Neutral diversity in experimental metapopulations.

New automated and high-throughput methods allow the manipulation and selection of numerous bacterial populations. In this manuscript we are interested in the neutral diversity patterns that emerge from such a setup in which many bacterial populations are grown in parallel serial transfers, in some cases with population-wide extinction and splitting events. We model bacterial growth by a birth-death process and use the theory of coalescent point processes. We show that there is a dilution factor that optimises the expected amount of neutral diversity for a given number of cycles, and study the power law behaviour of the mutation frequency spectrum for different experimental regimes. We also explore how neutral variation diverges between two recently split populations by establishing a new formula for the expected number of shared and private mutations. Finally, we show the interest of such a setup to select a phenotype of interest that requires multiple mutations.

Interpreting the pervasive observation of U-shaped Site Frequency Spectra.

The standard neutral model of molecular evolution has traditionally been used as the null model for population genomics. We gathered a collection of 45 genome-wide site frequency spectra from a diverse set of species, most of which display an excess of low and high frequency variants compared to the expectation of the standard neutral model, resulting in U-shaped spectra. We show that multiple merger coalescent models often provide a better fit to these observations than the standard Kingman coalescent. Hence, in many circumstances these under-utilized models may serve as the more appropriate reference for genomic analyses. We further discuss the underlying evolutionary processes that may result in the widespread U-shape of frequency spectra.

Bottlenecks can constrain and channel evolutionary paths.

Population bottlenecks are commonplace in experimental evolution, specifically in serial passaging experiments where microbial populations alternate between growth and dilution. Natural populations also experience such fluctuations caused by seasonality, resource limitation, or host-to-host transmission for pathogens. Yet, how unlimited growth with periodic bottlenecks influence the adaptation of populations is not fully understood. Here, we study theoretically the effects of bottlenecks on the accessibility of evolutionary paths and on the rate of evolution. We model an asexual population evolving on a minimal fitness landscape consisting of two types of beneficial mutations with the empirically supported trade-off between mutation rate and fitness advantage, in the regime where multiple beneficial mutations may segregate simultaneously. In the limit of large population sizes and small mutation rates, we show the existence of a unique most likely evolutionary scenario, determined by the size of the wild-type population at the beginning and at the end of each cycle. These two key demographic parameters determine which adaptive paths may be taken by the evolving population by controlling the supply of mutants during growth and the loss of mutants at the bottleneck. We do not only show that bottlenecks act as a deterministic control of evolutionary paths but also that each possible evolutionary scenario can be forced to occur by tuning demographic parameters. This work unveils the effects of demography on adaptation of periodically bottlenecked populations and can guide the design of evolution experiments.

Evaluating cancer etiology and risk with a mathematical model of tumor evolution.

Recent evidence arising from DNA sequencing of healthy human tissues has clearly indicated that our organs accumulate a relevant number of somatic mutations due to normal endogenous mutational processes, in addition to those caused by environmental factors. A deeper understanding of the evolution of this endogenous mutational load is critical for understanding what causes cancer. Here we present a mathematical model of tumor evolution that is able to predict the expected number of endogenous somatic mutations present in various tissue types of a patient at a given age. These predictions are then compared to those observed in patients. We also obtain an improved fitting of the variation in cancer incidence across cancer types, showing that the endogenous mutational processes can explain 4/5 of the variation in cancer risk. Overall, these results offer key insights into cancer etiology, by providing further evidence for the major role these endogenous processes play in cancer.

From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics.

We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual's infection age, i.e., the time elapsed since infection, has three benefits. First, regardless of the number of types, the age distribution of the population can be described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick-von Foerster equation. The frequency of type i is simply obtained by integrating the probability of being in state i at a given age against the age distribution. This representation induces a simple methodology based on the additional assumption of Poisson sampling to infer and forecast the epidemic. We illustrate this technique using French data from the COVID-19 epidemic. Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ordinary differential equations (ODEs) to account for disease complexity. We show that such models can always be rewritten in our framework, thus, providing a low-dimensional yet equivalent representation of these complex models. Third, beyond the simplicity of the approach, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models, where the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual.

A Minimal yet Flexible Likelihood Framework to Assess Correlated Evolution.

