Biology subjects

Steel, M.

Publications and source records attributed to Steel, M..

At least 19 recordsLinked to original sources

bioRxiv2024

The probability of a unique gene occurrence at the tips of a phylogenetic tree in the absence of horizontal gene transfer (the last-one-out)

Gene loss is an important process in gene and genome evolution. If a gene is present at the root of a rooted binary phylogenetic tree and can be lost in one descendant lineage, it can be lost in other descendant lineages as well, and potentially can be lost in all of them, leading to extinction of the gene on the tree. In that case, just before the gene goes extinct in the rooted phylogeny, there will be one lineage that still retains the gene for some period of time, representing a last-one-out distribution. If there are many (hundreds) of leaves in one clade of a phylogenetic tree, yet only one leaf possesses the gene, it will look like the result of a recent gene acquisition, even though the distribution at the tips was generated by loss. Here we derive the probability of observing last-one-out distributions under a Markovian loss model and a given gene loss rate {micro}. We find that the probability of observing such cases can be calculated mathematically, and can be surprisingly high, depending upon the tree and the rate of gene loss. Examples from real data show that gene loss can readily account for the observed frequency of last-one-out gene distribution patterns that might otherwise be attributed to lateral gene transfer.

evolutionary biology↗

bioRxiv2023

Self-generating autocatalytic networks: structural results, algorithms, and their relevance to evolutionary processes

The concept of an autocatalytic network of reactions that can form and persist, starting from just an available food source, has been formalised by the notion of a Reflexively-Autocatalytic and Food generated (RAF) set. The theory and algorithmic results concerning RAFs have been applied to a range of settings, from metabolic questions arising at the origin of life, to ecological networks, and cognitive models in cultural evolution. In this paper, we present new structural and algorithmic results concerning RAF sets, by studying more complex modes of catalysis that allow certain reactions to require multiple catalysts (or to not require catalysis at all), and discuss the differing ways catalysis has been viewed in the literature. We then focus on the structure and analysis of minimal RAFs, and derive structural results and polynomial-time algorithms, with applications to metabolic network data described briefly.

evolutionary biology↗

bioRxiv2023

Labellable phylogenetic networks

AO_SCPLOWBSTRACTC_SCPLOWPhylogenetic networks are mathematical representations of evolutionary history that are able to capture both tree-like evolutionary processes (speciations), and non-tree-like "reticulate" processes such as hybridization or horizontal gene transfer. The additional complexity that comes with this capacity, however, makes networks harder to infer from data, and more complicated to work with as mathematical objects. In this paper we define a new, large class of phylogenetic networks, that we call labellable, and show that they are in bijection with the set of "expanding covers" of finite sets. This correspondence is a generalisation of the encoding of phylogenetic forests by partitions of finite sets. Labellable networks can be characterised by a simple combinatorial condition, and we describe the relationship between this large class and other commonly studied classes. Furthermore, we show that all phylogenetic networks have a quotient network that is labellable.

evolutionary biology↗

bioRxiv2023

Spaces of phylogenetic diversity indices: combinatorial and geometric properties

Biodiversity is a concept most naturally quantified and measured across sets of species. However, for some applications, such as prioritising species for conservation efforts, a species-by-species approach is desirable. Phylogenetic diversity indices are functions that apportion the total biodiversity value of a set of species across its constituent members. As such, they aim to measure each species individual contribution to, and embodiment of, the diversity present in that set. However, no clear definition exists that encompasses the diversity indices in current use. This paper presents conditions that define diversity indices arising from the phylogenetic diversity measure on rooted phylogenetic trees. In this context, the diversity index score given to a species represents a measure of its unique and shared evolutionary history as displayed in the underlying phylogenetic tree. Our definition generalises the diversity index notion beyond the popular Fair Proportion and Equal-Splits indices. These particular indices may now be seen as two points in a convex space of possible diversity indices, for which the boundary conditions are determined by the underlying shape of each phylogenetic tree. We calculated the dimension of the convex space associated with each tree shape and described the extremal points.

evolutionary biology↗

bioRxiv2022

The expected loss of feature diversity (versus phylogenetic diversity) following rapid extinction at the present

