Survival probability of beneficial mutations in bacterial batch culture

Neutral diversity in experimental metapopulations

New automated and high-throughput methods allow the manipulation and selection of numerous bacterial populations. In this manuscript we are interested in the neutral diversity patterns that emerge from such a setup in which many bacterial populations are grown in parallel serial transfers, in some cases with population-wide extinction and splitting events. We model bacterial growth by a birth-death process and use the theory of coalescent point processes. We show that there is a dilution factor that optimises the expected amount of neutral diversity for a given number of cycles, and study the power law behaviour of the mutation frequency spectrum for different experimental regimes. We also explore how neutral variation diverges between two recently split populations by establishing a new formula for the expected number of shared and private mutations. Finally, we show the interest of such a setup to select a phenotype of interest that requires multiple mutations.

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.

Selection bias in mutation accumulation

Mutation accumulation (MA) experiments, in which de novo mutations are sampled and subsequently characterized, are an essential tool in understanding the processes underlying evolution. In microbial populations, MA protocols typically involve a period of population growth between severe bottlenecks, such that a single individual can form a visible colony. While it has long been appreciated that the action of positive selection during this growth phase cannot be eliminated, it is typically assumed to be negligible. Here, we quantify the effect of both positive and negative selection in MA studies, demonstrating that selective effects can substantially bias the distribution of fitness effects (DFE) and mutation rates estimated from typical MA protocols in microbes. We then present a simple correction for this bias which applies to both beneficial and deleterious mutations, and can be used to correct the observed DFE in multiple environments. We use simulated MA experiments to illustrate the extent to which the MA-inferred DFE differs from the underlying true DFE, and demonstrate that the proposed correction accurately reconstructs the true DFE over a wide range of scenarios; we also provide an example of these corrections applied to experimental data. These results highlight that positive selection during microbial MA experiments is in fact not negligible, but can be corrected to gain a more accurate understanding of fundamental evolutionary parameters. This article is protected by copyright. All rights reserved.

Phage strategies facilitate bacterial coexistence under environmental variability

Bacterial communities are often exposed to temporal variations in resource availability, which exceed bacterial generation times and thereby affect bacterial coexistence. Bacterial population dynamics are also shaped by bacteriophages, which are a main cause of bacterial mortality. Several strategies are proposed in the literature to describe infections by phages, such as "Killing the Winner", "Piggyback the loser" (PtL) or "Piggyback the Winner" (PtW). The two temperate phage strategies PtL and PtW are defined by a change from lytic to lysogenic infection when the host density changes, from high to low or from low to high, respectively. To date, the occurrence of different phage strategies and their response to environmental variability is poorly understood. In our study, we developed a microbial trophic network model using ordinary differential equations (ODEs) and performed 'in silico' experiments. To model the switch from the lysogenic to the lytic cycle, we modified the lysis rate of infected bacteria and their growth was turned on or off using a density-dependent switching point. We addressed whether and how the different phage strategies facilitate bacteria coexistence competing for limiting resources. We also studied the impact of a fluctuating resource inflow to evaluate the response of the different phage strategies to environmental variability. Our results show that the viral shunt (i.e. nutrient release after bacterial lysis) leads to an enrichment of the system. This enrichment enables bacterial coexistence at lower resource concentrations. We were able to show that an established, purely lytic model leads to stable bacterial coexistence despite fluctuating resources. Both temperate phage models differ in their coexistence patterns. The model of PtW yields stable bacterial coexistence at a limited range of resource supply and is most sensitive to resource fluctuations. Interestingly, the purely lytic phage strategy and PtW both result in stable bacteria coexistence at oligotrophic conditions. The PtL model facilitates stable bacterial coexistence over a large range of stable and fluctuating resource inflow. An increase in bacterial growth rate results in a higher resilience to resource variability for the PtL and the lytic infection model. We propose that both temperate phage strategies represent different mechanisms of phages coping with environmental variability. Our study demonstrates how phage strategies can maintain bacterial coexistence in constant and fluctuating environments.

Evolution of Microbial Growth Traits Under Serial Dilution

Selection of mutants in a microbial population depends on multiple cellular traits. In serial-dilution evolution experiments, three key traits are the lag time when transitioning from starvation to growth, the exponential growth rate, and the yield (number of cells per unit resource). Here, we investigate how these traits evolve in laboratory evolution experiments using a minimal model of population dynamics, where the only interaction between cells is competition for a single limiting resource. We find that the fixation probability of a beneficial mutation depends on a linear combination of its growth rate and lag time relative to its immediate ancestor, even under clonal interference. The relative selective pressure on growth rate and lag time is set by the dilution factor; a larger dilution factor favors the adaptation of growth rate over the adaptation of lag time. The model shows that yield, however, is under no direct selection. We also show how the adaptation speeds of growth and lag depend on experimental parameters and the underlying supply of mutations. Finally, we investigate the evolution of covariation between these traits across populations, which reveals that the population growth rate and lag time can evolve a nonzero correlation even if mutations have uncorrelated effects on the two traits. Altogether these results provide useful guidance to future experiments on microbial evolution.

