Adaptive evolution on neutral networks

We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation takes place as regions with more advantageous distributions of neutral genotypes are discovered. Since these discoveries are typically rare events, the population dynamics can be subdivided into separate epochs, with rapid transitions between them. Within one epoch, the average fitness in the population is approximately constant. The transitions between epochs, however, are generally accompanied by a significant increase in the average fitness. We verify our theoretical considerations with two analytically tractable bitstring models.     

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.     

Clonal interference and the periodic selection of new beneficial mutations in Escherichia coli

The conventional model of adaptation in asexual populations implies sequential fixation of new beneficial mutations via rare selective sweeps that purge all variation and preserve the clonal genotype. However, in large populations multiple beneficial mutations may co-occur, causing competition among them, a phenomenon called "clonal interference." Clonal interference is thus expected to lead to longer fixation times and larger fitness effects of mutations that ultimately become fixed, as well as to a genetically more diverse population. Here, we study the significance of clonal interference in populations consisting of mixtures of differently marked wild-type and mutator strains of Escherichia coli that adapt to a minimal-glucose environment for 400 generations. We monitored marker frequencies during evolution and measured the competitive fitness of random clones from each marker state after evolution. The results demonstrate the presence of multiple beneficial mutations in these populations and slower and more erratic invasion of mutants than expected by the conventional model, showing the signature of clonal interference. We found that a consequence of clonal interference is that fitness estimates derived from invasion trajectories were less than half the magnitude of direct estimates from competition experiments, thus revealing fundamental problems with this fitness measure. These results force a reevaluation of the conventional model of periodic selection for asexual microbes.     

Minimal models of growth and decline of microbial populations

Dynamics of growth and decline of microbial populations were analysed and respective models were developed in this investigation. Analysis of the dynamics was based on general considerations concerning the main properties of microorganisms and their interactions with the environment which was supposed to be affected by the activity of the population. Those considerations were expressed mathematically by differential equations or systems of the equations containing minimal sets of parameters characterizing those properties. It has been found that: (1) the factors leading to the decline of the population have to be considered separately, namely, accumulation of metabolites (toxins) in the medium and the exhaustion of resources; the latter have to be separated again into renewable (‘building materials’) and non-renewable (sources of energy); (2) decline of the population is caused by the exhaustion of sources of energy but no decline is predicted by the model because of the exhaustion of renewable resources; (3) the model determined by the accumulation of metabolites (toxins) in the medium does not suggest the existence of a separate ‘stationary phase’; (4) in the model determined by the exhaustion of energy resources the ‘stationary’ and ‘decline’ phases are quite discernible; and (5) there is no symmetry in microbial population dynamics, the decline being slower than the rise. Mathematical models are expected to be useful in getting insight into the process of control of the dynamics of microbial populations. The models are in agreement with the experimental data.     

Clonal interference, multiple mutations and adaptation in large asexual populations

Two important problems affect the ability of asexual populations to accumulate beneficial mutations and hence to adapt. First, clonal interference causes some beneficial mutations to be outcompeted by more-fit mutations that occur in the same genetic background. Second, multiple mutations occur in some individuals, so even mutations of large effect can be outcompeted unless they occur in a good genetic background that contains other beneficial mutations. In this article, we use a Monte Carlo simulation to study how these two factors influence the adaptation of asexual populations. We find that the results depend qualitatively on the shape of the distribution of the fitness effects of possible beneficial mutations. When this distribution falls off slower than exponentially, clonal interference alone reasonably describes which mutations dominate the adaptation, although it gives a misleading picture of the evolutionary dynamics. When the distribution falls off faster than exponentially, an analysis based on multiple mutations is more appropriate. Using our simulations, we are able to explore the limits of validity of both of these approaches, and we explore the complex dynamics in the regimes where neither one is fully applicable.     

