Algorithms for the quantitative Lock/Key model of cytoplasmic incompatibility

Cytoplasmic incompatibility (CI) relates to the manipulation by the parasite Wolbachia of its host reproduction. Despite its widespread occurrence, the molecular basis of CI remains unclear and theoretical models have been proposed to understand the phenomenon. We consider in this paper the quantitative Lock-Key model which currently represents a good hypothesis that is consistent with the data available. CI is in this case modelled as the problem of covering the edges of a bipartite graph with the minimum number of chain subgraphs. This problem is already known to be NP-hard, and we provide an exponential algorithm with a non trivial complexity. It is frequent that depending on the dataset, there may be many optimal solutions which can be biologically quite different among them. To rely on a single optimal solution may therefore be problematic. To this purpose, we address the problem of enumerating (listing) all minimal chain subgraph covers of a bipartite graph and show that it can be solved in quasi-polynomial time. Interestingly, in order to solve the above problems, we considered also the problem of enumerating all the maximal chain subgraphs of a bipartite graph and improved on the current results in the literature for the latter. Finally, to demonstrate the usefulness of our methods we show an application on a real dataset

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

Some Problems Related to the Space of Optimal Tree Reconciliations (Invited Talk)

Tree reconciliation is a general framework for investigating the evolution of strongly dependent systems as hosts and parasites or genes and species, based on their phylogenetic information. Indeed, informally speaking, it reconciles any differences between two phylogenetic trees by means of biological events. Tree reconciliation is usually computed according to the parsimony principle, that is, to each evolutionary event a cost is assigned and the goal is to find tree reconciliations of minimum total cost. Unfortunately, the number of optimal reconciliations is usually huge and many biological applications require to enumerate and to examine all of them, so it is necessary to handle them. In this paper we list some problems connected with the management of such a big space of tree reconciliations and, for each of them, discuss some known solutions

Comparing related phylogenetic trees

In phylogenetics, several classical distances exist to compare two phylogenetic trees. However, when the evolution in one tree has been influenced by the evolution in the other (e.g. two ecologically linked groups of organisms as hosts and their symbionts), other methods are more appropriate to compare the trees. Among the most used ones, there is phylogenetic tree reconciliation, i.e. mapping of one tree into the other according to certain rules, with a quantification of its quality; we refer to distances based on this concept as reconciliation distances. They bring useful information but are unfortunately NP-hard to be computed. It is then interesting to understand whether a polynomial phylogenetic tree distance is correlated to the reconciliation distances. In this communication we announce a systematic study to compare clas- sical and reconciliation distances and we show that there is not much correlation between them. We then introduce a new distance that is in- stead correlated with the reconciliation distances and can be computed in polynomial time, hence it represents an efficient alternative to them