A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees

Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for binary trees, exact solvers struggle to solve instances with reticulation number larger than 40-50. Here we present CycleKiller and NonbinaryCycleKiller, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Using simulations, we demonstrate that these algorithms run quickly for large and difficult instances, producing solutions that are very close to optimality. As a spin-off from our simulations we also present TerminusEst, which is the fastest exact method currently available that can handle nonbinary trees: this is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All three methods are based on extensions of previous theoretical work and are publicly available. We also apply our methods to real data

A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm is combinatorial and its running time is quadratic in the input size. To prove the approximation guarantee, we construct a feasible dual solution for a novel linear programming formulation. In addition, we show this linear program is stronger than previously known formulations, and we give a compact formulation, showing that it can be solved in polynomial tim

Analyzing tree distribution and abundance in Yukon-Charley Rivers National Preserve: developing geostatistical Bayesian models with count data

Master's Project (M.S.) University of Alaska Fairbanks, 2018Species distribution models (SDMs) describe the relationship between where a species occurs and underlying environmental conditions. For this project, I created SDMs for the five tree species that occur in Yukon-Charley Rivers National Preserve (YUCH) in order to gain insight into which environmental covariates are important for each species, and what effect each environmental condition has on that species' expected occurrence or abundance. I discuss some of the issues involved in creating SDMs, including whether or not to incorporate spatially explicit error terms, and if so, how to do so with generalized linear models (GLMs, which have discrete responses). I ran a total of 10 distinct geostatistical SDMs using Markov Chain Monte Carlo (Bayesian methods), and discuss the results here. I also compare these results from YUCH with results from a similar analysis conducted in Denali National Park and Preserve (DNPP)

Cycle killer... qu'est-ce que c'est? On the comparative approximability of hybridization number and directed feedback vertex set

We show that the problem of computing the hybridization number of two rooted binary phylogenetic trees on the same set of taxa X has a constant factor polynomial-time approximation if and only if the problem of computing a minimum-size feedback vertex set in a directed graph (DFVS) has a constant factor polynomial-time approximation. The latter problem, which asks for a minimum number of vertices to be removed from a directed graph to transform it into a directed acyclic graph, is one of the problems in Karp's seminal 1972 list of 21 NP-complete problems. However, despite considerable attention from the combinatorial optimization community it remains to this day unknown whether a constant factor polynomial-time approximation exists for DFVS. Our result thus places the (in)approximability of hybridization number in a much broader complexity context, and as a consequence we obtain that hybridization number inherits inapproximability results from the problem Vertex Cover. On the positive side, we use results from the DFVS literature to give an O(log r log log r) approximation for hybridization number, where r is the value of an optimal solution to the hybridization number problem

Approximating subtree distances between Phylogenies

We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete by Bordewich and Semple [5]. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances such as Rodrigues et al. [24] and Hein et al. [13]. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a \cascading" scheme that accounts for possible wrong moves. This accounting is missing from previous analysis of tree distance approximation algorithms. Further, we show how all algorithms of this type can be implemented in linear time and give experimental results

The value of native biodiversity enhancement in New Zealand: A case study of the greater Wellington area

New Zealand’s biodiversity consists of over 80,000 native plants, animals and fungi, many of which are indigenous and located on private property. To enhance native biodiversity and discourage activities that may deplete it, policies can be introduced that can encourage individual self-interest to coincide with social interest. Economic values for biodiversity can help to determine the best policy tools to use. In this project, we surveyed Greater Wellington Region households to determine their biodiversity enhancement values using the contingent valuation approach. Greater Wellington respondents placed a significant value on both private land biodiversity as well as public land biodiversity

Plant height and hydraulic vulnerability to drought and cold

Understanding how plants survive drought and cold is increasingly important as plants worldwide experience dieback with drought in moist places and grow taller with warming in cold ones. Crucial in plant climate adaptation are the diameters of water-transporting conduits. Sampling 537 species across climate zones dominated by angiosperms, we find that plant size is unambiguously the main driver of conduit diameter variation. And because taller plants have wider conduits, and wider conduits within species are more vulnerable to conduction-blocking embolisms, taller conspecifics should be more vulnerable than shorter ones, a prediction we confirm with a plantation experiment. As a result, maximum plant size should be short under drought and cold, which cause embolism, or increase if these pressures relax. That conduit diameter and embolism vulnerability are inseparably related to plant size helps explain why factors that interact with conduit diameter, such as drought or warming, are altering plant heights worldwide

A parsimony-based metric for phylogenetic trees

In evolutionary biology various metrics have been defined and studied for comparing phylogenetic trees. Such metrics are used, for example, to compare competing evolutionary hypotheses or to help organize algorithms that search for optimal trees. Here we introduce a new metric dpdp on the collection of binary phylogenetic trees each labeled by the same set of species. The metric is based on the so-called parsimony score, an important concept in phylogenetics that is commonly used to construct phylogenetic trees. Our main results include a characterization of the unit neighborhood of a tree in the dpdp metric, and an explicit formula for its diameter, that is, a formula for the maximum possible value of dpdp over all possible pairs of trees labeled by the same set of species. We also show that dpdp is closely related to the well-known tree bisection and reconnection (tbr) and subtree prune and regraft (spr) distances, a connection which will hopefully provide a useful new approach to understanding properties of these and related metrics