An evolutionary process is reflected in the sequence of changes of any trait (e.g., morphological or molecular) through time. Yet, a better understanding of evolution would be procured by characterizing correlated evolution, or when two or more evolutionary processes interact. Previously developed parametric methods often require significant computing time as they rely on the estimation of many parameters. Here, we propose a minimal likelihood framework modeling the joint evolution of two traits on a known phylogenetic tree. The type and strength of correlated evolution are characterized by a few parameters tuning mutation rates of each trait and interdependencies between these rates. The framework can be applied to study any discrete trait or character ranging from nucleotide substitution to gain or loss of a biological function. More specifically, it can be used to 1) test for independence between two evolutionary processes, 2) identify the type of interaction between them, and 3) estimate parameter values of the most likely model of interaction. In the current implementation, the method takes as input a phylogenetic tree with discrete evolutionary events mapped on its branches. The method then maximizes the likelihood for one or several chosen scenarios. The strengths and limits of the method, as well as its relative power compared to a few other methods, are assessed using both simulations and data from 16S rRNA sequences in a sample of 54 $\gamma$-enterobacteria. We show that, even with data sets of fewer than 100 species, the method performs well in parameter estimation and in evolutionary model selection. [Correlated evolution; maximum likelihood; model.].

[Biochemical and statistical lessons from the evolution of the SARS-CoV-2 virus: paths for novel antiviral warfare]. / Leçons biochimiques et statistiques de l'évolution du virus SARS-CoV-2 : nouveaux chemins pour combattre les virus.

In the fight against the spread of COVID-19 the emphasis is on vaccination or on reactivating existing drugs used for other purposes. The tight links that necessarily exist between the virus as it multiplies and the metabolism of its host are systematically ignored. Here we show that the metabolism of all cells is coordinated by the availability of a core building block of the cell's genome, cytidine triphosphate (CTP). This metabolite is also the key to the synthesis of the viral envelope and to the translation of its genome into proteins. This unique role explains why evolution has led to the early emergence in animals of an antiviral immunity enzyme, viperin, that synthesizes a toxic analogue of CTP. The constraints arising from this dependency guide the evolution of the virus. With this in mind, we explored the real-time experiment taking place before our eyes using probabilistic modelling approaches to the molecular evolution of the virus. We have thus followed, almost on a daily basis, the evolution of the composition of the viral genome to link it to the progeny produced over time, particularly in the form of blooms that sparked a firework of viral mutations. Some of those certainly increase the propagation of the virus. This led us to make out the critical role in this evolution of several proteins of the virus, such as its nucleocapsid N, and more generally to begin to understand how the virus ties up the host metabolism to its own benefit. A way for the virus to escape CTP-dependent control in cells would be to infect cells that are not expected to grow, such as neurons. This may account for unexpected body sites of viral development in the present epidemic.

Dans la lutte contre la propagation de la COVID-19 l'accent est mis sur la vaccination, d'une part, et sur le redéploiement de traitements utilisés pour d'autres usages, d'autre part. Les liens qui existent nécessairement entre la multiplication du virus et le métabolisme de l'hôte sont systématiquement ignorés. Ici nous montrons que le métabolisme de toutes les cellules est coordonné par l'accessibilité d'un composant central du génome cellulaire, le triphosphate de cytidine (CTP). Ce métabolite est aussi la clé de la synthèse de l'enveloppe virale et de la traduction de son génome en protéines. Ce rôle unique explique pourquoi l'évolution a fait apparaître très tôt chez les animaux une activité enzymatique de l'immunité antivirale, la vipérine, destinée à synthétiser un analogue toxique du CTP. Les contraintes nées de cette dépendance orientent l'évolution du virus. Avec cette servitude à l'esprit, nous avons exploré l'expérience en vraie grandeur qui se déroule sous nos yeux au moyen d'approches de modélisation probabiliste de l'évolution moléculaire du virus. Nous avons ainsi suivi, presque au jour le jour, le devenir de la composition du génome viral pour la relier à la descendance produite au cours du temps, en particulier sous la forme d'efflorescences où apparaît un véritable feu d'artifice de mutations virales. Certaines d'entre elles augmentent certainement la propagation du virus. Cela nous conduit à proposer un rôle important dans cette évolution à certaines protéines du virus, comme celle de la nucléocapside N et plus généralement de commencer à comprendre comment le virus asservit à son bénéfice le métabolisme de l'hôte. L'un des moyens possibles pour le virus d'échapper au contrôle par le CTP serait d'infecter des cellules qui ne se multiplient pas, comme les neurones. Cela pourrait expliquer les sites de développement viral inattendus qu'on observe dans l'épidémie actuelle.

