Genome structure and the benefit of sex

We examine the behavior of sexual and asexual populations in modular multipeaked fitness landscapes and show that sexuals can systematically reach different, higher fitness adaptive peaks than asexuals. Whereas asexuals must move against selection to escape local optima, sexuals reach higher fitness peaks reliably because they create specific genetic variants that "skip over" fitness valleys, moving from peak to peak in the fitness landscape. This occurs because recombination can supply combinations of mutations in functional composites or "modules," that may include individually deleterious mutations. Thus when a beneficial module is substituted for another less-fit module by sexual recombination it provides a genetic variant that would require either several specific simultaneous mutations in an asexual population or a sequence of individual mutations some of which would be selected against. This effect requires modular genomes, such that subsets of strongly epistatic mutations are tightly physically linked. We argue that such a structure is provided simply by virtue of the fact that genomes contain many genes each containing many strongly epistatic nucleotides. We briefly discuss the connections with "building blocks" in the evolutionary computation literature. We conclude that there are conditions in which sexuals can systematically evolve high-fitness genotypes that are essentially unevolvable for asexuals.     

A population genetics model for multiple quantitative traits exhibiting pleiotropy and epistasis

We study a population genetics model of an organism with a genome of L(tot)loci that determine the values of T quantitative traits. Each trait is controlled by a subset of L loci assigned randomly from the genome. There is an optimum value for each trait, and stabilizing selection acts on the phenotype as a whole to maintain actual trait values close to their optima. The model contains pleiotropic effects (loci can affect more than one trait) and epistasis in fitness. We use adaptive walk simulations to find high-fitness genotypes and to study the way these genotypes are distributed in sequence space. We then simulate the evolution of haploid and diploid populations on these fitness landscapes and show that the genotypes of populations are able to drift through sequence space despite stabilizing selection on the phenotype. We study the way the rate of drift and the extent of the accessible region of sequence space is affected by mutation rate, selection strength, population size, recombination rate, and the parameters L and T that control the landscape shape. There are three regimes of the model. If LTL(tot), there are many small peaks that can be spread over a wide region of sequence space. Compensatory neutral mutations are important in the population dynamics in this case.     

Fixation of clonal lineages under Muller's ratchet

For clonal lineages of finite size that differ in their deleterious mutational effects, the probability of fixation is investigated by mathematical theory and Monte Carlo simulations. If these fitness effects are sufficiently small in one or both lineages, then the lineage with the less deleterious effects will become fixed with high probability. If, however, in both lineages the deleterious effects are larger than a threshold s(c), then the probability of fixation is independent of the fitness effects and depends only on the initial frequencies of the lineages. This threshold decreases with decreasing genomic mutation rate U and increases with population size N. (For N = 10(5), we have s(c) approximately = 0.1 if U = 1, and s(c) approximately = 0.015 if U = 0.1). Above the threshold, the competition is not driven by the ratio of mean fitnesses of the lineages, but by the relative sizes of the zero-mutation classes, which are independent of the fitness effects of the mutations. After the loss of the zero-mutation class of a lineage, the other lineage will spread to fixation with high probability and within a short time span. If the mutation rates of the lineages differ substantially, the lineage with the lower mutation rate is fixed with very high probability unless the lineage with the larger mutation rate has very slightly deleterious mutational effects. If the mutation rates differ by not more than a few percent, then the lineage with the higher mutation rate and the more deleterious effects can become fixed with appreciable probability for a certain range of parameters. The independence of the fixation probability on the fitness effects in a single population leads to dramatic effects in metapopulations: lineages with more deleterious effects have a much higher fixation probability. The critical value s(c), above which this phenomenon occurs, decreases as the migration rate between the subpopulations decreases.     

Rate of adaptive peak shifts with partial genetic robustness

How adaptive evolution occurs with individually deleterious but jointly beneficial mutations has been one of the major problems in population genetics theory. Adaptation in this case is commonly described as a population's escape from a local peak to a higher peak on Sewall Wright's fitness landscape. Recent molecular genetic and computational studies have suggested that genetic robustness can facilitate such peak shifts. If phenotypic expressions of new mutations are suppressed under genetic robustness, mutations that are otherwise deleterious can accumulate in the population as neutral variants. When the robustness is perturbed by an environmental change or a major mutation, these variants become exposed to natural selection. It is argued that this process promotes adaptation because allelic combinations enriched under genetic robustness can then be positively selected. Here, I propose simple two- and three-locus models of adaptation with partial genetic robustness as suggested by recent studies. The waiting time until the fixation of an adaptive haplotype was observed in stochastic simulations and compared to the expectation without robustness. It is shown that peak shifts can be delayed or accelerated depending on the conditions of genetic robustness. The evolutionary significance of these processes is discussed.     

