The fixation probability of beneficial mutations

Complex vaccination strategies prevent the emergence of vaccine resistance

Vaccination is the most effective tool to control infectious diseases. However, the evolution of vaccine resistance, exemplified by vaccine resistance in SARS-CoV-2, remains a concern. Here, we model complex vaccination strategies against a pathogen with multiple epitopes-molecules targeted by the vaccine. We found that a vaccine targeting one epitope was ineffective in preventing vaccine escape. Vaccine resistance in highly infectious pathogens was prevented by the full-epitope vaccine, that is, one targeting all available epitopes, but only when the rate of pathogen evolution was low. Strikingly, a bet-hedging strategy of random administration of vaccines targeting different epitopes was the most effective in preventing vaccine resistance in pathogens with the low rate of infection and high rate of evolution. Thus, complex vaccination strategies, when biologically feasible, may be preferable to the currently used single-vaccine approaches for long-term control of disease outbreaks, especially when applied to livestock with near 100% vaccination rates.

Multiple distinct evolutionary mechanisms govern the dynamics of selfish mitochondrial genomes in Caenorhabditis elegans

Cells possess multiple mitochondrial DNA (mtDNA) copies, which undergo semi-autonomous replication and stochastic inheritance. This enables mutant mtDNA variants to arise and selfishly compete with cooperative (wildtype) mtDNA. Selfish mitochondrial genomes are subject to selection at different levels: they compete against wildtype mtDNA directly within hosts and indirectly through organism-level selection. However, determining the relative contributions of selection at different levels has proven challenging. We overcome this challenge by combining mathematical modeling with experiments designed to isolate the levels of selection. Applying this approach to many selfish mitochondrial genotypes in Caenorhabditis elegans reveals an unexpected diversity of evolutionary mechanisms. Some mutant genomes persist at high frequency for many generations, despite a host fitness cost, by aggressively outcompeting cooperative genomes within hosts. Conversely, some mutant genomes persist by evading inter-organismal selection. Strikingly, the mutant genomes vary dramatically in their susceptibility to genetic drift. Although different mechanisms can cause high frequency of selfish mtDNA, we show how they give rise to characteristically different distributions of mutant frequency among individuals. Given that heteroplasmic frequency represents a key determinant of phenotypic severity, this work outlines an evolutionary theoretic framework for predicting the distribution of phenotypic consequences among individuals carrying a selfish mitochondrial genome.

Correlated evolution of conspicuous colouration and burrowing in crayfish

Conspicuous colours have fascinated biologists for centuries, leading to research on the evolution and functional significance of colour traits. In many cases, research suggests that conspicuous colours are adaptive and serve a function in sexual or aposematic signalling. In other cases, a lack of evidence for the adaptive value of conspicuous colours garners interest from biologists, such as when organisms that live underground and are rarely exposed to the surface are nevertheless colourful. Here, we use phylogenetic comparative methods to investigate colour evolution throughout freshwater crayfishes that vary in burrowing ability. Within the taxa we analysed, conspicuous colours have evolved independently over 50 times, and these colours are more common in semi-terrestrial crayfishes that construct extensive burrows. The intuitive but not evolutionarily justified assumption when presented with these results is to assume that these colours are adaptive. But contrary to this intuition, we discuss the hypothesis that colouration in crayfish is neutral. Supporting these ideas, the small population sizes and reduced gene flow within semi-terrestrial burrowing crayfishes may lead to the fixation of colour-phenotype mutations. Overall, our work brings into question the traditional view of animal colouration as a perfectly adapted phenotype.

Sweepstakes reproduction facilitates rapid adaptation in highly fecund populations

Adaptation enables natural populations to survive in a changing environment. Understanding the mechanics of adaptation is therefore crucial for learning about the evolution and ecology of natural populations. We focus on the impact of random sweepstakes on selection in highly fecund haploid and diploid populations partitioned into two genetic types, with one type conferring selective advantage. For the diploid populations, we incorporate various dominance mechanisms. We assume that the populations may experience recurrent bottlenecks. In random sweepstakes, the distribution of individual recruitment success is highly skewed, resulting in a huge variance in the number of offspring contributed by the individuals present in any given generation. Using computer simulations, we investigate the joint effects of random sweepstakes, recurrent bottlenecks and dominance mechanisms on selection. In our framework, bottlenecks allow random sweepstakes to have an effect on the time to fixation, and in diploid populations, the effect of random sweepstakes depends on the dominance mechanism. We describe selective sweepstakes that are approximated by recurrent sweeps of strongly beneficial allelic types arising by mutation. We demonstrate that both types of sweepstakes reproduction may facilitate rapid adaptation (as defined based on the average time to fixation of a type conferring selective advantage conditioned on fixation of the type). However, whether random sweepstakes cause rapid adaptation depends also on their interactions with bottlenecks and dominance mechanisms. Finally, we review a case study in which a model of recurrent sweeps is shown to essentially explain population genomic data from Atlantic cod.

Developmental hematopoietic stem cell variation explains clonal hematopoiesis later in life

Clonal hematopoiesis becomes increasingly common with age, but its cause is enigmatic because driver mutations are often absent. Serial observations infer weak selection indicating variants are acquired much earlier in life with unexplained initial growth spurts. Here we use fluctuating CpG methylation as a lineage marker to track stem cell clonal dynamics of hematopoiesis. We show, via the shared prenatal circulation of monozygotic twins, that weak selection conferred by stem cell variation created before birth can reliably yield clonal hematopoiesis later in life. Theory indicates weak selection will lead to dominance given enough time and large enough population sizes. Human hematopoiesis satisfies both these conditions. Stochastic loss of weakly selected variants is naturally prevented by the expansion of stem cell lineages during development. The dominance of stem cell clones created before birth is supported by blood fluctuating CpG methylation patterns that exhibit low correlation between unrelated individuals but are highly correlated between many elderly monozygotic twins. Therefore, clonal hematopoiesis driven by weak selection in later life appears to reflect variation created before birth.

Frequent, infinitesimal bottlenecks maximize the rate of microbial adaptation

Serial passaging is a fundamental technique in experimental evolution. The choice of bottleneck severity and frequency poses a dilemma: longer growth periods allow beneficial mutants to arise and grow over more generations, but simultaneously necessitate more severe bottlenecks with a higher risk of those same mutations being lost. Short growth periods require less severe bottlenecks, but come at the cost of less time between transfers for beneficial mutations to establish. The standard laboratory protocol of 24-h growth cycles with severe bottlenecking has logistical advantages for the experimenter but limited theoretical justification. Here we demonstrate that contrary to standard practice, the rate of adaptive evolution is maximized when bottlenecks are frequent and small, indeed infinitesimally so in the limit of continuous culture. This result derives from revising key assumptions underpinning previous theoretical work, notably changing the metric of optimization from adaptation per serial transfer to per experiment runtime. We also show that adding resource constraints and clonal interference to the model leaves the qualitative results unchanged. Implementing these findings will require liquid-handling robots to perform frequent bottlenecks, or chemostats for continuous culture. Further innovation in and adoption of these technologies has the potential to accelerate the rate of discovery in experimental evolution.