The genomic view of diversification.

The process of species diversification is traditionally summarized by a single tree, the species tree, whose reconstruction from molecular data is hindered by frequent conflicts between gene genealogies. Here, we argue that instead of seeing these conflicts as nuisances, we can exploit them to inform the diversification process itself. We adopt a gene-based view of diversification to model the ubiquitous presence of gene flow between diverging lineages, one of the most important processes explaining disagreements among gene trees. We propose a new framework for modelling the joint evolution of gene and species lineages relaxing the hierarchy between the species tree and gene trees inherent to the standard view, as embodied in a popular model known as the multispecies coalescent (MSC). We implement this framework in two alternative models called the gene-based diversification models (GBD): (a) GBD-forward following all evolving genomes through time and (b) GBD-backward based on coalescent theory. They feature four parameters tuning colonization, gene flow, genetic drift and genetic differentiation. We propose an inference method based on differences between gene trees. Applied to two empirical data sets prone to gene flow, we find better support for the GBD-backward model than for the MSC model. Along with the increasing awareness of the extent of gene flow, this work shows the importance of considering the richer signal contained in genomic histories, rather than in the mere species tree, to better apprehend the complex evolutionary history of species.

Eco-evolutionary dynamics of nested Darwinian populations and the emergence of community-level heredity.

Interactions among microbial cells can generate new chemistries and functions, but exploitation requires establishment of communities that reliably recapitulate community-level phenotypes. Using mechanistic mathematical models, we show how simple manipulations to population structure can exogenously impose Darwinian-like properties on communities. Such scaffolding causes communities to participate directly in the process of evolution by natural selection and drives the evolution of cell-level interactions to the point where, despite underlying stochasticity, derived communities give rise to offspring communities that faithfully re-establish parental phenotype. The mechanism is akin to a developmental process (developmental correction) that arises from density-dependent interactions among cells. Knowledge of ecological factors affecting evolution of developmental correction has implications for understanding the evolutionary origin of major egalitarian transitions, symbioses, and for top-down engineering of microbial communities.

Model-Based Inference of Punctuated Molecular Evolution.

In standard models of molecular evolution, DNA sequences evolve through asynchronous substitutions according to Poisson processes with a constant rate (called the molecular clock) or a rate that can vary (relaxed clock). However, DNA sequences can also undergo episodes of fast divergence that will appear as synchronous substitutions affecting several sites simultaneously at the macroevolutionary timescale. Here, we develop a model, which we call the Relaxed Clock with Spikes model, combining basal, clock-like molecular substitutions with episodes of fast divergence called spikes arising at speciation events. Given a multiple sequence alignment and its time-calibrated species phylogeny, our model is able to detect speciation events (including hidden ones) cooccurring with spike events and to estimate the probability and amplitude of these spikes on the phylogeny. We identify the conditions under which spikes can be distinguished from the natural variance of the clock-like component of molecular substitutions and from variations of the clock. We apply the method to genes underlying snake venom proteins and identify several spikes at gene-specific locations in the phylogeny. This work should pave the way for analyses relying on whole genomes to inform on modes of species diversification.

Testing for population decline using maximal linkage disequilibrium blocks.

Only 6% of known species have a conservation status. Methods that assess conservation statuses are often based on individual counts and are thus too laborious to be generalized to all species. Population genomics methods that infer past variations in population size are easy to use but limited to the relatively distant past. Here we propose a population genomics approach that tests for recent population decline and may be used to assess species conservation statuses. More specifically, we study Maximal Recombination Free (MRF) blocks, that are segments of a sequence alignment inherited from a common ancestor without recombination. MRF blocks are relatively longer in small than in large populations. We use the distribution of MRF block lengths rescaled by their mean to test for recent population decline. However, because MRF blocks are difficult to detect, we also consider Maximal Linkage Disequilibrium (MLD) blocks, which are runs of single nucleotide polymorphisms compatible with a single tree. We develop a new method capable of inferring a very recent decline (e.g. with a detection power of 50% for populations whose size was halved to N, 0.05 ×N generations ago) from rescaled MLD block lengths. Our framework could serve as a basis for quantitative tools to assess conservation status in a wide range of species.

