Self-generating autocatalytic networks: structural results, algorithms and their relevance to early biochemistry.

The concept of an autocatalytic network of reactions that can form and persist, starting from just an available food source, has been formalized 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 article, 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 also focus on the structure and analysis of minimal RAFs and derive structural results and polynomial-time algorithms. We then apply these new methods to a large metabolic network to gain insights into possible biochemical scenarios near the origin of life.

Phylogenetic network classes through the lens of expanding covers.

It was recently shown that a large class of phylogenetic networks, the 'labellable' networks, is in bijection with the set of 'expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks can be characterised purely in terms of properties of their associated covers. These classes include the tree-based, tree-child, orchard, tree-sibling, and normal networks. In the opposite direction, we give an example of how a restriction on the set of expanding covers can define a new class of networks, which we call 'spinal' phylogenetic networks.

Phylogenetic Biodiversity Metrics Should Account for Both Accumulation and Attrition of Evolutionary Heritage.

Phylogenetic 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 generalization of PD that is founded on the joint processes of accumulation and attrition of features. We argue that while 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.

Interior Operators and Their Relationship to Autocatalytic Networks.

The emergence of an autocatalytic network from an available set of elements is a fundamental step in early evolutionary processes, such as the origin of metabolism. Given the set of elements, the reactions between them (chemical or otherwise), and with various elements catalysing certain reactions, a Reflexively Autocatalytic F-generated (RAF) set is a subset R[Formula: see text] of reactions that is self-generating from a given food set, and with each reaction in R[Formula: see text] being catalysed from within R[Formula: see text]. RAF theory has been applied to various phenomena in theoretical biology, and a key feature of the approach is that it is possible to efficiently identify and classify RAFs within large systems. This is possible because RAFs can be described as the (nonempty) subsets of the reactions that are the fixed points of an (efficiently computable) interior map that operates on subsets of reactions. Although the main generic results concerning RAFs can be derived using just this property, we show that for systems with at least 12 reactions there are generic results concerning RAFs that cannot be proven using the interior operator property alone.Kindly check and confirm the edit made in the title.I confirm that the edit is fine.

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, analyzing the point mutations of standard markers is often too crude and slow for fine-scale phylogenetics. Nevertheless, genome dynamics (GD) events provide alternative, often 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 modeled 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, no precise and provably consistent estimators could be derived, resulting in heuristic solutions. Here, we extend this modeling approach by using techniques from birth-death theory to derive explicit expressions of the system's probabilistic dynamics in the form of rational functions of the model parameters. This, in turn, allows us to infer analytically accurate distances between organisms based on their SI. Subsequently, we establish additivity of this estimated evolutionary distance (a desirable property yielding phylogenetic consistency). Applying the new measure in simulation studies shows that it provides accurate results in realistic settings and even under model extensions such as gene gain/loss or over a tree structure. 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. To the best of our knowledge, this is the largest gene-order-based tree constructed and it overcomes shortcomings found in previous approaches. Constructing a GD-based tree allows to confirm and contrast findings based on other phylogenetic approaches, as we show.

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 [Formula: see text] 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 [Formula: see text]. We derive an exact mathematical expression for the ratio [Formula: see text] of the two expected feature diversities (prior to and following an extinction event at the present) as t becomes large. We find that although [Formula: see text] has a similar behaviour to [Formula: see text] (and coincides with it for [Formula: see text]), when [Formula: see text], [Formula: see text] is described by a function that is different from [Formula: see text]. 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.

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.

Labellable Phylogenetic Networks.

Phylogenetic 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.

The EDGE2 protocol: Advancing the prioritisation of Evolutionarily Distinct and Globally Endangered species for practical conservation action.

The conservation of evolutionary history has been linked to increased benefits for humanity and can be captured by phylogenetic diversity (PD). The Evolutionarily Distinct and Globally Endangered (EDGE) metric has, since 2007, been used to prioritise threatened species for practical conservation that embody large amounts of evolutionary history. While there have been important research advances since 2007, they have not been adopted in practice because of a lack of consensus in the conservation community. Here, building from an interdisciplinary workshop to update the existing EDGE approach, we present an "EDGE2" protocol that draws on a decade of research and innovation to develop an improved, consistent methodology for prioritising species conservation efforts. Key advances include methods for dealing with uncertainty and accounting for the extinction risk of closely related species. We describe EDGE2 in terms of distinct components to facilitate future revisions to its constituent parts without needing to reconsider the whole. We illustrate EDGE2 by applying it to the world's mammals. As we approach a crossroads for global biodiversity policy, this Consensus View shows how collaboration between academic and applied conservation biologists can guide effective and practical priority-setting to conserve biodiversity.

