Selection-Like Biases Emerge in Population Models with Recurrent Jackpot Events

Detecting deviations from Kingman coalescence using 2-site frequency spectra

Demographic inference methods in population genetics typically assume that the ancestry of a sample can be modeled by the Kingman coalescent. A defining feature of this stochastic process is that it generates genealogies that are binary trees: no more than 2 ancestral lineages may coalesce at the same time. However, this assumption breaks down under several scenarios. For example, pervasive natural selection and extreme variation in offspring number can both generate genealogies with "multiple-merger" events in which more than 2 lineages coalesce instantaneously. Therefore, detecting violations of the Kingman assumptions (e.g. due to multiple mergers) is important both for understanding which forces have shaped the diversity of a population and for avoiding fitting misspecified models to data. Current methods to detect deviations from Kingman coalescence in genomic data rely primarily on the site frequency spectrum (SFS). However, the signatures of some non-Kingman processes (e.g. multiple mergers) in the SFS are also consistent with a Kingman coalescent with a time-varying population size. Here, we present a new statistical test for determining whether the Kingman coalescent with any population size history is consistent with population data. Our approach is based on information contained in the 2-site joint frequency spectrum (2-SFS) for pairs of linked sites, which has a different dependence on the topologies of genealogies than the SFS. Our statistical test is global in the sense that it can detect when the genome-wide genetic diversity is inconsistent with the Kingman model, rather than detecting outlier regions, as in selection scan methods. We validate this test using simulations and then apply it to demonstrate that genomic diversity data from Drosophila melanogaster is inconsistent with the Kingman coalescent.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations

Large stochastic population abundance fluctuations are ubiquitous across the tree of life, impacting the predictability and outcomes of population dynamics. It is generally thought that abundance fluctuations with a Taylor's law exponent of two do not strongly impact evolution. However, we argue that such abundance fluctuations can lead to substantial genotype frequency fluctuations if different genotypes in a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related Escherichia coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from genetic drift. We develop an effective model explaining that the abundance fluctuations arise from correlated offspring numbers between individuals, and the large frequency fluctuations result from (even slight) decoupling in offspring number correlations between genotypes. The model quantitatively predicts the observed abundance and frequency fluctuation scaling. Initially close trajectories diverge exponentially, suggesting that chaotic dynamics may underpin the excess frequency fluctuations. Our findings suggest that decoupling noise is also present in mixed-genotype Saccharomyces cerevisiae populations. Theoretical analyses demonstrate that decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of these frequency fluctuations, we expect them to be widespread across biological populations.

Eco-evolutionary dynamics of adapting pathogens and host immunity

As pathogens spread in a population of hosts, immunity is built up, and the pool of susceptible individuals are depleted. This generates selective pressure, to which many human RNA viruses, such as influenza virus or SARS-CoV-2, respond with rapid antigenic evolution and frequent emergence of immune evasive variants. However, the host's immune systems adapt, and older immune responses wane, such that escape variants only enjoy a growth advantage for a limited time. If variant growth dynamics and reshaping of host-immunity operate on comparable time scales, viral adaptation is determined by eco-evolutionary interactions that are not captured by models of rapid evolution in a fixed environment. Here, we use a Susceptible/Infected model to describe the interaction between an evolving viral population in a dynamic but immunologically diverse host population. We show that depending on strain cross-immunity, heterogeneity of the host population, and durability of immune responses, escape variants initially grow exponentially, but lose their growth advantage before reaching high frequencies. Their subsequent dynamics follows an anomalous random walk determined by future escape variants and results in variant trajectories that are unpredictable. This model can explain the apparent contradiction between the clearly adaptive nature of antigenic evolution and the quasi-neutral dynamics of high-frequency variants observed for influenza viruses.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations

Large stochastic population abundance fluctuations are ubiquitous across the tree of life1-7, impacting the predictability of population dynamics and influencing eco-evolutionary outcomes. It has generally been thought that these large abundance fluctuations do not strongly impact evolution, as the relative frequencies of alleles in the population will be unaffected if the abundance of all alleles fluctuate in unison. However, we argue that large abundance fluctuations can lead to significant genotype frequency fluctuations if different genotypes within a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related E. coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from models of genetic drift. We develop a flexible, effective model that explains the abundance fluctuations as arising from correlated offspring numbers between individuals, and the large frequency fluctuations result from even slight decoupling in offspring numbers between genotypes. This model accurately describes the observed abundance and frequency fluctuation scaling behaviors. Our findings suggest chaotic dynamics underpin these giant fluctuations, causing initially similar trajectories to diverge exponentially; subtle environmental changes can be magnified, leading to batch correlations in identical growth conditions. Furthermore, we present evidence that such decoupling noise is also present in mixed-genotype S. cerevisiae populations. We demonstrate that such decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of asynchronous fluctuations, we anticipate that they are widespread in biological populations, significantly affecting evolutionary and ecological dynamics.