The Price equation and evolutionary epidemiology.

The Price equation has found widespread application in many areas of evolutionary biology, including the evolutionary epidemiology of infectious diseases. In this paper, we illustrate the utility of this approach to modelling disease evolution by first deriving a version of Price's equation that can be applied in continuous time and to populations with overlapping generations. We then show how this version of Price's equation provides an alternative perspective on pathogen evolution by considering the epidemiological meaning of each of its terms. Finally, we extend these results to the case where population size is small and generates demographic stochasticity. We show that the particular partitioning of evolutionary change given by Price's equation is also a natural way to partition the evolutionary consequences of demographic stochasticity, and demonstrate how such stochasticity tends to weaken selection on birth rate (e.g. the transmission rate of an infectious disease) and enhance selection on mortality rate (e.g. factors, like virulence, that cause the end of an infection). In the long term, if there is a trade-off between virulence and transmission across parasite strains, the weaker selection on transmission and stronger selection on virulence that arises from demographic stochasticity will tend to drive the evolution of lower levels of virulence. This article is part of the theme issue 'Fifty years of the Price equation'.

Population persistence under high mutation rate: From evolutionary rescue to lethal mutagenesis.

Populations may genetically adapt to severe stress that would otherwise cause their extirpation. Recent theoretical work, combining stochastic demography with Fisher's geometric model of adaptation, has shown how evolutionary rescue becomes unlikely beyond some critical intensity of stress. Increasing mutation rates may however allow adaptation to more intense stress, raising concerns about the effectiveness of treatments against pathogens. This previous work assumes that populations are rescued by the rise of a single resistance mutation. However, even in asexual organisms, rescue can also stem from the accumulation of multiple mutations in a single genome. Here, we extend previous work to study the rescue process in an asexual population where the mutation rate is sufficiently high so that such events may be common. We predict both the ultimate extinction probability of the population and the distribution of extinction times. We compare the accuracy of different approximations covering a large range of mutation rates. Moderate increase in mutation rates favors evolutionary rescue. However, larger increase leads to extinction by the accumulation of a large mutation load, a process called lethal mutagenesis. We discuss how these results could help design "evolution-proof" antipathogen treatments that even highly mutable strains could not overcome.

The Species Problem from the Modeler's Point of View.

How to define a partition of individuals into species is a long-standing question called the species problem in systematics. Here, we focus on this problem in the thought experiment where individuals reproduce clonally and both the differentiation process and the population genealogies are explicitly known. We specify three desirable properties of species partitions: (A) Heterotypy between species, (B) Homotypy within species and (M) Genealogical monophyly of each species. We then ask: How and when is it possible to delineate species in a way satisfying these properties? We point out that the three desirable properties cannot in general be satisfied simultaneously, but that any two of them can. We mathematically prove the existence of the finest partition satisfying (A) and (M) and the coarsest partition satisfying (B) and (M). For each of them, we propose a simple algorithm to build the associated phylogeny out of the genealogy. The ways we propose to phrase the species problem shed new light on the interaction between the genealogical and phylogenetic scales in modeling work. The two definitions centered on the monophyly property can readily be used at a higher taxonomic level as well, e.g., to cluster species into monophyletic genera.

Pathogen evolution in finite populations: slow and steady spreads the best.

The theory of life-history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens. It assumes, however, that host populations are large and that one can neglect the effects of demographic stochasticity. Here, we expand the theory to account for the effects of finite population size on the evolution of pathogen virulence. We show that demographic stochasticity introduces additional evolutionary forces that can qualitatively affect the dynamics and the evolutionary outcome. We discuss the importance of the shape of the pathogen fitness landscape on the balance between mutation, selection and genetic drift. This analysis reconciles Adaptive Dynamics with population genetics in finite populations and provides a new theoretical toolbox to study life-history evolution in realistic ecological scenarios.

Clade diversification dynamics and the biotic and abiotic controls of speciation and extinction rates.