The Effect of Population Bottleneck Size and Selective Regime on Genetic Diversity and Evolvability in Bacteria

Population bottlenecks leading to a drastic reduction of the population size are common in the evolutionary dynamics of natural populations; their occurrence is known to have implications for genome evolution due to genetic drift, the consequent reduction in genetic diversity, and the rate of adaptation. Nevertheless, an empirical characterization of the effect of population bottleneck size on evolutionary dynamics of bacteria is currently lacking. In this study, we show that selective conditions have a stronger effect on the evolutionary history of bacteria in comparison to population bottlenecks. We evolved Escherichia coli populations under three different population bottleneck sizes (small, medium, and large) in two temperature regimes (37 °C and 20 °C). We find a high genetic diversity in the large in comparison to the small bottleneck size. Nonetheless, the cold temperature led to reduced genetic diversity regardless the bottleneck size; hence, the temperature has a stronger effect on the genetic diversity in comparison to the bottleneck size. A comparison of the fitness gain among the evolved populations reveals a similar pattern where the temperature has a significant effect on the fitness. Our study demonstrates that population bottlenecks are an important determinant of bacterial evolvability; their consequences depend on the selective conditions and are best understood via their effect on the standing genetic variation.

Predicting microbial growth in a mixed culture from growth curve data

Determining the fitness of specific microbial genotypes has extensive application in microbial genetics, evolution, and biotechnology. While estimates from growth curves are simple and allow high throughput, they are inaccurate and do not account for interactions between costs and benefits accruing over different parts of a growth cycle. For this reason, pairwise competition experiments are the current "gold standard" for accurate estimation of fitness. However, competition experiments require distinct markers, making them difficult to perform between isolates derived from a common ancestor or between isolates of nonmodel organisms. In addition, competition experiments require that competing strains be grown in the same environment, so they cannot be used to infer the fitness consequence of different environmental perturbations on the same genotype. Finally, competition experiments typically consider only the end-points of a period of competition so that they do not readily provide information on the growth differences that underlie competitive ability. Here, we describe a computational approach for predicting density-dependent microbial growth in a mixed culture utilizing data from monoculture and mixed-culture growth curves. We validate this approach using 2 different experiments with Escherichia coli and demonstrate its application for estimating relative fitness. Our approach provides an effective way to predict growth and infer relative fitness in mixed cultures.

Trade-offs between microbial growth phases lead to frequency-dependent and non-transitive selection

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 that 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 population dynamics when there are trade-offs between phases: multiple strains can coexist or exhibit bistability due to frequency-dependent selection, and strains can engage in rock-paper-scissors interactions due to non-transitive selection. We characterize the environmental conditions and patterns of traits necessary to realize these phenomena, which we show to be readily accessible to experiments. Our results provide a theoretical framework for analysing high-throughput measurements of microbial growth traits, especially interpreting the pleiotropy and correlations between traits across mutants. This work also highlights the need for more comprehensive measurements of selection in simple microbial systems, where the concept of an ordinary fitness landscape breaks down.

Effects of Transmission Bottlenecks on the Diversity of Influenza A Virus

We investigate the fate of de novo mutations that occur during the in-host replication of a pathogenic virus, predicting the probability that such mutations are passed on during disease transmission to a new host. Using influenza A virus as a model organism, we develop a life-history model of the within-host dynamics of the infection, deriving a multitype branching process with a coupled deterministic model to capture the population of available target cells. We quantify the fate of neutral mutations and mutations affecting five life-history traits: clearance, attachment, budding, cell death, and eclipse phase timing. Despite the severity of disease transmission bottlenecks, our results suggest that in a single transmission event, several mutations that appeared de novo in the donor are likely to be transmitted to the recipient. Even in the absence of a selective advantage for these mutations, the sustained growth phase inherent in each disease transmission cycle generates genetic diversity that is not eliminated during the transmission bottleneck.

Mutation in populations governed by a Galton-Watson branching process

A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is presented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral mutations. The asymptotic stationary solution is obtained and has the property that the extant population partitions into subpopulations whose relative sizes are determined by mutation rates. An approximate time-dependent solution is obtained in the limit of low mutation rates. This solution has the property that the system undergoes a rapid transition from a drift-dominated phase to a mutation-dominated phase in which the distribution collapses onto the asymptotic stationary distribution. The changeover point of the transition is determined by the per-generation growth factor and mutation rate. The approximate solution is confirmed using numerical simulations.

Exploring genetic suppression interactions on a global scale

Genetic suppression occurs when the phenotypic defects caused by a mutation in a particular gene are rescued by a mutation in a second gene. To explore the principles of genetic suppression, we examined both literature-curated and unbiased experimental data, involving systematic genetic mapping and whole-genome sequencing, to generate a large-scale suppression network among yeast genes. Most suppression pairs identified novel relationships among functionally related genes, providing new insights into the functional wiring diagram of the cell. In addition to suppressor mutations, we identified frequent secondary mutations,in a subset of genes, that likely cause a delay in the onset of stationary phase, which appears to promote their enrichment within a propagating population. These findings allow us to formulate and quantify general mechanisms of genetic suppression.

