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Keywords:

  • adaptation;
  • beneficial mutation;
  • clonal interference;
  • Escherichia coli;
  • experimental evolution

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

In asexual populations, the rate of adaptation is basically limited by the frequency and properties of spontaneous beneficial mutations. Hence, knowledge of these mutational properties and how they are affected by particular evolutionary conditions is a precondition for understanding the process of adaptation. Here, we address how the rate of adaptation of asexual populations is limited by its population size and mutation rate, as well as by two factors affecting the fraction of mutations that confer a benefit, i.e. the initial adaptedness of the population and the variability of the environment. These factors both influence which mutations are likely to occur, as well as the probability that they will ultimately contribute to adaptation. We attempt to separate the consequences of these basic population features in terms of their effect on the rate of adaptation by using results from evolution experiments with microorganisms.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

Adaptive evolution has led to an endless catalogue of complex organismal features, including physiological and behavioural adaptations to particular stresses such as heat or starvation. Although the traits resulting from adaptive evolution are often complex, the processes that underlie their emergence are relatively uncomplicated, because just two factors are required: mutation and selection. Hence, determining the number and properties (most importantly: fitness consequences) of spontaneous mutations constitutes the first important step towards understanding the mechanisms of adaptation. Variables that affect the number of mutations that arise each generation include the size of the population and the mutation rate of its members, whereas the fraction of mutations with a positive effect on fitness depends, among others, on the initial adaptedness of the population and the variability of the environment. Understanding how selection acts upon new mutations – in other words, how selection affects the fate of mutations – is the second important step towards a mechanistic model of adaptation. Over a broad set of conditions, the same evolutionary variables that determine the number and kind of mutations that are generated by a population, also affect their subsequent fate. How this is achieved is the topic of the present paper.

To circumvent the slow pace of evolution, the use of microorganisms in laboratory evolution experiments has increasingly placed the study of adaptive evolution in the realm of experimentalists (Elena & Lenski, 2003). Microorganisms allow large populations to be maintained for many generations in simple laboratory environments, while they mutate and adapt to these novel conditions. Because they evolve so rapidly, hypotheses about the process of adaptation can be tested in rigorous experiments by manipulating the responsible variables and comparing the outcome of different evolutionary treatments. The fact that microorganisms can be stored in a nonevolving state in the freezer facilitates studying the dynamics of the process of adaptation by enabling the comparison of evolutionary intermediates in contemporary assays. These developments, together with recent theoretical work (Gerrish & Lenski, 1998; Orr, 2000, 2003; Gerrish, 2001; Rozen et al., 2002; Wilke, 2004), have led to several new insights into the variables that determine the dynamics of adaptation in asexual populations.

Mutation and selection in asexual populations

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

Adaptive evolution of asexual populations results from the substitution by natural selection of beneficial mutations via the process of ‘periodic selection’ (Atwood et al., 1951). Assuming no epistasis among beneficial mutations, the rate of adaptation (i.e. the rate of fitness improvement per time interval) can be estimated as the product of the substitution rate and average fitness effect of fixed beneficial mutations. These two variables, in turn, depend on the underlying distribution of mutational fitness effects, as well as on population size, mutation rate, and on factors that affect the fraction of all mutations conferring a benefit.

There is general agreement that beneficial mutations constitute only a small fraction of all mutations, but very few empirical estimates of the rate of beneficial mutations exist. The lack of such estimates in part reflects the practical difficulties involved in studying such rare events experimentally. We estimated the rate of beneficial mutations to be 5.9 × 10−8 per genome per generation for a particular strain of Escherichia coli in one laboratory environment [Rozen et al., 2002; see Miralles et al. (1999) and a recent review by Zeyl (2004) for other estimates]. Given an overall mutation rate for E. coli of about 0.0025 per genome per generation (Drake et al., 1998), this implies that on average only one in every 104–105 mutations is beneficial. Estimates of fitness effects of beneficial mutations are equally scarce for the same reasons. We estimated the average fitness effect of spontaneous beneficial mutations to be 0.024 (i.e. increasing fitness by 2.4%) for the same E. coli strain as above, whereas the fitness effects of beneficial mutations that ultimately reached fixation were on average three to four times larger (Rozen et al., 2002), thus demonstrating the role of natural selection in determining the competitive outcome among existing beneficial mutations.