Predicting Long Pendant Edges in Model Phylogenies, with Applications to Biodiversity and Tree Inference.

In 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 $\frac{1}{2\lambda}$ as $t$ grows and thus is essentially independent of $t$. However, the behavior of the length $L$ of the longest pendant edge reveals remarkably different behavior: $L$ converges to $t/2$ as the expected number of leaves grows. Extending this model to allow an extinction rate $\mu$ (where $\mu<\lambda$), we also establish a similar result for birth-death trees, except that $t/2$ is replaced by $t/2 \cdot (1-\mu/\lambda)$. 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. [Birth-death process; phylogenetic diversification models; phylogenetic diversity.].

Autocatalytic Sets Arising in a Combinatorial Model of Chemical Evolution.

The idea that chemical evolution led to the origin of life is not new, but still leaves open the question of how exactly it could have led to a coherent and self-reproducing collective of molecules. One possible answer to this question was proposed in the form of the emergence of an autocatalytic set: a collection of molecules that mutually catalyze each other's formation and that is self-sustaining given some basic "food" source. Building on previous work, here we investigate in more detail when and how autocatalytic sets can arise in a simple model of chemical evolution based on the idea of combinatorial innovation with random catalysis assignments. We derive theoretical results, and compare them with computer simulations. These results could suggest a possible step towards the (or an) origin of life.

Counting and optimising maximum phylogenetic diversity sets.

In conservation biology, phylogenetic diversity (PD) provides a way to quantify the impact of the current rapid extinction of species on the evolutionary 'Tree of Life'. This approach recognises that extinction not only removes species but also the branches of the tree on which unique features shared by the extinct species arose. In this paper, we investigate three questions that are relevant to PD. The first asks how many sets of species of given size k preserve the maximum possible amount of PD in a given tree. The number of such maximum PD sets can be very large, even for moderate-sized phylogenies. We provide a combinatorial characterisation of maximum PD sets, focusing on the setting where the branch lengths are ultrametric (e.g. proportional to time). This leads to a polynomial-time algorithm for calculating the number of maximum PD sets of size k by applying a generating function; we also investigate the types of tree shapes that harbour the most (or fewest) maximum PD sets of size k. Our second question concerns optimising a linear function on the species (regarded as leaves of the phylogenetic tree) across all the maximum PD sets of a given size. Using the characterisation result from the first question, we show how this optimisation problem can be solved in polynomial time, even though the number of maximum PD sets can grow exponentially. Our third question considers a dual problem: If k species were to become extinct, then what is the largest possible loss of PD in the resulting tree? For this question, we describe a polynomial-time solution based on dynamical programming.

The Probability of Joint Monophyly of Samples of Gene Lineages for 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 (JM), has been used to evaluate phylogenetic and phylogeographic hypotheses, as well as to delimit species. These applications often make use of a probability of JM under models of gene lineage evolution. Studies in coalescent theory have computed this JM probability for small numbers of separate groups in arbitrary species trees and for arbitrary numbers of separate groups in trivial species trees. In this study, generalizing existing results on monophyly probabilities under the multispecies coalescent, we derive the probability of JM 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 JM. We obtain relatively simple lower and upper bounds on the JM probability. Our results expand the scope of JM calculations beyond small numbers of species, subsuming past formulas that have been used in simpler cases.

Combined Histo-endoscopic Remission but not Endoscopic Healing Alone in Ulcerative Colitis is Associated with a Mucosal Transcriptional Profile Resembling Healthy Mucosa.

