on the Yule-Harding model [23] or on a continuoustime Markov model of speciation to a birth-hybridization Markov model [53,42]. The hybrid edges can either be added during the process of building a tree or after a tree is generated.…”

“…The hybrid edges can either be added during the process of building a tree or after a tree is generated. For these methods, there is also an option to add the hybrid edges in a way that favours shortdistance (local) hybrid edges [42,43].…”

Orchard Networks are Trees with Additional Horizontal Arcs

“…Hence, they are closely related to the class of LGT networks (Pons et al. 2019 ), because the horizontal arcs can be used to model LGT events. However, note that, in contrast to LGT networks, orchard networks do not (necessarily) specify which arcs are horizontal.…”