The loss of sex in clonal plants

Most plants combine sexual and clonal reproduction, and the balance between the two may vary widely between and within species. There are many anecdotal reports of plants that appear to have abandoned sex for clonal reproduction, yet few studies have quantified the degree of sexual variation in clonal plants and fewer still have determined the underlying ecological and/or genetic factors. Recent empirical work has shown that some clonal plants exhibit very wide variation in sexual reproduction that translates into striking variation in genotypic diversity and differentiation of natural populations. Reduced sexual reproduction may be particularly common at the geographical margins of species' ranges. Although seed production and sexual recruitment may often be limited by biotic and abiotic aspects of the environment in marginal populations, genetic factors, including changes in ploidy and sterility mutations, may also play a significant role in causing reduced sexual fertility. Moreover, environmental suppression of sexual recruitment may facilitate the evolution of genetic sterility because natural selection no longer strongly maintains the many traits involved in sex. In addition to the accumulation of neutral sterility mutations in highly clonal populations, the evolution of genetic infertility may be facilitated if sterility is associated with enhanced vegetative growth, clonal propagation or survival through either resource reallocation or pleiotropy. However, there are almost no experimental data with which to distinguish among these possibilities. Ultimately, wide variation in genotypic diversity and gene flow associated with the loss of sex may constrain local adaptation and the evolution of the geographical range limit in clonal plants.     

Compensatory evolution in diploid populations

Compensatory mutations are individually deleterious but harmless in appropriate combinations either at more than two sites within a gene or on separate genes. Considering that dominance effects of selection and heterodimer formation of gene products may affect the rate of compensatory evolution, we investigate compensatory neutral mutation models for diploid populations. Our theoretical analysis on the average time until fixation of compensatory mutations shows that these factors play an important role in reducing the fixation time of compensatory mutations if mutation rates are not low. Compensatory evolution of heterodimers is shown to occur more easily if the deleterious effects of single mutants are recessive.     

Selection for intermediate mortality and reproduction rates in a spatially structured population

How local interactions influence both population and evolutionary dynamics is currently a key topic in theoretical ecology. We use a 'well-mixed' analytical model and spatially explicit individual-based models to investigate a system where a population is subject to rare disturbance events. The disturbance can only propagate through regions of the population where the density of individuals is sufficiently high and individuals affected by the disturbance die shortly after. We find that populations where individuals are sessile often exhibit very different dynamic behaviour when compared to populations where individuals are mobile and spatially well mixed. When mutations are allowed which affect either offspring birth rates or mortality rates, the well-mixed populations always evolve to a state where a single disturbance event leads to extinction. Populations often persist substantially longer if individuals are sessile and they disperse their offspring locally. We also find that for sessile populations selection may favour short-lived individuals with limited offspring production. Population dynamics are found to be strongly influenced by the host characters that are evolving and the rate at which host variation is introduced into the system.     

New Statistical Tests of Neutrality for DNA Samples from a Population

The purpose of this paper is to develop statistical tests of the neutral model of evolution against a class of alternative models with the common characteristic of having an excess of mutations that occurred a long time ago or a reduction of recent mutations compared to the neutral model. This class of population genetics models include models for structured populations, models with decreasing effective population size and models of selection and mutation balance. Four statistical tests were proposed in this paper for DNA samples from a population. Two of these tests, one new and another a modification of an existing test, are based on EWENS'' sampling formula, and the other two new tests make use of the frequencies of mutations of various classes. Using simulated samples and regression analyses, the critical values of these tests can be computed from regression equations. This approach for computing the critical values of a test was found to be appropriate and quite effective. We examined the powers of these four tests using simulated samples from structured populations, populations with linearly decreasing sizes and models of selection and mutation balance and found that they are more powerful than existing statistical tests of the neutral model of evolution.     

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.     

Two measures of effective population size for graphs

Effective population size is a key parameter in population ecology because it allows prediction of the dynamics of genetic variation and the rate of genetic drift and inbreeding. It is important for the definition of "nearly neutral" mutations and, hence, has consequences for the fixation or extinction probabilities of advantageous and deleterious mutations. As graph-based population models become increasingly popular for studying evolution in spatially or socially structured populations, a neutral theory for evolution on graphs is called for. Here, we derive formulae for two alternative measures of effective population size, the variance effective and inbreeding effective size of general unweighted and undirected graphs. We show how these two quantities relate to each other and we derive effective sizes for the complete graph the cycle and bipartite graphs. For one-dimensional lattices and small-world graphs, we estimate the inbreeding effective size using simulations. The presented method is suitable for any structured population of haploid individuals with overlapping generations.     

