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An equidistant X-cactus is a type of rooted, arc-weighted, directed acyclic graph with leaf set X, that is used in biology to represent the evolutionary history of a set X of species. In this paper, we introduce and investigate the space of equidistant X-cactuses. This space contains, as a subset, the space of ultrametric trees on X that was introduced by Gavryushkin and Drummond. We show that equidistant-cactus space is a CAT(0)-metric space which implies, for example, that there are unique geodesic paths between points. As a key step to proving this, we present a combinatorial result concerning ranked rooted X-cactuses. In particular, we show that such graphs can be encoded in terms of a pairwise compatibility condition arising from a poset of collections of pairs of sub- sets of X that satisfy certain set-theoretic properties. As a corollary, we also obtain an encoding of ranked, rooted X-trees in terms of partitions of X, which provides an alternative proof that the space of ultrametric trees on X is CAT(0). We expect that our results will provide the basis for novel ways to perform statistical analyses on collections of equidistant X-cactuses, as well as new directions for defining and understanding spaces of more general, arc-weighted phylogenetic networks. 

Phylogenetic trees are fundamental for understanding evolutionary history. However, finding maximum likelihood trees is challenging due to the complexity of the likelihood landscape and the size of tree space. Based on the Billera-Holmes-Vogtmann (BHV) distance between trees, we describe a method to generate intermediate trees on the shortest path between two trees, called pathtrees. These pathtrees give a structured way to generate and visualize part of treespace. They allow investigating intermediate regions between trees of interest, exploring locally optimal trees in topological clusters of treespace, and potentially finding trees of high likelihood unexplored by tree search algorithms. We compared our approach against other tree search tools (P aup *, RA x ML, and R ev B ayes ) using the highest likelihood trees and number of new topologies found, and validated the accuracy of the generated treespace. We assess our method using two datasets. The first consists of 23 primate species (CytB, 1141 bp), leading to well-resolved relationships. The second is a dataset of 182 milksnakes (CytB, 1117 bp), containing many similar sequences and complex relationships among individuals. Our method visualizes the treespace using log likelihood as a fitness function. It finds similarly optimal trees as heuristic methods and presents the likelihood landscape at different scales. It found relevant trees that were not found with MCMC methods. The validation measures indicated that our method performed well mapping treespace into lower dimensions. Our method complements heuristic search analyses, and the visualization allows the inspection of likelihood terraces and exploration of treespace areas not visited by heuristic searches. 

Rescue, rehabilitation, and release (‘rescue-rehab-release’) of wildlife is an increasingly widespread practice across ecosystems, largely driven by habitat loss, wildlife exploitation and a changing climate. Despite this, its conservation value has not been realized, in part due to the scarcity of what has been termed “the 4th R”, research. Similar to conservation breeding and headstarting, rescue and rehabilitation entails close association of humans and the wildlife in their care over impressionable and extended periods. However, unlike these interventions, rescue and rehabilitation require an initial, and sometimes sustained, focus on crisis management and veterinary needs which can impede the development of natural behaviors and promote habituation to humans, both of which can compromise post-release survival and recruitment. In this perspective, we discuss the pathways toward, and implications of, behavioral incompetence and highlight opportunities for testable interventions to curtail negative outcomes post-release, without compromising the health or welfare of rescued individuals. We propose that practitioners ‘switch gears’ from triage to fostering behavioral competence as early in the rehabilitation process as is possible, and that research be implemented in order to develop an evidence-base for best practices that can be shared amongst practitioners. We focus on four mammalian species to illustrate specific contexts and considerations for fostering behavioral competence by building on research in the conservation translocation literature. Finally, we discuss a way forward that calls for greater cross-pollination among translocation scenarios involving extended time under human care during developmentally sensitive periods. 

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of Francis, Semple, and Steel about the complexity of determining how far a phylogenetic network is from being tree-based, including non-binary phylogenetic networks. We show that finding a phylogenetic tree covering the maximum number of nodes in a phylogenetic network can be computed in polynomial time via an encoding into a minimum-cost flow problem.