Reconstruction of certain phylogenetic networks from the genomes at their leaves

Defining phylogenetic networks using ancestral profiles

Rooted phylogenetic networks provide a more complete representation of the ancestral relationship between species than phylogenetic trees when reticulate evolutionary processes are at play. One way to reconstruct a phylogenetic network is to consider its 'ancestral profile' (the number of paths from each ancestral vertex to each leaf). In general, this information does not uniquely determine the underlying phylogenetic network. A recent paper considered a new class of phylogenetic networks called 'orchard networks' where this uniqueness was claimed to hold. Here we show that an additional restriction on the network, that of being 'stack-free', is required in order for the original uniqueness claim to hold. On the other hand, if the additional stack-free restriction is lifted, we establish an alternative result; namely, there is uniqueness within the class of orchard networks up to the resolution of vertices of high in-degree.

NCHB: A method for constructing rooted phylogenetic networks from rooted triplets based on height function and binarization

Phylogenetics is a field that studies and models the evolutionary history of currently living species. The rooted phylogenetic network is an important approach that models non-tree-like events between currently living species. Rooted triplets are one type of inputs in constructing rooted phylogenetic networks. Constructing an optimal rooted phylogenetic network that contains all given rooted triplets is a NP-hard problem. To overcome this challenge efficiently, a novel heuristic method called NCHB is introduced in this paper. NCHB produces an optimal rooted phylogenetic network that covers all given rooted triplets. The NCHB optimality criterions in building a rooted phylogenetic network are minimizing the number of reticulation nodes, and minimizing the level of the final network. In NCHB, the two concepts: the height function and the binarization of a network are considered innovatively. In order to study the performance of NCHB, our proposed method is compared with the three state of the art algorithms that are LEV1ATHAN, SIMPLISTIC and TripNet in two scenarios. In the first scenario, triplet sets are generated under biological presumptions and our proposed method is compared with SIMPLISTIC and TripNet. The results show that NCHB outperforms TripNet and SIMPLISTIC according to the optimality criterions. In the second scenario, we designed a software for generating level-k networks. Then all triplets consistent with each network are obtained and are used as input for NCHB, LEV1THAN, SIMPLISTIC, and TripNet. LEV1ATHEN is just applicable for level-1 networks while the other algorithms can be performed to obtain higher level networks. The results show that the NCHB and LEV1ATHAN outputs are almost the same when we are restricted to level-1 networks. Also the results show that NCHB outperforms TripNet and SIMPLISTIC. Moreover NCHB outputs are very close to the generated networks (that are optimal) with respect to the criterions.

Regular networks can be uniquely constructed from their trees

A rooted acyclic digraph N with labeled leaves displays a tree T when there exists a way to select a unique parent of each hybrid vertex resulting in the tree T. Let Tr(N) denote the set of all trees displayed by the network N. In general, there may be many other networks M, such that Tr(M) = Tr(N). A network is regular if it is isomorphic with its cover digraph. If N is regular and D is a collection of trees displayed by N, this paper studies some procedures to try to reconstruct N given D. If the input is D = Tr(N), one procedure is described, which will reconstruct N. Hence, if N and M are regular networks and Tr(N) = Tr(M), it follows that N = M, proving that a regular network is uniquely determined by its displayed trees. If D is a (usually very much smaller) collection of displayed trees that satisfies certain hypotheses, modifications of the procedure will still reconstruct N given D.

Phylogeny of the rock wallabies, Petrogale (Marsupialia: Macropodidae). Part II: Detection of hybridisation among macropodines

Phylogenetic relationships among rock-wallabies, Petrogale (Marsupialia: Macropodidae), have proven difficult to resolve. Given the documented interspecific hybridisation in the wild and the ease with which hybrids can be bred in captivity, introgression and hybrid speciation are likely explanations for these difficulties. In this paper, an attempt is made at using a phylogenetic approach to identify Petrogale hybrids of known origin. The Hybrid Detection Criterion (HDC) test is applied to DNA–DNA hybridisation data for 15 full species, two natural yard-bred hybrids, and two artificial hybrids from the same pairs of parental species. While the yard-bred hybrids elude detection with this technique, the artificial hybrids, consisting of equimolar mixture of parental extracts, are easily identified. Moreover, splitsgraphs constructed from five pairs of natural and artificial hybrids, including those evaluated with HDC, and their parents show that, in all cases but one, these two kinds of hybrids do not group together. Because the HDC assumes an intermediate phylogenetic position of the hybrid between its postulated parents, it is likely that unequal crossing-over, or another recombination event, affects the results of the test. These conclusions cast some doubt on the possibility of accurately detecting Petrogale hybrids with a phylogenetic approach.

Metrics for phylogenetic networks I: generalizations of the Robinson-Foulds metric

The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the first in a series of papers devoted to the analysis and comparison of metrics for tree-child time consistent phylogenetic networks on the same set of taxa. In this paper, we study three metrics that have already been introduced in the literature: the Robinson-Foulds distance, the tripartitions distance and the mu-distance. They generalize to networks the classical Robinson-Foulds or partition distance for phylogenetic trees. We analyze the behavior of these metrics by studying their least and largest values and when they achieve them. As a by-product of this study, we obtain tight bounds on the size of a tree-child time consistent phylogenetic network.