To Prosper, Live Long: Understanding the Sources of Reproductive Skew and Extreme Reproductive Success in Structured Populations

AbstractIn many species, a few individuals produce most of the next generation. How much of this reproductive skew is driven by variation among individuals in fixed traits, how much by external factors, and how much by random chance? And what does it take to have truly exceptional lifetime reproductive output (LRO)? In the past, we and others have partitioned the variance of LRO as a proxy for reproductive skew. Here we explain how to partition LRO skewness itself into contributions from fixed trait variation, four forms of "demographic luck" (birth state, fecundity luck, survival trajectory luck, and growth trajectory luck), and two kinds of "environmental luck" (birth environment and environment trajectory). Each of these is further partitioned into contributions at different ages. We also determine what we can infer about individuals with exceptional LRO. We find that reproductive skew is largely driven by random variation in lifespan, and exceptional LRO generally results from exceptional lifespan. Other kinds of luck frequently bring skewness down rather than increasing it. In populations where fecundity varies greatly with environmental conditions, getting a good year at the right time can be an alternate route to exceptional LRO, so that LRO is less predictive of lifespan.

A dynamical limit to evolutionary adaptation

Natural selection makes evolutionary adaptation possible even if the overwhelming majority of new mutations are deleterious. However, in rapidly evolving populations where numerous linked mutations occur and segregate simultaneously, clonal interference and genetic hitchhiking can limit the efficiency of selection, allowing deleterious mutations to accumulate over time. This can in principle overwhelm the fitness increases provided by beneficial mutations, leading to an overall fitness decline. Here, we analyze the conditions under which evolution will tend to drive populations to higher versus lower fitness. Our analysis focuses on quantifying the boundary between these two regimes, as a function of parameters such as population size, mutation rates, and selection pressures. This boundary represents a state in which adaptation is precisely balanced by Muller's ratchet, and we show that it can be characterized by rapid molecular evolution without any net fitness change. Finally, we consider the implications of global fitness-mediated epistasis and find that under some circumstances, this can drive populations toward the boundary state, which can thus represent a long-term evolutionary attractor.

Evolutionary dynamics in non-Markovian models of microbial populations

In the past decade, great strides have been made to quantify the dynamics of single-cell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of single-cell growth and division influence evolutionary dynamics. This requires us to connect processes on the single-cell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the single-cell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarse-grained so that the forces of natural selection and genetic drift can be expressed in terms of the long-term fitness? We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the single-cell dynamics affect the fate of a new mutant independently from how they affect the long-term growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multispecies generalization of the Euler-Lotka equation.

Proliferating active matter

The fascinating patterns of collective motion created by autonomously driven particles have fuelled active-matter research for over two decades. So far, theoretical active-matter research has often focused on systems with a fixed number of particles. This constraint imposes strict limitations on what behaviours can and cannot emerge. However, a hallmark of life is the breaking of local cell number conservation by replication and death. Birth and death processes must be taken into account, for example, to predict the growth and evolution of a microbial biofilm, the expansion of a tumour, or the development from a fertilized egg into an embryo and beyond. In this Perspective, we argue that unique features emerge in these systems because proliferation represents a distinct form of activity: not only do the proliferating entities consume and dissipate energy, they also inject biomass and degrees of freedom capable of further self-proliferation, leading to myriad dynamic scenarios. Despite this complexity, a growing number of studies document common collective phenomena in various proliferating soft-matter systems. This generality leads us to propose proliferation as another direction of active-matter physics, worthy of a dedicated search for new dynamical universality classes. Conceptual challenges abound, from identifying control parameters and understanding large fluctuations and nonlinear feedback mechanisms to exploring the dynamics and limits of information flow in self-replicating systems. We believe that, by extending the rich conceptual framework developed for conventional active matter to proliferating active matter, researchers can have a profound impact on quantitative biology and reveal fascinating emergent physics along the way.