Evolutionary rescue on genotypic fitness landscapes

Populations facing adverse environments, novel pathogens or invasive competitors may be destined to extinction if they are unable to adapt rapidly. Quantitative predictions of the probability of survival through adaptation, evolutionary rescue, have been previously developed for one of the most natural and well-studied mappings from an organism's traits to its fitness, Fisher's geometric model (FGM). While FGM assumes that all possible trait values are accessible via mutation, in many applications only a finite set of rescue mutations will be available, such as mutations conferring resistance to a parasite, predator or toxin. We predict the probability of evolutionary rescue, via de novo mutation, when this underlying genetic structure is included. We find that rescue probability is always reduced when its genetic basis is taken into account. Unlike other known features of the genotypic FGM, however, the probability of rescue increases monotonically with the number of available mutations and approaches the behaviour of the classical FGM as the number of available mutations approaches infinity.

Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance

There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behaviour leading to the coexistence of resistant and sensitive cells in large populations and static environments. This picture is, however, greatly altered by the fluctuations arising in volatile environments, in which microbial communities commonly evolve. Here, we study the eco-evolutionary dynamics of a population consisting of an antimicrobial-resistant strain and microbes sensitive to antimicrobial drugs in a time-fluctuating environment, modelled by a carrying capacity randomly switching between states of abundance and scarcity. We assume that antimicrobial resistance (AMR) is a shared public good when the number of resistant cells exceeds a certain threshold. Eco-evolutionary dynamics is thus characterised by demographic noise (birth and death events) coupled to environmental fluctuations which can cause population bottlenecks. By combining analytical and computational means, we determine the environmental conditions for the long-lived coexistence and fixation of both strains, and characterise a fluctuation-driven AMR eradication mechanism, where resistant microbes experience bottlenecks leading to extinction. We also discuss the possible applications of our findings to laboratory-controlled experiments.

Symmetry in models of natural selection

Symmetry arguments are frequently used-often implicitly-in mathematical modelling of natural selection. Symmetry simplifies the analysis of models and reduces the number of distinct population states to be considered. Here, I introduce a formal definition of symmetry in mathematical models of natural selection. This definition applies to a broad class of models that satisfy a minimal set of assumptions, using a framework developed in previous works. In this framework, population structure is represented by a set of sites at which alleles can live, and transitions occur via replacement of some alleles by copies of others. A symmetry is defined as a permutation of sites that preserves probabilities of replacement and mutation. The symmetries of a given selection process form a group, which acts on population states in a way that preserves the Markov chain representing selection. Applying classical results on group actions, I formally characterize the use of symmetry to reduce the states of this Markov chain, and obtain bounds on the number of states in the reduced chain.

Mutant fixation in the presence of a natural enemy

The literature about mutant invasion and fixation typically assumes populations to exist in isolation from their ecosystem. Yet, populations are part of ecological communities, and enemy-victim (e.g. predator-prey or pathogen-host) interactions are particularly common. We use spatially explicit, computational pathogen-host models (with wild-type and mutant hosts) to re-visit the established theory about mutant fixation, where the pathogen equally attacks both wild-type and mutant individuals. Mutant fitness is assumed to be unrelated to infection. We find that pathogen presence substantially weakens selection, increasing the fixation probability of disadvantageous mutants and decreasing it for advantageous mutants. The magnitude of the effect rises with the infection rate. This occurs because infection induces spatial structures, where mutant and wild-type individuals are mostly spatially separated. Thus, instead of mutant and wild-type individuals competing with each other, it is mutant and wild-type "patches" that compete, resulting in smaller fitness differences and weakened selection. This implies that the deleterious mutant burden in natural populations might be higher than expected from traditional theory.

Mutation and Selection Induce Correlations between Selection Coefficients and Mutation Rates

AbstractThe joint distribution of selection coefficients and mutation rates is a key determinant of the genetic architecture of molecular adaptation. Three different distributions are of immediate interest: (1) the "nominal" distribution of possible changes, prior to mutation or selection; (2) the "de novo" distribution of realized mutations; and (3) the "fixed" distribution of selectively established mutations. Here, we formally characterize the relationships between these joint distributions under the strong-selection/weak-mutation (SSWM) regime. The de novo distribution is enriched relative to the nominal distribution for the highest rate mutations, and the fixed distribution is further enriched for the most highly beneficial mutations. Whereas mutation rates and selection coefficients are often assumed to be uncorrelated, we show that even with no correlation in the nominal distribution, the resulting de novo and fixed distributions can have correlations with any combination of signs. Nonetheless, we suggest that natural systems with a finite number of beneficial mutations will frequently have the kind of nominal distribution that induces negative correlations in the fixed distribution. We apply our mathematical framework, along with population simulations, to explore joint distributions of selection coefficients and mutation rates from deep mutational scanning and cancer informatics. Finally, we consider the evolutionary implications of these joint distributions together with two additional joint distributions relevant to parallelism and the rate of adaptation.

Universality of evolutionary trajectories under arbitrary forms of self-limitation and competition

The assumption of constant population size is central in population genetics. It led to a large body of results that is robust to modeling choices and that has proven successful to understand evolutionary dynamics. In reality, allele frequencies and population size are both determined by the interaction between a population and the environment. Relaxing the constant-population assumption has two big drawbacks. It increases the technical difficulty of the analysis, and it requires specifying a mechanism for the saturation of the population size, possibly making the results contingent on model details. Here we develop a framework that encompasses a great variety of systems with an arbitrary mechanism for population growth limitation. By using techniques based on scale separation for stochastic processes, we are able to calculate analytically properties of evolutionary trajectories, such as the fixation probability. Remarkably, these properties assume a universal form with respect to our framework, which depends on only three parameters related to the intergeneration timescale, the invasion fitness, and the carrying capacity of the strains. In other words, different systems, such as Lotka-Volterra or a chemostat model (contained in our framework), share the same evolutionary outcomes after a proper remapping of their parameters. An important and surprising consequence of our results is that the direction of selection can be inverted, with a population evolving to reach lower values of invasion fitness.

Self-loops in evolutionary graph theory: Friends or foes?

