Natalia Rutecka

We present a novel problem, called MetaEC, which aims to infer gene-species assignments in a collection of gene trees with missing labels by minimizing the size of duplication episode clustering (EC). This problem is particularly relevant in metagenomics, where incomplete data often poses a challenge in the accurate reconstruction of gene histories. To solve MetaEC, we propose a polynomial time dynamic programming (DP) formulation that verifies the existence of a set of duplication episodes from a predefined set of episode candidates. In addition, we design a method to infer distributions of gene-species mappings. We then demonstrate how to use DP to design an algorithm that solves MetaEC. Although the algorithm is exponential in the worst case, we introduce a heuristic modification of the algorithm that provides a solution with the knowledge that it is exact. To evaluate our method, we perform two computational experiments on simulated and empirical data containing whole genome dup...

Gene trees inferred from alignments of molecular sequences are usually unrooted. Since the root of a gene tree is often the desired property, one of the most classical problems in computational biology is gene tree rooting, where the goal is to infer the most credible rooting edge in an unrooted gene tree. One way to solve it is to apply unrooted reconciliation, where the rooting edge is postulated based on a given split of a rooted species tree. Here, we address a novel variant of the rooting problem, where the gene tree root is inferred using a given phylogenetic network of the species present in the gene tree. One can apply unrooted reconciliation to obtain the best rooting, where the unrooted gene tree is jointly reconciled with a set of splits inferred from the given network. Natural candidates are splits induced by display trees of the network. However, such an approach is computationally prohibiting due to the exponential size of the set. Therefore, we propose a broader and e...

We address the problem of inferring an optimal tree displayed by a network, given a gene tree G and a tree-child network N , under the deep coalescence cost. We propose an O(|G||N |)-time dynamic programming algorithm (DP) to compute a lower bound of the optimal displayed tree cost, where |G| and |N | are the sizes of G and N , respectively. This algorithm has the ability to state whether the cost is exact or is a lower bound. In addition, our algorithm provides a set of reticulation edges that correspond to the obtained cost. If the cost is exact, the set induces an optimal displayed tree that yields the cost. If the cost is a lower bound, the set contains pairs of conflicting edges, that is, edges sharing a reticulation node. Next, we show a conflict resolution algorithm that requires 2r+1 − 1 invocations of DP in the worst case, where r is a number of reticulations. We propose a similar O(2|G||N |)-time algorithm for level-k networks and a branch and bound solution to compute low...