Phylogenetic Diversity Indices from an Affine and Projective Viewpoint.

Phylogenetic diversity indices are commonly used to rank the elements in a collection of species or populations for conservation purposes. The derivation of these indices is typically based on some quantitative description of the evolutionary history of the species in question, which is often given in terms of a phylogenetic tree. Both rooted and unrooted phylogenetic trees can be employed, and there are close connections between the indices that are derived in these two different ways. In this paper, we introduce more general phylogenetic diversity indices that can be derived from collections of subsets (clusters) and collections of bipartitions (splits) of the given set of species. Such indices could be useful, for example, in case there is some uncertainty in the topology of the tree being used to derive a phylogenetic diversity index. As well as characterizing some of the indices that we introduce in terms of their special properties, we provide a link between cluster-based and split-based phylogenetic diversity indices that uses a discrete analogue of the classical link between affine and projective geometry. This provides a unified framework for many of the various phylogenetic diversity indices used in the literature based on rooted and unrooted phylogenetic trees, generalizations and new proofs for previous results concerning tree-based indices, and a way to define some new phylogenetic diversity indices that naturally arise as affine or projective variants of each other or as generalizations of tree-based indices.

Association between psychological distress trajectories from adolescence to midlife and mental health during the pandemic: evidence from two British birth cohorts.

BACKGROUND: This paper examined whether distinct life-course trajectories of psychological distress from adolescence to midlife were associated with poorer mental health outcomes during the pandemic. METHODS: We present a secondary analysis of two nationally representative British birth cohorts, the 1958 National Child Development Study (NCDS) and 1970 British Cohort Study (BCS70). We used latent variable mixture models to identify pre-pandemic longitudinal trajectories of psychological distress and a modified Poisson model with robust standard errors to estimate associations with psychological distress, life satisfaction and loneliness at different points during the pandemic. RESULTS: Our analysis identified five distinct pre-pandemic trajectories of psychological distress in both cohorts. All trajectories with prior symptoms of psychological distress irrespective of age of onset, severity and chronicity were associated with a greater relative risk of poorer mental health outcomes during the pandemic and the probability of poorer mental health associated with psychological distress trajectories remained fairly constant. The relationship was not fully attenuated when most recent pre-pandemic psychological distress and other midlife factors were controlled for. CONCLUSIONS: Whilst life-course trajectories with any prior symptoms of psychological distress put individuals at greater risk of poor mental health outcomes during the pandemic, those with chronic and more recent occurrences were at highest risk. In addition, prior poor mental health during the adult life-course may mean individuals are less resilient to shocks, such as pandemics. Our findings show the importance of considering heterogeneous mental health trajectories across the life-course in the general population in addition to population average trends.

Adult life-course trajectories of psychological distress and economic outcomes in midlife during the COVID-19 pandemic: evidence from the 1958 and 1970 British birth cohorts.

PURPOSE: Financial adversity in times of economic recession have been shown to have an unequal effect on individuals with prior mental health problems. This study investigated the relationship between mental health groupings across the adult life-course and change in financial situation and employment status during the COVID-19 pandemic, as well as the use of financial measures to mitigate the economic shock. METHODS: Using two nationally representative British birth cohorts, the National Child Development Study (1958) n = 17,415 and 1970 British Cohort Study n = 17,198, we identified 5 different life-course trajectories of psychological distress from adolescence to midlife which were similar but not identical across the two cohorts. We explored their relation to changes in financial and employment circumstances at different stages during the pandemic from May 2020 to March 2021, applying multinomial logistic regression and controlling for numerous early life covariates, including family socio-economic status (SES). In addition, we ran modified Poisson models with robust standard errors to identify whether different mental health trajectories were supported by government and used other methods to mitigate their financial situation. RESULTS: We found that the financial circumstances of pre-pandemic trajectories of psychological distress with differential onset, severity, and chronicity across the life-course were exacerbated by the COVID-19 economic shock. The 'stable-high' (persistent severe symptoms) and 'adult-onset' (symptoms developing in 30s, but later decreasing) groups were vulnerable to job loss. Compared to pre-pandemic trajectory groupings with no, minor, or psychological distress symptoms in early adulthood, the 'stable-high', 'midlife-onset' (symptoms developing in midlife), and 'adult-onset' trajectory groups were more likely to seek support from the UK governments economic response package. However, trajectories with pre-pandemic psychological distress were also at greater risk of reducing consumption, dis-saving, relying on increased financial help from family and friends, and also taking payment holidays (agreements with lenders to pause mortgage, credit card or loan payments for a set period) and borrowing. CONCLUSION: This work highlights different trajectories of pre-pandemic psychological distress, compared to groups with no symptoms were more vulnerable to pandemic-related economic shock and job loss. By adopting unsustainable mitigating measures (borrowing and payment holidays) to support their financial circumstances during COVID-19, these mental health trajectories are at even more risk of lasting adverse impacts and future economic difficulties.

