Random ultrametric trees and applications

Ultrametric trees are trees whose leaves lie at the same distance from the root. They are used to model the genealogy of a population of particles co-existing at the same point in time. We show how the boundary of an ultrametric tree, like any compact ultrametric space, can be represented in a simple way via the so-called comb metric. We display a variety of examples of random combs and explain how they can be used in applications. In particular, we review some old and recent results regarding the genetic structure of the population when throwing neutral mutations on the skeleton of the tree.Comment: 20 pages, 7 figures, proceedings of MAS 2016, Grenoble, France (Stochastic modeling and Statistics Conference, French Society for Applied and Industrial Math, SMAI

Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective

Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with "big data," as well as the complication that their discrete geometric structure results in a non-Euclidean phylogenetic tree space, which poses computational and statistical limitations. We propose and study a novel framework to study sets of phylogenetic trees based on tropical geometry. In particular, we focus on characterizing our framework for statistical analyses of evolutionary biological processes represented by phylogenetic trees. Our setting exhibits analytic, geometric, and topological properties that are desirable for theoretical studies in probability and statistics, as well as increased computational efficiency over the current state-of-the-art. We demonstrate our approach on seasonal influenza data.Comment: 28 pages, 5 figures, 1 tabl

A hierarchical loss and its problems when classifying non-hierarchically

Failing to distinguish between a sheepdog and a skyscraper should be worse and penalized more than failing to distinguish between a sheepdog and a poodle; after all, sheepdogs and poodles are both breeds of dogs. However, existing metrics of failure (so-called "loss" or "win") used in textual or visual classification/recognition via neural networks seldom leverage a-priori information, such as a sheepdog being more similar to a poodle than to a skyscraper. We define a metric that, inter alia, can penalize failure to distinguish between a sheepdog and a skyscraper more than failure to distinguish between a sheepdog and a poodle. Unlike previously employed possibilities, this metric is based on an ultrametric tree associated with any given tree organization into a semantically meaningful hierarchy of a classifier's classes. An ultrametric tree is a tree with a so-called ultrametric distance metric such that all leaves are at the same distance from the root. Unfortunately, extensive numerical experiments indicate that the standard practice of training neural networks via stochastic gradient descent with random starting points often drives down the hierarchical loss nearly as much when minimizing the standard cross-entropy loss as when trying to minimize the hierarchical loss directly. Thus, this hierarchical loss is unreliable as an objective for plain, randomly started stochastic gradient descent to minimize; the main value of the hierarchical loss may be merely as a meaningful metric of success of a classifier.Comment: 19 pages, 4 figures, 7 table

Optimizing Phylogenetic Supertrees Using Answer Set Programming

The supertree construction problem is about combining several phylogenetic trees with possibly conflicting information into a single tree that has all the leaves of the source trees as its leaves and the relationships between the leaves are as consistent with the source trees as possible. This leads to an optimization problem that is computationally challenging and typically heuristic methods, such as matrix representation with parsimony (MRP), are used. In this paper we consider the use of answer set programming to solve the supertree construction problem in terms of two alternative encodings. The first is based on an existing encoding of trees using substructures known as quartets, while the other novel encoding captures the relationships present in trees through direct projections. We use these encodings to compute a genus-level supertree for the family of cats (Felidae). Furthermore, we compare our results to recent supertrees obtained by the MRP method.Comment: To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 201

Plant DNA barcodes and assessment of phylogenetic community structure of a tropical mixed dipterocarp forest in Brunei Darussalam (Borneo)

DNA barcoding is a fast and reliable tool to assess and monitor biodiversity and, via community phylogenetics, to investigate ecological and evolutionary processes that may be responsible for the community structure of forests. In this study, DNA barcodes for the two widely used plastid coding regions rbcL and matK are used to contribute to identification of morphologically undetermined individuals, as well as to investigate phylogenetic structure of tree communities in 70 subplots (10 × 10m) of a 25-ha forest-dynamics plot in Brunei (Borneo, Southeast Asia). The combined matrix (rbcL + matK) comprised 555 haplotypes (from ≥154 genera, 68 families and 25 orders sensu APG, Angiosperm Phylogeny Group, 2016), making a substantial contribution to tree barcode sequences from Southeast Asia. Barcode sequences were used to reconstruct phylogenetic relationships using maximum likelihood, both with and without constraining the topology of taxonomic orders to match that proposed by the Angiosperm Phylogeny Group. A third phylogenetic tree was reconstructed using the program Phylomatic to investigate the influence of phylogenetic resolution on results. Detection of non-random patterns of community assembly was determined by net relatedness index (NRI) and nearest taxon index (NTI). In most cases, community assembly was either random or phylogenetically clustered, which likely indicates the importance to community structure of habitat filtering based on phylogenetically correlated traits in determining community structure. Different phylogenetic trees gave similar overall results, but the Phylomatic tree produced greater variation across plots for NRI and NTI values, presumably due to noise introduced by using an unresolved phylogenetic tree. Our results suggest that using a DNA barcode tree has benefits over the traditionally used Phylomatic approach by increasing precision and accuracy and allowing the incorporation of taxonomically unidentified individuals into analyses