EXPERIMENTAL STUDIES OF PLEIOTROPY AND EPISTASIS IN ESCHERICHIA COLI. II. COMPENSATION FOR MALADAPTIVE EFFECTS ASSOCIATED WITH RESISTANCE TO VIRUS T4

Mutations in Escherichia coli that confer resistance to virus T4 also have maladaptive effects that reduce competitive fitness. After resistant populations had evolved for 400 generations in the absence of T4, their fitness approached that of sensitive populations allowed to evolve under identical conditions. However, the resistant populations had not reverted to sensitivity. Instead, this convergence in fitness resulted from genetic changes that compensated for maladaptive pleiotropic effects of the resistance mutations. An allele selected in an evolving resistant population reduced the competitive disadvantage associated with resistance by almost half. Interestingly, this allele was also beneficial in sensitive populations, although its fitness advantage was only about one-fifth as great as it was in the resistant population. These results run counter to a commonly held view that trade-offs between components of fitness should become more pronounced as populations approach their “selective equilibria.” If a trade-off derives from some limiting energetic or material currency, then it is likely to become more pronounced as a population becomes more finely adapted. If a trade-off derives from the disruption of genetic integration, then it is likely to be diminished with further adaptation.     

Phenotype Switching and Mutations in Random Environments

Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here, we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genotypes with different switching rates, and analyze how the optimal switching rates depend on the frequency of environmental changes. If environmental changes are as rare as mutations, then the optimal switching rates mimic the rates of environmental changes. If the environment changes more frequently, then the optimal genotype either maximally favors fitness in the more common environment or has the maximal switching rate to each phenotype. Our results also explain why the optimum is relatively insensitive to fitness in each environment.     

ON THE FINDABILITY OF GENOTYPES

Can we define a measure that describes how easy or difficult it is for a population to evolve to a specific genotype? For populations evolving under weak mutation on a time‐invariant fitness landscape, I argue that one appropriate measure is the expected waiting time, starting from equilibrium, for a population to become fixed for a given genotype. Under this definition for the “findability” of genotypes, I show that for any pair of genotypes (1) a population at equilibrium is always more likely to fix at the more findable before the less findable genotype and (2) the expected time to evolve from the more findable to the less findable genotype is always greater that the expected time to evolve in the opposite direction. Although increasing the fitness of a genotype always increases its findability, in general there is no simple relationship between the rank ordering of genotypes by fitness and the rank ordering of genotypes by findability. I also present a method for quantifying the relative contributions of mutation, selection, substitution rate, and probability of reversion to a genotype's findability.     

The Rate of Compensatory Evolution

A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, k(c), is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, k(c) depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, k(c) is given by the rate at which favorable combinations of double mutants are produced by compensatory mutation. For r>0, k(c) decreases exponentially with r. In contrast, k(c) becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to WRIGHT's shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.     

Environmental change exposes beneficial epistatic interactions in a catalytic RNA

Natural selection drives populations of individuals towards local peaks in a fitness landscape. These peaks are created by the interactions between individual mutations. Fitness landscapes may change as an environment changes. In a previous contribution, we discovered a variant of the Azoarcus group I ribozyme that represents a local peak in the RNA fitness landscape. The genotype at this peak is distinguished from the wild-type by four point mutations. We here report ribozyme fitness data derived from constructing all possible combinations of these point mutations. We find that these mutations interact epistatically. Importantly, we show that these epistatic interactions change qualitatively in the three different environments that we studied. We find examples where the relative fitness of a ribozyme can change from neutral or negative in one environment, to positive in another. We also show that the fitness effect of a specific GC-AU base pair switch is dependent on both the environment and the genetic context. Moreover, the mutations that we study improve activity at the cost of decreased structural stability. Environmental change is ubiquitous in nature. Our results suggest that such change can facilitate adaptive evolution by exposing new peaks of a fitness landscape. They highlight a prominent role for genotype-environment interactions in doing so.     

Evolutionary dynamics of two related malignant plasma cell lines

Cancer is the consequence of sequential acquisition of mutations within somatic cells. Mutations alter the relative reproductive fitness of cells, enabling the population to evolve in time as a consequence of selection. Cancer therapy itself can select for or against specific subclones. Given the large population of tumor cells, subclones inevitably emerge and their fate will depend on the evolutionary dynamics that define the interactions between such clones. Using a combination of in vitro studies and mathematical modeling, we describe the dynamic behavior of two cell lines isolated from the same patient at different time points of disease progression and show how the two clones relate to one another. We provide evidence that the two clones coexisted at the time of initial presentation. The dominant clone presented with biopsy proven cardiac AL amyloidosis. Initial therapy selected for the second clone that expanded leading to a change in the diagnosis to multiple myeloma. The evolutionary dynamics relating the two cell lines are discussed and a hypothesis is generated in regard to the mechanism of one of the phenotypic characteristics that is shared by these two cell lines.     