Evolutionary dynamics in spatially structured populations has been studied for a long time. More recently, the focus has been to construct structures that amplify selection by fixing beneficial mutations with higher probability than the well-mixed population and lower probability of fixation for deleterious mutations. It has been shown that for a structure to substantially amplify selection, self-loops are necessary when mutants appear predominately in nodes that change often. As a result, for low mutation rates, self-looped amplifiers attain higher steady-state average fitness in the mutation-selection balance than well-mixed populations. But what happens when the mutation rate increases such that fixation probabilities alone no longer describe the dynamics? We show that self-loops effects are detrimental outside the low mutation rate regime. In the intermediate and high mutation rate regime, amplifiers of selection attain lower steady-state average fitness than the complete graph and suppressors of selection. We also provide an estimate of the mutation rate beyond which the mutation-selection dynamics on a graph deviates from the weak mutation rate approximation. It involves computing average fixation time scaling with respect to the population sizes for several graphs.

Segregational drift hinders the evolution of antibiotic resistance on polyploid replicons

The emergence of antibiotic resistance under treatment depends on the availability of resistance alleles and their establishment in the population. Novel resistance alleles are encoded either in chromosomal or extrachromosomal genetic elements; both types may be present in multiple copies within the cell. However, the effect of polyploidy on the emergence of antibiotic resistance remains understudied. Here we show that the establishment of resistance alleles in microbial populations depends on the ploidy level. Evolving bacterial populations under selection for antibiotic resistance, we demonstrate that resistance alleles in polyploid elements are lost frequently in comparison to alleles in monoploid elements due to segregational drift. Integrating the experiments with a mathematical model, we find a remarkable agreement between the theoretical and empirical results, confirming our understanding of the allele segregation process. Using the mathematical model, we further show that the effect of polyploidy on the establishment probability of beneficial alleles is strongest for low replicon copy numbers and plateaus for high replicon copy numbers. Our results suggest that the distribution of fitness effects for mutations that are eventually fixed in a population depends on the replicon ploidy level. Our study indicates that the emergence of antibiotic resistance in bacterial pathogens depends on the pathogen ploidy level.

Quantifying stochastic establishment of mutants in microbial adaptation

Studies of microbial evolution, especially in applied contexts, have focused on the role of selection in shaping predictable, adaptive responses to the environment. However, chance events - the appearance of novel genetic variants and their establishment, i.e. outgrowth from a single cell to a sizeable population - also play critical initiating roles in adaptation. Stochasticity in establishment has received little attention in microbiology, potentially due to lack of awareness as well as practical challenges in quantification. However, methods for high-replicate culturing, mutant labelling and detection, and statistical inference now make it feasible to experimentally quantify the establishment probability of specific adaptive genotypes. I review methods that have emerged over the past decade, including experimental design and mathematical formulas to estimate establishment probability from data. Quantifying establishment in further biological settings and comparing empirical estimates to theoretical predictions represent exciting future directions. More broadly, recognition that adaptive genotypes may be stochastically lost while rare is significant both for interpreting common lab assays and for designing interventions to promote or inhibit microbial evolution.

Categorizing update mechanisms for graph-structured metapopulations

The structure of a population strongly influences its evolutionary dynamics. In various settings ranging from biology to social systems, individuals tend to interact more often with those present in their proximity and rarely with those far away. A common approach to model the structure of a population is evolutionary graph theory. In this framework, each graph node is occupied by a reproducing individual. The links connect these individuals to their neighbours. The offspring can be placed on neighbouring nodes, replacing the neighbours-or the progeny of its neighbours can replace a node during the course of ongoing evolutionary dynamics. Extending this theory by replacing single individuals with subpopulations at nodes yields a graph-structured metapopulation. The dynamics between the different local subpopulations is set by an update mechanism. There are many such update mechanisms. Here, we classify update mechanisms for structured metapopulations, which allows to find commonalities between past work and illustrate directions for further research and current gaps of investigation.

The role of migration in mutant dynamics in fragmented populations

Mutant dynamics in fragmented populations have been studied extensively in evolutionary biology. Yet, open questions remain, both experimentally and theoretically. Some of the fundamental properties predicted by models still need to be addressed experimentally. We contribute to this by using a combination of experiments and theory to investigate the role of migration in mutant distribution. In the case of neutral mutants, while the mean frequency of mutants is not influenced by migration, the probability distribution is. To address this empirically, we performed in vitro experiments, where mixtures of GFP-labelled ("mutant") and non-labelled ("wid-type") murine cells were grown in wells (demes), and migration was mimicked via cell transfer from well to well. In the presence of migration, we observed a change in the skewedness of the distribution of the mutant frequencies in the wells, consistent with previous and our own model predictions. In the presence of de novo mutant production, we used modelling to investigate the level at which disadvantageous mutants are predicted to exist, which has implications for the adaptive potential of the population in case of an environmental change. In panmictic populations, disadvantageous mutants can persist around a steady state, determined by the rate of mutant production and the selective disadvantage (selection-mutation balance). In a fragmented system that consists of demes connected by migration, a steady-state persistence of disadvantageous mutants is also observed, which, however, is fundamentally different from the mutation-selection balance and characterized by higher mutant levels. The increase in mutant frequencies above the selection-mutation balance can be maintained in small ( N < N c ) demes as long as the migration rate is sufficiently small. The migration rate above which the mutants approach the selection-mutation balance decays exponentially with N / N c . The observed increase in the mutant numbers is not explained by the change in the effective population size. Implications for evolutionary processes in diseases are discussed, where the pre-existence of disadvantageous drug-resistant mutant cells or pathogens drives the response of the disease to treatments.

Genome interpretation using in silico predictors of variant impact

Estimating the effects of variants found in disease driver genes opens the door to personalized therapeutic opportunities. Clinical associations and laboratory experiments can only characterize a tiny fraction of all the available variants, leaving the majority as variants of unknown significance (VUS). In silico methods bridge this gap by providing instant estimates on a large scale, most often based on the numerous genetic differences between species. Despite concerns that these methods may lack reliability in individual subjects, their numerous practical applications over cohorts suggest they are already helpful and have a role to play in genome interpretation when used at the proper scale and context. In this review, we aim to gain insights into the training and validation of these variant effect predicting methods and illustrate representative types of experimental and clinical applications. Objective performance assessments using various datasets that are not yet published indicate the strengths and limitations of each method. These show that cautious use of in silico variant impact predictors is essential for addressing genome interpretation challenges.