Population genetic models for the spatial spread of adaptive variants: A review in light of SARS-CoV-2 evolution

Theoretical population genetics has long studied the arrival and geographic spread of adaptive variants through the analysis of mathematical models of dispersal and natural selection. These models take on a renewed interest in the context of the COVID-19 pandemic, especially given the consequences that novel adaptive variants have had on the course of the pandemic as they have spread through global populations. Here, we review theoretical models for the spatial spread of adaptive variants and identify areas to be improved in future work, toward a better understanding of variants of concern in Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) evolution and other contemporary applications. As we describe, characteristics of pandemics such as COVID-19-such as the impact of long-distance travel patterns and the overdispersion of lineages due to superspreading events-suggest new directions for improving upon existing population genetic models.

Recommendations for improving statistical inference in population genomics

The field of population genomics has grown rapidly in response to the recent advent of affordable, large-scale sequencing technologies. As opposed to the situation during the majority of the 20th century, in which the development of theoretical and statistical population genetic insights outpaced the generation of data to which they could be applied, genomic data are now being produced at a far greater rate than they can be meaningfully analyzed and interpreted. With this wealth of data has come a tendency to focus on fitting specific (and often rather idiosyncratic) models to data, at the expense of a careful exploration of the range of possible underlying evolutionary processes. For example, the approach of directly investigating models of adaptive evolution in each newly sequenced population or species often neglects the fact that a thorough characterization of ubiquitous nonadaptive processes is a prerequisite for accurate inference. We here describe the perils of these tendencies, present our consensus views on current best practices in population genomic data analysis, and highlight areas of statistical inference and theory that are in need of further attention. Thereby, we argue for the importance of defining a biologically relevant baseline model tuned to the details of each new analysis, of skepticism and scrutiny in interpreting model fitting results, and of carefully defining addressable hypotheses and underlying uncertainties.

Population genetics of polymorphism and divergence in rapidly evolving populations

In rapidly evolving populations, numerous beneficial and deleterious mutations can arise and segregate within a population at the same time. In this regime, evolutionary dynamics cannot be analyzed using traditional population genetic approaches that assume that sites evolve independently. Instead, the dynamics of many loci must be analyzed simultaneously. Recent work has made progress by first analyzing the fitness variation within a population, and then studying how individual lineages interact with this traveling fitness wave. However, these "traveling wave" models have previously been restricted to extreme cases where selection on individual mutations is either much faster or much slower than the typical coalescent timescale Tc. In this work, we show how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (Tcs) are neither large nor small compared to one. This enables us to describe the dynamics of populations subject to a wide range of fitness effects, and in particular, in cases where it is not immediately clear which mutations are most important in shaping the dynamics and statistics of genetic diversity. We use this approach to derive new expressions for the fixation probabilities and site frequency spectra of mutations as a function of their scaled fitness effects, along with related results for the coalescent timescale Tc and the rate of adaptation or Muller's ratchet. We find that competition between linked mutations can have a dramatic impact on the proportions of neutral and selected polymorphisms, which is not simply summarized by the scaled selection coefficient Tcs. We conclude by discussing the implications of these results for population genetic inferences.

Evolution during primary HIV infection does not require adaptive immune selection

Modern HIV research depends crucially on both viral sequencing and population measurements. To directly link mechanistic biological processes and evolutionary dynamics during HIV infection, we developed multiple within-host phylodynamic models of HIV primary infection for comparative validation against viral load and evolutionary dynamics data. The optimal model of primary infection required no positive selection, suggesting that the host adaptive immune system reduces viral load but surprisingly does not drive observed viral evolution. Rather, the fitness (infectivity) of mutant variants is drawn from an exponential distribution in which most variants are slightly less infectious than their parents (nearly neutral evolution). This distribution was not largely different from either in vivo fitness distributions recorded beyond primary infection or in vitro distributions that are observed without adaptive immunity, suggesting the intrinsic viral fitness distribution may drive evolution. Simulated phylogenetic trees also agree with independent data and illuminate how phylogenetic inference must consider viral and immune-cell population dynamics to gain accurate mechanistic insights.