The current rapid extinction of species leads not only to their loss but also the disappearance of the unique features they harbour, which have evolved along the branches of the underlying evolutionary tree. One proxy for estimating the feature diversity (FD) of a set S of species at the tips of a tree is phylogenetic diversity (PD): the sum of the branch lengths of the subtree connecting the species in S. For a phylogenetic tree that evolves under a standard birth-death process, and which is then subject to a sudden extinction event at the present (the simple field of bullets model with a survival probability of s per species) the proportion of the original PD that is retained after extinction at the present is known to converge quickly to a particular concave function{varphi} PD(s) as t grows. To investigate how the loss of FD mirrors the loss of PD for a birth-death tree, we model FD by assuming that distinct discrete features arise randomly and independently along the branches of the tree at rate r and are lost at a constant rate v. We derive an exact mathematical expression for the ratio{varphi} FD(s) of the two expected feature diversities (prior to and following an extinction event at the present) as t becomes large. We find that although{varphi} FD has a similar behaviour to{varphi} PD (and coincides with it for v = 0), when v > 0,{varphi} FD(s) is described by a function that is different from{varphi} PD(s). We also derive an exact expression for the expected number of features that are present in precisely one extant species. Our paper begins by establishing some generic properties of FD in a more general (non-phylogenetic) setting and applies this to fixed trees, before considering the setting of random (birth-death) trees.

evolutionary biology↗

bioRxiv2022

Information Accumulation and Loss as a Foundation for Sound Phylogenetic Biodiversity Metrics

AO_SCPLOWBSTRACTC_SCPLOWPhylogenetic metrics are essential tools used in the study of ecology, evolution and conservation. Phylogenetic diversity (PD) in particular is one of the most prominent measures of biodiversity, and is based on the idea that biological features accumulate along the edges of phylogenetic trees that are summed. We argue that PD and many other phylogenetic biodiversity metrics fail to capture an essential process that we term attrition. Attrition is the gradual loss of features through causes other than extinction. Here we introduce EvoHeritage, a generalisation of PD that is founded on the joint processes of accumulation and attrition of features. We argue that whilst PD measures evolutionary history, EvoHeritage is required to capture a more pertinent subset of evolutionary history including only components that have survived attrition. We show that EvoHeritage is not the same as PD on a tree with scaled edges; instead, accumulation and attrition interact in a more complex non-monophyletic way that cannot be captured by edge lengths alone. This leads us to speculate that the one dimensional edge lengths of classic trees may be insufficiently flexible to capture the nuances of evolutionary processes. We derive a measure of EvoHeritage and show that it elegantly reproduces species richness and PD at opposite ends of a continuum based on the intensity of attrition. We demonstrate the utility of EvoHeritage in ecology as a predictor of community productivity compared with species richness and PD. We also show how EvoHeritage can quantify living fossils and resolve their associated controversy. We suggest how the existing calculus of PD-based metrics and other phylogenetic biodiversity metrics can and should be recast in terms of EvoHeritage accumulation and attrition. Candidate cover image O_FIG O_LINKSMALLFIG WIDTH=186 HEIGHT=200 SRC="FIGDIR/small/499419v5_ufig1.gif" ALT="Figure 1"> View larger version (70K): org.highwire.dtl.DTLVardef@1a4b8cforg.highwire.dtl.DTLVardef@16145dborg.highwire.dtl.DTLVardef@1316b1eorg.highwire.dtl.DTLVardef@16fb06b_HPS_FORMAT_FIGEXP M_FIG C_FIG Artistic cover image prepared for this manuscript. The central tree depicts the gain and loss of Evolutionary Heritage (EvoHeritage) along each edge with its many coloured sections. EvoHeritage is proposed as an expansion of the concept of phylogenetic diversity. Around the outside of the tree are species that feature in our two practical applications of the EvoHeritage calculus: mammals identified as living fossils and plants included in our study of community productivity. The cover image was generated by James Rosin-dell following discussions with co-authors. The Caenolestes outline (representing shrew opossums) and Dromiciops outline (monito del monte) used as components of this image are credited to Sarah Werning and provided under a CC BY 3.0 license; both images were recoloured in brown and placed over a shaded circle. All other images used as components are from the public domain. We thank Mina Mincheva for useful feedback on earlier drafts of the cover image.

evolutionary biology↗

bioRxiv2022

EDGE2: advancing the prioritisation of threatened evolutionary history for conservation action