Laws of Spatially Structured Population Dynamics on a Lattice

We consider spatial population dynamics on a lattice, following a type of a contact (birth–death) stochastic process. We show that simple mathematical approximations for the density of cells can be obtained in a variety of scenarios. In the case of a homogeneous cell population, we derive the cellular density for a two-dimensional (2D) spatial lattice with an arbitrary number of neighbors, including the von Neumann, Moore, and hexagonal lattice.are not allowed in the abstract, please move them to the main text, please remember to check the order of references in the full text after revision. We then turn our attention to evolutionary dynamics, where mutant cells of different properties can be generated. For disadvantageous mutants, we derive an approximation for the equilibrium density representing the selection–mutation balance. For neutral and advantageous mutants, we show that simple scaling (power) laws for the numbers of mutants in expanding populations hold in 2D and 3D, under both flat (planar) and range population expansion. These models have relevance for studies in ecology and evolutionary biology, as well as biomedical applications including the dynamics of drug-resistant mutants in cancer and bacterial biofilms.

Stochastic establishment of β-lactam-resistant Escherichia coli mutants reveals conditions for collective resistance

For antibiotic resistance to arise, new resistant mutants must establish in a bacterial population before they can spread via natural selection. Comprehending the stochastic factors that influence mutant establishment is crucial for a quantitative understanding of antibiotic resistance emergence. Here, we quantify the single-cell establishment probability of four Escherichia coli strains expressing β-lactamase alleles with different activity against the antibiotic cefotaxime, as a function of antibiotic concentration in both unstructured (liquid) and structured (agar) environments. We show that concentrations well below the minimum inhibitory concentration (MIC) can substantially hamper establishment, particularly for highly resistant mutants. While the pattern of establishment suppression is comparable in both tested environments, we find greater variability in establishment probability on agar. Using a simple branching model, we investigate possible sources of this stochasticity, including environment-dependent lineage variability, but cannot reject other possible causes. Lastly, we use the single-cell establishment probability to predict each strain's MIC in the absence of social interactions. We observe substantially higher measured than predicted MIC values, particularly for highly resistant strains, which indicates cooperative effects among resistant cells at large cell numbers, such as in standard MIC assays.

Martingales and the fixation time of evolutionary graphs with arbitrary dimensionality

Evolutionary graph theory (EGT) investigates the Moran birth-death process constrained by graphs. Its two principal goals are to find the fixation probability and time for some initial population of mutants on the graph. The fixation probability of graphs has received considerable attention. Less is known about the distribution of fixation time. We derive clean, exact expressions for the full conditional characteristic functions (CCFs) of a close proxy to fixation and extinction times. That proxy is the number of times that the mutant population size changes before fixation or extinction. We derive these CCFs from a product martingale that we identify for an evolutionary graph with any number of partitions. The existence of that martingale only requires that the connections between those partitions are of a certain type. Our results are the first expressions for the CCFs of any proxy to fixation time on a graph with any number of partitions. The parameter dependence of our CCFs is explicit, so we can explore how they depend on graph structure. Martingales are a powerful approach to study principal problems of EGT. Their applicability is invariant to the number of partitions in a graph, so we can study entire families of graphs simultaneously.

OPTIMAL CONTROL OF GENETIC DIVERSITY IN THE MORAN MODEL WITH POPULATION GROWTH

In the Moran model of drift and selection of a mutant allele with population growth, instead of examining the consequences of pre-specified selection and population growth, the coexistence of the wild allele and the mutant allele becomes the maximization of the expected sojourn time in a given set. The process is controlled by the additional mortality of the mutant and by population growth. This makes it possible to retroactively assign fitness values as functions of the constraints, thus guiding a conservation policy or the achievement of a wishful proportion of mutants. This also gives the optimal conditions that have allowed an observed coexistence.

Gene surfing of underdominant alleles promotes formation of hybrid zones

The distribution of genetic diversity over geographical space has long been investigated in population genetics and serves as a useful tool to understand evolution and history of populations. Within some species or across regions of contact between two species, there are instances where there is no apparent ecological determinant of sharp changes in allele frequencies or divergence. To further understand these patterns of spatial genetic structure and potential species divergence, we model the establishment of clines that occur due to the surfing of underdominant alleles during range expansions. We provide analytical approximations for the fixation probability of underdominant alleles at expansion fronts and demonstrate that gene surfing can lead to clines in one-dimensional range expansions. We extend these results to multiple loci via a mixture of analytical theory and individual-based simulations. We study the interaction between the strength of selection against heterozygotes, migration rates, and local recombination rates on the formation of stable hybrid zones. Clines created by surfing at different loci can attract each other and align after expansion, if they are sufficiently close in space and in terms of recombination distance. Our findings suggest that range expansions can set the stage for parapatric speciation due to the alignment of multiple selective clines, even in the absence of ecologically divergent selection. This article is part of the theme issue 'Species' ranges in the face of changing environments (part I)'.

Selection on the gametophyte: Modeling alternation of generations in plants

PREMISE

The degree of gametophyte dependence on the sporophyte life stage is a major feature that differentiates the life cycles of land plants, yet the evolutionary consequences of this difference remain poorly understood. Most evolutionary models assume organisms are either haploid or diploid for their entire lifespan, which is not appropriate for simulating plant life cycles. Here, we introduce shadie (Simulating Haploid-Diploid Evolution), a new, simple Python program for implementing simulations with biphasic life cycles and analyzing their results, using SLiM 3 as a simulation back end.

METHODS

We implemented evolutionary simulations under three realistic plant life cycle models supported in shadie, using either standardized or biologically realistic parameter settings to test how variation in plant life cycles and sexual systems affects patterns of genome diversity.

RESULTS

The dynamics of single beneficial mutation fixation did not vary dramatically between different models, but the patterns of spatial variation did differ, demonstrating that different life histories and model parameters affect both genetic diversity and linkage disequilibrium. The rate of linkage disequilibrium decay away from selected sites varied depending on model parameters such as cloning and selfing rates, through their impact on effective population sizes.

DISCUSSION

Evolutionary simulations are an exciting, underutilized approach in evolutionary research and education. shadie can aid plant researchers in developing null hypotheses, examining theory, and designing empirical studies, in order to investigate the role of the gametophyte life stage, and the effects of variation in plant life cycles, on plant genome evolution.

Haldane's formula in Cannings models: the case of moderately strong selection

For a class of Cannings models we prove Haldane’s formula, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi (s_N) \sim \frac{2s_N}{\rho ^2}$$\end{document}π(sN)∼2sNρ2, for the fixation probability of a single beneficial mutant in the limit of large population size N and in the regime of moderately strong selection, i.e. for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_N \sim N^{-b}$$\end{document}sN∼N-b and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0< b<1/2$$\end{document}0<b<1/2. Here, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_N$$\end{document}sN is the selective advantage of an individual carrying the beneficial type, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho ^2$$\end{document}ρ2 is the (asymptotic) offspring variance. Our assumptions on the reproduction mechanism allow for a coupling of the beneficial allele’s frequency process with slightly supercritical Galton–Watson processes in the early phase of fixation.