DYNAMICS OF HYBRID INCOMPATIBILITY IN GENE NETWORKS IN A CONSTANT ENVIRONMENT

After an ancestral population splits into two allopatric populations, different mutations may fix in each. When pairs of mutations are brought together in a hybrid offspring, epistasis may cause reduced fitness. Such pairs are known as Bateson–Dobzhansky–Muller (BDM) incompatibilities. A well-known model of BDM incompatibility due to Orr suggests that the fitness load on hybrids should initially accelerate, and continue to increase as the number of potentially incompatible substitutions increases (the "snowball effect"). In the gene networks model, which violates a key assumption of Orr's model (independence of fixation probabilities), the snowball effect often does not occur. Instead, we describe three possible dynamics in a constant environment: (1) Stabilizing selection can constrain two allopatric populations to remain near-perfectly compatible. (2) Despite constancy of environment, punctuated evolution may obtain; populations may experience rare adaptations asynchronously, permitting incompatibility. (3) Despite stabilizing selection, developmental system drift may permit genetic change, allowing two populations to drift in and out of compatibility. We reinterpret Orr's model in terms of genetic distance. We extend Orr's model to the finite loci case, which can limit incompatibility. Finally, we suggest that neutral evolution of gene regulation in nature, to the point of speciation, is a distinct possibility.     

Adaptation,Clonal Interference,and Frequency-Dependent Interactions in a Long-Term Evolution Experiment with Escherichia coli

Twelve replicate populations of Escherichia coli have been evolving in the laboratory for >25 years and 60,000 generations. We analyzed bacteria from whole-population samples frozen every 500 generations through 20,000 generations for one well-studied population, called Ara−1. By tracking 42 known mutations in these samples, we reconstructed the history of this population’s genotypic evolution over this period. The evolutionary dynamics of Ara−1 show strong evidence of selective sweeps as well as clonal interference between competing lineages bearing different beneficial mutations. In some cases, sets of several mutations approached fixation simultaneously, often conveying no information about their order of origination; we present several possible explanations for the existence of these mutational cohorts. Against a backdrop of rapid selective sweeps both earlier and later, two genetically diverged clades coexisted for >6000 generations before one went extinct. In that time, many additional mutations arose in the clade that eventually prevailed. We show that the clades evolved a frequency-dependent interaction, which prevented the immediate competitive exclusion of either clade, but which collapsed as beneficial mutations accumulated in the clade that prevailed. Clonal interference and frequency dependence can occur even in the simplest microbial populations. Furthermore, frequency dependence may generate dynamics that extend the period of coexistence that would otherwise be sustained by clonal interference alone.     

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.     

The Effect of Deleterious Mutations on Neutral Molecular Variation

Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.     

Compensatory evolution of interacting gene products through multifunctional intermediates

When two mutations are singly deleterious but neutral or beneficial together, compensatory evolution can occur. The accumulation of derived, compensated genotypes contributes to the evolution of genetic incompatibilities between diverging populations or species. Previous two locus/two allele models have shown that compensatory evolution is appreciable only with tight linkage, the possibility of nearly simultaneous mutations, and/or a way to overcome negative selection against the singly mutated genotype. These conditions are often not met. Even when they are met, compensatory evolution is still predicted to be extremely slow, and in many scenarios selective advantage of the compensated genotype does little to accelerate it. Despite these obstacles, empirical studies suggest that it occurs readily. We describe here a set of related two locus/three allele models that invoke plausible neutral intermediates capable of productive interaction with both ancestral and compensated products of the interacting locus. These models are explored with analytical and computer simulation methods. The effect of these stepping-stone alleles on the evolution of ancestor-descendant incompatibilities is often profound, making the difference between evolution and stasis in several situations, including in small populations, when codominance or haploidy prevents shielding of mismatched genotypes, and in the absence of positive selection on the derived genotype. However, in large populations these intermediates can either speed or slow the evolution of incompatible genotypes relative to the two-allele case, depending on the specific fitness model. These results suggest that population size, the source of adaptive benefit, and the structural details of heteromeric gene product complexes interact to influence the path by which intergenic incompatibility evolves.     

Dynamics of molecular evolution in RNA virus populations depend on sudden versus gradual environmental change

Understanding the dynamics of molecular adaptation is a fundamental goal of evolutionary biology. While adaptation to constant environments has been well characterized, the effects of environmental complexity remain seldom studied. One simple but understudied factor is the rate of environmental change. Here we used experimental evolution with RNA viruses to investigate whether evolutionary dynamics varied based on the rate of environmental turnover. We used whole‐genome next‐generation sequencing to characterize evolutionary dynamics in virus populations adapting to a sudden versus gradual shift onto a novel host cell type. In support of theoretical models, we found that when populations evolved in response to a sudden environmental change, mutations of large beneficial effect tended to fix early, followed by mutations of smaller beneficial effect; as predicted, this pattern broke down in response to a gradual environmental change. Early mutational steps were highly parallel across replicate populations in both treatments. The fixation of single mutations was less common than sweeps of associated “cohorts” of mutations, and this pattern intensified when the environment changed gradually. Additionally, clonal interference appeared stronger in response to a gradual change. Our results suggest that the rate of environmental change is an important determinant of evolutionary dynamics in asexual populations.     