Forest-Based Networks.

In evolutionary studies, it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has occurred in the past, a tree may not provide a complete picture of their history. In such cases, tree-based phylogenetic networks can provide a useful, more refined representation of the species' evolution. Such a network is essentially a phylogenetic tree with some arcs added between the tree's edges so as to represent reticulate events such as gene transfer, hybridization and recombination. Even so, this model does not permit the direct representation of evolutionary scenarios where reticulate events have taken place between different subfamilies or lineages of species. To represent such scenarios, in this paper we introduce the notion of a forest-based network, that is, a collection of leaf-disjoint phylogenetic trees on a set of species with arcs added between the edges of distinct trees within the collection. Forest-based networks include the recently introduced class of overlaid species forests which can be used to model introgression. As we shall see, even though the definition of forest-based networks is closely related to that of tree-based networks, they lead to new mathematical theory which complements that of tree-based networks. As well as studying the relationship of forest-based networks with other classes of phylogenetic networks, such as tree-child networks and universal tree-based networks, we present some characterizations of some special classes of forest-based networks. We expect that our results will be useful for developing new models and algorithms to understand reticulate evolution, such as introgression and gene transfer between species.

Correction to: Tree-Based Unrooted Phylogenetic Networks.

The level-5 example of a network presented in Fig. 4 of Francis et al. (2018) is tree-based even though it states in the caption and in the text that this is not the case.

Tree-Based Unrooted Phylogenetic Networks.

Phylogenetic networks are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An unrooted phylogenetic network on a non-empty, finite set X of taxa, or network, is a connected, simple graph in which every vertex has degree 1 or 3 and whose leaf set is X. It is called a phylogenetic tree if the underlying graph is a tree. In this paper we consider properties of tree-based networks, that is, networks that can be constructed by adding edges into a phylogenetic tree. We show that although they have some properties in common with their rooted analogues which have recently drawn much attention in the literature, they have some striking differences in terms of both their structural and computational properties. We expect that our results could eventually have applications to, for example, detecting horizontal gene transfer or hybridization which are important factors in the evolution of many organisms.

Minimum triplet covers of binary phylogenetic X-trees.

Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed from the distances between the leaves (when the edges are given any strictly positive lengths). Moreover, a linear number of these pairwise distance values suffices to determine both the tree and its edge lengths. A natural set of pairs of leaves is provided by any 'triplet cover' of the tree (based on the fact that each non-leaf vertex is the median vertex of three leaves). In this paper we describe a number of new results concerning triplet covers of minimum size. In particular, we characterize such covers in terms of an associated graph being a 2-tree. Also, we show that minimum triplet covers are 'shellable' and thereby provide a set of pairs for which the inter-leaf distance values will uniquely determine the underlying tree and its associated branch lengths.

Generating Functions for Multi-labeled Trees.

Multi-labeled trees are a generalization of phylogenetic trees that are used, for example, in the study of gene versus species evolution and as the basis for phylogenetic network construction. Unlike phylogenetic trees, in a leaf-multi-labeled tree it is possible to label more than one leaf by the same element of the underlying label set. In this paper we derive formulae for generating functions of leaf-multi-labeled trees and use these to derive recursions for counting such trees. In particular, we prove results which generalize previous theorems by Harding on so-called tree-shapes, and by Otter on relating the number of rooted and unrooted phylogenetic trees.

S-system parameter estimation for noisy metabolic profiles using newton-flow analysis.

Biochemical systems are commonly modelled by systems of ordinary differential equations (ODEs). A particular class of such models called S-systems have recently gained popularity in biochemical system modelling. The parameters of an S-system are usually estimated from time-course profiles. However, finding these estimates is a difficult computational problem. Moreover, although several methods have been recently proposed to solve this problem for ideal profiles, relatively little progress has been reported for noisy profiles. We describe a special feature of a Newton-flow optimisation problem associated with S-system parameter estimation. This enables us to significantly reduce the search space, and also lends itself to parameter estimation for noisy data. We illustrate the applicability of our method by applying it to noisy time-course data synthetically produced from previously published 4- and 30-dimensional S-systems. In addition, we propose an extension of our method that allows the detection of network topologies for small S-systems. We introduce a new method for estimating S-system parameters from time-course profiles. We show that the performance of this method compares favorably with competing methods for ideal profiles, and that it also allows the determination of parameters for noisy profiles.

Imputing supertrees and supernetworks from quartets.