Maximum levels of cross-contamination for 24 antimicrobial active substances in non-target feed. Part 1: Methodology, general data gaps and uncertainties

The European Commission requested EFSA to assess, in collaboration with EMA, the specific concentrations of antimicrobials resulting from cross-contamination in non-target feed for food-producing animals below which there would not be an effect on the emergence of, and/or selection for, resistance in microbial agents relevant for human and animal health, as well as the levels of the antimicrobials which could have a growth promotion/increase yield effect. The assessment was performed for 24 antimicrobial active substances, as specified in the mandate. This scientific opinion describes the methodology used, and the main associated data gaps and uncertainties. To estimate the antimicrobial levels in the non-target feed that would not result in emergence of, and/or selection for, resistance, a model was developed. This 'Feed Antimicrobial Resistance Selection Concentration' (FARSC) model is based on the minimal selective concentration (MSC), or the predicted MSC (PMSC) if MSC for the most susceptible bacterial species is unavailable, the fraction of antimicrobial dose available for exposure to microorganisms in the large intestine or rumen (considering pharmacokinetic parameters), the daily faecal output or rumen volume and the daily feed intake. Currently, lack of data prevents the establishment of PMSC and/or FARSC for several antimicrobials and animal species. To address growth promotion, data from an extensive literature search were used. Specific assessments of the different substances grouped by antimicrobial classes are addressed in separate scientific opinions. General conclusions and recommendations were made.

Antibiotic Breakdown by Susceptible Bacteria Enhances the Establishment of β-Lactam Resistant Mutants

For a better understanding of the evolution of antibiotic resistance, it is imperative to study the factors that determine the initial establishment of mutant resistance alleles. In addition to the antibiotic concentration, the establishment of resistance alleles may be affected by interactions with the surrounding susceptible cells from which they derive, for instance via the release of nutrients or removal of the antibiotic. Here, we investigate the effects of social interactions with surrounding susceptible cells on the establishment of Escherichia coli mutants with increasing β-lactamase activity (i.e., the capacity to hydrolyze β-lactam antibiotics) from single cells under the exposure of the antibiotic cefotaxime (CTX) on agar plates. We find that relatively susceptible cells, expressing a β-lactamase with very low antibiotic-hydrolyzing activity, increase the probability of mutant cells to survive and outgrow into colonies due to the active breakdown of the antibiotic. However, the rate of breakdown by the susceptible strain is much higher than expected based on its low enzymatic activity. A detailed theoretical model suggests that this observation may be explained by cell filamentation causing delayed lysis. While susceptible cells may hamper the spread of higher-resistant β-lactamase mutants at relatively high frequencies, our findings show that they promote their initial establishment.

Viral transmission and evolution dynamics of SARS-CoV-2 in shipboard quarantine

OBJECTIVE

To examine transmission and evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in shipboard quarantine of the Diamond Princess cruise ship.

METHODS

We obtained the full SARS-CoV-2 genome sequences of 28 samples from the Global Initiative on Sharing All Influenza Data database. The samples were collected between 10 and 25 February 2020 and came for individuals who had been tested for SARS-CoV-2 during the quarantine on the cruise ship. These samples were later sequenced in either Japan or the United States of America. We analysed evolution dynamics of SARS-CoV-2 using computational tools of phylogenetics, natural selection pressure and genetic linkage.

FINDINGS

The SARS-CoV-2 outbreak in the cruise most likely originated from either a single person infected with a virus variant identical to the WIV04 isolates, or simultaneously with another primary case infected with a virus containing the 11083G > T mutation. We identified a total of 24 new viral mutations across 64.2% (18/28) of samples, and the virus evolved into at least five subgroups. Increased positive selection of SARS-CoV-2 were statistically significant during the quarantine (Tajima's D: -2.03, P < 0.01; Fu and Li's D: -2.66, P < 0.01; and Zeng's E: -2.37, P < 0.01). Linkage disequilibrium analysis confirmed that ribonucleic acid (RNA) recombination with the11083G > T mutation also contributed to the increase of mutations among the viral progeny.

CONCLUSION

The findings indicate that the 11083G > T mutation of SARS-CoV-2 spread during shipboard quarantine and arose through de novo RNA recombination under positive selection pressure.

Effects of synonymous mutations beyond codon bias: The evidence for adaptive synonymous substitutions from microbial evolution experiments

Synonymous mutations are often assumed to be neutral with respect to fitness because they do not alter the encoded amino acid and so cannot be 'seen' by natural selection. Yet a growing body of evidence suggests that synonymous mutations can have fitness effects that drive adaptive evolution through their impacts on gene expression and protein folding. Here, we review what microbial experiments have taught us about the contribution of synonymous mutations to adaptation. A survey of site-directed mutagenesis experiments reveals the distributions of fitness effects for nonsynonymous and synonymous mutations are more similar, especially for beneficial mutations, than expected if all synonymous mutations were neutral, suggesting they should drive adaptive evolution more often than is typically observed. A review of experimental evolution studies where synonymous mutations have contributed to adaptation shows they can impact fitness through a range of mechanisms including the creation of illicit RNA polymerase binding sites impacting transcription and changes to mRNA folding stability that modulate translation. We suggest that clonal interference in evolving microbial populations may be the reason synonymous mutations play a smaller role in adaptive evolution than expected based on their observed fitness effects. We finish by discussing the impacts of falsely assuming synonymous mutations are neutral and discuss directions for future work exploring the role of synonymous mutations in adaptive evolution.

Understanding evolutionary and ecological dynamics using a continuum limit

Continuum limits in the form of stochastic differential equations are typically used in theoretical population genetics to account for genetic drift or more generally, inherent randomness of the model. In evolutionary game theory and theoretical ecology, however, this method is used less frequently to study demographic stochasticity. Here, we review the use of continuum limits in ecology and evolution. Starting with an individual-based model, we derive a large population size limit, a (stochastic) differential equation which is called continuum limit. By example of the Wright-Fisher diffusion, we outline how to compute the stationary distribution, the fixation probability of a certain type, and the mean extinction time using the continuum limit. In the context of the logistic growth equation, we approximate the quasi-stationary distribution in a finite population.