A Well-Resolved Phylogeny of the Trees of Puerto Rico Based on DNA Barcode Sequence Data

Background: The use of phylogenetic information in community ecology and conservation has grown in recent years. Two key issues for community phylogenetics studies, however, are (i) low terminal phylogenetic resolution and (ii) arbitrarilydefined species pools. Methodology/principal findings: We used three DNA barcodes (plastid DNA regions rbcL, matK, and trnH-psbA) to infer a phylogeny for 527 native and naturalized trees of Puerto Rico, representing the vast majority of the entire tree flora of the island (89%). We used a maximum likelihood (ML) approach with and without a constraint tree that enforced monophyly of recognized plant orders. Based on 50% consensus trees, the ML analyses improved phylogenetic resolution relative to a comparable phylogeny generated with PHYLOMATIC (proportion of internal nodes resolved:constrained ML = 74%, unconstrained ML = 68%, PHYLOMATIC = 52%). We quantified the phylogenetic composition of 15 protected forests in Puerto Rico using the constrained ML and PHYLOMATIC phylogenies. We found some evidence that tree communities in areas of high water stress were relatively phylogenetically clustered. Reducing the scale at which the species pool was defined (from island to soil types) changed some of our results depending on which phylogeny (ML vs. PHYLOMATIC) was used. Overall, the increased terminal resolution provided by the ML phylogeny revealed additional patterns that were not observed with a less-resolved phylogeny. Conclusions/significance: With the DNA barcode phylogeny presented here (based on an island-wide species pool), we show that a more fully resolved phylogeny increases power to detect nonrandom patterns of community composition in several Puerto Rican tree communities. Especially if combined with additional information on species functional traits and geographic distributions, this phylogeny will (i) facilitate stronger inferences about the role of historical processes in governing the assembly and composition of Puerto Rican forests, (ii) provide insight into Caribbean biogeography, and (iii) aid in incorporating evolutionary history into conservation planning

A genome-scale mining strategy for recovering novel rapidly-evolving nuclear single-copy genes for addressing shallow-scale phylogenetics in Hydrangea

Background: Identifying orthologous molecular markers that potentially resolve relationships at and below species level has been a major challenge in molecular phylogenetics over the past decade. Non-coding regions of nuclear low-or single-copy markers are a vast and promising source of data providing information for shallow-scale phylogenetics. Taking advantage of public transcriptome data from the One Thousand Plant Project (1KP), we developed a genome-scale mining strategy for recovering potentially orthologous single-copy markers to address low-scale phylogenetics. Our marker design targeted the amplification of intron-rich nuclear single-copy regions from genomic DNA. As a case study we used Hydrangea section Cornidia, one of the most recently diverged lineages within Hydrangeaceae (Cornales), for comparing the performance of three of these nuclear markers to other "fast" evolving plastid markers. Results: Our data mining and filtering process retrieved 73 putative nuclear single-copy genes which are potentially useful for resolving phylogenetic relationships at a range of divergence depths within Cornales. The three assessed nuclear markers showed considerably more phylogenetic signal for shallow evolutionary depths than conventional plastid markers. Phylogenetic signal in plastid markers increased less markedly towards deeper evolutionary divergences. Potential phylogenetic noise introduced by nuclear markers was lower than their respective phylogenetic signal across all evolutionary depths. In contrast, plastid markers showed higher probabilities for introducing phylogenetic noise than signal at the deepest evolutionary divergences within the tribe Hydrangeeae (Hydrangeaceae). Conclusions: While nuclear single-copy markers are highly informative for shallow evolutionary depths without introducing phylogenetic noise, plastid markers might be more appropriate for resolving deeper-level divergences such as the backbone relationships of the Hydrangeaceae family and deeper, at which non-coding parts of nuclear markers could potentially introduce noise due to elevated rates of evolution. The herein developed and demonstrated transcriptome based mining strategy has a great potential for the design of novel and highly informative nuclear markers for a range of plant groups and evolutionary scales