Evaluating the impact of population bottlenecks in experimental evolution

Experimental evolution involves severe, periodic reductions in population size when fresh media are inoculated during serial transfer. These bottlenecks affect the dynamics of evolution, reducing the probability that a beneficial mutation will reach fixation. We quantify the impact of these bottlenecks on the evolutionary dynamics, for populations that grow exponentially between transfers and for populations in which growth is curbed by a resource-limited environment. We find that in both cases, mutations that survive bottlenecks are equally likely to occur, per unit time, at all times during the growth phase. We estimate the total fraction of beneficial mutations that are lost due to bottlenecks during experimental evolution protocols and derive the "optimal" dilution ratio, the ratio that maximizes the number of surviving beneficial mutations. Although more severe dilution ratios are often used in the literature, we find that a ratio of 0.1-0.2 minimizes the chances that rare beneficial mutations are lost. Finally, we provide a number of useful approximate results and illustrate our approach with applications to experimental evolution protocols in the literature.     

Frequent beneficial mutations during single-colony serial transfer of Streptococcus pneumoniae

The appearance of new mutations within a population provides the raw material for evolution. The consistent decline in fitness observed in classical mutation accumulation studies has provided support for the long-held view that deleterious mutations are more common than beneficial mutations. Here we present results of a study using a mutation accumulation design with the bacterium Streptococcus pneumoniae in which the fitness of the derived populations increased. This rise in fitness was associated specifically with adaptation to survival during brief stationary phase periods between single-colony population bottlenecks. To understand better the population dynamics behind this unanticipated adaptation, we developed a maximum likelihood model describing the processes of mutation and stationary-phase selection in the context of frequent population bottlenecks. Using this model, we estimate that the rate of beneficial mutations may be as high as 4.8×10(-4) events per genome for each time interval corresponding to the pneumococcal generation time. This rate is several orders of magnitude higher than earlier estimates of beneficial mutation rates in bacteria but supports recent results obtained through the propagation of small populations of Escherichia coli. Our findings indicate that beneficial mutations may be relatively frequent in bacteria and suggest that in S. pneumoniae, which develops natural competence for transformation, a steady supply of such mutations may be available for sampling by recombination.     

The effect of population bottlenecks on mutation rate evolution in asexual populations

In the absence of recombination, a mutator allele can spread through a population by hitchhiking with beneficial mutations that appear in its genetic background. Theoretical studies over the past decade have shown that the survival and fixation probability of beneficial mutations can be severely reduced by population size bottlenecks. Here, we use computational modelling and evolution experiments with the yeast S. cerevisiae to examine whether population bottlenecks can affect mutator dynamics in adapting asexual populations. In simulation, we show that population bottlenecks can inhibit mutator hitchhiking with beneficial mutations and are most effective at lower beneficial mutation supply rates. We then subjected experimental populations of yeast propagated at the same effective population size to three different bottleneck regimes and observed that the speed of mutator hitchhiking was significantly slower at smaller bottlenecks, consistent with our theoretical expectations. Our results, thus, suggest that bottlenecks can be an important factor in mutation rate evolution and can in certain circumstances act to stabilize or, at least, delay the progressive elevation of mutation rates in asexual populations. Additionally, our findings provide the first experimental support for the theoretically postulated effect of population bottlenecks on beneficial mutations and demonstrate the usefulness of studying mutator frequency dynamics for understanding the underlying dynamics of fitness‐affecting mutations.     

THE ADAPTATION RATE OF ASEXUALS: DELETERIOUS MUTATIONS,CLONAL INTERFERENCE AND POPULATION BOTTLENECKS

The rate at which a population adapts to its environment is a cornerstone of evolutionary theory, and recent experimental advances in microbial populations have renewed interest in predicting and testing this rate. Efforts to understand the adaptation rate theoretically are complicated by high mutation rates, to both beneficial and deleterious mutations, and by the fact that beneficial mutations compete with each other in asexual populations (clonal interference). Testable predictions must also include the effects of population bottlenecks, repeated reductions in population size imposed by the experimental protocol. In this contribution, we integrate previous work that addresses each of these issues, developing an overall prediction for the adaptation rate that includes: beneficial mutations with probabilistically distributed effects, deleterious mutations of arbitrary effect, population bottlenecks, and clonal interference.     