Inferring species phylogenies is an important part of understanding molecular evolution. Even so, it is well known that an accurate phylogenetic tree reconstruction for a single gene does not always necessarily correspond to the species phylogeny. One commonly accepted strategy to cope with this problem is to sequence many genes; the way in which to analyze the resulting collection of genes is somewhat more contentious. Supermatrix and supertree methods can be used, although these can suppress conflicts arising from true differences in the gene trees caused by processes such as lineage sorting, horizontal gene transfer, or gene duplication and loss. In 2004, Huson et al. (IEEE/ACM Trans. Comput. Biol. Bioinformatics 1:151-158) presented the Z-closure method that can circumvent this problem by generating a supernetwork as opposed to a supertree. Here we present an alternative way for generating supernetworks called Q-imputation. In particular, we describe a method that uses quartet information to add missing taxa into gene trees. The resulting trees are subsequently used to generate consensus networks, networks that generalize strict and majority-rule consensus trees. Through simulations and application to real data sets, we compare Q-imputation to the matrix representation with parsimony (MRP) supertree method and Z-closure, and demonstrate that it provides a useful complementary tool.

Phylogenetic networks from multi-labelled trees.

It is now quite well accepted that the evolutionary past of certain species is better represented by phylogenetic networks as opposed to trees. For example, polyploids are typically thought to have resulted through hybridization and duplication, processes that are probably not best represented as bifurcating speciation events. Based on the knowledge of a multi-labelled tree relating collection of polyploids, we present a canonical construction of a phylogenetic network that exhibits the tree. In addition, we prove that the resulting network is in some well-defined sense a minimal network having this property.

The MinMax Squeeze: guaranteeing a minimal tree for population data.

We report that for population data, where sequences are very similar to one another, it is often possible to use a two-pronged (MinMax Squeeze) approach to prove that a tree is the shortest possible under the parsimony criterion. Such population data can be in a range where parsimony is a maximum likelihood estimator. This is in sharp contrast to the case with species data, where sequences are much further apart and the problem of guaranteeing an optimal phylogenetic tree is known to be computationally prohibitive for realistic numbers of species, irrespective of whether likelihood or parsimony is the optimality criterion. The Squeeze uses both an upper bound (the length of the shortest tree known) and a lower bound derived from partitions of the columns (the length of the shortest tree possible). If the two bounds meet, the shortest known tree is thus proven to be a shortest possible tree. The implementation is first tested on simulated data sets and then applied to 53 complete human mitochondrial genomes. The shortest possible trees for those data have several significant improvements from the published tree. Namely, a pair of Australian lineages comes deeper in the tree (in agreement with archaeological data), and the non-African part of the tree shows greater agreement with the geographical distribution of lineages.

Phylogenetic analysis of the full-length SARS-CoV sequences: evidence for phylogenetic discordance in three genomic regions.

The origin of the severe acute respiratory syndrome-coronavirus (SARS-CoV) remains unclear. Evidence based on Bayesian scanning plots and phylogenetic analysis using maximum likelihood (ML) and Bayesian methods indicates that SARS-CoV, for the largest part of the genome ( approximately 80%), is more closely related to Group II coronaviruses sequences, whereas in three regions in the ORF1ab gene it shows no apparent similarity to any of the previously characterized groups of coronaviruses. There is discordant phylogenetic clustering of SARS-CoV and coronaviruses sequences, throughout the genome, compatible with either ancient recombination events or altered evolutionary rates in different lineages, or a combination of both.

Delta plots: a tool for analyzing phylogenetic distance data.

A method is described that allows the assessment of treelikeness of phylogenetic distance data before tree estimation. This method is related to statistical geometry as introduced by Eigen, Winkler-Oswatitsch, and Dress (1988 [Proc. Natl. Acad. Sci. USA. 85:5913-5917]), and in essence, displays a measure for treelikeness of quartets in terms of a histogram that we call a delta plot. This allows identification of nontreelike data and analysis of noisy data sets arising from processes such as, for example, parallel evolution, recombination, or lateral gene transfer. In addition to an overall assessment of treelikeness, individual taxa can be ranked by reference to the treelikeness of the quartets to which they belong. Removal of taxa on the basis of this ranking results in an increase in accuracy of tree estimation. Recombinant data sets are simulated, and the method is shown to be capable of identifying single recombinant taxa on the basis of distance information alone, provided the parents of the recombinant sequence are sufficiently divergent and the mixture of tree histories is not strongly skewed toward a single tree. delta Plots and taxon rankings are applied to three biological data sets using distances derived from sequence alignment, gene order, and fragment length polymorphism.

Pruned median networks: a technique for reducing the complexity of median networks.