Modeling the selective advantage of new amino acids on the hemagglutinin of H1N1 influenza viruses using their patient age distributions

In 2009, a new strain of H1N1 influenza A virus caused a pandemic, and its descendant strains are causing seasonal epidemics worldwide. Given the high mutation rate of influenza viruses, variant strains having different amino acids on hemagglutinin (HA) continuously emerge. To prepare vaccine strains for the next influenza seasons, it is an urgent task to predict which variants will be selected in the viral population. An analysis of 24,681 pairs of an amino acid sequence of HA of H1N1pdm2009 viruses and its patient age showed that the empirical fixation probability of new amino acids on HA significantly differed depending on their frequencies in the population, patient age distributions, and epitope flags. The selective advantage of a variant strain having a new amino acid was modeled by linear combinations of patients age distributions and epitope flags, and then the fixation probability of the new amino acid was modeled using Kimura’s formula for advantageous selection. The parameters of models were estimated from the sequence data and models were tested with four-fold cross validations. The frequency of new amino acids alone can achieve high sensitivity, specificity, and precision in predicting the fixation of a new amino acid of which frequency is more than 0.11. The estimated parameter suggested that viruses with a new amino acid having a frequency in the population higher than 0.11 have a significantly higher selective advantage compared to viruses with the old amino acid at the same position. The model considering the Z-value of patient age rank-sums of new amino acids predicted amino acid substitutions on HA with a sensitivity of 0.78, specificity of 0.86, and precision of 0.83, showing significant improvement compared to the constant selective advantage model, which used only the frequency of the amino acid. These results suggested that H1N1 viruses tend to be selected in the adult population, and frequency of viruses having new amino acids and their patient ages are useful to predict amino acid substitutions on HA.

Concerns about SARS-CoV-2 evolution should not hold back efforts to expand vaccination

When vaccines are in limited supply, expanding the number of people who receive some vaccine, such as by halving doses or increasing the interval between doses, can reduce disease and mortality compared with concentrating available vaccine doses in a subset of the population. A corollary of such dose-sparing strategies is that the vaccinated individuals may have less protective immunity. Concerns have been raised that expanding the fraction of the population with partial immunity to SARS-CoV-2 could increase selection for vaccine-escape variants, ultimately undermining vaccine effectiveness. We argue that, although this is possible, preliminary evidence instead suggests such strategies should slow the rate of viral escape from vaccine or naturally induced immunity. As long as vaccination provides some protection against escape variants, the corresponding reduction in prevalence and incidence should reduce the rate at which new variants are generated and the speed of adaptation. Because there is little evidence of efficient immune selection of SARS-CoV-2 during typical infections, these population-level effects are likely to dominate vaccine-induced evolution.

Genetic Context Significantly Influences the Maintenance and Evolution of Degenerate Pathways

Understanding the evolution of novel physiological traits is highly relevant for expanding the characterization and manipulation of biological systems. Acquisition of new traits can be achieved through horizontal gene transfer (HGT). Here, we investigate drivers that promote or deter the maintenance of HGT-driven degeneracy, occurring when processes accomplish identical functions through nonidentical components. Subsequent evolution can optimize newly acquired functions; for example, beneficial alleles identified in an engineered Methylorubrum extorquens strain allowed it to utilize a “Foreign” formaldehyde oxidation pathway substituted for its Native pathway for methylotrophic growth. We examined the fitness consequences of interactions between these alleles when they were combined with the Native pathway or both (Dual) pathways. Unlike the Foreign pathway context where they evolved, these alleles were often neutral or deleterious when moved into these alternative genetic backgrounds. However, there were instances where combinations of multiple alleles resulted in higher fitness outcomes than individual allelic substitutions could provide. Importantly, the genetic context accompanying these allelic substitutions significantly altered the fitness landscape, shifting local fitness peaks and restricting the set of accessible evolutionary trajectories. These findings highlight how genetic context can negatively impact the probability of maintaining native and HGT-introduced functions together, making it difficult for degeneracy to evolve. However, in cases where the cost of maintaining degeneracy was mitigated by adding evolved alleles impacting the function of these pathways, we observed rare opportunities for pathway coevolution to occur. Together, our results highlight the importance of genetic context and resulting epistasis in retaining or losing HGT-acquired degenerate functions.

Evolutionary graph theory derived from eco-evolutionary dynamics

A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The evolutionary graph theory model, which considers evolutionary dynamics only, is derived as a special case, highlighting additional assumptions that diverge from real biological processes. This is achieved by introducing a negative ecological feedback loop that suppresses ecological dynamics by forcing births and deaths to be coupled. We also investigate how fitness, a measure of reproductive success used in evolutionary graph theory, is related to the life-history of individuals in terms of their birth and death rates. In simple networks, these ecologically motivated dynamics are used to provide new insight into the spread of adaptive mutations, both with and without clonal interference. For example, the star network, which is known to be an amplifier of selection in evolutionary graph theory, can inhibit the spread of adaptive mutations when individuals can die naturally.

Fixation probabilities in evolutionary dynamics under weak selection

In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as it depends on the mutation's effect on the organism as well as the population's spatial structure, mating patterns, and other factors. In this study, we consider weak selection, which means that the mutation's effect on the organism is small. We obtain a weak-selection perturbation expansion of a mutant's fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which the size and spatial structure are arbitrary (but fixed). The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We conclude by applying these methods to obtain new results for evolutionary dynamics on graphs.

The population genetics of ploidy change in unicellular fungi

Changes in ploidy are a significant type of genetic variation, describing the number of chromosome sets per cell. Ploidy evolves in natural populations, clinical populations, and lab experiments, particularly in fungi. Despite a long history of theoretical work on this topic, predicting how ploidy will evolve has proven difficult, as it is often unclear why one ploidy state outperforms another. Here, we review what is known about contemporary ploidy evolution in diverse fungal species through the lens of population genetics. As with typical genetic variants, ploidy evolution depends on the rate that new ploidy states arise by mutation, natural selection on alternative ploidy states, and random genetic drift. However, ploidy variation also has unique impacts on evolution, with the potential to alter chromosomal stability, the rate and patterns of point mutation, and the nature of selection on all loci in the genome. We discuss how ploidy evolution depends on these general and unique factors and highlight areas where additional experimental evidence is required to comprehensively explain the ploidy transitions observed in the field and the lab.

Rapid parallel adaptation despite gene flow in silent crickets

Gene flow is predicted to impede parallel adaptation via de novo mutation, because it can introduce pre-existing adaptive alleles from population to population. We test this using Hawaiian crickets (Teleogryllus oceanicus) in which 'flatwing' males that lack sound-producing wing structures recently arose and spread under selection from an acoustically-orienting parasitoid. Morphometric and genetic comparisons identify distinct flatwing phenotypes in populations on three islands, localized to different loci. Nevertheless, we detect strong, recent and ongoing gene flow among the populations. Using genome scans and gene expression analysis we find that parallel evolution of flatwing on different islands is associated with shared genomic hotspots of adaptation that contain the gene doublesex, but the form of selection differs among islands and corresponds to known flatwing demographics in the wild. We thus show how parallel adaptation can occur on contemporary timescales despite gene flow, indicating that it could be less constrained than previously appreciated.

Adapt or Perish: Evolutionary Rescue in a Gradually Deteriorating Environment

We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can survive only if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime.

