An efficient exact algorithm for computing all pairwise distances between reconciliations in the duplication-transfer-loss model

Abstract

BackgroundMaximum parsimony reconciliation in the duplication-transfer-loss model is widely used in studying the evolutionary histories of genes and species and in studying coevolution of parasites and their hosts and pairs of symbionts. While efficient algorithms are known for finding maximum parsimony reconciliations, the number of reconciliations can grow exponentially in the size of the trees. An understanding of the space of maximum parsimony reconciliations is necessary to determine whether a single reconciliation can adequately represent the space or whether multiple representative reconciliations are needed.ResultsWe show that for any instance of the reconciliation problem, the distribution of pairwise distances can be computed exactly by an efficient polynomial-time algorithm with respect to several different distance metrics. We describe the algorithm, analyze its asymptotic worst-case running time, and demonstrate its utility and viability on a large biological dataset.ConclusionsThis result provides new insights into the structure of the space of maximum parsimony reconciliations. These insights are likely to be useful in the wide range of applications that employ reconciliation methods.

Tree Reconciliation Methods for Host-Symbiont Cophylogenetic Analyses

“…It is known that the number of MPRs can grow exponentially in the size of the two trees [ 15 ] and that these reconciliations can differ substantially [ 16 ]. In some datasets with at most 100 tips in each tree, the number of MPRs for a given set of event costs can exceed [ 17 ] which is comparable to the number of particles in the known universe!…”

“…Santichaivekin et al described an efficient algorithm for visualizing the diversity of MPRs [ 17 ]. For a given set of MPRs, the pairwise distance histogram is a histogram of the distances between all pairs of reconciliations in that set with respect to the symmetric set distance described above (where losses are included in the distance in addition to cospeciation, duplication, and host switch events).…”

Phylogenetic reconciliation

“…EMPRess [ 72 ] can group similar reconciliations through clustering [ 82 ], with all pairwise distance between reconciliations computable in polynomial time (independently of the number of most parsimonious reconciliations) [ 83 ]. With the same aim, Capybara [ 84 ] defines equivalence classes among reconciliations, efficiently computing representative for all classes, and outputs with linear delay a given number of reconciliations (first optimal ones, then sub optimal).…”

Efficiently Sparse Listing of Classes of Optimal Cophylogeny Reconciliations

“…However, as the optimal reconciliation space can be both large and heterogeneous [17], this does not guarantee that important information is not lost. Other methods try to understand the structure of the space of solutions by computing some global properties such as the frequency of the events across the space [16], the diameter of the space [17], the pairwise distance among the optimal reconciliations [18]. In a similar direction, other methods propose a single reconciliation (e.g.…”

“…a "median" reconciliation) to represent the whole space of optimal ones [19,11,14]. However, the results presented in [12,14,17,18] show that the space can be very diverse and making inferences from a single reconciliation might lead to conclusions that can be contradicted by other optimal reconciliations. The method in [19] has been generalized in [20] in order to find a set of k medoids, or k centers that represent the space.…”