The Cophylogeny Reconstruction Problem is NP-Complete

The cophylogeny reconstruction problem arises in the study of host-parasite relationships. Specif- ically, we are given a host tree H, a parasite tree P, and a function \u27 mapping the leaves (extant taxa) of P to the leaves of H. Four biologically plausible operations are considered: cospeciation, duplication, host switching, and loss (Figure 1). A host switch is permitted in conjunction with a duplication event but not with a cospeciation event [1]

On the Computational Complexity of the Reticulate Cophylogeny Reconstruction Problem

The cophylogeny reconstruction problem is that of finding minimal cost explanations of differences between evolutionary histories of ecologically linked groups of biological organisms. We present a proof that shows that the general problem of reconciling evolutionary histories is NP-complete and provide a sharp boundary where this intractability begins. We also show that a related problem, that of finding Pareto optimal solutions, is NP-hard. As a byproduct of our results, we give a framework by which meta-heuristics can be applied to find good solutions to this problem

Jane: A New Tool for the Cophylogeny Reconstruction Problem

Background This paper describes the theory and implementation of a new software tool, called Jane, for the study of historical associations. This problem arises in parasitology (associations of hosts and parasites), molecular systematics (associations of orderings and genes), and biogeography (associations of regions and orderings). The underlying problem is that of reconciling pairs of trees subject to biologically plausible events and costs associated with these events. Existing software tools for this problem have strengths and limitations, and the new Jane tool described here provides functionality that complements existing tools. Results The Jane software tool uses a polynomial time dynamic programming algorithm in conjunction with a genetic algorithm to find very good, and often optimal, solutions even for relatively large pairs of trees. The tool allows the user to provide rich timing information on both the host and parasite trees. In addition the user can limit host switch distance and specify multiple host switch costs by specifying regions in the host tree and costs for host switches between pairs of regions. Jane also provides a graphical user interface that allows the user to interactively experiment with modifications to the solutions found by the program. Conclusions Jane is shown to be a useful tool for cophylogenetic reconstruction. Its functionality complements existing tools and it is therefore likely to be of use to researchers in the areas of parasitology, molecular systematics, and biogeography

Jane: a new tool for the cophylogeny reconstruction problem

<p>Abstract</p> <p>Background</p> <p>This paper describes the theory and implementation of a new software tool, called <it>Jane</it>, for the study of historical associations. This problem arises in parasitology (associations of hosts and parasites), molecular systematics (associations of orderings and genes), and biogeography (associations of regions and orderings). The underlying problem is that of reconciling pairs of trees subject to biologically plausible events and costs associated with these events. Existing software tools for this problem have strengths and limitations, and the new <it>Jane </it>tool described here provides functionality that complements existing tools.</p> <p>Results</p> <p>The <it>Jane </it>software tool uses a polynomial time dynamic programming algorithm in conjunction with a genetic algorithm to find very good, and often optimal, solutions even for relatively large pairs of trees. The tool allows the user to provide rich timing information on both the host and parasite trees. In addition the user can limit host switch distance and specify multiple host switch costs by specifying regions in the host tree and costs for host switches between pairs of regions. <it>Jane </it>also provides a graphical user interface that allows the user to interactively experiment with modifications to the solutions found by the program.</p> <p>Conclusions</p> <p><it>Jane </it>is shown to be a useful tool for cophylogenetic reconstruction. Its functionality complements existing tools and it is therefore likely to be of use to researchers in the areas of parasitology, molecular systematics, and biogeography.</p

Cophylogeny reconstruction via an approximate bayesian computation

Despite an increasingly vast literature on cophylogenetic reconstructions for studying host-parasite associations, understanding the common evolutionary history of such systems remains a problem that is far from being solved. Most algorithms for host-parasite reconciliation use an event-based model, where the events include in general (a subset of) cospeciation, duplication, loss, and host switch. All known parsimonious event-based methods then assign a cost to each type of event in order to find a reconstruction of minimum cost. The main problem with this approach is that the cost of the events strongly influences the reconciliation obtained. Some earlier approaches attempt to avoid this problem by finding a Pareto set of solutions and hence by considering event costs under some minimization constraints. To deal with this problem, we developed an algorithm, called Coala, for estimating the frequency of the events based on an approximate Bayesian computation approach. The benefits of this method are 2-fold: (i) it provides more confidence in the set of costs to be used in a reconciliation, and (ii) it allows estimation of the frequency of the events in cases where the data set consists of trees with a large number of taxa. We evaluate our method on simulated and on biological data sets. We show that in both cases, for the same pair of host and parasite trees, different sets of frequencies for the events lead to equally probable solutions. Moreover, often these solutions differ greatly in terms of the number of inferred events. It appears crucial to take this into account before attempting any further biological interpretation of such reconciliations. More generally, we also show that the set of frequencies can vary widely depending on the input host and parasite trees. Indiscriminately applying a standard vector of costs may thus not be a good strategy

