In exponentially proliferating populations of microbes, the population typically doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population's growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a population's growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a non-monotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.
The outcomes of evolution are determined by which mutations occur and fix. In rapidly adapting microbial populations, this process is particularly hard to predict because lineages with different beneficial mutations often spread simultaneously and interfere with one another's fixation. Hence to predict the fate of any individual variant, we must know the rate at which new mutations create competing lineages of higher fitness. Here, we directly measured the effect of this interference on the fates of specific adaptive variants in laboratory Saccharomyces cerevisiae populations and used these me…
Evolutionary experiments with microbes are a powerful tool to study mutations and natural selection. These experiments, however, are often limited to the well-mixed environments of a test tube or a chemostat. Since spatial organization can significantly affect evolutionary dynamics, the need is growing for evolutionary experiments in spatially structured environments. The surface of a Petri dish provides such an environment, but a more detailed understanding of microbial growth on Petri dishes is necessary to interpret such experiments. We formulate a simple deterministic reaction-diffusion mo…
We obtain general inequalities constraining the difference between the average of an arbitrary function of a phenotypic trait, which includes the fitness landscape of the trait itself, in the presence or in the absence of natural selection. These inequalities imply bounds on the strength of selection, which can be measured from the statistics of trait values and divisions along lineages. The upper bound is related to recent generalizations of linear response relations in Stochastic Thermodynamics, and shares common features with Fisher's fundamental theorem of natural selection, and with its g…
Here, we study the evolution of specialization using realistic computer simulations of bacteria that secrete two public goods in a dynamic fluid. Through this first principles approach, we find physical factors such as diffusion, flow patterns, and decay rates are as influential as fitness economics in governing the evolution of community structure, to the extent that when mechanical factors are taken into account, (1) Generalist communities can resist becoming specialists, despite the invasion fitness of specialization, (2) Generalist and specialists can both resist cheaters despite the invas…
Antibiotics resistance has caused much complication in the treatment of diseases, where the pathogen is no longer susceptible to specific antibiotics and the use of such antibiotics are no longer effective for treatment. A recent study that utilizes digital organisms suggests that complete elimination of specific antibiotic resistance is unlikely after the disuse of antibiotics, assuming that there are no fitness costs for maintaining resistance once resistance are established. Fitness cost are referred to as reaction to change in environment, where organism improves its' abilities in one area…
This is supplementary information for arXiv:1204.4896, which also appeared in Physical Biology 9, 026008 (2012). Main text abstract: Evolutionary experiments with microbes are a powerful tool to study mutations and natural selection. These experiments, however, are often limited to the well-mixed environments of a test tube or a chemostat. Since spatial organization can significantly affect evolutionary dynamics, the need is growing for evolutionary experiments in spatially structured environments. The surface of a Petri dish provides such an environment, but a more detailed understanding of m…
Horizontal gene transfer is an important factor in bacterial evolution that can act across species boundaries. Yet, we know little about rate and genomic targets of cross-lineage gene transfer, and about its effects on the recipient organism's physiology and fitness. Here, we address these questions in a parallel evolution experiment with two Bacillus subtilis lineages of 7% sequence divergence. We observe rapid evolution of hybrid organisms: gene transfer swaps ~12% of the core genome in just 200 generations, and 60% of core genes are replaced in at least one population. By genomics, transcri…
We consider the adaptation dynamics of an asexual population that walks uphill on a rugged fitness landscape which is endowed with large number of local fitness peaks. We work in a parameter regime where only those mutants that are single mutation away are accessible, as a result of which the population eventually gets trapped at a local fitness maximum and the adaptive walk terminates. We study how the number of adaptive steps taken by the population before reaching a local fitness peak depends on the initial fitness of the population, the extreme value distribution of the beneficial mutation…
We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a trade-off relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the resp…
This chapter gives a synopsis of recent approaches to model and analyse the evolution of microbial populations under selection. The first part reviews two population genetic models of Lenski's long-term evolution experiment with Escherichia coli, where models aim at explaining the observed curve of the evolution of the mean fitness. The second part describes a model of a host-pathogen system where the population of pathogenes experiences balancing selection, migration, and mutation, as motivated by observations of the genetic diversity of HCMV (the human cytomegalovirus) across hosts.