Modeling of typical microbial cell growth in batch culture

A mathematical model was developed, based on the time dependent changes of the specific growth rate, for prediction of the typical microbial cell growth in batch cultures. This model could predict both the lag growth phase and the stationary growth phase of batch cultures, and it was tested with the batch growth ofTrichoderma reesei andLactobacillus delbrucckii.     

A Genetic Strategy to Demonstrate the Occurrence of Spontaneous Mutations in Nondividing Cells within Colonies of Escherichia Coli

A genetic strategy was designed to examine the occurrence of mutations in stationary-phase populations. In this strategy, a parental population of cells is able to survive under both permissive and restrictive conditions whereas mutants at a particular target locus exhibit a conditional-lethal phenotype. Thus, by growing the population to stationary phase under restrictive conditions and then shifting it to permissive conditions, mutations that had arisen in stationary phase can be studied without confounding effects caused by the occurrence of similar mutations during growth of the population. In two different applications of this strategy, we have studied the reversion to Lac(+) in stationary phase of several Lac(-) mutations in Escherichia coli. Our results indicate that a variety of spontaneous point mutations and deletions, particularly those that are sensitive to the mechanisms of replication slippage (for their generation) and methyl-directed mismatch repair (for their correction), can arise in nondividing populations of cells within a colony. The frequency of their occurrence was also elevated in mutS strains, which are defective in such mismatch repair. These data have relevance to the ongoing debate on adaptive or directed mutations in bacteria.     

ADAPTATION RATES OF LYTIC VIRUSES DEPEND CRITICALLY ON WHETHER HOST CELLS SURVIVE THE BOTTLENECK

We use a branching process approach to estimate the substitution rate, the rate at which beneficial mutations occur and fix, in populations of lytic viruses whose growth is controlled by periodic population bottlenecks. Our model predicts that substitution rates, and by extension adaptation rates, are profoundly affected by the survival of infected host cells at the bottleneck. In particular, we find that direct transfer (or environmental) bottlenecks, in which some fraction of both free virus and host cells are preserved, are associated with relatively slow adaptation rates for the virus. In contrast, viruses can adapt much more quickly when only free virus is transferred to a new host population, as is typical in an epidemiological setting. Finally, when premature lysis of the host‐cell population is induced at the bottleneck, we predict that adaptation rates for the virus will, in general, be faster still. These results hold irrespective of the life‐history trait affected by the beneficial mutation. The substitution rates in the presence of environmental bottlenecks are predicted to be as much as an order of magnitude lower than in the other two cases.     

Cell cycle operation during batch growth of fission yeast populations

Batch cultivation provides a continuous sequence of different environments useful for studying responses of cell cycle controls. Flow cytometry measurements have been made of the frequency functions for protein, RNA, and DNA at different times during batch growth of the fission yeast Schizosaccharomyces pombe. The mean cellular protein and RNA contents and their variances tend to increase with increasing population specific growth rates. Analysis of the mid-exponential phase DNA frequency function data indicates that DNA synthesis occupies 12% of the total cell cycle time and is completed at the same time as cell separation. Coordination of DNA synthesis and cell separation is less precise when population growth rate is low in late lag and early stationary phases.     

Using Raman spectroscopy and chemometrics to identify the growth phase of <Emphasis Type="Italic">Lactobacillus casei</Emphasis> Zhang during batch culture at the single-cell level

Background

As microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins, and other constituents, the detailed identification and discrimination of the growth phases of bacterial populations in batch culture is challenging. Cell analysis is indispensable for quality control and cell enrichment.

Methods

In this paper, we report the results of our investigation on the use of single-cell Raman spectrometry (SCRS) for real-time analysis and prediction of cells in different growth phases during batch culture of Lactobacillus (L.) casei Zhang. A targeted analysis of defined cell growth phases at the level of the single cell, including lag phase, log phase, and stationary phase, was facilitated by SCRS.

