Characterization of phylogenetic networks with NetTest

<p>Abstract</p> <p>Background</p> <p>Typical evolutionary events like recombination, hybridization or gene transfer make necessary the use of phylogenetic networks to properly depict the evolution of DNA and protein sequences. Although several theoretical classes have been proposed to characterize these networks, they make stringent assumptions that will likely not be met by the evolutionary process. We have recently shown that the complexity of simulated networks is a function of the population recombination rate, and that at moderate and large recombination rates the resulting networks cannot be categorized. However, we do not know whether these results extend to networks estimated from real data.</p> <p>Results</p> <p>We introduce a web server for the categorization of explicit phylogenetic networks, including the most relevant theoretical classes developed so far. Using this tool, we analyzed statistical parsimony phylogenetic networks estimated from ~5,000 DNA alignments, obtained from the NCBI PopSet and Polymorphix databases. The level of characterization was correlated to nucleotide diversity, and a high proportion of the networks derived from these data sets could be formally characterized.</p> <p>Conclusions</p> <p>We have developed a public web server, <it>NetTest </it>(freely available from the software section at <url>http://darwin.uvigo.es</url>), to formally characterize the complexity of phylogenetic networks. Using NetTest we found that most statistical parsimony networks estimated with the program TCS could be assigned to a known network class. The level of network characterization was correlated to nucleotide diversity and dependent upon the intra/interspecific levels, although no significant differences were detected among genes. More research on the properties of phylogenetic networks is clearly needed.</p

Spaces of phylogenetic networks from generalized nearest-neighbor interchange operations

Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are used to represent the evolution of species which have undergone reticulate evolution. In this paper we consider spaces of such networks defined by some novel local operations that we introduce for converting one phylogenetic network into another. These operations are modeled on the well-studied nearest-neighbor interchange (NNI) operations on phylogenetic trees, and lead to natural generalizations of the tree spaces that have been previously associated to such operations. We present several results on spaces of some relatively simple networks, called level-1 networks, including the size of the neighborhood of a fixed network, and bounds on the diameter of the metric defined by taking the smallest number of operations required to convert one network into another.We expect that our results will be useful in the development of methods for systematically searching for optimal phylogenetic networks using, for example, likelihood and Bayesian approaches

On the challenge of reconstructing level-1 phylogenetic networks from triplets and clusters

Phylogenetic networks have gained prominence over the years due to their ability to represent complex non-treelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet systems and cluster systems, the motivation being that any network $N$ induces a triplet system $\mathcal R(N)$ and a softwired cluster system $\mathcal S(N)$. Since in real-world studies it cannot be guaranteed that all triplets/softwired clusters induced by a network are available, it is of particular interest to understand whether subsets of $\mathcal R(N)$ or $\mathcal S(N)$ allow one to uniquely reconstruct the underlying network $N$. Here we show that even within the highly restricted yet biologically interesting space of level-1 phylogenetic networks it is not always possible to uniquely reconstruct a level-1 network $N$\kelk{,} even when all triplets in $\mathcal R(N)$ or all clusters in $\mathcal S(N)$ are available. On the positive side, we introduce a reasonably large subclass of level-1 networks the members of which are uniquely determined by their induced triplet/softwired cluster systems. Along the way, we also establish various enumerative results, both positive and negative, including results which show that certain special subclasses of level-1 networks $N$ can be uniquely reconstructed from proper subsets of $\mathcal R(N)$ and $\mathcal S(N)$. We anticipate these results to be of use in the design of algorithms for phylogenetic network inference

Uprooted Phylogenetic Networks

The need for structures capable of accommodating complex evolutionary signals such as those found in, for example, wheat has fueled research into phylogenetic networks. Such structures generalize the standard model of a phylogenetic tree by also allowing for cycles and have been introduced in rooted and unrooted form. In contrast to phylogenetic trees or their unrooted versions, rooted phylogenetic networks are notoriously difficult to understand. To help alleviate this, recent work on them has also centered on their “uprooted” versions. By focusing on such graphs and the combinatorial concept of a split system which underpins an unrooted phylogenetic network, we show that not only can a so-called (uprooted) 1-nested network N be obtained from the Buneman graph (sometimes also called a median network) associated with the split system  Σ(N)Σ(N)  induced on the set of leaves of N but also that that graph is, in a well-defined sense, optimal. Along the way, we establish the 1-nested analogue of the fundamental “splits equivalence theorem” for phylogenetic trees and characterize maximal circular split systems

Computing consensus networks for collections of 1-nested phylogenetic networks

An important and well-studied problem in phylogenetics is to compute a consensus tree so as to summarize the common features within a collection of rooted phylogenetic trees, all whose leaf-sets are bijectively labeled by the same set X of species. More recently, however, it has become of interest to find a consensus for a collection of more general, rooted directed acyclic graphs all of whose sink-sets are bijectively labeled by X, so called rooted phylogenetic networks. These networks are used to analyze the evolution of species that cross with one another, such as plants and viruses. In this paper, we introduce an algorithm for computing a consensus for a collection of so-called 1-nested phylogenetic networks. Our approach builds on a previous result by Rosell´o et al. that describes an encoding for any 1-nested phylogenetic network in terms of a collection of ordered pairs of subsets of X. More specifically, we characterize those collections of ordered pairs that arise as the encoding of some 1-nested phylogenetic network, and then use this characterization to compute a consensus network for a collection of t ≥ 1 1-nested networks in O(t|X|2 + |X|3) time. Applying our algorithm to a collection of phylogenetic trees yields the well-known majority rule consensus tree. Our approach leads to several new directions for future work, and we expect that it should provide a useful new tool to help understand complex evolutionary scenarios

Species network inference under the multispecies coalescent model

Dissertation (Ph.D.) University of Alaska Fairbanks, 2019Species network inference is a challenging problem in phylogenetics. In this work, we present two results on this. The first shows that many topological features of a level-1 network are identifable under the network multispecies coalescent model (NMSC). Specifcally, we show that one can identify from gene tree frequencies the unrooted semidirected species network, after suppressing all cycles of size less than 4. The second presents the theory behind a new, statistically consistent, practical method for the inference of level-1 networks under the NMSC. The input for this algorithm is a collection of unrooted topological gene trees, and the output is an unrooted semidirected species network.Chapter 1: Introduction -- Chapter 2: The network multispecies coalescent model -- 1. The coalescent model -- 2. The network multispecies coalescent model (NMSC) -- Chapter 3: Identifying species network features from gene tree quartets under the coalescent model -- 1. Introduction -- 2. Phylogenetic networks -- 3. Structure of level-1 networks -- 4. The network multispecies coalescent model and quartet concordance factors -- 5. Computing quartet concordance factors -- 6. The cycle property -- 7. The big cycle property -- 8. Identifying cycles in networks -- 9. Further results in 32-cycles -- 10. Discussion -- 11. Appendix -- Chapter 4: NANUQ: A method for inferring species networks from gene trees under the coalescent model -- 1. Introduction -- 2. Phylogenetic networks -- 3. The network multispecies coalescent model and quartet concordance factors -- 4. Network split systems and distances -- 5. Quartet distance for level-1 networks -- 6. Split networks from the network quartet distance -- 7. The NANUQ algorithm for inference of phylogenetic networks -- 8. Examples -- Chapter 5: Conclusions and future work - References