Sex ratio polymorphism: The impact of mutation and drift on evolution

This paper addresses the question, which sex ratio will evolve in a population that is subject to mutation and drift. The problem is analyzed using a simulation model as well as analytical methods. A detailed simulation model for the evolution of a population's allele distribution shows that for the sex ratio game a wide spectrum of different population states may evolve from on the one hand a monomorphic state with one predominant allele and with all other alleles suppressed by the forces of selection, to on the other hand a polymorphism determined by recurrent mutations. Which of these states will evolve depends on the population size, the mating system and the rate of mutations. For the sex ratio game the evolutionary stable strategy (ESS), as defined by evolutionary game theory, can only predict the population sex ratio but not the underlying stable population state. A comparison of different approaches to the problem shows that false predictions of the stable population states might result from two simplifying assumptions that are fairly common in evolutionary biology: a) it is assumed that mutations are rare events and there is never more than one mutant gene present in a population at any one time; b) a deterministic relationship is assumed between the fitness assigned to an individual's strategy and the individual's contribution to the gene pool of future generations.     

VARIANCE-INDUCED PEAK SHIFTS

The increase in phenotypic variance that occurs in some populations as a result of bottlenecks and founder events can cause a dramatic increase in the probability of a peak shift from one adaptive state to another. Periods of small population size allow drift in the amount of phenotypic variance. Increases in phenotypic variance, coupled with a constant individual fitness function with multiple peaks, can cause the mean fitness landscape to change from bimodal to unimodal, thereby allowing the population's mean phenotype to change deterministically by selection. As the amount of phenotypic variance is returned to an equilibrium state, the multiple peaks reemerge, but the population has moved from one stable state to another. These variance-induced peak shifts allow punctuational evolution from one peak to another at a rate that can be much higher than that predicted by Wright's shifting-balance process alone.     

Very low levels of direct additive genetic variance in fitness and fitness components in a red squirrel population

A trait must genetically correlate with fitness in order to evolve in response to natural selection, but theory suggests that strong directional selection should erode additive genetic variance in fitness and limit future evolutionary potential. Balancing selection has been proposed as a mechanism that could maintain genetic variance if fitness components trade off with one another and has been invoked to account for empirical observations of higher levels of additive genetic variance in fitness components than would be expected from mutation–selection balance. Here, we used a long‐term study of an individually marked population of North American red squirrels (Tamiasciurus hudsonicus) to look for evidence of (1) additive genetic variance in lifetime reproductive success and (2) fitness trade‐offs between fitness components, such as male and female fitness or fitness in high‐ and low‐resource environments. “Animal model” analyses of a multigenerational pedigree revealed modest maternal effects on fitness, but very low levels of additive genetic variance in lifetime reproductive success overall as well as fitness measures within each sex and environment. It therefore appears that there are very low levels of direct genetic variance in fitness and fitness components in red squirrels to facilitate contemporary adaptation in this population.     

Genetic loads under fitness‐dependent mutation rates

Abstract Although much theory depends on the genome‐wide rate of deleterious mutations, good estimates of the mutation rate are scarce and remain controversial. Furthermore, mutation rate may not be constant, and a recent study suggests that mutation rates are higher in mildly stressful environments. If mutation rate is a function of condition, then individuals carrying more mutations will tend to be in worse condition and therefore produce more mutations. Here I examine the mean fitnesses of sexual and asexual populations evolving under such condition‐dependent mutation rates. The equilibrium mean fitness of a sexual population depends on the shape of the curve relating fitness to mutation rate. If mutation rate declines synergistically with increasing condition the mean fitness will be much lower than if mutation rate declines at a diminishing rate. In contrast, asexual populations are less affected by condition‐dependent mutation rates. The equilibrium mean fitness of an asexual population only depends on the mutation rate of the individuals in the least loaded class. Because such individuals have high fitness and therefore a low mutation rate, asexual populations experience less genetic load than sexual populations, thus increasing the twofold cost of sex.     