The evolution of antimicrobial resistance generally occurs in an environment where antimicrobial concentration is variable, which has dramatic consequences on the microorganisms' fitness landscape, and thus on the evolution of resistance. We investigate the effect of these time-varying patterns of selection within a stochastic model. We consider a homogeneous microbial population of fixed size subjected to periodic alternations of phases of absence and presence of an antimicrobial that stops growth. Combining analytical approaches and stochastic simulations, we quantify how the time necessary …
We construct a pathwise formulation of a growing population of cells, based on two different samplings of lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called fluctuation relation relates these two samplings, independently of the model used to generate divisions and growth in the cell population. These relations lead to estimators of the population growth rate, which can be very efficient as we demonstrate by an analysis of a set of mother machine data. These fluctuation relations lead to general and important inequalities …
The evolution of microbial and viral organisms often generates clonal interference, a mode of competition between genetic clades within a population. In this paper, we show that interference strongly constrains the genetic and phenotypic complexity of evolving systems. Our analysis uses biophysically grounded evolutionary models for an organism's quantitative molecular phenotypes, such as fold stability and enzymatic activity of genes. We find a generic mode of asexual evolution called phenotypic interference with strong implications for systems biology: it couples the stability and function o…
We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length $L$. The population evolves in a maximally rugged fitness landscape with a large number of local optima. We find that whether the evolutionary trajectory is deterministic or stochastic depends on the effective mutational distance $d_{\mathrm{eff}}$ upto which the population can spread in genotype space. For $d_{\mathrm{eff}}=L$, the deterministic quasispecies theory operates while for $d_{\mathrm{eff}} < 1$, the evolution is completely stochastic. Between thes…
Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple life-history traits to selection is a critical question for evolutionary biology as we seek to predict the evolutionary fates of mutations. Here we use a model of microbial growth to show there are two distinct components of selection corresponding to the growth and lag phases, while the yield modulates their relative importance. The model predicts rich popu…
When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population concurrently. In an asexual population, these different mutant lineages interfere and not all can fix simultaneously. In addition, further beneficial mutations can accumulate in mutant lineages while these are still a minority of the population. In this paper, we analyze the dynamics of such multiple mutations and the interplay between multiple mutations and inter…
Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depend on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the f…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and environment is important in modeling cancer initiation, microbial evolution and evolution of drug resistance. Environmental interactions can be asymmetric, that is, they affect the fitness of one type more than the other. The question is how local environmental variations in network population structures change the selection dynamics in a finite population setting.…
Zooplankton have evolved several mechanisms to deal with environmental threats, such as ultraviolet radiation (UVR), and in order to identify strategies inherent to organisms exposed to different UVR environments, we here examine life-history traits of two lineages of Daphnia pulex. The lineages differed in the UVR dose they had received at their place of origin from extremely high UVR stress at high-altitude Bolivian lakes to low UVR stress near the sea level in temperate Sweden. Nine life-history variables of each lineage were analyzed in laboratory experiments in the presence and the absenc…
The evolutionary spread of cheater strategies can destabilize populations engaging in cooperative behaviors, thus demonstrating that evolutionary changes can have profound implications for populations dynamics. At the same time, the relative fitness of cooperative traits often depends upon population density, thus leading to the potential for bidirectional coupling between population density and the evolution of a cooperative trait. Despite the potential importance of these eco evolutionary feedback loops, they have not yet been demonstrated experimentally in social species and their ecologica…
Stochastic phenotype switching has been suggested to play a beneficial role in microbial populations by leading to the division of labour among cells, or ensuring that at least some of the population survives an unexpected change in environmental conditions. Here we use a computational model to investigate an alternative possible function of stochastic phenotype switching - as a way to adapt more quickly even in a static environment. We show that when a genetic mutation causes a population to become less fit, switching to an alternative phenotype with higher fitness (growth rate) may give the …
Mounting evidence suggests that natural populations can harbor extensive fitness diversity with numerous genomic loci under selection. It is also known that genealogical trees for populations under selection are quantifiably different from those expected under neutral evolution and described statistically by Kingman's coalescent. While differences in the statistical structure of genealogies have long been used as a test for the presence of selection, the full extent of the information that they contain has not been exploited. Here we shall demonstrate that the shape of the reconstructed geneal…
Bacteria evolve resistance to antibiotics by a multitude of mechanisms. A central, yet unsolved question is how resistance evolution affects cell growth at different drug levels. Here we develop a fitness model that predicts growth rates of common resistance mutants from their effects on cell metabolism. We map metabolic effects of resistance mutations in drug-free environments and under drug challenge; the resulting fitness trade-off defines a Pareto surface of resistance evolution. We predict evolutionary trajectories of dosage-dependent growth rates and resistance levels, as well as the pre…
Given a sample of genome sequences from an asexual population, can one predict its evolutionary future? Here we demonstrate that the branching patterns of reconstructed genealogical trees contains information about the relative fitness of the sampled sequences and that this information can be used to predict successful strains. Our approach is based on the assumption that evolution proceeds by accumulation of small effect mutations, does not require species specific input and can be applied to any asexual population under persistent selection pressure. We demonstrate its performance using hist…
Spatial models where growth is limited to the edge of the expansions have been instrumental to understand the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular tumours. A complete characterization of the coalescence process generated by spatial growth is still lacking, limiting our ability to apply classic population genetics inference to spatially growing populations. Here, we start filling this gap by investigating the statistical properties of the cell lineages generated by the two dimensional Eden model, leveraging…
Classic experiments on the distribution of ducks around separated food sources found consistency with the `ideal free' distribution in which the local population is proportional to the local supply rate. Motivated by this experiment and others, we examine the analogous problem in the microbial world: the distribution of chemotactic bacteria around multiple nearby food sources. In contrast to the optimization of uptake rate that may hold at the level of a single cell in a spatially varying nutrient field, nutrient consumption by a population of chemotactic cells will modify the nutrient field, …
Genome sizes have evolved to vary widely, from 250 bases in viroids to 670 billion bases in amoeba. This remarkable variation in genome size is the outcome of complex interactions between various evolutionary factors such as point mutation rate, population size, insertions and deletions, and genome editing mechanisms that may be specific to certain taxonomic lineages. While comparative genomics analyses have uncovered some of the relationships between these diverse evolutionary factors, we still do not understand what drives genome size evolution. Specifically, it is not clear how primordial m…