Results

Spectral shifts were identified in different states of cell growth that reflect biochemical changes specific to each cell growth phase. Raman peaks associated with DNA and RNA displayed a decrease in intensity over time, whereas protein-specific and lipid-specific Raman vibrations increased at different rates. Furthermore, a supervised classification model (Random Forest) was used to specify the lag phase, log phase, and stationary phase of cells based on SCRS, and a mean sensitivity of 90.7% and mean specificity of 90.8% were achieved. In addition, the correct cell type was predicted at an accuracy of approximately 91.2%.

Conclusions

To conclude, Raman spectroscopy allows label-free, continuous monitoring of cell growth, which may facilitate more accurate estimates of the growth states of lactic acid bacterial populations during fermented batch culture in industry.

     

Fixation probability for lytic viruses: the attachment-lysis model

The fixation probability of a beneficial mutation is extremely sensitive to assumptions regarding the organism's life history. In this article we compute the fixation probability using a life-history model for lytic viruses, a key model organism in experimental studies of adaptation. The model assumes that attachment times are exponentially distributed, but that the lysis time, the time between attachment and host cell lysis, is constant. We assume that the growth of the wild-type viral population is controlled by periodic sampling (population bottlenecks) and also include the possibility that clearance may occur at a constant rate, for example, through washout in a chemostat. We then compute the fixation probability for mutations that increase the attachment rate, decrease the lysis time, increase the burst size, or reduce the probability of clearance. The fixation probability of these four types of beneficial mutations can be vastly different and depends critically on the time between population bottlenecks. We also explore mutations that affect lysis time, assuming that the burst size is constrained by the lysis time, for experimental protocols that sample either free phage or free phage and artificially lysed infected cells. In all cases we predict that the fixation probability of beneficial alleles is remarkably sensitive to the time between population bottlenecks.     

THE EFFECTS OF POPULATION BOTTLENECKS ON CLONAL INTERFERENCE, AND THE ADAPTATION EFFECTIVE POPULATION SIZE

Clonal interference refers to the competition that arises in asexual populations when multiple beneficial mutations segregate simultaneously. A large body of theoretical and experimental work now addresses this issue. Although much of the experimental work is performed in populations that grow exponentially between periodic population bottlenecks, the theoretical work to date has addressed only populations of a constant size. We derive an analytical approximation for the rate of adaptation in the presence of both clonal interference and bottlenecks, and compare this prediction to the results of an individual-based simulation, showing excellent agreement in the parameter regime in which clonal interference prevails. We also derive an appropriate definition for the effective population size for adaptive evolution experiments in the presence of population bottlenecks. This "adaptation effective population size" allows for a good approximation of the expected rate of adaptation, either in the strong-selection weak-mutation regime, or when clonal interference comes into play. In the multiple mutation regime, when the product of the population size and mutation rate is extremely large, these results no longer hold.     

Probabilistic neural networks using Bayesian decision strategies and a modified Gompertz model for growth phase classification in the batch culture of Bacillus subtilis

Probabilistic neural networks (PNNs) were used in conjunction with the Gompertz model for bacterial growth to classify the lag, logarithmic, and stationary phases in a batch process. Using the fermentation time and the optical density of diluted cell suspensions, sampled from a culture of Bacillus subtilis, PNNs enabled a reliable determination of the growth phases. Based on a Bayesian decision strategy, the Gompertz based PNN used newly proposed definition of the lag and logarithmic phases to estimate the latent, logarithmic and stationary phases. This network topology has the potential for use with on-line turbidimeter for the automation and control of cultivation processes.     

The impact of host-cell dynamics on the fixation probability for lytic viruses

Lytic viruses are obligate parasites whose population dynamics are necessarily coupled to the dynamics of their host-cell population. The adaptation rate of these viruses has attracted considerable scientific interest, as they are a key model organism in experimental evolution. Nevertheless, to date mathematical models of experimental evolution have largely ignored the host-cell population. In this paper we incorporate two important features of host-cell dynamics—the possibility of clearance or death of an infected cell before lysis, and the possibility of changing host-cell density—into previous models for the fixation probability of lytic viruses. We compute the fixation probabilities of rare alleles that confer reproductive benefit through either an increase in attachment rate or burst size, or a reduction in lysis time. We find that host-cell clearance significantly reduces the fixation probabilities of all types of beneficial mutations, having the largest impact on mutations which reduce the lysis time, but has only modest effects on the pattern of fixation probabilities previously observed. We further predict that exponential growth of the host-cell population preferentially selects for mutations that affect burst size or lysis time, and exacerbates the sensitive dependence of fixation probabilities on the time between population bottlenecks. Even when burst size and lysis time are constrained to vary together, our results suggest that lytic viruses should readily adapt to optimize these traits to the timing between population bottlenecks.     