Dynamic sampling bias and overdispersion induced by skewed offspring distributions

Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population expansions. The resulting allele-frequency fluctuations are large and, therefore, challenge standard models of population genetics, which assume sufficiently narrow offspring distributions. While the neutral dynamics backward in time can be readily analyzed using coalescent approaches, we still know little about the effect of broad offspring distributions on the forward-in-time dynamics, especially with selection. Here, we employ an asymptotic analysis combined with a scaling hypothesis to demonstrate that over-dispersed frequency trajectories emerge from the competition of conventional forces, such as selection or mutations, with an emerging time-dependent sampling bias against the minor allele. The sampling bias arises from the characteristic time-dependence of the largest sampled family size within each allelic type. Using this insight, we establish simple scaling relations for allele-frequency fluctuations, fixation probabilities, extinction times, and the site frequency spectra that arise when offspring numbers are distributed according to a power law.

Genealogical structure changes as range expansions transition from pushed to pulled

Range expansions accelerate evolution through multiple mechanisms, including gene surfing and genetic drift. The inference and control of these evolutionary processes ultimately rely on the information contained in genealogical trees. Currently, there are two opposing views on how range expansions shape genealogies. In invasion biology, expansions are typically approximated by a series of population bottlenecks producing genealogies with only pairwise mergers between lineages-a process known as the Kingman coalescent. Conversely, traveling wave models predict a coalescent with multiple mergers, known as the Bolthausen-Sznitman coalescent. Here, we unify these two approaches and show that expansions can generate an entire spectrum of coalescent topologies. Specifically, we show that tree topology is controlled by growth dynamics at the front and exhibits large differences between pulled and pushed expansions. These differences are explained by the fluctuations in the total number of descendants left by the early founders. High growth cooperativity leads to a narrow distribution of reproductive values and the Kingman coalescent. Conversely, low growth cooperativity results in a broad distribution, whose exponent controls the merger sizes in the genealogies. These broad distribution and non-Kingman tree topologies emerge due to the fluctuations in the front shape and position and do not occur in quasi-deterministic simulations. Overall, our results show that range expansions provide a robust mechanism for generating different types of multiple mergers, which could be similar to those observed in populations with strong selection or high fecundity. Thus, caution should be exercised in making inferences about the origin of non-Kingman genealogies.

Quantifying the relationship between genetic diversity and population size suggests natural selection cannot explain Lewontin's Paradox

Neutral theory predicts that genetic diversity increases with population size, yet observed levels of diversity across metazoans vary only two orders of magnitude while population sizes vary over several. This unexpectedly narrow range of diversity is known as Lewontin's Paradox of Variation (1974). While some have suggested selection constrains diversity, tests of this hypothesis seem to fall short. Here, I revisit Lewontin's Paradox to assess whether current models of linked selection are capable of reducing diversity to this extent. To quantify the discrepancy between pairwise diversity and census population sizes across species, I combine previously-published estimates of pairwise diversity from 172 metazoan taxa with newly derived estimates of census sizes. Using phylogenetic comparative methods, I show this relationship is significant accounting for phylogeny, but with high phylogenetic signal and evidence that some lineages experience shifts in the evolutionary rate of diversity deep in the past. Additionally, I find a negative relationship between recombination map length and census size, suggesting abundant species have less recombination and experience greater reductions in diversity due to linked selection. However, I show that even assuming strong and abundant selection, models of linked selection are unlikely to explain the observed relationship between diversity and census sizes across species.

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.

Tuning environmental timescales to evolve and maintain generalists

Natural environments can present diverse challenges, but some genotypes remain fit across many environments. Such "generalists" can be hard to evolve, outcompeted by specialists fitter in any particular environment. Here, inspired by the search for broadly neutralizing antibodies during B cell affinity maturation, we demonstrate that environmental changes on an intermediate timescale can reliably evolve generalists, even when faster or slower environmental changes are unable to do so. We find that changing environments on timescales comparable with evolutionary transients in a population enhance the rate of evolving generalists from specialists, without enhancing the reverse process. The yield of generalists is further increased in more complex dynamic environments, such as a "chirp" of increasing frequency. Our work offers design principles for how nonequilibrium fitness "seascapes" can dynamically funnel populations to genotypes unobtainable in static environments.