Despite a scarcity of experimental data on the rate of beneficial mutations, there is general theoretical agreement about the shape of the distribution of their fitness effects. Arguments from extreme-value theory (Gillespie, 1991; Rozen et al., 2002; Orr, 2003; Wilke, 2004) suggest that the fitness effects of beneficial mutations are distributed exponentially. Empirical observations of the distribution of fixed beneficial effects in E. coli are in agreement with theoretical expectations (Rozen et al., 2002). In other words, most mutations confer small fitness benefits and only few have large beneficial effects. The form of the distribution has a number of important consequences for the rate of adaptation as well as for the repeatability of evolution, which will be addressed below.

An important determinant of which beneficial mutations will be ultimately successful is population size. If a population is small, it will spend most of its time waiting for beneficial mutations to arise, and selective sweeps will tend to occur as rapid isolated events (Fig. 1a). Hence, the rate of adaptation of such populations will be limited by the production of beneficial mutations rather than by their substitution. Increases of the population size and mutation rate can reduce this waiting time and provide access to new beneficial mutations, which will initially lead to more rapid adaptation.

image

Figure 1. Adaptation in asexual populations according to Muller (1932). (a) Small populations spend most time waiting for beneficial mutations, and when one occurs (and survives drift) it rapidly fixes. (b) Large populations spend less time waiting for beneficial mutations. Instead, several beneficial mutations will be present in different clones simultaneously and will subsequently interfere with each others’ spread, a phenomenon called ‘clonal interference’. As a result, the ultimately successful beneficial mutation takes longer to fix, but confers a larger fitness benefit. The combination of these two effects leads to a net decline of the rate of adaptation.

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When the population size increases, the occurrence of mutations – including beneficial mutations – increases proportionally, which leads to the simultaneous presence of clones carrying different beneficial mutations (Fig. 1b). Because these beneficial mutations cannot recombine in asexual organisms, they will instead interfere with each others’ spread, a process referred to as ‘clonal interference’ (Muller, 1932, 1964; Haigh, 1978; Gerrish & Lenski, 1998). The consequences of clonal interference for adaptation are that (i) small mutations that survived drift are removed from the population, thereby increasing the fitness effect of ultimately successful mutations, (ii) the fixation time of ultimately successful mutations increases, and (iii) beneficial mutations are substituted in an orderly fashion, with large-effect mutations first. As a net result, (iv) the rate of adaptation will approach a maximum (Gerrish & Lenski, 1998), or at least become disproportional (Wilke, 2004), with increasing population size. Increases of the mutation rate have somewhat similar, but still essentially different effects on the rate of adaptation (Gerrish & Lenski, 1998; Orr, 2000, 2003; Wilke, 2004), as we will discuss below.

Here, we use published and novel results from evolution experiments with bacteria and other microorganisms to address how the rate of adaptation depends on (i) population size, (ii) mutation rate, (iii) initial adaptedness of the population, and (iv) variability of the environment, specifically that mediated by antagonistic coevolution. We limit our survey to the simplest of all situations, i.e. isolated asexual populations where adaptation depends entirely on mutation and selection. Many other factors affect the rate of adaptation in asexual populations that will be neglected here, including other forms of temporal and spatial environmental heterogeneity (see review by Elena, 2002), and several aspects of the genetic architecture of organisms, such as pleiotropy leading to trade-offs between adaptations and reduced adaptability (Buckling et al., 2003), and antagonistic epistasis among beneficial mutations that slows down later adaptation (Sanjuán et al., 2004b).

Population size and mutation rate

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

The size of a population and the mutation rate of its individuals have subtly different roles in adaptive evolution. Although the rate at which beneficial mutations are produced is a linear function of both variables, their impact on the subsequent fate of these mutations is rather different. For instance, in very small populations genetic drift may cause adaptation to decline, whereas low (but not zero) mutation rates do not have similar effects. At the other extreme, increased population sizes are associated with longer fixation times, whereas this is not true for increased mutation rates. In addition, increases of the mutation rate, but not increases of population size, cause deleterious mutations to accumulate in backgrounds carrying beneficial mutations, which lower the net fitness benefit of fixed mutations (Orr, 2000).