Mutant Evolution in Spatially Structured and Fragmented Expanding Populations

Mutant evolution in spatially structured systems is important for a range of biological systems, but aspects of it still require further elucidation. Adding to previous work, we provide a simple derivation of growth laws that characterize the number of mutants of different relative fitness in expanding populations in spatial models of different dimensionalities. These laws are universal and independent of "microscopic" modeling details. We further study the accumulation of mutants and find that, with advantageous and neutral mutants, more of them are present in spatially structured, compared to well-mixed colonies of the same size. The behavior of disadvantageous mutants is subtle: if they are disadvantageous through a reduction in division rates, the result is the same, and it is the opposite if the disadvantage is due to a death rate increase. Finally, we show that in all cases, the same results are observed in fragmented, nonspatial patch models. This suggests that the patterns observed are the consequence of population fragmentation, and not spatial restrictions per se We provide an intuitive explanation for the complex dependence of disadvantageous mutant evolution on spatial restriction, which relies on desynchronized dynamics in different locations/patches, and plays out differently depending on whether the disadvantage is due to a lower division rate or a higher death rate. Implications for specific biological systems, such as the evolution of drug-resistant cell mutants in cancer or bacterial biofilms, are discussed.

Stochastic bacterial population dynamics restrict the establishment of antibiotic resistance from single cells

A better understanding of how antibiotic exposure impacts the evolution of resistance in bacterial populations is crucial for designing more sustainable treatment strategies. The conventional approach to this question is to measure the range of concentrations over which resistant strain(s) are selectively favored over a sensitive strain. Here, we instead investigate how antibiotic concentration impacts the initial establishment of resistance from single cells, mimicking the clonal expansion of a resistant lineage following mutation or horizontal gene transfer. Using two Pseudomonas aeruginosa strains carrying resistance plasmids, we show that single resistant cells have <5% probability of detectable outgrowth at antibiotic concentrations as low as one-eighth of the resistant strain's minimum inhibitory concentration (MIC). This low probability of establishment is due to detrimental effects of antibiotics on resistant cells, coupled with the inherently stochastic nature of cell division and death on the single-cell level, which leads to loss of many nascent resistant lineages. Our findings suggest that moderate doses of antibiotics, well below the MIC of resistant strains, may effectively restrict de novo emergence of resistance even though they cannot clear already-large resistant populations.

Evolutionary Rescue and Drug Resistance on Multicopy Plasmids

Bacteria often carry "extra DNA" in the form of plasmids in addition to their chromosome. Many plasmids have a copy number greater than one such that the genes encoded on these plasmids are present in multiple copies per cell. This has evolutionary consequences by increasing the mutational target size, by prompting the (transitory) co-occurrence of mutant and wild-type alleles within the same cell, and by allowing for gene dosage effects. We develop and analyze a mathematical model for bacterial adaptation to harsh environmental change if adaptation is driven by beneficial alleles on multicopy plasmids. Successful adaptation depends on the availability of advantageous alleles and on their establishment probability. The establishment process involves the segregation of mutant and wild-type plasmids to the two daughter cells, allowing for the emergence of mutant homozygous cells over the course of several generations. To model this process, we use the theory of multitype branching processes, where a type is defined by the genetic composition of the cell. Both factors-the availability of advantageous alleles and their establishment probability-depend on the plasmid copy number, and they often do so antagonistically. We find that in the interplay of various effects, a lower or higher copy number may maximize the probability of evolutionary rescue. The decisive factor is the dominance relationship between mutant and wild-type plasmids and potential gene dosage effects. Results from a simple model of antibiotic degradation indicate that the optimal plasmid copy number may depend on the specific environment encountered by the population.

Virus epidemics, plant-controlled population bottlenecks and the durability of plant resistance

Plant qualitative resistances to viruses are natural exhaustible resources that can be impaired by the emergence of resistance-breaking (RB) virus variants. Mathematical modelling can help determine optimal strategies for resistance durability by a rational deployment of resistance in agroecosystems. Here, we propose an innovative approach, built up from our previous empirical studies, based on plant cultivars combining qualitative resistance with quantitative resistance narrowing population bottlenecks exerted on viruses during host-to-host transmission and/or within-host infection. Narrow bottlenecks are expected to slow down virus adaptation to plant qualitative resistance. To study the effect of bottleneck size on yield, we developed a stochastic epidemic model with mixtures of susceptible and resistant plants, relying on continuous-time Markov chain processes. Overall, narrow bottlenecks are beneficial when the fitness cost of RB virus variants in susceptible plants is intermediate. In such cases, they could provide up to 95 additional percentage points of yield compared with deploying a qualitative resistance alone. As we have shown in previous works that virus population bottlenecks are at least partly heritable plant traits, our results suggest that breeding and deploying plant varieties exposing virus populations to narrowed bottlenecks will increase yield and delay the emergence of RB variants. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Resist or perish: Fate of a microbial population subjected to a periodic presence of antimicrobial

The evolution of antimicrobial resistance can be strongly affected by variations of antimicrobial concentration. Here, we study the impact of periodic alternations of absence and presence of antimicrobial on resistance evolution in a microbial population, using a stochastic model that includes variations of both population composition and size, and fully incorporates stochastic population extinctions. We show that fast alternations of presence and absence of antimicrobial are inefficient to eradicate the microbial population and strongly favor the establishment of resistance, unless the antimicrobial increases enough the death rate. We further demonstrate that if the period of alternations is longer than a threshold value, the microbial population goes extinct upon the first addition of antimicrobial, if it is not rescued by resistance. We express the probability that the population is eradicated upon the first addition of antimicrobial, assuming rare mutations. Rescue by resistance can happen either if resistant mutants preexist, or if they appear after antimicrobial is added to the environment. Importantly, the latter case is fully prevented by perfect biostatic antimicrobials that completely stop division of sensitive microorganisms. By contrast, we show that the parameter regime where treatment is efficient is larger for biocidal drugs than for biostatic drugs. This sheds light on the respective merits of different antimicrobial modes of action.

A compartment size-dependent selective threshold limits mutation accumulation in hierarchical tissues

Renewed tissues of multicellular organism accumulate mutations that lead to aging and cancer. To mitigate these effects, self-renewing tissues produce cells along differentiation hierarchies, which have been shown to suppress somatic evolution both by limiting the number of cell divisions, and thus reducing mutational load, and by differentiation “washing out” mutations. Our analytical results reveal the existence of a third mechanism: a compartment size-dependent threshold in proliferative advantage, below which mutations cannot persist, but are rapidly expelled from the tissue by differentiation. In sufficiently small compartments, the resulting selective barrier can greatly slow down somatic evolution and reduce the risk of cancer by preventing the accumulation of mutations even if even they confer substantial proliferative advantage.

