Section: New Results

Efficient tree reconciliation enumerator plus cophylogeny reconstruction algorithm via an Approximate Bayesian Computation

Phylogenetic tree reconciliation is the approach of choice for investigating the co-evolution of sets of organisms such as hosts and parasites. It consists in a mapping between the parasite tree and the host tree using event-based maximum parsimony. Given a cost model for the events, many optimal reconciliations are however possible. Any further biological interpretation of them must therefore take this into account, making the capacity to enumerate all optimal solutions a crucial point. Only two algorithms currently exist that attempt such enumeration; in one case not all possible solutions are produced while in the other not all cost vectors are currently handled. Our objective in addressing this problem was two-fold. The first was to fill this gap, and the second was to test whether the number of solutions generally observed can be an issue in terms of interpretation.

We presented a polynomial-delay algorithm called Eucalypt for enumerating all optimal reconciliations [12] . We showed that in general many solutions exist. We gave an example where, for two pairs of host-parasite trees having each less than 41 leaves, the number of solutions is 5120, even when only time-feasible ones are kept. To facilitate their interpretation, those solutions were also classified in terms of how many of each event they contain. The number of different classes of solutions may thus be notably smaller than the number of solutions, yet they may remain high enough, in particular for the cases where losses have cost 0. In fact, depending on the cost vector, both numbers of solutions and of classes thereof may increase considerably (for the same instance, to respectively 4080384 and 275). To further deal with this problem, we introduced and analysed a restricted version where host-switches are allowed to happen only between species that are within some fixed distance along the host tree. This restriction allows us to reduce the number of time-feasible solutions while preserving the same optimal cost, as well as to find time-feasible solutions with a cost close to the optimal in the cases where no time-feasible solution is found.

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. This is what we did ourselves in Eucalypt . The main problem with this approach is that the cost of the events strongly influences the reconciliation obtained.

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 [8] . The benefits of this method are twofold: (1) it provides more confidence in the set of costs to be used in a reconciliation, and (2) it allows estimation of the frequency of the events in cases where the dataset consists of trees with a large number of taxa.

We evaluated our method on simulated and on biological datasets. We showed 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 showed 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.