CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under aThe copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/194050 doi: bioRxiv preprint first posted online Sep. 28, 2017; 40 The evolutionary history of species is known to shape the present-day distribution
51In contrast, the first assumption has not been questioned until now (Jhwueng and 52 O'Meara 2017). However, phylogenetic trees are not always adapted to capture 53 relationships between species, and phylogenetic networks are sometimes needed.
54Phylogenetic networks differ from trees by added reticulation points, where two distinct known to be common in some groups of organisms (Mallet 2005(Mallet , 2007 computational burden, we believe that the use of these networks will increase in the future.
64The goal of this work is to propose an adaptation of standard PCMs to a group of species 65 with reticulate evolution, related by a network instead of a tree.
66We describe an extension of the BM model of trait evolution to a network. The 67 main modeling choice is about the fate of hybrid species. How should these species inherit 68 their trait from their two parents? In this work, we first choose a weighted-average merging 69 rule: the trait of a hybrid is a mixture of its two parents', weighted by their relative genetic 70 contributions. This rule can be seen as a reasonable null model. But in some cases, the 71 trait of a hybrid is observed to be outside of the range of its two parents. This phenomenon
84In the following, we first describe this BM model of trait evolution and show how it 85 fits into the standard PCM framework. We then show how to add shifts in the trait values
86. CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/194050 doi: bioRxiv preprint first posted online Sep. 28, 2017; to model transgressive evolution. We propose a statistical test for transgressive evolution.
87These methods are validated with a simulation study, and with the theoretical study of the and weighted phylogenetic network that describes the relationships between a set of 99 observed species (Huson et al. 2010). In such a network, reticulations, or hybrids, are nodes 100 that have two parent nodes. They receive a given proportion of their genetic material from 101 each parent. This proportion is controlled by a weight γ e that represents the inheritance 102 probability associated with each branch e of the network. A branch that is tree-like, i.e.
103that ends at a non-hybrid node, has a weight γ e = 1. We further assume that the length e 104 of a branch e represents evolutionary time. In the example in Figure 1a, the two hybrid At the root node ρ, we assume that X ρ = µ is fixed.
122.
CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under aThe copyright holder for this preprint (which was not . http://dx....