Drift vs. selection

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

When populations are very small and governed largely by genetic drift, fitness is expected to decay over time due to the chance accumulation of the much more abundant deleterious mutations via Muller's ratchet (Lynch et al., 1999; Elena & Lenski, 2003). Small population size in studies of drift decay with microbes is often achieved by severely bottlenecking the population during transfer of the population to fresh medium. A general, and perhaps surprising, conclusion from these experiments is that actual fitness declines due to genetic drift are only observed in extremely small populations that use bottlenecks of a single or a few individuals. In one experiment, asexual wild-type and mutator populations of the yeast Saccharomyces cerevisiae were serially transferred by bottlenecking populations to about 25 cells at each transfer (leading to an effective population size of ∼250; see Lenski et al., 1991). Mutator populations had an estimated ∼100-fold increased mutation rate in all its genes due to a defective msh2 function, involved in DNA mismatch repair. Yet, contrary to the expectation of significant fitness loss or even extinction (Muller, 1964; Lynch & Gabriel, 1990), only two of 12 mutator populations went extinct, whereas most wild-type – and several of the other mutator – populations actually increased fitness during the 3000 generations of the experiment (Zeyl et al., 2001). Thus, despite conditions idealized for genetic drift decay, fitness loss remained an infrequent outcome. Possibly, the occasional chance fixation of a deleterious mutation in small populations was rapidly countered in subsequent generations by beneficial mutations that specifically compensated the negative effects of these mutations (Wagner & Gabriel, 1990; Moore et al., 2000). The apparent ubiquity of compensatory mutations has only been recently appreciated, but their presence has already become an important countering feature of models of fitness decay by Muller's ratchet (Poon & Otto, 2000; Whitlock et al., 2003). In general, these studies indicate the power of natural selection, even in very small asexual populations where one might expect drift to cause maladaptation.

Fitness effects of fixed beneficial mutations

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

Once populations are large enough to escape fitness decay by genetic drift, the size of the population still remains important. According to the clonal interference model, increases in population size and mutation rate can cause larger-effect beneficial mutations to become fixed. We tested these predictions in two studies using evolving populations of E. coli. In the first study, we were interested in characterizing the fitness effects of fixed beneficial mutations (Rozen et al., 2002). We allowed 60 populations consisting of a mixture of two genetically marked strains of E. coli to adapt to a minimal-glucose medium for 400 generations. Combinations of isogenic strains with wild-type mutation rate and combinations of a mutator (a mutS-deficient strain with a ∼33-fold increased mutation rate) and a wild-type strain were started at varying initial ratios (implying different population sizes because total effective population size remained constant), and passaged by daily serial transfer. Populations were plated at regular intervals to determine the relative frequencies of the marked subpopulations. Sudden deviations of the marker ratio would indicate that one strain had invaded by fixing a beneficial mutation. Following mutant invasion, successful clones were collected and the fitness effects of their mutations were measured in competition with the ancestral strain. When the fitness effects of these beneficial mutations are regressed against population size, a significant positive effect of population size is revealed for both the wild-type (F1,86 = 21.72, P < 0.0001; Fig. 2a) and mutator populations (F1,23 = 13.39, P < 0.01; Fig. 2a), as predicted by the clonal interference model. Using two-way anova of wild-type and mutator populations of similar size only, we found that the 33-fold increase of the mutation rate also has the predicted positive effect on the fitness benefit of fixed mutations (F1,49 = 40.94, P < 0.0001; Fig. 2a); that is, at the same population size the mutator fixes larger-effect beneficial mutations. However, the dependence of fitness effects on population size was not different for wild-type and mutator populations (F2,49 = 0.328, n.s.), suggesting that both population size and mutation rate exert their influence through a qualitatively similar mechanism, i.e. the enhancement of clonal interference. Positive relationships between population size and the size of the fitness effect of fixed beneficial mutations have also been shown for RNA viruses φ6 (Burch & Chao, 1999) and VSV (Miralles et al., 1999).

image

Figure 2. (a) Average fitness effects of fixed beneficial mutations (selection coefficient S) in evolving populations of E. coli of varying effective size (Ne). Filled squares are for the strain with a wild-type mutation rate, open circles for a mutS-deficient, but otherwise isogenic, strain with an estimated ∼33-fold increased mutation rate. (b) Coefficient of variation (CV) of fitness effects of fixed beneficial mutations of the same E. coli populations. [Data from wild-type populations were used by Rozen et al. (2002) to study the distribution of mutational fitness effects].