ADAPTIVE WALKS AND DISTRIBUTION OF BENEFICIAL FITNESS EFFECTS

We study the adaptation dynamics of a maladapted asexual population on rugged fitness landscapes with many local fitness peaks. The distribution of beneficial fitness effects is assumed to belong to one of the three extreme value domains, viz. Weibull, Gumbel, and Fréchet. We work in the strong selection‐weak mutation regime in which beneficial mutations fix sequentially, and the population performs an uphill walk on the fitness landscape until a local fitness peak is reached. A striking prediction of our analysis is that the fitness difference between successive steps follows a pattern of diminishing returns in the Weibull domain and accelerating returns in the Fréchet domain, as the initial fitness of the population is increased. These trends are found to be robust with respect to fitness correlations. We believe that this result can be exploited in experiments to determine the extreme value domain of the distribution of beneficial fitness effects. Our work here differs significantly from the previous ones that assume the selection coefficient to be small. On taking large effect mutations into account, we find that the length of the walk shows different qualitative trends from those derived using small selection coefficient approximation.     

The role of deleterious mutations in allopatric speciation

Allopatric speciation is often assumed to occur as a consequence of adaptive divergence between two isolated populations. However, there are some scenarios in which reproductive isolation can be favored due to accumulated unconditionally deleterious mutations. If deleterious mutations have synergistic epistatic effects, it is shown here that the average fitness of recombinants between two parental lines with a given number of fixed mutations is lower than that of the parents in both the F1 and F2 generations. If individual mutations are only slightly deleterious, then they will tend to fixation at a high enough rate to cause lower hybrid fitness. If the fitness effects of mutation give rise to antagonistic epistasis, the hybrids tend to have a higher average fitness than the parental lines, suggesting a possible scenario for the origin of hybrid vigor. The other model of deleterious mutations investigated is the accumulation of knockout mutants in a duplicated gene family. While neutral in the parental lines, upon contact the F1 and later generations have a significant probability of carrying double knockouts. Under this scenario, selection may also favor reproductive isolation between the two lines. Even when the selection coefficients generated are too low to drive speciation, epistatic interactions between deleterious mutations offer a possible explanation for both outbreeding depression and hybrid vigor.     

Evolutionary dynamics of two related malignant plasma cell lines

Cancer is the consequence of sequential acquisition of mutations within somatic cells. Mutations alter the relative reproductive fitness of cells, enabling the population to evolve in time as a consequence of selection. Cancer therapy itself can select for or against specific subclones. Given the large population of tumor cells, subclones inevitably emerge and their fate will depend on the evolutionary dynamics that define the interactions between such clones. Using a combination of in vitro studies and mathematical modeling, we describe the dynamic behavior of two cell lines isolated from the same patient at different time points of disease progression and show how the two clones relate to one another. We provide evidence that the two clones coexisted at the time of initial presentation. The dominant clone presented with biopsy-proven cardiac AL amyloidosis. Initial therapy selected for the second clone that expanded leading to a change in the diagnosis to multiple myeloma. The evolutionary dynamics relating the two cell lines are discussed and a hypothesis is generated in regard to the mechanism of one of the phenotypic characteristics that is shared by these two cell lines.Key words: multiple myeloma, amyloidosis, chemotherapy, clonal evolution, selection     

Defined order of evolutionary adaptations: experimental evidence

Organisms often adapt to new conditions by means of beneficial mutations that become fixed in the population. Often, full adaptation requires several different mutations in the same cell, each of which may affect a different aspect of the behavior. Can one predict order in which these mutations become fixed? To address this, we experimentally studied evolution of Escherichia coli in a growth medium in which the effects of different adaptations can be easily classified as affecting growth rate or the lag‐phase duration. We find that adaptations are fixed in a defined and reproducible order: first reduction of lag phase, and then an increase of the exponential growth rate. A population genetics theory explains this order, and suggests growth conditions in which the order of adaptations is reversed. We experimentally find this order reversal under the predicted conditions. This study supports a view in which the evolutionary path to adaptation in a new environment can be captured by theory and experiment.     

The speed of evolution and maintenance of variation in asexual populations

BACKGROUND: The rate at which beneficial mutations accumulate determines how fast asexual populations evolve, but this is only partially understood. Some recent clonal-interference models suggest that evolution in large asexual populations is limited because smaller beneficial mutations are outcompeted by larger beneficial mutations that occur in different lineages within the same population. This analysis assumes that the important mutations fix one at a time; it ignores multiple beneficial mutations that occur in the lineage of an earlier beneficial mutation, before the first mutation in the series can fix. We focus on the effects of such multiple mutations. RESULTS: Our analysis predicts that the variation in fitness maintained by a continuously evolving population increases as the logarithm of the population size and logarithm of the mutation rate and thus yields a similar logarithmic increase in the speed of evolution. To test these predictions, we evolved asexual budding yeast in glucose-limited media at a range of population sizes and mutation rates. CONCLUSIONS: We find that their evolution is dominated by the accumulation of multiple mutations of moderate effect. Our results agree with our theoretical predictions and are inconsistent with the one-by-one fixation of mutants assumed by recent clonal-interference analysis.