The global biodiversity crisis threatens the natural world and its capacity to provide benefits to humans into the future. The conservation of evolutionary history, captured by the measure phylogenetic diversity (PD), is linked to the maintenance of these benefits and future options. The Evolutionarily Distinct and Globally Endangered (EDGE) metric has, since 2007, been used to identify species for conservation action that embody large amounts of threatened evolutionary history. In 2017, we convened a workshop to update the EDGE metric to incorporate advances in the field of phylogenetically-informed conservation. Building on that workshop, we devised the metric EDGE2, which we present here. EDGE2 uses a modular, tiered approach to provide priority rankings--and associated measures of uncertainty in both phylogenetic and extinction risk data--for all species in a clade. EDGE2 takes into account the extinction risk of closely-related species to better reflect the contribution a species is expected to make to overall PD in the future. We applied EDGE2 to the worlds mammals to identify an updated list of priority EDGE species and compare the results with the original EDGE approach. Despite similarity in the priority lists produced between EDGE and EDGE2, EDGE2 places greater priority on species with fewer close relatives on the Tree of Life. As we approach a crossroads for global biodiversity policy, EDGE2 exemplifies how academic and applied conservation biologists can collaborate to guide effective priority-setting to conserve the most irreplaceable components of biodiversity upon which humanity depends.

zoology↗

bioRxiv2022

Gene Transfer based Phylogenetics: Analytical Expressions and Additivity via Birth/Death Theory

The genomic era has opened up vast opportunities in molecular systematics, one of which is deciphering the evolutionary history in fine detail. Under this mass of data, analysing the point mutations of standard markers is too crude and slow for fine-scale phylogenetics. Nevertheless, genome dynamics events provide far richer information. The synteny index (SI) between a pair of genomes combines gene order and gene content information, allowing the comparison of genomes of unequal gene content, together with order considerations of their common genes. Recently, genome dynamics has been modelled as a continuous-time Markov process, and gene distance in the genome as a birth-death-immigration process. Nevertheless, due to complexities arising in this setting such as overlapping neighbourhoods and other confounding factors, no precise and provably consistent estimators could be derived. Here, we extend this modelling approach by using techniques from birth-death theory to derive explicit expressions of the systems probabilistic dynamics in the form of rational functions of the model parameters. This, in turn, allows us to infer analytically the expected distances between organisms based on a transformation of their SI. Despite the complexity of the expressions obtained, we establish additivity of this estimated evolutionary distance (a desirable property yielding phylogenetic consistency). Applying the new measure in simulation studies shows that it attains very accurate results in realistic settings and even under model extensions. In the real-data realm, we applied the new formulation to unique data structure that we constructed - the ordered orthology DB - based on a new version of the EggNOG database, to construct a tree with more than 4.5K taxa. The resulted tree was compared it with a NCBI taxonomy for these organisms. To the best of our knowledge, this is the largest gene-order-based tree constructed and it overcomes flaws found in previous approaches.

evolutionary biology↗

bioRxiv2021

The probability of joint monophyly of all species in an arbitrary species tree.

Monophyly is a feature of a set of genetic lineages in which every lineage in the set is more closely related to all other members of the set than it is to any lineage outside the set. Multiple sets of lineages that are separately monophyletic are said to be reciprocally monophyletic, or jointly monophyletic. The prevalence of reciprocal monophyly, or joint monophyly, has been used to evaluate phylogenetic and phylogeographic hypotheses, as well as to delimit species. These applications often make use of a probability of joint monophyly under models of gene lineage evolution. Studies in coalescent theory have computed this joint monophyly probability for small numbers of separate groups in arbitrary species trees, and for arbitrary numbers of separate groups in trivial species trees. Here, generalizing existing results on monophyly probabilities under the multispecies coalescent, we derive the probability of joint monophyly for arbitrary numbers of separate groups in arbitrary species trees. We illustrate how our result collapses to previously examined cases. We also study the effect of tree height, sample size, and number of species on the probability of joint monophyly. The result also enables computation of relatively simple lower and upper bounds on the joint monophyly probability. Our results expand the scope of joint monophyly calculations beyond small numbers of species, subsuming past formulas that have been used in simpler cases.

evolutionary biology↗

bioRxiv2021

Predicting long pendant edges in model phylogenies, with applications to biodiversity and tree inference