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An interesting implication of the observed relationship between population size or mutation rate and the fitness effect of fixed mutations concerns the repeatability of adaptation at the genotype level. Large population sizes and high mutation rates lead to adaptation via mutations of large effect. At the same time, the exponential shape of the underlying distribution of beneficial mutational effects indicates that such large-effect mutations are fewer in number. Hence, adaptation of independent populations is expected to depend more often on the same beneficial mutations in large than in small populations, and also – perhaps counter-intuitively – in populations with high vs. low mutation rates. We tested these expectations by regressing the coefficient of variation (CV) of fitness effects of fixed beneficial mutations against population size for both strains (Fig. 2b). The CV seems the appropriate measure of phenotypic variance, because it removes the inherent association between mean and variance of mutational effects due to variation in population size (large populations sample from a broader distribution of beneficial mutations, that contains bigger-effect mutations, than small populations). As expected, a negative relationship is apparent between CV and population size for both strains, although only significantly so for the wild-type populations (wild-type populations: F1,3 = 15.81, P < 0.05; mutator populations: F1,3 = 1.42, n.s.). We also find that the CV of mutational fitness effects is smaller in mutator than wild-type populations of the same size (Fig. 2b; t-test with pooled variance: t4 = 3.72, two-tailed P < 0.05). Although clonal interference is likely the primary reason for this pattern, the exponential shape of the underlying distribution of mutational effects will also contribute to this outcome, because it implies that mutations with large effect are much more likely to occur in large populations or those with increased mutation rates.

Rate of adaptation

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

Population size and mutation rate influence the short-term rate of adaptation by affecting the size of the fitness advantage of fixing beneficial mutations. In the longer term, the rate of adaptation also depends on the substitution rate of these fixing mutations. In a second study, we attempted to quantify the net effect of population size and mutation rate on the rate of adaptation in the longer term (de Visser et al., 1999). Here, we allowed 48 populations of E. coli to adapt for 1000 generations to the same minimal-glucose environment as used in the previous study on fitness effects of beneficial mutations. We manipulated population size by adjusting the number of cells that were transferred daily to fresh medium, which resulted in a 50-fold difference in effective population size between small and large populations. The mutation rate was manipulated by inserting deficient alleles of mismatch-repair genes mutY and mutS in copies of the same strain, resulting in ∼three- and 33-fold increased mutation rates (as established in fluctuation tests), respectively. The baseline strain had no previous evolutionary history in the minimal-glucose environment, and was thus referred to as ‘nonadapted’. We then plotted the rate of fitness improvement of these populations against their mutation supply rate, i.e. the product of population size and mutation rate (Fig. 3a). Increases of the mutation supply rate by several orders of magnitude resulted in a much less than proportional increase of the rate of adaptation, indicated by the significantly better fit of a hyperbolic than a linear model (de Visser et al., 1999). This was consistent with clonal interference causing the rate of adaptation to become relatively independent of the mutation supply rate. These data lack the statistical power to distinguish between an absolute limit on the rate of adaptation at higher mutation supplies – as the hyperbolic model suggests, and other forms of disproportionality (Wilke, 2004). A similar disproportionality between population size and the rate of adaptation was observed in vesicular stomatitis virus (Miralles et al., 1999).

image

Figure 3. Rate of adaptation as a function of the relative mutation supply rate (i.e. population size × mutation rate) of evolving populations of E. coli. (a) Populations founded by a nonadapted strain. Circles for small, squares for large populations (50-fold difference); open symbols for wild-type, grey for mutY-deficient (three-fold increased mutation rate), and black for mutS-deficient (33-fold increased mutation rate) populations. The curve is a hyperbolic regression, which fits the data better than a linear regression. (b) Populations founded by a strain that had previously adapted to this environment for 10 000 generations. The curve is a linear regression, which appears exponential due to the log-scale of the x-axis. A hyperbolic regression provides no significant improvement. [Data from de Visser et al. (1999)].

