An ABC method for estimating the rate and distribution of effects of beneficial mutations

Neural networks enable efficient and accurate simulation-based inference of evolutionary parameters from adaptation dynamics

The rate of adaptive evolution depends on the rate at which beneficial mutations are introduced into a population and the fitness effects of those mutations. The rate of beneficial mutations and their expected fitness effects is often difficult to empirically quantify. As these 2 parameters determine the pace of evolutionary change in a population, the dynamics of adaptive evolution may enable inference of their values. Copy number variants (CNVs) are a pervasive source of heritable variation that can facilitate rapid adaptive evolution. Previously, we developed a locus-specific fluorescent CNV reporter to quantify CNV dynamics in evolving populations maintained in nutrient-limiting conditions using chemostats. Here, we use CNV adaptation dynamics to estimate the rate at which beneficial CNVs are introduced through de novo mutation and their fitness effects using simulation-based likelihood-free inference approaches. We tested the suitability of 2 evolutionary models: a standard Wright-Fisher model and a chemostat model. We evaluated 2 likelihood-free inference algorithms: the well-established Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) algorithm, and the recently developed Neural Posterior Estimation (NPE) algorithm, which applies an artificial neural network to directly estimate the posterior distribution. By systematically evaluating the suitability of different inference methods and models, we show that NPE has several advantages over ABC-SMC and that a Wright-Fisher evolutionary model suffices in most cases. Using our validated inference framework, we estimate the CNV formation rate at the GAP1 locus in the yeast Saccharomyces cerevisiae to be 10-4.7 to 10-4 CNVs per cell division and a fitness coefficient of 0.04 to 0.1 per generation for GAP1 CNVs in glutamine-limited chemostats. We experimentally validated our inference-based estimates using 2 distinct experimental methods-barcode lineage tracking and pairwise fitness assays-which provide independent confirmation of the accuracy of our approach. Our results are consistent with a beneficial CNV supply rate that is 10-fold greater than the estimated rates of beneficial single-nucleotide mutations, explaining the outsized importance of CNVs in rapid adaptive evolution. More generally, our study demonstrates the utility of novel neural network-based likelihood-free inference methods for inferring the rates and effects of evolutionary processes from empirical data with possible applications ranging from tumor to viral evolution.

SodaPop: a forward simulation suite for the evolutionary dynamics of asexual populations on protein fitness landscapes

Motivation

Protein evolution is determined by forces at multiple levels of biological organization. Random mutations have an immediate effect on the biophysical properties, structure and function of proteins. These same mutations also affect the fitness of the organism. However, the evolutionary fate of mutations, whether they succeed to fixation or are purged, also depends on population size and dynamics. There is an emerging interest, both theoretically and experimentally, to integrate these two factors in protein evolution. Although there are several tools available for simulating protein evolution, most of them focus on either the biophysical or the population-level determinants, but not both. Hence, there is a need for a publicly available computational tool to explore both the effects of protein biophysics and population dynamics on protein evolution.

Results

To address this need, we developed SodaPop, a computational suite to simulate protein evolution in the context of the population dynamics of asexual populations. SodaPop accepts as input several fitness landscapes based on protein biochemistry or other user-defined fitness functions. The user can also provide as input experimental fitness landscapes derived from deep mutational scanning approaches or theoretical landscapes derived from physical force field estimates. Here, we demonstrate the broad utility of SodaPop with different applications describing the interplay of selection for protein properties and population dynamics. SodaPop is designed such that population geneticists can explore the influence of protein biochemistry on patterns of genetic variation, and that biochemists and biophysicists can explore the role of population size and demography on protein evolution.

Availability and implementation

Source code and binaries are freely available at https://github.com/louisgt/SodaPop under the GNU GPLv3 license. The software is implemented in C++ and supported on Linux, Mac OS/X and Windows.

Supplementary information

Supplementary data are available at Bioinformatics online.

Multidrug-resistant bacteria compensate for the epistasis between resistances

Mutations conferring resistance to antibiotics are typically costly in the absence of the drug, but bacteria can reduce this cost by acquiring compensatory mutations. Thus, the rate of acquisition of compensatory mutations and their effects are key for the maintenance and dissemination of antibiotic resistances. While compensation for single resistances has been extensively studied, compensatory evolution of multiresistant bacteria remains unexplored. Importantly, since resistance mutations often interact epistatically, compensation of multiresistant bacteria may significantly differ from that of single-resistant strains. We used experimental evolution, next-generation sequencing, in silico simulations, and genome editing to compare the compensatory process of a streptomycin and rifampicin double-resistant Escherichia coli with those of single-resistant clones. We demonstrate that low-fitness double-resistant bacteria compensate faster than single-resistant strains due to the acquisition of compensatory mutations with larger effects. Strikingly, we identified mutations that only compensate for double resistance, being neutral or deleterious in sensitive or single-resistant backgrounds. Moreover, we show that their beneficial effects strongly decrease or disappear in conditions where the epistatic interaction between resistance alleles is absent, demonstrating that these mutations compensate for the epistasis. In summary, our data indicate that epistatic interactions between antibiotic resistances, leading to large fitness costs, possibly open alternative paths for rapid compensatory evolution, thereby potentially stabilizing costly multiple resistances in bacterial populations.

