When two trees go to war

Rooted phylogenetic 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. In general, the model chosen influences the minimum number of reticulation events required. However, when one obtains the input data from two binary 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 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

Phylogenetic Networks Do not Need to Be Complex: Using Fewer Reticulations to Represent Conflicting Clusters

Phylogenetic trees are widely used to display estimates of how groups of species 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 data sets (e.g. for different genes), then their clusters are often contradicting. Consequently, the set of all clusters of such a data set 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 in the freely available Dendroscope software

Reconstructing phylogenetic level-1 networks from nondense binet and trinet sets

Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxon set X, and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an O(3^{|X|} poly(|X|)) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted 1 phylogenetic networks

Constructing a Smallest Refining Galled Phylogenetic Network

Lecture Notes in Bioinformatics (Subseries of Lecture Notes in Computer Science)3500265-28

The radical integration of science, religion, and poetry in the writings of Loren Eiseley and Richard Wilbur

In a postmodern world turning away from the rigid categories of the past and "the univocal literalism" (Tarnas) of the modern mind, Loren Eiseley and Richard Wilbur bridge the schism between religion and science. Their essays and poems reinvigorate the romantic reconciliation between the mind and nature, subject and object, because, like Goethe, Wilbur and Eiseley see the human mind as a product of nature and the agent of nature's self revelation