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Different impacts of population size and mutation rate

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

Despite their similar roles in enhancing the mutation supply rate and increasing the fitness effect of fixed beneficial mutations, population size and mutation rate differ in their impact on the subsequent fate of beneficial mutations, and thus on the rate of adaptation. We examined this by testing the separate effects of variation in mutation rate and population size on the rate of adaptation for the 24 E. coli populations that were initiated with a nonadapted strain (de Visser et al., 1999; Fig. 3a). Analysis of variance was used to examine the effect of variation in mutation rate (up to 33-fold) and population size (50-fold) on the logarithm of fitness improvement. (The data were log-transformed because the combined effect of mutation rate and population size is expected to be roughly multiplicative.) Although population size and interaction term show no significant effect, the effect of mutation rate is significant (Table 1). The lack of a significant effect of population size and interaction term – despite the good fit of a hyperbolic model in Fig. 3a– is likely due to the variation among the few data points and their position on the asymptote where effects from both variables are strongly reduced. Moreover, the interaction term approaches significance, because its P-value may roughly be halved due to our directional prediction (i.e. less effect of increasing population size and mutation rate when the other variable is already high). However, the lack of power applies to the effect of mutation rate as well as population size, and hence these results suggest that increases of the mutation rate have a stronger effect on the long-term rate of adaptation than similar increases in population size. In contrast, theoretical studies of clonal interference predict that, depending on the actual values of these variables, either both have a similar effect (Gerrish & Lenski, 1998) or population size has a slightly stronger effect (Wilke, 2004). A possible explanation for this discrepancy is the fact that increases in population size will also cause longer fixation times (proportional to the logarithm of the population size). The models ignore this reality, and assume steady-state dynamics where differences in fixation time are of no influence. In our experiment, however, populations were initiated from clones and required time to generate beneficial mutations, a process which may have been more rapid in the small populations with increased mutation rates.

Table 1. anova of the logarithm of fitness improvement during 1000 generations of the 24 E. coli populations founded by the nonadapted ancestor of Fig. 3a.
Sourced.f.Mean squareFP
  1. Mutation rate was three- and 33-fold higher than wild-type in mutY and mutS populations, respectively. Population size differed 50-fold between small and large populations. Data from de Visser et al. (1999).

Population size10.01561.1440.299
Mutation rate20.06194.5510.025
Population size × mutation rate20.02852.0990.152
Error180.0136  

This short-term adaptation advantage of small populations with increased mutation rates implies an invasion advantage for mutator mutants. The argument is illustrated graphically in Fig. 4a. Consider two populations with equal mutation supply rate, a large population with low mutation rate (N), and a small population with high mutation rate (M). When these two populations adapt to the same environment, it is easy to see that population M will invade. Both populations have on average the same waiting time (tW) for a given successful beneficial mutation (as their mutation supply rates are equal), but M will fix the mutation sooner than N (tM < tN). Once M has fixed its mutation, it will increase in size to exactly that of N before N fixes its beneficial mutation. Without direct fitness costs for the mutator, therefore, a small mutator population is expected to increase in frequency relative to a large wild-type population by a factor equal to its strength (i.e. relative increase of the mutation rate) per selective sweep (Painter, 1975; Mao et al., 1997; Tanaka et al., 2003). Only when the size of the mutator subpopulation becomes too low to produce a successful beneficial mutation before the wild-type majority fixes its mutation will this advantage break down. Consequently, in finite populations the invasion of a mutator will be frequency dependent (Chao & Cox, 1983), but the threshold for invasion will often be lower than the ratio of their mutation supply rates would predict.