BACKGROUND AND AIMS: A composite endpoint of histological and endoscopic remission is proposed to be the most complete measure of mucosal healing in ulcerative colitis [UC]. We aim to establish the prognosis, and transcriptional and microbial features of histo-endoscopic remission and activity. METHODS: A cross-sectional endoscopic rectosigmoid colon sample collection from UC patients and healthy controls [HC] was performed for histopathology and host genome-wide RNA-sequencing. Histo-endoscopic remission and histo-endoscopic activity were defined as Mayo endoscopic subscore [MES] 0-1 with and without histological activity, respectively. UC relapse, defined as symptomatic and endoscopic worsening, was retrospectively recorded for survival analysis. Unsupervised and differential gene expression analyses were performed, and the interaction between transcriptomics and mucosal gut microbiota was analysed based on the 16S rRNA gene sequencing profile. RESULTS: UC patients with histo-endoscopic remission showed a significantly lower risk of relapse compared to histo-endoscopic activity. Unsupervised analysis of the transcriptomic profile showed that histo-endoscopic remission and histo-endoscopic activity samples clustered with HC and MES 2-3 samples, respectively. A total of 452 host genes enriched for humoral immune response, antimicrobial defence, chemokine and TH17 signalling pathway were upregulated in histo-endoscopic activity compared to histo-endoscopic remission. A set of host genes with antimicrobial properties showed significant associations with mucosal microbiota. CONCLUSIONS: The rectosigmoid mucosa transcriptional profile of UC patients in histo-endoscopic remission resembles that of HC mucosa and confers a lower risk of relapse. These data support that the combination of histo-endoscopic remission could be the most appropriate definition of mucosal healing in UC.

Accuracy in Near-Perfect Virus Phylogenies.

Phylogenetic 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.[Ebolavirus; epidemic; HIV; homoplasy; mumps virus; perfect phylogeny; SARS-CoV-2; virus; West Nile virus; Yule-Harding model; Zika virus.].

An Autocatalytic Network Model of Conceptual Change.

In reflexively autocatalytic foodset (RAF)-generated networks, nodes are not only passive transmitters of activation, but they also actively galvanize, or "catalyze" the synthesis of novel ("foodset-derived") nodes from existing ones (the "foodset"). Thus, RAFs are uniquely suited to modeling how new structure grows out of currently available structure, and analyzing phase transitions in potentially very large networks. RAFs have been used to model the origins of evolutionary processes, both biological (the origin of life) and cultural (the origin of cumulative innovation), and may potentially provide an overarching framework that integrates evolutionary and developmental approaches to cognition. Applied to cognition, the foodset consists of information obtained through social learning or individual learning of pre-existing information, and foodset-derived items arise through mental operations resulting in new information. Thus, mental representations are not only propagators of spreading activation, but they also trigger the derivation of new mental representations. To illustrate the application of RAF networks in cognitive science, we develop a step-by-step process model of conceptual change (i.e., the process by which a child becomes an active participant in cultural evolution), focusing on childrens' mental models of the shape of the Earth. Using results from (Vosniadou & Brewer, 1992), we model different trajectories from the flat Earth model to the spherical Earth model, as well as the impact of other factors, such as pretend play, on cognitive development. As RAFs increase in size and number, they begin to merge, bridging previously compartmentalized knowledge, and get subsumed by a giant RAF (the maxRAF) that constrains and enables the scaffolding of new conceptual structure. At this point, the cognitive network becomes self-sustaining and self-organizing. The child can reliably frame new knowledge and experiences in terms of previous ones, and engage in recursive representational redescription and abstract thought. We suggest that individual differences in the reactivity of mental representations, that is, their proclivity to trigger conceptual change, culminate in different cognitive networks and concomitant learning trajectories.

The Expected Number of Viable Autocatalytic Sets in Chemical Reaction Systems.

The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modeling how living systems first arose. It has been known for several decades that such networks will form within systems of polymers (under cleavage and ligation reactions) under a simple process of random catalysis, and this process has since been mathematically analyzed. In this paper, we provide an exact expression for the expected number of self-sustaining autocatalytic networks that will form in a general chemical reaction system, and the expected number of these networks that will also be uninhibited (by some molecule produced by the system). Using these equations, we are able to describe the patterns of catalysis and inhibition that maximize or minimize the expected number of such networks. We apply our results to derive a general theorem concerning the trade-off between catalysis and inhibition, and to provide some insight into the extent to which the expected number of self-sustaining autocatalytic networks coincides with the probability that at least one such system is present.

An evolutionary process 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 Darwin's 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 reorganization (SOR) because it involves internal self-organizing 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.

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.

Normalising phylogenetic networks.

Rooted phylogenetic networks provide a way to describe species' relationships when evolution departs from the simple model of a tree. However, networks inferred from genomic data can be highly tangled, making it difficult to discern the main reticulation signals present. In this paper, we describe a natural way to transform any rooted phylogenetic network into a simpler canonical network, which has desirable mathematical and computational properties, and is based only on the 'visible' vertices in the original network. The method has been implemented and we demonstrate its application to some examples.