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.
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.
Forest-Based Networks Huber, K. T.; Moulton, V.; Scholz, G. E.
Bulletin of mathematical biology,
2022/10, Volume:
84, Issue:
10
Journal Article
Peer reviewed
Open access
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.
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.
Phylogenetic networks are a generalization of phylogenetic trees that are used in biology to represent reticulate or non-treelike evolution. Recently, several algorithms have been developed which aim ...to construct phylogenetic networks from biological data using
triplets
, i.e. binary phylogenetic trees on 3-element subsets of a given set of species. However, a fundamental problem with this approach is that the triplets displayed by a phylogenetic network do not necessarily uniquely determine or
encode
the network. Here we propose an alternative approach to encoding and constructing phylogenetic networks, which uses phylogenetic networks on 3-element subsets of a set, or
trinets
, rather than triplets. More specifically, we show that for a special, well-studied type of phylogenetic network called a 1-nested network, the trinets displayed by a 1-nested network always encode the network. We also present an efficient algorithm for deciding whether a
dense
set of trinets (i.e. one that contains a trinet on every 3-element subset of a set) can be displayed by a 1-nested network or not and, if so, constructs that network. In addition, we discuss some potential new directions that this new approach opens up for constructing and comparing phylogenetic networks.
Introgression is an evolutionary process in which genes or other types of genetic material are introduced into a genome. It is an important evolutionary process that can, for example, play a ...fundamental role in speciation. Recently the concept of an overlaid species forest (OSF) was introduced as a discrete way to model introgression. Basically, an OSF consists of a gene history in the form of a phylogenetic tree, a collection of lineage trees or forest for some species of interest, and a map that overlays the gene tree onto the forest. In this paper we shall study mathematical properties of OSFs and their relationship with other structures in phylogenetics, such as lateral gene transfer models, subtree prune and regraft operations, and phylogenetic networks. In particular, we show that a certain algorithm called OSF-Builder for constructing an OSF is guaranteed to produce a special type of OSF with a minimum number of introgressions, as well as providing some characterizations for networks that can arise from OSFs. We also give bounds on how much an OSF can change when the underlying gene tree or forest is perturbed. We expect that these results will be useful in developing new algorithms for deriving introgression histories, a rapidly growing area of interest in phylogenomics.
•Overlaid species forests (OSFs) model genes jumping between species lineages.•OSF-Builder algorithm produces a minimal OSF with a special structure.•We characterize phylogenetic networks that can arise from OSFs.•We quantify and bound OSF change when perturbing the underlying graph structure.
Injective Split Systems Hellmuth, M.; Huber, K. T.; Moulton, V. ...
Graphs and combinatorics,
08/2023, Volume:
39, Issue:
4
Journal Article
Peer reviewed
Open access
A split system
S
on a finite set
X
,
|
X
|
≥
3
, is a set of bipartitions or splits of
X
which contains all splits of the form
{
x
,
X
-
{
x
}
}
,
x
∈
X
. To any such split system
S
we can associate ...the Buneman graph
B
(
S
)
which is essentially a median graph with leaf-set
X
that displays the splits in
S
. In this paper, we consider properties of injective split systems, that is, split systems
S
with the property that
med
B
(
S
)
(
Y
)
≠
med
B
(
S
)
(
Y
′
)
for any 3-subsets
Y
,
Y
′
in
X
, where
med
B
(
S
)
(
Y
)
denotes the median in
B
(
S
)
of the three elements in
Y
considered as leaves in
B
(
S
)
. In particular, we show that for any set
X
there always exists an injective split system on
X
, and we also give a characterization for when a split system is injective. We also consider how complex the Buneman graph
B
(
S
)
needs to become in order for a split system
S
on
X
to be injective. We do this by introducing a quantity for |
X
| which we call the injective dimension for |
X
|, as well as two related quantities, called the injective 2-split and the rooted-injective dimension. We derive some upper and lower bounds for all three of these dimensions and also prove that some of these bounds are tight. An underlying motivation for studying injective split systems is that they can be used to obtain a natural generalization of symbolic tree maps. An important consequence of our results is that any three-way symbolic map on
X
can be represented using Buneman graphs.
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.
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.
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