Cophylogenetic analysis of dated trees

Parasites and the associations they form with their hosts is an important area of research due to the associated health risks which parasites pose to the human population. The associations parasites form with their hosts are responsible for a number of the worst emerging diseases impacting global health today, including Ebola, HIV, and malaria. Macro-scale coevolutionary research aims to analyse these associations to provide further insights into these deadly diseases. This approach, first considered by Fahrenholz in 1913, has been applied to hundreds of coevolutionary systems and remains the most robust means to infer the underlying relationships which form between coevolving species. While reconciling the coevolutionary relationships between a pair of evolutionary systems is NP-Hard, it has been shown that if dating information exists there is a polynomial solution. These solutions however are computationally expensive, and are quickly becoming infeasible due to the rapid growth of phylogenetic data. If the rate of growth continues in line with the last three decades, the current means for analysing dated systems will become computationally infeasible. Within this thesis a collection of algorithms are introduced which aim to address this problem. This includes the introduction of the most efficient solution for analysing dated coevolutionary systems optimally, along with two linear time heuristics which may be applied where traditional algorithms are no longer feasible, while still offering a high degree of accuracy 91%. Finally, this work integrates these incremental results into a single model which is able to handle widespread parasitism, the case where parasites infect multiple hosts. This proposed model reconciles two competing theories of widespread parasitism, while also providing an accuracy improvement of 21%, one of the largest single improvements provided in this field to date. As such, the set of algorithms introduced within this thesis offers another step toward a unified coevolutionary analysis framework, consistent with Fahrenholz original coevolutionary analysis model

Unifying Parsimonious Tree Reconciliation

Evolution is a process that is influenced by various environmental factors, e.g. the interactions between different species, genes, and biogeographical properties. Hence, it is interesting to study the combined evolutionary history of multiple species, their genes, and the environment they live in. A common approach to address this research problem is to describe each individual evolution as a phylogenetic tree and construct a tree reconciliation which is parsimonious with respect to a given event model. Unfortunately, most of the previous approaches are designed only either for host-parasite systems, for gene tree/species tree reconciliation, or biogeography. Hence, a method is desirable, which addresses the general problem of mapping phylogenetic trees and covering all varieties of coevolving systems, including e.g., predator-prey and symbiotic relationships. To overcome this gap, we introduce a generalized cophylogenetic event model considering the combinatorial complete set of local coevolutionary events. We give a dynamic programming based heuristic for solving the maximum parsimony reconciliation problem in time O(n^2), for two phylogenies each with at most n leaves. Furthermore, we present an exact branch-and-bound algorithm which uses the results from the dynamic programming heuristic for discarding partial reconciliations. The approach has been implemented as a Java application which is freely available from http://pacosy.informatik.uni-leipzig.de/coresym.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Phylogenetic framework for coevolutionary studies: A compass for exploring jungles of tangled trees

Phylogenetics is used to detect past evolutionary events, from how species originated to how their ecological interactions with other species arose, which can mirror cophylogenetic patterns. Cophylogenetic reconstructions uncover past ecological relationships between taxa through inferred coevolutionary events on trees, for example, codivergence, duplication, host-switching, and loss. These events can be detected by cophylogenetic analyses based on nodes and the length and branching pattern of the phylogenetic trees of symbiotic associations, for example, host-parasite. In the past 2 decades, algorithms have been developed for cophylogetenic analyses and implemented in different software, for example, statistical congruence index and event-based methods. Based on the combination of these approaches, it is possible to integrate temporal information into cophylogenetical inference, such as estimates of lineage divergence times between 2 taxa, for example, hosts and parasites. Additionally, the advances in phylogenetic biogeography applying methods based on parametric process models and combined Bayesian approaches, can be useful for interpreting coevolutionary histories in a scenario of biogeographical area connectivity through time. This article briefly reviews the basics of parasitology and provides an overview of software packages in cophylogenetic methods. Thus, the objective here is to present a phylogenetic framework for coevolutionary studies, with special emphasis on groups of parasitic organisms. Researchers wishing to undertake phylogeny-based coevolutionary studies can use this review as a "compass" when "walking" through jungles of tangled phylogenetic trees.Facultad de Ciencias Naturales y Muse