The Multilocus Multispecies Coalescent: A Flexible New Model of Gene Family Evolution

Abstract

Incomplete lineage sorting (ILS), the interaction between coalescence and speciation, can generate incongruence between gene trees and species trees, as can gene duplication (D), transfer (T) and loss (L). These processes are usually modelled independently, but in reality, ILS can affect gene copy number polymorphism, i.e., interfere with DTL. This has been previously recognised, but not treated in a satisfactory way, mainly because DTL events are naturally modelled forward-in-time, while ILS is naturally modelled backwards-in-time with the coalescent. Here we consider the joint action of ILS and DTL on the gene tree/species tree problem in all its complexity. In particular, we show that the interaction between ILS and duplications/transfers (without losses) can result in patterns usually interpreted as resulting from gene loss, and that the realised rate of D, T and L becomes non-homogeneous in time when ILS is taken into account. We introduce algorithmic solutions to these problems. Our new model, the multilocus multispecies coalescent (MLMSC), which also accounts for any level of linkage between loci, generalises the multispecies coalescent model and offers a versatile, powerful framework for proper simulation and inference of gene family evolution.

Species Tree Inference Methods Intended to Deal with Incomplete Lineage Sorting Are Robust to the Presence of Paralogs

“…It is important to highlight, as well, that great strides have been made in developing methods for phylogenetic network inference in the presence of ILS ( Elworth et al. 2019 ), but no probabilistic methods currently incorporate gene duplication and loss (see Li et al (2021) for a very interesting alternative approach). We believe methods along the lines described in the previous section could be promising for accurate and scalable phylogenomic inferences without sacrificing much of the data.…”

“…An obvious way to handle data sets where ILS and GDL could have simultaneously acted on gene families is to employ models of gene evolution that go beyond the MSC in order to incorporate GDL as well. Indeed, such models are beginning to emerge ( Rasmussen and Kellis 2012 ; Li et al 2021 ). However, the more complex the models of gene family evolution, the more computationally prohibitive statistical inference under these models becomes ( Du and Nakhleh 2018 ), rendering their applicability infeasible except for very small data sets in terms of the number of species and gene families.…”

Classes of Explicit Phylogenetic Networks and their Biological and Mathematical Significance

“…An exception to this, however, is NetRAX (Lutteropp et al, 2021), which infers networks using maximum likelihood under a single-locus model (i.e., a model that assumes that a single network underlies the entire data set). On the other hand, recent work has extended the available coalescent-based models to include not only the coalescent process, but also models of gene duplication and loss (see, e.g., Du et al (2019); Li et al (2020)). Network inference in model-based settings such as these is especially challenging, however, because even for phylogenetic trees the likelihood cannot generally be computed explicitly (Kubatko, 2019).…”

The bounded coalescent model: conditioning a genealogy on a minimum root date

“…Consequently, the bounded coalescent model is used in many multi-species coalescent models, to enforce the full coalescence of members of a same species before the speciation event (Mallo et al, 2016;Du et al, 2019;Hill et al, 2020;Li et al, 2021). The bounded coalescent model is also used in work on homologous recombination resulting in ancestral recombination graphs (Ferretti et al, 2013;Rasmussen et al, 2014).…”

“…In this context, the bound condition is used to deal with incomplete lineage sorting, which could cause a gene tree to be incongruent with the species tree (Maddison, 1997; Maddison and Knowles, 2006). Consequently, the bounded coalescent model is used in many multi-species coalescent models, to enforce the full coalescence of members of a same species before the speciation event (Mallo et al, 2016; Du et al, 2019; Hill et al, 2020; Li et al, 2021). The bounded coalescent model is also used in work on homologous recombination resulting in ancestral recombination graphs (Ferretti et al, 2013; Rasmussen et al, 2014).…”