High mutation rates, bottlenecks, and robustness of RNA viral quasispecies

Population bottlenecks are stochastic events that strongly condition the structure and evolution of natural populations. Their effects are readily observable in highly heterogeneous populations, such as RNA viruses, since bottlenecks cause a fast accumulation of mutations. Considering that most mutations are deleterious, it was predicted that the frequent application of bottlenecks would yield a population unable to replicate. However, in vitro as well as in vivo systems evolving through bottlenecks present a remarkable resistance to extinction. This observation reveals the robustness of RNA viruses and points to the existence of internal mechanisms which must confer a high degree of adaptability to fast mutating populations. In this contribution, we review experimental observations regarding the survival of RNA viruses, both in laboratory experiments and in natural populations. By means of a simple theoretical model of evolution which incorporates strong reductions of the population size, we explore the relationship between the number of replication rounds that a single founder particle undergoes before the next bottleneck is applied, and the mutation rate in a particular environment. Our numerical results reveal that the mutation rate has evolved in a concerted way with the degree of optimization achieved by the population originated from the founder particle. We hypothesize that this mechanism generates a mutation-selection equilibrium in natural populations that maximizes adaptability while maintaining their structure.     

Inbreeding depression in the partially self-incompatible endemic plant species <Emphasis Type="Italic">Scalesia affinis</Emphasis> (Asteraceae) from Galápagos islands

A previous study showed that some individuals of the tetraploid Galápagos endemic Scalesia affinis were able to produce offspring after selfing. The present study compares the fitness of self-pollinated offspring with the fitness of cross-pollinated offspring. Germination success, seedling survival, and four different growth parameters was measured. In most of the studied characters selfed offspring were significantly inferior to outcrossed progeny. The effect was very clear in germination and survival. Outcrossed embryos were 3.4 times more likely to germinate than those that were selfed-fertilized, and the mortality was 84% higher among selfed individuals. Also, there was no genetic variation in inbreeding depression. The present study is based on material from a large population on Isabela Island, Galápagos. At other localities in the archipelago, populations have been through recent dramatic bottlenecks due to the grazing of introduced mammals. Considering the significant inbreeding depression found in the large population and the presence of a partial self-incompatibility system, these small populations are likely to be highly vulnerable and their future survival critically threatened.     

Why are viral genomes so fragile? The bottleneck hypothesis

If they undergo new mutations at each replication cycle, why are RNA viral genomes so fragile, with most mutations being either strongly deleterious or lethal? Here we provide theoretical and numerical evidence for the hypothesis that genetic fragility is partly an evolutionary response to the multiple population bottlenecks experienced by viral populations at various stages of their life cycles. Modelling within-host viral populations as multi-type branching processes, we show that mutational fragility lowers the rate at which Muller’s ratchet clicks and increases the survival probability through multiple bottlenecks. In the context of a susceptible-exposed-infectious-recovered epidemiological model, we find that the attack rate of fragile viral strains can exceed that of more robust strains, particularly at low infectivities and high mutation rates. Our findings highlight the importance of demographic events such as transmission bottlenecks in shaping the genetic architecture of viral pathogens.     