The multifurcating skyline plot

A variety of methods based on coalescent theory have been developed to infer demographic history from gene sequences sampled from natural populations. The 'skyline plot' and related approaches are commonly employed as flexible prior distributions for phylogenetic trees in the Bayesian analysis of pathogen gene sequences. In this work we extend the classic and generalized skyline plot methods to phylogenies that contain one or more multifurcations (i.e. hard polytomies). We use the theory of Λ-coalescents (specifically, Beta ( 2 - α , α ) -coalescents) to develop the 'multifurcating skyline plot', which estimates a piecewise constant function of effective population size through time, conditional on a time-scaled multifurcating phylogeny. We implement a smoothing procedure and extend the method to serially sampled (heterochronous) data, but we do not address here the problem of estimating trees with multifurcations from gene sequence alignments. We validate our estimator on simulated data using maximum likelihood and find that parameters of the Beta ( 2 - α , α ) -coalescent process can be estimated accurately. Furthermore, we apply the multifurcating skyline plot to simulated trees generated by tracking transmissions in an individual-based model of epidemic superspreading. We find that high levels of superspreading are consistent with the high-variance assumptions underlying Λ-coalescents and that the estimated parameters of the Λ-coalescent model contain information about the degree of superspreading.

Inferring Demography and Selection in Organisms Characterized by Skewed Offspring Distributions

The recent increase in time-series population genomic data from experimental, natural, and ancient populations has been accompanied by a promising growth in methodologies for inferring demographic and selective parameters from such data. However, these methods have largely presumed that the populations of interest are well-described by the Kingman coalescent. In reality, many groups of organisms, including viruses, marine organisms, and some plants, protists, and fungi, typified by high variance in progeny number, may be best characterized by multiple-merger coalescent models. Estimation of population genetic parameters under Wright-Fisher assumptions for these organisms may thus be prone to serious mis-inference. We propose a novel method for the joint inference of demography and selection under the Ψ-coalescent model, termed Multiple-Merger Coalescent Approximate Bayesian Computation, or MMC-ABC. We first demonstrate mis-inference under the Kingman, and then exhibit the superior performance of MMC-ABC under conditions of skewed offspring distributions. In order to highlight the utility of this approach, we reanalyzed previously published drug-selection lines of influenza A virus. We jointly inferred the extent of progeny-skew inherent to viral replication and identified putative drug-resistance mutations.

Effective models and the search for quantitative principles in microbial evolution

Microbes evolve rapidly. Yet they do so in idiosyncratic ways, which depend on the specific mutations that are beneficial or deleterious in a given situation. At the same time, some population-level patterns of adaptation are strikingly similar across different microbial systems, suggesting that there may also be simple, quantitative principles that unite these diverse scenarios. We review the search for simple principles in microbial evolution, ranging from the biophysical level to emergent evolutionary dynamics. A key theme has been the use of effective models, which coarse-grain over molecular and cellular details to obtain a simpler description in terms of a few effective parameters. Collectively, these theoretical approaches provide a set of quantitative principles that facilitate understanding, prediction, and potentially control of evolutionary phenomena, though formidable challenges remain due to the ecological complexity of natural populations.

The Effect of Strong Purifying Selection on Genetic Diversity

Purifying selection reduces genetic diversity, both at sites under direct selection and at linked neutral sites. This process, known as background selection, is thought to play an important role in shaping genomic diversity in natural populations. Yet despite its importance, the effects of background selection are not fully understood. Previous theoretical analyses of this process have taken a backward-time approach based on the structured coalescent. While they provide some insight, these methods are either limited to very small samples or are computationally prohibitive. Here, we present a new forward-time analysis of the trajectories of both neutral and deleterious mutations at a nonrecombining locus. We find that strong purifying selection leads to remarkably rich dynamics: neutral mutations can exhibit sweep-like behavior, and deleterious mutations can reach substantial frequencies even when they are guaranteed to eventually go extinct. Our analysis of these dynamics allows us to calculate analytical expressions for the full site frequency spectrum. We find that whenever background selection is strong enough to lead to a reduction in genetic diversity, it also results in substantial distortions to the site frequency spectrum, which can mimic the effects of population expansions or positive selection. Because these distortions are most pronounced in the low and high frequency ends of the spectrum, they become particularly important in larger samples, but may have small effects in smaller samples. We also apply our forward-time framework to calculate other quantities, such as the ultimate fates of polymorphisms or the fitnesses of their ancestral backgrounds.