A Model for Designing Adaptive Laboratory Evolution Experiments

The occurrence of mutations is a cornerstone of the evolutionary theory of adaptation, capitalizing on the rare chance that a mutation confers a fitness benefit. Natural selection is increasingly being leveraged in laboratory settings for industrial and basic science applications. Despite increasing deployment, there are no standardized procedures available for designing and performing adaptive laboratory evolution (ALE) experiments. Thus, there is a need to optimize the experimental design, specifically for determining when to consider an experiment complete and for balancing outcomes with available resources (i.e., laboratory supplies, personnel, and time). To design and to better understand ALE experiments, a simulator, ALEsim, was developed, validated, and applied to the optimization of ALE experiments. The effects of various passage sizes were experimentally determined and subsequently evaluated with ALEsim, to explain differences in experimental outcomes. Furthermore, a beneficial mutation rate of 10^-6.9 to 10^-8.4 mutations per cell division was derived. A retrospective analysis of ALE experiments revealed that passage sizes typically employed in serial passage batch culture ALE experiments led to inefficient production and fixation of beneficial mutations. ALEsim and the results described here will aid in the design of ALE experiments to fit the exact needs of a project while taking into account the resources required and will lower the barriers to entry for this experimental technique.IMPORTANCE ALE is a widely used scientific technique to increase scientific understanding, as well as to create industrially relevant organisms. The manner in which ALE experiments are conducted is highly manual and uniform, with little optimization for efficiency. Such inefficiencies result in suboptimal experiments that can take multiple months to complete. With the availability of automation and computer simulations, we can now perform these experiments in an optimized fashion and can design experiments to generate greater fitness in an accelerated time frame, thereby pushing the limits of what adaptive laboratory evolution can achieve.

Prophage Provide a Safe Haven for Adaptive Exploration in Temperate Viruses

Prophage sequences constitute a substantial fraction of the temperate virus gene pool. Although subject to mutational decay, prophage sequences can also be an important source of adaptive mutations for these viral populations. Here we develop a life-history model for temperate viruses, including both the virulent (lytic) and the temperate phases of the life cycle. We then examine the survival of mutations that increase fitness during the lytic phase (attachment rate, burst size), increase fitness in the temperate phase (increasing host survival), or affect transitions between the two phases (integration or induction probability). We find that beneficial mutations are much more likely to survive, ultimately, if they first occur in the prophage state. This conclusion applies even to traits that are only expressed during the lytic phase, and arises due to the substantially lower variance in the offspring distribution during the temperate cycle. This observation, however, is balanced by the fact that many more mutations can be generated during lytic replication. Overall we predict that the prophage state provides a refuge, relatively shielded from genetic drift, in which temperate viruses can explore possible adaptive steps.

Benefits of a Recombination-Proficient Escherichia coli System for Adaptive Laboratory Evolution

Adaptive laboratory evolution typically involves the propagation of organisms asexually to select for mutants with the desired phenotypes. However, asexual evolution is prone to competition among beneficial mutations (clonal interference) and the accumulation of hitchhiking and neutral mutations. The benefits of horizontal gene transfer toward overcoming these known disadvantages of asexual evolution were characterized in a strain of Escherichia coli engineered for superior sexual recombination (genderless). Specifically, we experimentally validated the capacity of the genderless strain to reduce the mutational load and recombine beneficial mutations. We also confirmed that inclusion of multiple origins of transfer influences both the frequency of genetic exchange throughout the chromosome and the linkage of donor DNA. We built a simple kinetic model to estimate recombination frequency as a function of transfer size and relative genotype enrichment in batch transfers; the model output correlated well with the experimental data. Our results provide strong support for the advantages of utilizing the genderless strain over its asexual counterpart during adaptive laboratory evolution for generating beneficial mutants with reduced mutational load.

IMPORTANCE

Over 80 years ago Fisher and Muller began a debate on the origins of sexual recombination. Although many aspects of sexual recombination have been examined at length, experimental evidence behind the behaviors of recombination in many systems and the means to harness it remain elusive. In this study, we sought to experimentally validate some advantages of recombination in typically asexual Escherichia coli and determine if a sexual strain of E. coli can become an effective tool for strain development.

How Life History Can Sway the Fixation Probability of Mutants

In this work, we study the effects of demographic structure on evolutionary dynamics when selection acts on reproduction, survival, or both. In contrast to the previously discovered pattern that the fixation probability of a neutral mutant decreases while the population becomes younger, we show that a mutant with a constant selective advantage may have a maximum or a minimum of the fixation probability in populations with an intermediate fraction of young individuals. This highlights the importance of life history and demographic structure in studying evolutionary dynamics. We also illustrate the fundamental differences between selection on reproduction and selection on survival when age structure is present. In addition, we evaluate the relative importance of size and structure of the population in determining the fixation probability of the mutant. Our work lays the foundation for also studying density- and frequency-dependent effects in populations when demographic structures cannot be neglected.