Antibiotics target essential cellular functions, such as translation or cell wall biogenesis, and bacteria can become resistant to antibiotics by acquiring mutations in genes encoding those functions. This causes most drug-resistance mutations to be detrimental in the absence of the drug. However, bacteria can reduce this handicap by acquiring additional mutations, known as compensatory mutations. Compensatory evolution is crucial for the maintenance and dissemination of antibiotic resistances in bacterial populations. While compensation for single resistances has been extensively studied, compensatory evolution of multidrug-resistant bacteria remains unexplored. Importantly, interactions between resistance mutations are frequent, and this may cause compensation of multidrug-resistant bacteria to differ significantly from that of single-resistant strains. By comparing compensation of single- and double-drug–resistant E. coli, we found that double-drug–resistant bacteria compensate faster than single-drug–resistant strains. This is due to the acquisition of compensatory mutations with larger effects and possibly driven by the large fitness cost of double-drug resistance. Strikingly, we identified mutations that compensate specifically for the interaction between drug resistances, since they are beneficial only for double-drug–resistant bacteria and in conditions in which the interaction between resistances occurs. In summary, our data indicate that certain interactions between antibiotic-resistance mutations can open alternative paths for rapid compensatory evolution, thereby potentially stabilizing multiple drug resistances in bacterial populations.

Trade-Offs of Escherichia coli Adaptation to an Intracellular Lifestyle in Macrophages

The bacterium Escherichia coli exhibits remarkable genomic and phenotypic variation, with some pathogenic strains having evolved to survive and even replicate in the harsh intra-macrophage environment. The rate and effects of mutations that can cause pathoadaptation are key determinants of the pace at which E. coli can colonize such niches and become pathogenic. We used experimental evolution to determine the speed and evolutionary paths undertaken by a commensal strain of E. coli when adapting to intracellular life. We estimated the acquisition of pathoadaptive mutations at a rate of 10⁻⁶ per genome per generation, resulting in the fixation of more virulent strains in less than a hundred generations. Whole genome sequencing of independently evolved clones showed that the main targets of intracellular adaptation involved loss of function mutations in genes implicated in the assembly of the lipopolysaccharide core, iron metabolism and di- and tri-peptide transport, namely rfaI, fhuA and tppB, respectively. We found a substantial amount of antagonistic pleiotropy in evolved populations, as well as metabolic trade-offs, commonly found in intracellular bacteria with reduced genome sizes. Overall, the low levels of clonal interference detected indicate that the first steps of the transition of a commensal E. coli into intracellular pathogens are dominated by a few pathoadaptive mutations with very strong effects.

Genomic investigations of evolutionary dynamics and epistasis in microbial evolution experiments

Microbial evolution experiments enable us to watch adaptation in real time, and to quantify the repeatability and predictability of evolution by comparing identical replicate populations. Further, we can resurrect ancestral types to examine changes over evolutionary time. Until recently, experimental evolution has been limited to measuring phenotypic changes, or to tracking a few genetic markers over time. However, recent advances in sequencing technology now make it possible to extensively sequence clones or whole-population samples from microbial evolution experiments. Here, we review recent work exploiting these techniques to understand the genomic basis of evolutionary change in experimental systems. We first focus on studies that analyze the dynamics of genome evolution in microbial systems. We then survey work that uses observations of sequence evolution to infer aspects of the underlying fitness landscape, concentrating on the epistatic interactions between mutations and the constraints these interactions impose on adaptation.

Polyploidy can drive rapid adaptation in yeast

Polyploidy is observed across the tree of life, yet its influence on evolution remains incompletely understood^1–4. Polyploidy, usually whole genome duplication (WGD), is proposed to alter the rate of evolutionary adaptation. This could occur through complex effects on the frequency or fitness of beneficial mutations ^2,5–7. For example, in diverse cell types and organisms, immediately after a WGD, newly formed polyploids missegregate chromosomes and undergo genetic instability^8–13. The instability following WGDs is thought to provide adaptive mutations in microorganisms^13,14 and can promote tumorigenesis in mammalian cells^11,15. Polyploidy may also affect adaptation independent of beneficial mutations through ploidy-specific changes in cell physiology¹⁶. Here, we performed in vitro evolution experiments to directly test whether polyploidy can accelerate evolutionary adaptation. Compared to haploids and diploids, tetraploids underwent significantly faster adaptation. Mathematical modeling suggested that rapid adaptation of tetraploids was driven by higher rates of beneficial mutations with stronger fitness effects, which was supported by whole-genome sequencing and phenotypic analyses of evolved clones. Chromosome aneuploidy, concerted chromosome loss, and point mutations all provided large fitness gains. We identified several mutations whose beneficial effects were manifest specifically in the tetraploid strains. Together, these results provide direct quantitative evidence that in some environments polyploidy can accelerate evolutionary adaptation.