Dynamics of isolated <Emphasis Type="Italic">Saponaria bellidifolia</Emphasis> Sm. populations at northern range periphery

Four populations of Saponaria bellidifolia situated at the species’ northern range periphery (Apuseni Mountains, southeastern Carpathians) were monitored over a period of 5 years. They were chosen to represent different habitat types (rocky, fixed screes, open screes and grassy), disturbance regime (fire), and population sizes (categorized as large and small). The reproductive effort was quantified, and matrix models were used to describe the population dynamics and to assess population viability. Saponaria bellidifolia had very stable population dynamics in the harsh and stable abiotic conditions of the outcrops where populations occur. Habitat conditions exerted a notable influence on the species’ population reproductive performance, growth rate, and vital rates, whereas population size and climate did not have a clear-cut effect on the dynamics of the species. Saponaria bellidifolia maintains viable populations in the southeastern Carpathians, at its northern range periphery.     

Metastable evolutionary dynamics: Crossing fitness barriers or escaping via neutral paths?

We analytically study the dynamics of evolving populations that exhibit metastability on the level of phenotype or fitness. In constant selective environments, such metastable behavior is caused by two qualitatively different mechanisms. On the one hand, populations may become pinned at a local fitness optimum, being separated from higher-fitness genotypes by a fitness barrier of low-fitness genotypes. On the other hand, the population may only be metastable on the level of phenotype or fitness while, at the same time, diffusing over neutral networks of selectively neutral genotypes. Metastability occurs in this case because the population is separated from higher-fitness genotypes by an entropy barrier: the population must explore large portions of these neutral networks before it discovers a rare connection to fitter phenotypes. We derive analytical expressions for the barrier crossing times in both the fitness barrier and entropy barrier regime. In contrast with ‘landscape’ evolutionary models, we show that the waiting times to reach higher fitness depend strongly on the width of a fitness barrier and much less on its height. The analysis further shows that crossing entropy barriers is faster by orders of magnitude than fitness barrier crossing. Thus, when populations are trapped in a metastable phenotypic state, they are most likely to escape by crossing an entropy barrier, along a neutral path in genotype space. If no such escape route along a neutral path exists, a population is most likely to cross a fitness barrier where the barrier is narrowest, rather than where the barrier is shallowest.     

The evolution of senescence in multi-component systems

Actuarial senescence is characterized by an increase in mortality rate with increasing chronological age. The reliability theory of senescence proposes that organisms’ vital functions can be modelled as a suite of damageable, irreplaceable elements (typically genes or their products) that protect their bearer from condition-dependent death so long as at least one of the elements remains intact. Current incarnations of the reliability theory of senescence are continuous-time models with no explicit evolutionary component. Here, we use elementary probability theory and evolutionary dynamics analysis to derive a discrete-time version of the reliability theory of senescence. We include three variations on this theme: the ‘Series’ model in which damage to any of n elements results in death, the ‘Parallel’ model, in which damage accumulates in random order and damage to all n elements results in death, and the ‘Cascade’ (multi-stage) model, which is like the Parallel model, except the irreparable damage necessarily follows a strict sequence. For simplicity, we refer to the state of having multiple elements as ‘redundancy’, but this does not imply that the elements are necessarily identical. We show that redundancy leads to actuarial senescence in the Parallel and Cascade models but not in the Series model. We further demonstrate that in the Parallel and Cascade models, lifetime reproductive output (a potential proxy for fitness in populations with discrete generations) is a positive but decelerating function of redundancy. The positive nature of the fitness function leads to the prediction that redundancy and senescence should evolve from non-redundant, non-senescing ancestral populations; however, the deceleration of the fitness function leads to the prediction that this evolution towards increased redundancy will eventually be limited by mutation-selection balance. Using evolutionary dynamics analysis involving the discrete-generation quasispecies equation, we confirm these two predictions. Finally, we show that a population's equilibrium redundancy is sensitive to the environmental conditions that prevailed during its evolution, such as the rate of extrinsic mortality.