Expression of the multiple antibiotic resistance operon (mar) during growth of Escherichia coli as a biofilm

The multiple antibiotic resistance (mar) operon is a global regulator controlling the expression of various genes in Escherichia coli which constitutes the mar regulon. Upregulation of mar leads to a multi-drug resistant phenotype, which includes resistance towards structurally unrelated antibiotics, organic solvents and the disinfectant pine oil. Biofilms also display similar decreases in susceptibility to antimicrobial agents. A marOII-lacZ fusion strain (SPC105) of E. coli was used to monitor mar expression under various growth conditions including batch, continuous and biofilm culture. In chemically-defined media (CDM), mar expression was maximal in mid-log and declined in the stationary phase. Conversely, in rich media (Luria-Bertani broth), minimal expression in mid-log was followed by an increase in the stationary phase. In continuous culture, expression was inversely related to specific growth rate (mu = 0.05-0.4 h-1). LacZ expression by the marOII-lacZ fusion was generally low within the total biofilm population and equivalent to that of stationary phase cultures grown in batch culture. When the expression of mar in CDM batch culture was compared with that in biofilm populations, beta-galactosidase activity was generally higher throughout batch culture than in the attached population. Overall, these results suggest that while mar expression will be greatest within the depths of a biofilm where growth rates are suppressed, its probable induction within biofilms cannot explain the elevated levels of antibiotic resistance observed.     

Estimation of dormant Micrococcus luteus cells by penicillin lysis and by resuscitation in cell-free spent culture medium at high dilution

Abstract Micrococcus luteus starved for 2–7 months in spent medium following growth to stationary phase in batch culture exhibited a culturability (as estimated by direct plating on nutrient agar plates) of < 0.001%. However, following a lag, some 70% of the cells could be lysed upon inoculation into and cultivation in fresh lactate minimal medium containing penicillin, showing the capability of a significant portion of the cells at least to enlarge (and thus potentially to resuscitate). When the viable cell count was estimated using the most probable number method, by incubation of high dilutions of starved cells in liquid growth media, the number of culturable or resuscitable cells was very low, and little different from the viable cell count as assessed by plating on solid media. However, the apparent viability of these populations evidenced with the most probable number method was 1000–100 000-fold greater when samples were diluted into liquid media containing supernatants taken from the stationary phase of batch cultures of the organism, suggesting that viable cells can produce a factor which stimulates the resuscitation of dormant cells. Both approaches show, under conditions in which the growth of a limited number of viable cells during resuscitation is excluded, that a significant portion of the apparently non-viable cell population in an extended stationary phase is dormant, and not dead.     

Fixation probabilities when generation times are variable: the burst death model

Estimating the fixation probability of a beneficial mutation has a rich history in theoretical population genetics. Typically, to attain mathematical tractability, we assume that generation times are fixed, while the number of offspring per individual is stochastic. However, fixation probabilities are extremely sensitive to these assumptions regarding life history. In this article, we compute the fixation probability for a "burst-death" life-history model. The model assumes that generation times are exponentially distributed, but the number of offspring per individual is constant. We estimate the fixation probability for populations of constant size and for populations that grow exponentially between periodic population bottlenecks. We find that the fixation probability is, in general, substantially lower in the burst-death model than in classical models. We also note striking qualitative differences between the fates of beneficial mutations that increase burst size and mutations that increase the burst rate. In particular, once the burst size is sufficiently large relative to the wild type, the burst-death model predicts that fixation probability depends only on burst rate.     

Fixation probabilities depend on life history: fecundity, generation time and survival in a burst-death model

The burst-death model has been developed to describe the life history of organisms with variable generation times and a burst of a fixed number of offspring. The model also includes an optional constant clearance rate, such as washout from a chemostat, and the possibility of sustained periods of population growth followed by severe bottlenecks, as in serial passaging. In this model, a beneficial mutation can either increase the burst rate or the burst size, or reduce the clearance rate, thus increasing survival. In this article we examine the effects of these three possible mechanisms on both the Malthusian fitness and the fixation probability of the lineage. We find that equivalent relative increases in the burst rate or burst size confer equivalent increases in the Malthusian fitness of a lineage, whereas increasing survival typically has a more moderate effect on Malthusian fitness. In contrast, for beneficial mutations that confer the same increase in fitness, mutations that increase survival are the most likely to fix, followed by mutations that increase the burst rate. Mutations that increase the burst size are the least likely to fix. These results imply that mutant lineages with the highest Malthusian fitness are not, in many cases, the most likely to escape extinction.