image

Figure 4. (a) Graphical argument showing the short-term advantage of small over large populations with similar mutation supply rates. A small population with high mutation rate (M) and large population with low mutation rate (N) will on average wait equally long for a given beneficial mutation (tW), but M will fix the mutation faster due to its smaller size (tM < tN). This causes M to increase its frequency per selective sweep by a factor equal to the ratio of the mutation rates. In finite populations, this principle will break down where M becomes too small to produce a beneficial mutation before N fixes one. (b) Trajectories of the log ratio of differently marked mutator and wild-type populations of E. coli, with starting frequencies of the mutator of either 0.001 or 0.0001. The populations evolved in a minimal-glucose medium and changes of the ratio of the two subpopulations reflect the fixation of a beneficial mutation in one or the other subpopulation. Each line represents a different population started with a mixture of the same two strains. [For experimental details see Rozen et al. (2002)].

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Consistent with these predictions and with what Chao & Cox (1983) found for E. colimutT mutators, we observed the invasion of E. colimutS mutators when they were co-evolving with repair-proficient strains at lower mutation supply rates than these repair-proficient strains (Fig. 4b). In populations where the mutator subpopulation started at a frequency of 0.001, the mutator subpopulation increased in frequency in at least four of the five populations, despite its approximately 30-fold (i.e. 1000/33) lower mutation supply rate. Only when the mutator subpopulations were reduced even further in size, resulting in an effective population size of a few thousand cells only, did mutators decrease in frequency (Fig. 4b). These mutator populations were presumably too small to generate a successful beneficial mutation before the wild-type majority had fixed one.

To summarize, altering the size of the population may have profound effects on – and may even prevent – adaptation, if populations are small, but will hardly affect adaptation of already large populations. The effect of altering the mutation rate can be similar, but involves different processes. Experimental support from evolution experiments with E. coli has been presented for two predictions of the clonal interference model. Both experiments show results that are consistent with a qualitatively similar role of population size and mutation rate, i.e. increased fitness effects of fixed beneficial mutations and less-than-proportional increases of the rate of adaptation with increases of both variables. However, increases of the population size were shown to have less effect on the rate of adaptation than similar increases of the mutation rate, probably due to the longer fixation times associated with large population sizes.

Beneficial mutation fraction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

Level of adaptation

Mutations can be neutral, incur a cost, or have a fitness benefit. Because adaptation primarily relies on beneficial mutations, it is the supply rate of beneficial mutations that is of relevance for the rate of adaptation rather than the total mutation supply rate. Although population size and mutation rate affect the total number and type of mutations generated by a population, the initial level of adaptation of the population and the variability of the environment affect the relative frequency of beneficial mutations. If a population is not well adapted, more mutations are expected to confer a benefit than after it has already adapted to the same environment for many generations, and ‘used up’ several beneficial mutations. In addition, already well-adapted populations will often have access to beneficial mutations with small fitness effects only, because clonal interference is expected to cause large-effect mutations to be fixed first. This can be pictured by considering adaptation on a fitness landscape. Although unadapted, a population will sit at the base of a fitness peak. As it accumulates beneficial mutations that will allow it to climb to the summit, fewer new mutations will confer benefits, whereas at the same time a larger fraction will incur costs. Because of this shift in the relative fraction of beneficial and deleterious mutations, the predicted rate of adaptation will be higher in naïve vs. better adapted populations.

This was tested by allowing populations of E. coli founded with a strain that had not adapted to the evolutionary environment, and a strain that was derived from the first strain after 10 000 generations of adaptation to the same environment (de Visser et al., 1999). Two things are apparent from the observed relationship between mutation supply rate and rate of fitness improvement of these populations (Fig. 4b). First, the 10 000 generations of previous adaptation lead to a rate of fitness improvement that is about an order of magnitude lower than that of the nonadapted populations. Secondly, the rate of adaptation is limited by the mutation supply rate, as reflected by the significant fit of a linear model and lack of improvement of a hyperbolic model (de Visser et al., 1999). The likely reason for these observations is that the well-adapted populations had already fixed several beneficial mutations, and few beneficial mutations (of small effect) remained for their further adaptation. As a consequence, these populations had to spend more time waiting for beneficial mutations, thereby minimizing the effects of clonal interference, and preventing diminishing returns from the mutation supply rate as it did in the nonadapted populations (Fig. 4a).