AO_SCPLOWBSTRACTC_SCPLOWIn the simplest phylogenetic diversification model (the pure-birth Yule process), lineages split independently at a constant rate {lambda} for time t. The length of a randomly chosen edge (either interior or pendant) in the resulting tree has an expected value that rapidly converges to [Formula] as t grows, and thus is essentially independent of t. However, the behaviour of the length L of the longest pendant edge reveals remarkably different behaviour: L converges to t/2 as the expected number of leaves grows. Extending this model to allow an extinction rate (where < {lambda}), we also establish a similar result for birth-death trees, except that t/2 is replaced by t/2 {middle dot} (1 - /{lambda}). This complete tree may contain subtrees that have died out before time t; for the reduced tree that just involves the leaves present at time t and their direct ancestors, the longest pendant edge length L again converges to t/2. Thus, there is likely to be at least one extant species whose associated pendant branch attaches to the tree approximately half-way back in time to the origin of the entire clade. We also briefly consider the length of the shortest edges. Our results are relevant to phylogenetic diversity indices in biodiversity conservation, and to quantifying the length of aligned sequences required to correctly infer a tree. We compare our theoretical results with simulations, and with the branch lengths from a recent phylogenetic tree of all mammals.

evolutionary biology↗

bioRxiv2021

Accuracy in near-perfect virus phylogenies

AO_SCPLOWBSTRACTC_SCPLOWPhylogenetic trees from real-world data often include short edges with very few substitutions per site, which can lead to partially resolved trees and poor accuracy. Theory indicates that the number of sites needed to accurately reconstruct a fully resolved tree grows at a rate proportional to the inverse square of the length of the shortest edge. However, when inferred trees are partially resolved due to short edges, "accuracy" should be defined as the rate of discovering false splits (clades on a rooted tree) relative to the actual number found. Thus, accuracy can be high even if short edges are common. Specifically, in a "near-perfect" parameter space in which trees are large, the tree length{xi} (the sum of all edge lengths), is small, and rate variation is minimal, the expected false positive rate is less than{xi} /3; the exact value depends on tree shape and sequence length. This expected false positive rate is far below the false negative rate for small{xi} and often well below 5% even when some assumptions are relaxed. We show this result analytically for maximum parsimony and explore its extension to maximum likelihood using theory and simulations. For hypothesis testing, we show that measures of split "support" that rely on bootstrap resampling consistently imply weaker support than that implied by the false positive rates in near-perfect trees. The near-perfect parameter space closely fits several empirical studies of human virus diversification during outbreaks and epidemics, including Ebolavirus, Zika virus, and SARS-CoV-2, reflecting low substitution rates relative to high transmission/sampling rates in these viruses.

evolutionary biology↗

bioRxiv2021

Conditions under which distributions of edge length ratios on phylogenetic trees can be used to order evolutionary events

Two recent high profile studies have attempted to use edge (branch) length ratios from large sets of phylogenetic trees to determine the relative ages of genes of different origins in the evolution of eukaryotic cells. This approach can be straightforwardly justified if substitution rates are constant over the tree for a given protein. However, such strict molecular clock assumptions are not expected to hold on the billion-year timescale. Here we propose an alternative set of conditions under which comparisons of edge length distributions from multiple sets of phylogenies of proteins with different origins can be validly used to discern the order of their origins. We also point out scenarios where these conditions are not expected to hold and caution is warranted.

evolutionary biology↗

bioRxiv2020

Evolution Without Variation and Selection

Natural selection successfully explains how organisms accumulate adaptive change despite that traits acquired over a lifetime are eliminated at the end of each generation. However, in some domains that exhibit cumulative, adaptive change--e.g., cultural evolution, and earliest life--acquired traits are retained; these domains do not face the problem that Darwins theory was designed to solve. Lack of transmission of acquired traits occurs when germ cells are protected from environmental change, due to a self-assembly code used in two distinct ways: (i) actively interpreted during development to generate a soma, and (ii) passively copied without interpretation during reproduction to generate germ cells. Early life and cultural evolution appear not to involve a self-assembly code used in these two ways. We suggest that cumulative, adaptive change in these domains is due to a lower-fidelity evolutionary process, and model it using Reflexively Autocatalytic and Foodset-generated networks. We refer to this more primitive evolutionary process as Self-Other Reorganisation (SOR) because it involves internal self-organising and self-maintaining processes within entities, as well as interaction between entities. SOR encompasses learning but in general operates across groups. We discuss the relationship between SOR and Lamarckism, and illustrate a special case of SOR without variation.

