Steven Kelk

Ancient Dispersal of the Human Fungal Pathogen Cryptococcus gattii from the Amazon Rainforest

Over the past two decades, several fungal outbreaks have occurred, including the high-profile ‘Vancouver Island’ and ‘Pacific Northwest’ outbreaks, caused by Cryptococcus gattii, which has affected hundreds of otherwise healthy humans and animals. Over the same time period, C. gattii was the cause of several additional case clusters at localities outside of the tropical and subtropical climate zones where the species normally occurs. In every case, the causative agent belongs to a previously rare genotype of C. gattii called AFLP6/VGII, but the origin of the outbreak clades remains enigmatic. Here we used phylogenetic and recombination analyses, based on AFLP and multiple MLST datasets, and coalescence gene genealogy to demonstrate that these outbreaks have arisen from a highly-recombining C. gattii population in the native rainforest of Northern Brazil. Thus the modern virulent C. gattii AFLP6/VGII outbreak lineages derived from mating events in South America and then dispersed to temperate regions where they cause serious infections in humans and animals.

On the complexity of several haplotyping problems

We present several new results pertaining to haplotyping. The first set of results concerns the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype data. More specifically, we show that an interesting, restricted case of Minimum Error Correction (MEC) is NP-hard, question earlier claims about a related problem, and present a polynomial-time algorithm for the ungapped case of Longest Haplotype Reconstruction (LHR). Secondly, we present a polynomial time algorithm for the problem of resolving genotype data using as few haplotypes as possible (the Pure Parsimony Haplotyping Problem, PPH) where each genotype has at most two ambiguous positions, thus solving an open problem posed by Lancia et al in [15].

Constructing Level-2 Phylogenetic Networks from Triplets

Jansson and Sung showed that, given a dense set of input triplets T (representing hypotheses about the local evolutionary relationships of triplets of taxa), it is possible to determine in polynomial time whether there exists a level-1 network consistent with T, and if so, to construct such a network. Here, we extend this work by showing that this problem is even polynomial time solvable for the construction of level-2 networks. This shows that, assuming density, it is tractable to construct plausible evolutionary histories from input triplets even when such histories are heavily nontree-like. This further strengthens the case for the use of triplet-based methods in the construction of phylogenetic networks. We also implemented the algorithm and applied it to yeast data.

The Complexity of the Single Individual SNP Haplotyping Problem

We present several new results pertaining to haplotyping. These results concern the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype fragments. We consider the complexity of the problems Minimum Error Correction (MEC) and Longest Haplotype Reconstruction (LHR) for different restrictions on the input data. Specifically, we look at the gapless case, where every row of the input corresponds to a gapless haplotype-fragment, and the 1-gap case, where at most one gap per fragment is allowed. We prove that MEC is APX-hard in the 1-gap case and still NP-hard in the gapless case. In addition, we question earlier claims that MEC is NP-hard even when the input matrix is restricted to being completely binary. Concerning LHR, we show that this problem is NP-hard and APX-hard in the 1-gap case (and thus also in the general case), but is polynomial time solvable in the gapless case.

Phylogenetic networks do not need to be complex

Phylogenetic trees are widely used to display estimates of how groups of species are evolved. Each phylogenetic tree can be seen as a collection of clusters, subgroups of the species that evolved from a common ancestor. When phylogenetic trees are obtained for several datasets (e.g. for different genes), then their clusters are often contradicting. Consequently, the set of all clusters of such a dataset cannot be combined into a single phylogenetic tree. Phylogenetic networks are a generalization of phylogenetic trees that can be used to display more complex evolutionary histories, including reticulate events, such as hybridizations, recombinations and horizontal gene transfers. Here, we present the new Cass algorithm that can combine any set of clusters into a phylogenetic network. We show that the networks constructed by Cass are usually simpler than networks constructed by other available methods. Moreover, we show that Cass is guaranteed to produce a network with at most two reticulations per biconnected component, whenever such a network exists. We have implemented Cass and integrated it into the freely available Dendroscope software. Contact: l.j.j.v.iersel@gmail.com Supplementary information: Supplementary data are available at Bioinformatics online.

