Estimation of the rate and effect of new beneficial mutations in asexual populations

A branching process model of evolutionary rescue

Evolutionary rescue is the process whereby a declining population may start growing again, thus avoiding extinction, via an increase in the frequency of fitter genotypes. These genotypes may either already be present in the population in small numbers, or arise by mutation as the population declines. We present a simple two-type discrete-time branching process model and use it to obtain results such as the probability of rescue, the shape of the population growth curve of a rescued population, and the time until the first rescuing mutation occurs. Comparisons are made to existing results in the literature in cases where both the mutation rate and the selective advantage of the beneficial mutations are small.

Dynamics of bacterial adaptation

Determining pattern in the dynamics of population evolution is a long-standing focus of evolutionary biology. Complementing the study of natural populations, microbial laboratory evolution experiments have become an important tool for addressing these dynamics because they allow detailed and replicated analysis of evolution in response to controlled environmental and genetic conditions. Key findings include a tendency for smoothly declining rates of adaptation during selection in constant environments, at least in part a reflection of antagonism between accumulating beneficial mutations, and a large number of beneficial mutations available to replicate populations leading to significant, but relatively low genetic parallelism, even as phenotypic characteristics show high similarity. Together, there is a picture of adaptation as a process with a varied and largely unpredictable genetic basis leading to much more similar phenotypic outcomes. Increasing sophistication of sequencing and genetic tools will allow insight into mechanisms behind these and other patterns.

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.

Experimental Studies of Evolutionary Dynamics in Microbes

Evolutionary dynamics in laboratory microbial evolution experiments can be surprisingly complex. In the past two decades, observations of these dynamics have challenged simple models of adaptation and have shown that clonal interference, hitchhiking, ecological diversification, and contingency are widespread. In recent years, advances in high-throughput strain maintenance and phenotypic assays, the dramatically reduced cost of genome sequencing, and emerging methods for lineage barcoding have made it possible to observe evolutionary dynamics at unprecedented resolution. These new methods can now begin to provide detailed measurements of key aspects of fitness landscapes and of evolutionary outcomes across a range of systems. These measurements can highlight challenges to existing theoretical models and guide new theoretical work towards the complications that are most widely important.

Diminishing-returns epistasis decreases adaptability along an evolutionary trajectory

Populations evolving in constant environments exhibit declining adaptability. Understanding the basis of this pattern could reveal underlying processes determining the repeatability of evolutionary outcomes. In principle, declining adaptability can be due to a decrease in the effect size of beneficial mutations, a decrease in the rate at which they occur, or some combination of both. By evolving Escherichia coli populations started from different steps along a single evolutionary trajectory, we show that declining adaptability is best explained by a decrease in the size of available beneficial mutations. This pattern reflected the dominant influence of negative genetic interactions that caused new beneficial mutations to confer smaller benefits in fitter genotypes. Genome sequencing revealed that starting genotypes that were more similar to one another did not exhibit greater similarity in terms of new beneficial mutations, supporting the view that epistasis acts globally, having a greater influence on the effect than on the identity of available mutations along an adaptive trajectory. Our findings provide support for a general mechanism that leads to predictable phenotypic evolutionary trajectories.

Adaptation of Escherichia coli to glucose promotes evolvability in lactose

The selective history of a population can influence its subsequent evolution, an effect known as historical contingency. We previously observed that five of six replicate populations that were evolved in a glucose-limited environment for 2000 generations, then switched to lactose for 1000 generations, had higher fitness increases in lactose than populations started directly from the ancestor. To test if selection in glucose systematically increased lactose evolvability, we started 12 replay populations--six from a population subsample and six from a single randomly selected clone--from each of the six glucose-evolved founder populations. These replay populations and 18 ancestral populations were evolved for 1000 generations in a lactose-limited environment. We found that replay populations were initially slightly less fit in lactose than the ancestor, but were more evolvable, in that they increased in fitness at a faster rate and to higher levels. This result indicates that evolution in the glucose environment resulted in genetic changes that increased the potential of genotypes to adapt to lactose. Genome sequencing identified four genes--iclR, nadR, spoT, and rbs--that were mutated in most glucose-evolved clones and are candidates for mediating increased evolvability. Our results demonstrate that short-term selective costs during selection in one environment can lead to changes in evolvability that confer longer term benefits.

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.

Constraints on adaptation of Escherichia coli to mixed-resource environments increase over time

Can a population evolved in two resources reach the same fitness in both as specialist populations evolved in each of the individual resources? This question is central to theories of ecological specialization, the maintenance of genetic variation, and sympatric speciation, yet relatively few experiments have examined costs of generalism over long-term adaptation. We tested whether selection in environments containing two resources limits a population's ability to adapt to the individual resources by comparing the fitness of replicate Escherichia coli populations evolved for 6000 generations in the presence of glucose or lactose alone (specialists), or in varying presentations of glucose and lactose together (generalists). We found that all populations had significant fitness increases in both resources, though the magnitude and rate of these increases differed. For the first 4000 generations, most generalist populations increased in fitness as quickly in the individual resources as the corresponding specialist populations. From 5000 generations, however, a widespread cost of adaptation affected all generalists, indicating a growing constraint on their abilities to adapt to two resources simultaneously. Our results indicate that costs of generalism are prevalent, but may influence evolutionary trajectories only after a period of cost-free adaptation.

Systematic perturbation of cytoskeletal function reveals a linear scaling relationship between cell geometry and fitness

Diversification of cell size is hypothesized to have occurred through a process of evolutionary optimization, but direct demonstrations of causal relationships between cell geometry and fitness are lacking. Here, we identify a mutation from a laboratory-evolved bacterium that dramatically increases cell size through cytoskeletal perturbation and confers a large fitness advantage. We engineer a library of cytoskeletal mutants of different sizes and show that fitness scales linearly with respect to cell size over a wide physiological range. Quantification of the growth rates of single cells during the exit from stationary phase reveals that transitions between "feast-or-famine" growth regimes are a key determinant of cell-size-dependent fitness effects. We also uncover environments that suppress the fitness advantage of larger cells, indicating that cell-size-dependent fitness effects are subject to both biophysical and metabolic constraints. Together, our results highlight laboratory-based evolution as a powerful framework for studying the quantitative relationships between morphology and fitness.

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.

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

Determining the distribution of adaptive mutations available to natural selection is a difficult task. These are rare events and most of them are lost by chance. Some theoretical works propose that the distribution of newly arising beneficial mutations should be close to exponential. Empirical data are scarce and do not always support an exponential distribution. Analysis of the dynamics of adaptation in asexual populations of microorganisms has revealed that these can be summarized by two effective parameters, the effective mutation rate, U_e, and the effective selection coefficient of a beneficial mutation, S_e. Here, we show that these effective parameters will not always reflect the rate and mean effect of beneficial mutations, especially when the distribution of arising mutations has high variance, and the mutation rate is high. We propose a method to estimate the distribution of arising beneficial mutations, which is motivated by a common experimental setup. The method, which we call One Biallelic Marker Approximate Bayesian Computation, makes use of experimental data consisting of periodic measures of neutral marker frequencies and mean population fitness. Using simulations, we find that this method allows the discrimination of the shape of the distribution of arising mutations and that it provides reasonable estimates of their rates and mean effects in ranges of the parameter space that may be of biological relevance.