evolutionary biology↗

bioRxiv2020

The structure of autocatalytic networks, with application to early biochemistry

Metabolism across all known living systems combines two key features. First, all of the molecules that are required are either available in the environment or can be built up from available resources via other reactions within the system. Second, the reactions proceed in a fast and synchronised fashion via catalysts that are also produced within the system. Building on early work by Stuart Kauffman, a precise mathematical model for describing such self-sustaining autocatalytic systems (RAF theory) has been developed to explore the origins and organisation of living systems within a general formal framework. In this paper, we develop this theory further by establishing new relationships between classes of RAFs and related classes of networks, and developing new algorithms to investigate and visualise RAF structures in detail. We illustrate our results by showing how it reveals further details into the structure of archaeal and bacterial metabolism near the origin of life, and provide techniques to study and visualise the core aspects of primitive biochemistry.

evolutionary biology↗

bioRxiv2020

Terraces in Gene Tree Reconciliation-Based Species Tree Inference

AO_SCPLOWBSTRACTC_SCPLOWTerraces in phylogenetic tree space are sets of trees with identical optimality scores for a given data set, arising from missing data. These were first described for multilocus phylogenetic data sets in the context of maximum parsimony inference and maximum likelihood inference under certain model assumptions. Here we show how the mathematical properties that lead to terraces extend to gene tree - species tree problems in which the gene trees are incomplete. Inference of species trees from either sets of gene family trees subject to duplication and loss, or allele trees subject to incomplete lineage sorting, can exhibit terraces in their solution space. First, we show conditions that lead to a new kind of terrace, which stems from subtree operations that appear in reconciliation problems for incomplete trees. Then we characterize when terraces of both types can occur when the optimality criterion for tree search is based on duplication, loss or deep coalescence scores. Finally, we examine the impact of assumptions about the causes of losses: whether they are due to imperfect sampling or true evolutionary deletion.

evolutionary biology↗

bioRxiv2020

Formal Links between Feature Diversity and Phylogenetic Diversity

AO_SCPLOWBSTRACTC_SCPLOWThe extent to which phylogenetic diversity (PD) captures feature diversity (FD) is a topical and controversial question in biodiversity conservation. In this short paper, we formalise this question and establish a precise mathematical condition for FD (based on discrete characters) to coincide with PD. In this way, we make explicit the two main reasons why the two diversity measures might disagree for given data; namely, the presence of certain patterns of feature evolution and loss, and using temporal branch lengths for PD in settings that may not be appropriate (e.g. due to rapid evolution of certain features over short periods of time). Our paper also explores the relationship between the Fair Proportion index of PD and a simple index of FD (both of which correspond to Shapley values in cooperative game theory). In a second mathematical result, we show that the two indices can take identical values for any phylogenetic tree, provided the branch lengths in the tree are chosen appropriately.

evolutionary biology↗

bioRxiv2019

Autocatalytic chemical networks preceded proteins and RNA in evolution

Modern cells embody metabolic networks containing thousands of elements and form autocatalytic molecule sets that produce copies of themselves. How the first self-sustaining metabolic networks arose at life s origin is a major open question. Autocatalytic molecule sets smaller than metabolic networks were proposed as transitory intermediates at the origin of life, but evidence for their role in prebiotic evolution is lacking. Here we identify reflexively autocatalytic food-generated networks (RAFs)--self-sustaining networks that collectively catalyze all their reactions--embedded within microbial metabolism. RAFs in the metabolism of ancient anaerobic autotrophs that live from H2 and CO2 generate amino acids and bases, the monomeric components of protein and RNA, and acetyl-CoA, but amino acids and bases do not generate metabolic RAFs, indicating that small-molecule catalysis preceded polymers in biochemical evolution. RAFs uncover intermediate stages in the origin of metabolic networks, narrowing the gaps between early-Earth chemistry and life.

evolutionary biology↗

bioRxiv2018

A Darwinian Uncertainty Principle

Reconstructing ancestral characters and traits along a phylogenetic tree is central to evolutionary biology. It is the key to understanding morphology changes among species, inferring ancestral biochemical properties of life, and recovering migration routes in phylogeography. The goal is twofold: to reconstruct the character state at the tree root (e.g. the region of origin of some species), and to understand the process of state changes along the tree (e.g. species flow between countries). Although each goal can be achieved with high accuracy individually, we use mathematics and simulations to demonstrate that it is generally impossible to accurately estimate both the root state and the rates of state changes along the tree branches from the observed data at the tips of the tree. This inherent Darwinian uncertainty principle concerning the simultaneous estimation of pattern and process governs ancestral reconstructions in biology. Increasing the number of tips improves the joint estimation accuracy for certain tree shapes that arise in evolutionary models, however, for other trees shapes it does not.

evolutionary biology↗