MOTIVATION: Noncoding RNAs (ncRNAs) express their functions by adopting molecular structures. Specifically, RNA secondary structures serve as a relatively stable intermediate step before tertiary structures, offering a reliable signature of molecular function. Consequently, within an RNA functional family, secondary structures are generally more evolutionarily conserved than sequences. Conversely, homologous RNA families grouped within an RNA clan share ancestors but typically exhibit structural differences. Inferring the evolution of RNA structures within RNA families and clans is crucial for gaining insights into functional adaptations over time and providing clues about the Ancient RNA World Hypothesis. RESULTS: We introduce the median problem and the small parsimony problem for ncRNA families, where secondary structures are represented as leaf-labeled trees. We utilize the Robinson-Foulds (RF) tree distance, which corresponds to a specific edit distance between RNA trees, and a new metric called the Internal-Leafset (IL) distance. While the RF tree distance compares sets of leaves descending from internal nodes of two RNA trees, the IL distance compares the collection of leaf-children of internal nodes. The latter is better at capturing differences in structural elements of RNAs than the RF distance, which is more focused on base pairs. We also consider a more general tree edit distance that allows the mapping of base pairs that are not perfectly aligned. We study the theoretical complexity of the median problem and the small parsimony problem under the three distance metrics and various biologically relevant constraints, and we present polynomial-time maximum parsimony algorithms for solving some versions of the problems. Our algorithms are applied to ncRNA families from the RFAM database, illustrating their practical utility. AVAILABILITY AND IMPLEMENTATION: https://github.com/bmarchand/rna\_small\_parsimony.

MOTIVATION: It is largely established that all extant mitochondria originated from a unique endosymbiotic event integrating an α-proteobacterial genome into an eukaryotic cell. Subsequently, eukaryote evolution has been marked by episodes of gene transfer, mainly from the mitochondria to the nucleus, resulting in a significant reduction of the mitochondrial genome, eventually completely disappearing in some lineages. However, in other lineages such as in land plants, a high variability in gene repertoire distribution, including genes encoded in both the nuclear and mitochondrial genome, is an indication of an ongoing process of Endosymbiotic Gene Transfer (EGT). Understanding how both nuclear and mitochondrial genomes have been shaped by gene loss, duplication and transfer is expected to shed light on a number of open questions regarding the evolution of eukaryotes, including rooting of the eukaryotic tree. RESULTS: We address the problem of inferring the evolution of a gene family through duplication, loss and EGT events, the latter considered as a special case of horizontal gene transfer occurring between the mitochondrial and nuclear genomes of the same species (in one direction or the other). We consider both EGT events resulting in maintaining (EGTcopy) or removing (EGTcut) the gene copy in the source genome. We present a linear-time algorithm for computing the DLE (Duplication, Loss and EGT) distance, as well as an optimal reconciled tree, for the unitary cost, and a dynamic programming algorithm allowing to output all optimal reconciliations for an arbitrary cost of operations. We illustrate the application of our EndoRex software and analyze different costs settings parameters on a plant dataset and discuss the resulting reconciled trees. AVAILABILITY AND IMPLEMENTATION: EndoRex implementation and supporting data are available on the GitHub repository via https://github.com/AEVO-lab/EndoRex.