Environmental variability

Populations adapting to constant environmental conditions are expected to exhaust their supply of beneficial mutations as they approach their (local) fitness optimum. As a consequence, and as shown above, the rate of adaptation is expected to decline over time in a constant environment. And indeed, this is what is often seen in evolution experiments with bacteria and viruses in simple, constant environments: fitness gains are initially rapid but tend to decline over time (Elena & Lenski, 2003).

Although depletion of available beneficial mutations is the likely cause of the observed declining rate of adaptation, an alternative explanation is possible. It could be that the apparent decline in the rate of adaptation is an artefact of the way in which fitness is typically measured, and that in reality adaptation proceeds at the initially high rate. In evolution experiments, fitness of the evolved genotypes is usually measured by competing an evolved strain and its ancestor in the same evolutionary environment. However, it is possible that, despite the care put into maintaining constant environmental conditions (e.g. by using simple, chemically defined media, constant temperature, etc.), the environment changes over the course of evolution due to the activity of some of the evolved genotypes. For instance, genotypes may change the environment by evolving the ability to produce and excrete metabolites on which subsequent genotypes can specialize (Helling et al., 1988; Rozen & Lenski, 2000). Such uncontrolled environmental changes lead to nontransitive competitive hierarchies between population samples taken after different time intervals that may even result in fitness declines relative to the ancestor (Paquin & Adams, 1983). Although these nontransitive interactions are unpredictable, they will usually cause the real cumulative fitness improvement over the whole experiment to be underestimated by using the ancestor as the reference competitor.

We tested whether similar nontransitive interactions, indicating a changing environment, could explain the declining rate of adaptation of one of 12 E. coli populations that had been adapting to a simple and presumably constant laboratory environment for 20 000 generations (Cooper & Lenski, 2000). For this particular population (Ara-1) no evidence for nontransitive fitness interactions was found (de Visser & Lenski, 2002). Hence the evolutionary environment was essentially constant, and the observed decline in the rate of fitness improvement was inferred to be due to the fact that later adaptation relied on fewer (and smaller-effect) beneficial mutations.

However, in another of the 12 E. coli populations that had independently adapted to the same environment, the situation was quite different. In this unique population (Ara-2), two morphs evolved that have stably coexisted for more than 12 000 generations (Rozen & Lenski, 2000). One morph, producing small colonies on plates (S), had evolved to become specialized on an unknown product of the other morph, which produced large colonies on plates (L) and is a better competitor for the sole exogenously provided resource, i.e. glucose. Thus, for this population the evolutionary environment has changed, and perhaps changes continuously as a result of antagonistic coevolution between the two morphs (Van Valen, 1973). As a result, the rate of adaptation of both morphs might be higher than for similar genotypes adapting to a constant abiotic environment. For this to be true, two conditions must be met: (i) adaptation of each morph must (in part) depend on the presence of the other morph, and (ii) both morphs must continue to evolve in response to the other. A pilot experiment showed that at least the first condition may be met. When the fitness improvement of the small morph was measured over a 2000-generation interval (Fig. 5), it appeared to be ∼15% in the absence of the L morph, indicating that adaptation to the abiotic environment had taken place. When the L morph was present, the measured fitness improvement of S was significantly higher (∼40%), showing that total fitness improvement was dependent upon the presence of the L morph. At present, we are studying changes in the other morph and over more time intervals to determine whether adaptation in a changing (e.g. biotic) environment leads to continuously high rates of adaptation due to access to new beneficial mutations after every change, as predicted by the Red Queen model of antagonistic coevolution (Van Valen, 1973).

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Figure 5. Fitness improvement of one of the two morphs that stably coexisted for more than 12 000 generations in one of the 12 long-term evolving E. coli populations that are adapting to a minimal-glucose environment since 1988 [see Rozen & Lenski (2000) for details of the polymorphism, and Lenski (2004) for details of the broader experiment]. Shown is the fitness improvement of the S morph from 16 000 to 18 000 generations in the absence and presence of the L morph from 16 000 generations. Error bars represent 95% confidence intervals.