How ecological interactions, genetic processes, and environmental variability jointly shape the evolution of species diversity remains a challenging problem in biology. We developed an individual-based model of clade diversification to predict macroevolutionary dynamics when resource competition, genetic differentiation, and landscape fluctuations interact. Diversification begins with a phase of geographic adaptive radiation. Extinction rates rise sharply at the onset of the next phase. In this phase of niche self-structuring, speciation and extinction processes, albeit driven by biotic mechanisms (competition and hybridization), have essentially constant rates, determined primarily by the abiotic pace of landscape dynamics. The final phase of diversification begins when intense competition prevents dispersing individuals from establishing new populations. Species' ranges shrink, causing negative diversity-dependence of speciation rates. These results show how ecological and microevolutionary processes shape macroevolutionary dynamics and rates; they caution against the notion of ecological limits to diversity, and suggest new directions for the phylogenetic analysis of diversification.

Ranked Tree Shapes, Nonrandom Extinctions, and the Loss of Phylogenetic Diversity.

Phylogenetic diversity (PD) is a measure of the evolutionary legacy of a group of species, which can be used to define conservation priorities. It has been shown that an important loss of species diversity can sometimes lead to a much less important loss of PD, depending on the topology of the species tree and on the distribution of its branch lengths. However, the rate of decrease of PD strongly depends on the relative depths of the nodes in the tree and on the order in which species become extinct. We introduce a new, sampling-consistent, three-parameter model generating random trees with covarying topology, clades relative depths, and clades relative extinction risks. This model can be seen as an extension to Aldous' one parameter splitting model ($\beta$, which controls for tree balance) with two additional parameters: a new parameter $\alpha$ quantifying the relation between age and richness of subclades, and a parameter $\eta$ quantifying the relation between relative abundance and richness of subclades, taken herein as a proxy for overall extinction risk. We show on simulated phylogenies that loss of PD depends on the combined effect of all three parameters, $\beta$, $\alpha,$ and $\eta$. In particular, PD may decrease as fast as species diversity when high extinction risks are clustered within small, old clades, corresponding to a parameter range that we term the "danger zone" ($\beta<-1$ or $\alpha<0$; $\eta>1$). Besides, when high extinction risks are clustered within large clades, the loss of PD can be higher in trees that are more balanced ($\beta>0$), in contrast to the predictions of earlier studies based on simpler models. We propose a Monte-Carlo algorithm, tested on simulated data, to infer all three parameters. Applying it to a real data set comprising 120 bird clades (class Aves) with known range sizes, we show that parameter estimates precisely fall close to the danger zone: the combination of their ranking tree shape and nonrandom extinctions risks makes them prone to a sudden collapse of PD.

The coalescent of a sample from a binary branching process.

At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth-death process. Stop this process at time T>0. It is known that the tree spanned by the N tips alive at time T of the tree thus obtained (called a reduced tree or coalescent tree) is a coalescent point process (CPP), which basically means that the depths of interior nodes are independent and identically distributed (iid). Now select each of the N tips independently with probability y (Bernoulli sample). It is known that the tree generated by the selected tips, which we will call the Bernoulli sampled CPP, is again a CPP. Now instead, select exactly k tips uniformly at random among the N tips (a k-sample). We show that the tree generated by the selected tips is a mixture of Bernoulli sampled CPPs with the same parent CPP, over some explicit distribution of the sampling probability y. An immediate consequence is that the genealogy of a k-sample can be obtained by the realization of k random variables, first the random sampling probability Y and then the k-1 node depths which are iid conditional on Y=y.

Accuracy of Demographic Inferences from the Site Frequency Spectrum: The Case of the Yoruba Population.

Some methods for demographic inference based on the observed genetic diversity of current populations rely on the use of summary statistics such as the Site Frequency Spectrum (SFS). Demographic models can be either model-constrained with numerous parameters, such as growth rates, timing of demographic events, and migration rates, or model-flexible, with an unbounded collection of piecewise constant sizes. It is still debated whether demographic histories can be accurately inferred based on the SFS. Here, we illustrate this theoretical issue on an example of demographic inference for an African population. The SFS of the Yoruba population (data from the 1000 Genomes Project) is fit to a simple model of population growth described with a single parameter (e.g., founding time). We infer a time to the most recent common ancestor of 1.7 million years (MY) for this population. However, we show that the Yoruba SFS is not informative enough to discriminate between several different models of growth. We also show that for such simple demographies, the fit of one-parameter models outperforms the stairway plot, a recently developed model-flexible method. The use of this method on simulated data suggests that it is biased by the noise intrinsically present in the data.