Effects of new mutations on fitness: insights from models and data

The rates and properties of new mutations affecting fitness have implications for a number of outstanding questions in evolutionary biology. Obtaining estimates of mutation rates and effects has historically been challenging, and little theory has been available for predicting the distribution of fitness effects (DFE); however, there have been recent advances on both fronts. Extreme-value theory predicts the DFE of beneficial mutations in well-adapted populations, while phenotypic fitness landscape models make predictions for the DFE of all mutations as a function of the initial level of adaptation and the strength of stabilizing selection on traits underlying fitness. Direct experimental evidence confirms predictions on the DFE of beneficial mutations and favors distributions that are roughly exponential but bounded on the right. A growing number of studies infer the DFE using genomic patterns of polymorphism and divergence, recovering a wide range of DFE. Future work should be aimed at identifying factors driving the observed variation in the DFE. We emphasize the need for further theory explicitly incorporating the effects of partial pleiotropy and heterogeneity in the environment on the expected DFE.

The first steps of adaptation of Escherichia coli to the gut are dominated by soft sweeps

The accumulation of adaptive mutations is essential for survival in novel environments. However, in clonal populations with a high mutational supply, the power of natural selection is expected to be limited. This is due to clonal interference - the competition of clones carrying different beneficial mutations - which leads to the loss of many small effect mutations and fixation of large effect ones. If interference is abundant, then mechanisms for horizontal transfer of genes, which allow the immediate combination of beneficial alleles in a single background, are expected to evolve. However, the relevance of interference in natural complex environments, such as the gut, is poorly known. To address this issue, we have developed an experimental system which allows to uncover the nature of the adaptive process as Escherichia coli adapts to the mouse gut. This system shows the invasion of beneficial mutations in the bacterial populations and demonstrates the pervasiveness of clonal interference. The observed dynamics of change in frequency of beneficial mutations are consistent with soft sweeps, where different adaptive mutations with similar phenotypes, arise repeatedly on different haplotypes without reaching fixation. Despite the complexity of this ecosystem, the genetic basis of the adaptive mutations revealed a striking parallelism in independently evolving populations. This was mainly characterized by the insertion of transposable elements in both coding and regulatory regions of a few genes. Interestingly, in most populations we observed a complete phenotypic sweep without loss of genetic variation. The intense clonal interference during adaptation to the gut environment, here demonstrated, may be important for our understanding of the levels of strain diversity of E. coli inhabiting the human gut microbiota and of its recombination rate.

Adaptation to novel environments involves the accumulation of beneficial mutations. If these are rare the process will proceed slowly with each one sweeping to fixation on its own. On the contrary if they are common in clonal populations, individuals carrying different beneficial alleles will experience intense competition and only those clones carrying the stronger effect mutations will leave a future line of descent. This phenomenon is known as clonal interference and the extent to which it occurs in natural environments is unknown. One of the most complex natural environments for E. coli is the mammalian intestine, where it evolves in the presence of many species comprising the gut microbiota. We have studied the dynamics of adaptation of E. coli populations evolving in this relevant ecosystem. We show that clonal interference is pervasive in the mouse gut and that the targets of natural selection are similar in independently E. coli evolving populations. These results illustrate how experimental evolution in natural environments allows us to dissect the mechanisms underlying adaptation and its complex dynamics and further reveal the importance of mobile genetic elements in contributing to the adaptive diversification of bacterial populations in the gut.

The fates of mutant lineages and the distribution of fitness effects of beneficial mutations in laboratory budding yeast populations

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 measurements to infer the distribution of fitness effects of new beneficial mutations. To do so, we seeded marked lineages with different fitness advantages into replicate populations and tracked their subsequent frequencies for hundreds of generations. Our results illustrate the transition between strongly advantageous lineages that decisively sweep to fixation and more moderately advantageous lineages that are often outcompeted by new mutations arising during the course of the experiment. We developed an approximate likelihood framework to compare our data to simulations and found that the effects of these competing beneficial mutations were best approximated by an exponential distribution, rather than one with a single effect size. We then used this inferred distribution of fitness effects to predict the rate of adaptation in a set of independent control populations. Finally, we discuss how our experimental design can serve as a screen for rare, large-effect beneficial mutations.