Cancer is a genetic disease fueled by somatic evolution. Hierarchical tissue organization can slow somatic evolution by two qualitatively different mechanisms: by cell differentiation along the hierarchy “washing out” harmful mutations and by limiting the number of cell divisions required to maintain a tissue. Here we explore the effects of compartment size on somatic evolution in hierarchical tissues by considering cell number regulation that acts on cell division rates such that the number of cells in the tissue has the tendency to return to its desired homeostatic value. Introducing mutants with a proliferative advantage, we demonstrate the existence of a third fundamental mechanism by which hierarchically organized tissues are able to slow down somatic evolution. We show that tissue size regulation leads to the emergence of a threshold proliferative advantage, below which mutants cannot persist. We find that the most significant determinant of the threshold selective advantage is compartment size, with the threshold being higher the smaller the compartment. Our results demonstrate that, in sufficiently small compartments, even mutations that confer substantial proliferative advantage cannot persist, but are expelled from the tissue by differentiation along the hierarchy. The resulting selective barrier can significantly slow down somatic evolution and reduce the risk of cancer by limiting the accumulation of mutations that increase the proliferation of cells.

A multihost bacterial pathogen overcomes continuous population bottlenecks to adapt to new host species

While many bacterial pathogens are restricted to single host species, some have the capacity to undergo host switches, leading to the emergence of new clones that are a threat to human and animal health. However, the bacterial traits that underpin a multihost ecology are not well understood. Following transmission to a new host, bacterial populations are influenced by powerful forces such as genetic drift that reduce the fixation rate of beneficial mutations, limiting the capacity for host adaptation. Here, we implement a novel experimental model of bacterial host switching to investigate the ability of the multihost pathogen Staphylococcus aureus to adapt to new species under continuous population bottlenecks. We demonstrate that beneficial mutations accumulated during infection can overcome genetic drift and sweep through the population, leading to host adaptation. Our findings highlight the remarkable capacity of some bacteria to adapt to distinct host niches in the face of powerful antagonistic population forces.

Evolutionary simulations of Z-linked suppression gene drives

Synthetic gene drives may soon be used to suppress or eliminate populations of disease vectors, pathogens, invasive species, and agricultural pests. Recent proposals have focused on using Z-linked gene drives to control species with ZW sex determination, which include Lepidopteran pests, parasitic trematodes, and cane toads. These proposals include Z-linked 'W-shredders', which would suppress populations by cleaving the W chromosome and causing females to produce only sons, as well as Z-linked female-sterilizing gene drives. Here, I use eco-evolutionary simulations to evaluate the potential of some proposed Z-linked gene drives, and to produce recommendations regarding their design and use. The simulations show that W-shredders are likely to be highly effective at eradicating populations provided that resistance to W-shredding cannot evolve. However, W-shredder alleles can invade populations from very low frequencies, making it difficult to eliminate specific populations while leaving nearby populations untouched; this issue may restrict their possible uses.

Environmental spatial and temporal variability and its role in non-favoured mutant dynamics

Understanding how environmental variability (or randomness) affects evolution is of fundamental importance for biology. The presence of temporal or spatial variability significantly affects the competition dynamics in populations, and gives rise to some counterintuitive observations. In this paper, we consider both birth-death (BD) or death-birth (DB) Moran processes, which are set up on a circular or a complete graph. We investigate spatial and temporal variability affecting division and/or death parameters. Assuming that mutant and wild-type fitness parameters are drawn from an identical distribution, we study mutant fixation probability and timing. We demonstrate that temporal and spatial types of variability possess fundamentally different properties. Under temporal randomness, in a completely mixed system, minority mutants experience (i) higher than neutral fixation probability and a higher mean conditional fixation time, if the division rates are affected by randomness and (ii) lower fixation probability and lower mean conditional fixation time if the death rates are affected. Once spatial restrictions are imposed, however, these effects completely disappear, and mutants in a circular graph experience neutral dynamics, but only for the DB update rule in case (i) and for the BD rule in case (ii) above. In contrast to this, in the case of spatially variable environment, both for BD/DB processes, both for complete/circular graph and both for division/death rates affected, minority mutants experience a higher than neutral probability of fixation. Fixation time, however, is increased by randomness on a circle, while it decreases for complete graphs under random division rates. A basic difference between temporal and spatial kinds of variability is the types of correlations that occur in the system. Under temporal randomness, mutants are spatially correlated with each other (they simply have equal fitness values at a given moment of time; the same holds for wild-types). Under spatial randomness, there are subtler, temporal correlations among mutant and wild-type cells, which manifest themselves by cells of each type 'claiming' better spots for themselves. Applications of this theory include cancer generation and biofilm dynamics.

Motion, fixation probability and the choice of an evolutionary process

Seemingly minor details of mathematical and computational models of evolution are known to change the effect of population structure on the outcome of evolutionary processes. For example, birth-death dynamics often result in amplification of selection, while death-birth processes have been associated with suppression. In many biological populations the interaction structure is not static. Instead, members of the population are in motion and can interact with different individuals at different times. In this work we study populations embedded in a flowing medium; the interaction network is then time dependent. We use computer simulations to investigate how this dynamic structure affects the success of invading mutants, and compare these effects for different coupled birth and death processes. Specifically, we show how the speed of the motion impacts the fixation probability of an invading mutant. Flows of different speeds interpolate between evolutionary dynamics on fixed heterogeneous graphs and well-stirred populations; this allows us to systematically compare against known results for static structured populations. We find that motion has an active role in amplifying or suppressing selection by fragmenting and reconnecting the interaction graph. While increasing flow speeds suppress selection for most evolutionary models, we identify characteristic responses to flow for the different update rules we test. In particular we find that selection can be maximally enhanced or suppressed at intermediate flow speeds.

Whether a mutation spreads in a population or not is one of the most important questions in biology. The evolution of cancer and antibiotic resistance, for example, are mediated by invading mutants. Recent work has shown that population structure can have important consequences for the outcome of evolution. For instance, a mutant can have a higher or a lower chance of invasion than in unstructured populations. These effects can depend on seemingly minor details of the evolutionary model, such as the order of birth and death events. Many biological populations are in motion, for example due to external stirring. Experimentally this is known to be important; the performance of mutants in E. coli populations, for example, depends on the rate of mixing. Here, we focus on simulations of populations in a flowing medium, and compare the success of a mutant for different flow speeds. We contrast different evolutionary models, and identify what features of the evolutionary model affect mutant success for different speeds of the flow. We find that the chance of mutant invasion can be at its highest (or lowest) at intermediate flow speeds, depending on the order in which birth and death events occur in the evolutionary process.