Observations from molecular marker studies on recently diverged species indicate that substitution patterns in DNA sequences can often be complex and poorly described by tree-like bifurcating evolutionary models. These observations might result from processes of species diversification and/or processes of sequence evolution that are not tree-like. In these cases, bifurcating tree representations provide poor visualization of phylogenetic signals in sequence data. In this paper, we use median networks to study DNA sequence substitution patterns in plant nuclear and chloroplast markers. We describe how to prune median networks to obtain so called pruned median networks. These simpler networks may help to provide a useful framework for investigating the phylogenetic complexity of recently diverged taxa with hybrid origins.

Use of RNA secondary structure for studying the evolution of RNase P and RNase MRP.

Secondary structure is evaluated for determining evolutionary relationships between catalytic RNA molecules that are so distantly related they are scarcely alignable. The ribonucleoproteins RNase P (P) and RNase MRP (MRP) have been suggested to be evolutionarily related because of similarities in both function and secondary structure. However, their RNA sequences cannot be aligned with any confidence, and this leads to uncertainty in any trees inferred from sequences. We report several approaches to using secondary structures for inferring evolutionary trees and emphasize quantitative tests to demonstrate that evolutionary information can be recovered. For P and MRP, three hypotheses for the relatedness are considered. The first is that MRP is derived from P in early eukaryotes. The next is that MRP is derived from P from an early endosymbiont. The third is that both P and MRP evolved in the RNA-world (and the need for MRP has since been lost in prokaryotes). Quantitative comparisons of the pRNA and mrpRNA secondary structures have found that the possibility of an organellar origin of MRP is unlikely. In addition, comparison of secondary structures support the identity of an RNase P-like sequence in the maize chloroplast genome. Overall, it is concluded that RNA secondary structure is useful for evaluating evolutionary relatedness, even with sequences that cannot be aligned with confidence.

RNA folding argues against a hot-start origin of life.

Opinion is strongly divided on whether life arose on earth under hot or cold conditions, the hot-start and cold-start scenarios, respectively. The origin of life close to deep thermal vents appears as the majority opinion among biologists, but there is considerable biochemical evidence that high temperatures are incompatible with an RNA world. To be functional, RNA has to fold into a three-dimensional structure. We report both theoretical and experimental results on RNA folding and show that (as expected) hot conditions strongly reduce RNA folding. The theoretical results come from energy-minimization calculations of the average extent of folding of RNA, mainly from 0-90 degrees C, for both random sequences and tRNA sequences. The experimental results are from circular-dichroism measurements of tRNA over a similar range of temperatures. The quantitative agreement between calculations and experiment is remarkable, even to the shape of the curves indicating the cooperative nature of RNA folding and unfolding. These results provide additional evidence for a lower temperature stage being necessary in the origin of life.

Metrics on RNA secondary structures.

Many different programs have been developed for the prediction of the secondary structure of an RNA sequence. Some of these programs generate an ensemble of structures, all of which have free energy close to that of the optimal structure, making it important to be able to quantify how similar these different structures are. To deal with this problem, we define a new class of metrics, the mountain metrics, on the set of RNA secondary structures of a fixed length. We compare properties of these metrics with other well known metrics on RNA secondary structures. We also study some global and local properties of these metrics.

Likelihood analysis of phylogenetic networks using directed graphical models.

A method for computing the likelihood of a set of sequences assuming a phylogenetic network as an evolutionary hypothesis is presented. The approach applies directed graphical models to sequence evolution on networks and is a natural generalization of earlier work by Felsenstein on evolutionary trees, including it as a special case. The likelihood computation involves several steps. First, the phylogenetic network is rooted to form a directed acyclic graph (DAG). Then, applying standard models for nucleotide/amino acid substitution, the DAG is converted into a Bayesian network from which the joint probability distribution involving all nodes of the network can be directly read. The joint probability is explicitly dependent on branch lengths and on recombination parameters (prior probability of a parent sequence). The likelihood of the data assuming no knowledge of hidden nodes is obtained by marginalization, i.e., by summing over all combinations of unknown states. As the number of terms increases exponentially with the number of hidden nodes, a Markov chain Monte Carlo procedure (Gibbs sampling) is used to accurately approximate the likelihood by summing over the most important states only. Investigating a human T-cell lymphotropic virus (HTLV) data set and optimizing both branch lengths and recombination parameters, we find that the likelihood of a corresponding phylogenetic network outperforms a set of competing evolutionary trees. In general, except for the case of a tree, the likelihood of a network will be dependent on the choice of the root, even if a reversible model of substitution is applied. Thus, the method also provides a way in which to root a phylogenetic network by choosing a node that produces a most likely network.