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Conclusions and future directions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

The recent use of rapidly evolving organisms, such as bacteria, in laboratory evolution experiments has led to a growing understanding of the processes causing adaptation. Although these studies have so far largely neglected important factors such as migration and recombination, they have proven fruitful for studying the role of other variables of fundamental evolutionary impact. In this paper, we have highlighted how population size, mutation rate, initial adaptedness and environmental variability affect the rate of adaptation in asexual populations. We have shown that large populations, high mutation rates, and low initial adaptedness can lead to competition between beneficial clones, causing long fixation times of the large-effect beneficial mutations that will ultimately win. As a result, the long-term rate of adaptive evolution becomes relatively independent of the frequency of beneficial mutations in the population when they are abundant. In contrast, small populations, low mutation rates, and high adaptedness may all cause the rate of adaptation to be limited by the population's supply of beneficial mutations. One fundamental difference in the roles of population size and mutation rate is reflected by an invasion advantage for small populations with high mutation rates due to the associated shorter fixation time of beneficial mutations. Finally, continued variability of environmental conditions, for example, due to coevolving interacting organisms, may prevent the rate of adaptation to decline, as is often observed for populations adapting to constant environmental conditions.

Many questions about the factors that limit adaptation are still without answers, but may be addressed in future studies using experimental evolution with microorganisms. We just mention a few questions that we consider of interest and that immediately follow from our present survey. First, other aspects of the different roles of population size and mutation rate may be studied. For instance, very high mutation rates are predicted to lead to deleterious mutations in the background of beneficial mutations, resulting in an optimal rather than a maximal mutation rate that maximizes the rate of adaptation (e.g. Wilke, 2004). This prediction might be tested using microbes with varying mutation rates due to differences in particular defects in DNA proofreading and repair. Secondly, testing the prediction that large populations (and high mutation rates) lead to increased repeatability of adaptation is straightforward, especially when the target of selection is limited and repeatability can be verified at the genotype level (e.g. in the case of antibiotic resistance). Thirdly, distributions of fitness effects of beneficial mutations are needed as input for models of adaptive evolution. A powerful approach is the generation of random mutations via site-directed mutagenesis of small genomes (Sanjuán et al., 2004a). In addition, fitness distributions of beneficial mutations generated by various repair-deficient mutants, with different mutational spectra, may reveal unknown aspects of the process of adaptation. Such studies might, for instance, reveal a role for so-called ‘contingency loci’ with high mutation rates in adaptation of nonpathogenic microorganisms that is similar as previously observed for pathogens (Moxon et al., 1994). Fourthly, we still know very little about which environmental conditions trigger adaptive responses. For example, most evolution experiments have used simple, homogeneous environmental conditions, whereas natural environments usually involve some level of spatial heterogeneity. The consequences of such spatial structure for the dynamics of adaptation are complex, but if studied in single-factor experiments, individual aspects (e.g. population fragmentation, the presence of several niches, etc.) might be studied in more rigorous ways. Fifthly, to understand the effect of environmental variability on the rate of adaptation more fully we need to understand which environmental conditions may change as a consequence of evolution. For example, studying which potentially useful metabolites may be produced by different strains would help to predict the opportunities for cross-feeding interactions (Doebeli, 2002). Finally, given the predicted limiting effects of clonal interference on adaptation in asexual populations, it will be interesting to study under what conditions recombination is most effective in preventing clonal interference and causing accelerated adaptation (Colegrave, 2002).

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References

We would like to thank Volker Loeschke and Kuke Bijlsma for the invitation to contribute to this special issue on Stress, Adaptation and Evolution, Bruce Levin and Richard Lenski for discussing the role of population size and mutation rate, Jan Graffelman for statistical advise, and Santiago Elena and an anonymous reviewer for helpful comments. JAGMdV's research was supported by a fellowship from the Netherlands Organization of Scientific research (NWO).

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Mutation and selection in asexual populations
  5. Population size and mutation rate
  6. Drift vs. selection
  7. Fitness effects of fixed beneficial mutations
  8. Rate of adaptation
  9. Different impacts of population size and mutation rate
  10. Beneficial mutation fraction
  11. Conclusions and future directions
  12. Acknowledgments
  13. References