Constructing the Simplest Possible Phylogenetic Network from Triplets

A phylogenetic network is a directed acyclic graph that visualizes an evolutionary history containing so-called reticulations such as recombinations, hybridizations or lateral gene transfers. Here we consider the construction of a simplest possible phylogenetic network consistent with an input set T, where T contains at least one phylogenetic tree on three leaves (a triplet) for each combination of three taxa. To quantify the complexity of a network we consider both the total number of reticulations and the number of reticulations per biconnected component, called the level of the network. We give polynomial-time algorithms for constructing a level-1 respectively a level-2 network that contains a minimum number of reticulations and is consistent with T (if such a network exists). In addition, we show that if T is precisely equal to the set of triplets consistent with some network, then we can construct such a network with smallest possible level in time O(|T|k+1), if k is a fixed upper bound on the level of the network.

Worst-case optimal approximation algorithms for maximizing triplet consistency within phylogenetic networks

The study of phylogenetic networks is of great interest to computational evolutionary biology and numerous different types of such structures are known. This article addresses the following question concerning rooted versions of phylogenetic networks. What is the maximum value of p@?[0,1] such that for every input set T of rooted triplets, there exists some network N such that at least p|T| of the triplets are consistent with N? We call an algorithm that computes such a network (where p is maximum) worst-case optimal. Here we prove that the set containing all triplets (the full triplet set) in some sense defines p. Moreover, given a network N that obtains a fraction p^ for the full triplet set (for any p^), we show how to efficiently modify N to obtain a fraction >=p^ for any given triplet set T. We demonstrate the power of this insight by presenting a worst-case optimal result for level-1 phylogenetic networks improving considerably upon the 5/12 fraction obtained recently by Jansson, Nguyen and Sung. For level-2 phylogenetic networks we show that p>=0.61. We emphasize that, because we are taking |T| as a (trivial) upper bound on the size of an optimal solution for each specific input T, the results in this article do not exclude the existence of approximation algorithms that achieve approximation ratio better than p. Finally, we note that all the results in this article also apply to weighted triplet sets.

Uniqueness, intractability and exact algorithms : reflections on level-k phylogenetic networks

Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network determines how non-treelike the evolution can be, with level-0 networks being trees. We study the problem of constructing level-k phylogenetic networks from triplets, i.e. phylogenetic trees for three leaves (taxa). We give, for each k, a level-k network that is uniquely defined by its triplets. We demonstrate the applicability of this result by using it to prove that (1) for all k > or = 1 it is NP-hard to construct a level-k network consistent with all input triplets, and (2) for all k > or = 0 it is NP-hard to construct a level-k network consistent with a maximum number of input triplets, even when the input is dense. As a response to this intractability, we give an exact algorithm for constructing level-1 networks consistent with a maximum number of input triplets.

When two trees go to war

Rooted phylogenetic networks are used to model non-treelike evolutionary histories. Such networks are often constructed by combining trees, clusters, triplets or characters into a single network that in some well-defined sense simultaneously represents them all. We review these four models and investigate how they are related. Motivated by the parsimony principle, one often aims to construct a network that contains as few reticulations (non-treelike evolutionary events) as possible. In general, the model chosen influences the minimum number of reticulation events required. However, when one obtains the input data from two binary (i.e. fully resolved) trees, we show that the minimum number of reticulations is independent of the model. The number of reticulations necessary to represent the trees, triplets, clusters (in the softwired sense) and characters (with unrestricted multiple crossover recombination) are all equal. Furthermore, we show that these results also hold when not the number of reticulations but the level of the constructed network is minimised. We use these unification results to settle several computational complexity questions that have been open in the field for some time. We also give explicit examples to show that already for data obtained from three binary trees the models begin to diverge.

Constructing level-2 phylogenetic networks from triplets

Jansson and Sung showed that, given a dense set of input triplets T (representing hypotheses about the local evolutionary relationships of triplets of taxa), it is possible to determine in polynomial time whether there exists a level-1 network consistent with T, and if so to construct such a network [18]. Here we extend this work by showing that this problem is even polynomial-time solvable for the construction of level-2 networks. This shows that, assuming density, it is tractable to construct plausible evolutionary histories from input triplets even when such histories are heavily non-tree like. This further strengthens the case for the use of triplet-based methods in the construction of phylogenetic networks. We also implemented the algorithm and applied it to yeast data.