Phylogenetic networks represent the evolution of organisms that have undergone reticulate events, such as recombination, hybrid speciation or lateral gene transfer.

An important way to interpret a phylogenetic network is in terms of the trees it displays, which represent all the possible histories of the characters carried by the organisms in the network.

Given data that undenNent reticulate evolution, only the canonical form of the underlying phylogenetic network can be uniquely reconstructed.

We consider here an elementary question for the inference of phylogenetic networks: what networks can be reconstructed.

Indeed, whereas in theory it is always possible to reconstruct a phylogenetic tree, given sufficient data for this task, the same does not hold for phylogenetic networks: most notably, the relative order of consecutive reticulate events cannot be determined by standard network inference methods.

Here we propose limiting the space of reconstructible phylogenetic networks to what we call “canonical net-works”.

Explicit [1] or evolutionary [2, 3] phylogenetic networks are used to represent the evolution of organisms or genes that may inherit genetic material from more than one source.

They are called “explicit” to distinguish them from “implicit” [14], “abstract” [1] or “data-display” [3] phylogenetic networks, which are used to display collections of alternative evolutionary hypotheses supported by conflicting signals in the data.

This observation gives rise to the notion of trees displayed by a network, which are all the possible single-character histories implied by a phylogenetic network.

The viral population within each patient has descended from founder viruses and the population at the time of sampling may have some background correlation due to phylogenetic similarity.

confounded by such phylogenetic effects [40—44] , and a large literature has developed to account for such biases [44,45].

Firstly, strong selection pressure can create the environment for convergent evolution in which covariation dominates over phylogenetic effects [42,46,47]; indeed, drug resistance selection from reverse transcriptase (RT) inhibitors has been reported to generate a higher evolution rate in RT, thus f1Xing mutations, as compared to viral genes not under not under drug selection, such as envelope [48].

Phylogenetic correction to MI

We recognize that the Mutual Information (MI) does not account for correlations which arise from phylogenetic relationships among the population of interest.

In this specific study, where there is the population within each patient and the combined population of all patients, any phylogenetic correction to MI will only reduce phylogenetic influence in the combined population.