Epistasis and the adaptability of an RNA virus

We have explored the patterns of fitness recovery in the vesicular stomatitis RNA virus. We show that, in our experimental setting, reversions to the wild-type genotype were rare and fitness recovery was at least partially driven by compensatory mutations. We compared compensatory adaptation for genotypes carrying (1) mutations with varying deleterious fitness effects, (2) one or two deleterious mutations, and (3) pairs of mutations showing differences in the strength and sign of epistasis. In all cases, we found that the rate of fitness recovery and the proportion of reversions were positively affected by population size. Additionally, we observed that mutations with large fitness effect were always compensated faster than mutations with small fitness effect. Similarly, compensatory evolution was faster for genotypes carrying a single deleterious mutation than for those carrying pairs of mutations. Finally, for genotypes carrying two deleterious mutations, we found evidence of a negative correlation between the epistastic effect and the rate of compensatory evolution.     

Compensating for our load of mutations: freezing the meltdown of small populations

We have investigated the reduction of fitness caused by the fixation of new deleterious mutations in small populations within the framework of Fisher's geometrical model of adaptation. In Fisher's model, a population evolves in an n-dimensional character space with an adaptive optimum at the origin. The model allows us to investigate compensatory mutations, which restore fitness losses incurred by other mutations, in a context-dependent manner. We have conducted a moment analysis of the model, supplemented by the numerical results of computer simulations. The mean reduction of fitness (i.e., expected load) scaled to one is approximately n/(n+2Ne), where Ne is the effective population size. The reciprocal relationship between the load and Ne implies that the fixation of deleterious mutations is unlikely to cause extinction when there is a broad scope for compensatory mutations, except in very small populations. Furthermore, the dependence of load on n implies that pleiotropy plays a large role in determining the extinction risk of small populations. Differences and similarities between our results and those of a previous study on the effects of Ne and n are explored. That the predictions of this model are qualitatively different from studies ignoring compensatory mutations implies that we must be cautious in predicting the evolutionary fate of small populations and that additional data on the nature of mutations is of critical importance.     

Evolution by Gene Duplication and Compensatory Advantageous Mutations

Relaxation of selective constraint is thought to play an important role for evolution by gene duplication, in connection with compensatory advantageous mutant substitutions. Models were investigated by incorporating gene duplication by unequal crossing over, selection, mutation and random genetic drift into Monte Carlo simulations. Compensatory advantageous mutations were introduced, and simulations were carried out with and without relaxation, when genes are redundant on chromosomes. Relaxation was introduced by assuming that deleterious mutants have no effect on fitness, so long as one or more genes free of such mutations remain in the array. Compensatory mutations are characterized by the intermediate deleterious step of their substitutions, and therefore relaxation by gene redundancy is important. Through extensive Monte Carlo simulations, it was found that compensatory mutant substitutions require relaxation in addition to gene duplication, when mutant effects are large. However when mutant effects are small, such that the product of selection coefficient and population size is around unity, evolution by compensatory mutation is enhanced by gene duplication even without relaxation.     

The Interaction between Selection,Demography and Selfing and How It Affects Population Viability

Population extinction due to the accumulation of deleterious mutations has only been considered to occur at small population sizes, large sexual populations being expected to efficiently purge these mutations. However, little is known about how the mutation load generated by segregating mutations affects population size and, eventually, population extinction. We propose a simple analytical model that takes into account both the demographic and genetic evolution of populations, linking population size, density dependence, the mutation load, and self-fertilisation. Analytical predictions were found to be relatively good predictors of population size and probability of population viability when verified using an explicit individual based stochastic model. We show that initially large populations do not always reach mutation-selection balance and can go extinct due to the accumulation of segregating deleterious mutations. Population survival depends not only on the relative fitness and demographic stochasticity, but also on the interaction between the two. When deleterious mutations are recessive, self-fertilisation affects viability non-monotonically and genomic cold-spots could favour the viability of outcrossing populations.     

Mutation, multilevel selection, and the evolution of propagule size during the origin of multicellularity

Evolutionary transitions require the organization of genetic variation at two (or more) levels of selection so that fitness heritability may emerge at the new level. In this article, we consider the consequences for fitness variation and heritability of two of the main modes of reproduction used in multicellular organisms: vegetative reproduction and single-cell reproduction. We study a model where simple cell colonies reproduce by fragments or propagules of differing size, with mutations occurring during colony growth. Mutations are deleterious at the colony level but can be advantageous or deleterious at the cell level ("selfish" or "uniformly deleterious" mutants). Fragment size affects fitness in two ways: through a direct effect on adult group size (which in turn affects fitness) and by affecting the within- and between-group variances and opportunity for selection on mutations at the two levels. We show that the evolution of fragment size is determined primarily by its direct effects on group size except when mutations are selfish. When mutations are selfish, smaller propagule size may be selected, including single-cell reproduction, even though smaller propagule size has a direct fitness cost by virtue of producing smaller organisms, that is, smaller adult cell groups.     

Heterosis in an isolated, effectively small, and self-fertilizing population of the flowering plant Leavenworthia alabamica

Mildly deleterious mutations are thought to play a major role in the extinction of natural populations, especially those that are small, isolated, or inbred. Self-fertilization should reduce the effective size of populations and simultaneously reduce migration between populations. A history of self-fertilization should therefore cause a population to harbor a substantial "local drift load" caused by the fixation of mildly deleterious mutations. This hypothesis was tested in Leavenworthia alabamica, which contains large, self-incompatible populations and smaller self-compatible populations with adaptations for self-fertilization. The fitness of offspring from within- and between-population crosses was compared to quantify heterosis caused by the masking of deleterious alleles in the heterozygous state. Little heterosis was observed in crosses between five large, self-incompatible populations and two of the three small, self-fertilizing populations of L. alabamica. However, the most geographically isolated and genetically divergent self-fertilizing population (Tuscumbia) exhibited a 110.2% increase in germination and a 73.6% increase in fitness, which is consistent with a sizeable local drift load. The finding of substantial heterosis for fitness supports the idea that small effective size, reproductive isolation, and self-fertilization can make populations particularly vulnerable to mutation accumulation.     

Note on the computation of critical effective population sizes.

This work extends the work of Whitlock in examining the critical effective population sizes from the fixation of both deleterious and beneficial mutations under drift and selection to prevent mutation breakdown of the population. The validity of approximations for the probability of fixation depends on the nature of the assumed distribution for the fitness effect of both types of mutations. Using no approximation for the probability of fixation and assuming a heavy tailed fitness effect distribution, the current model indicates that the coefficients of variation for the fitness effect distributions of both types of mutations and the fitness effect distribution mean for the beneficial mutations are important predictors of the critical effective population size. The current model further predicts that very small populations can be sustained if the fitness effect variances for both types of mutations and the mean for beneficial mutations are large.     

The Properties of Adaptive Walks in Evolving Populations of Fungus

The rarity of beneficial mutations has frustrated efforts to develop a quantitative theory of adaptation. Recent models of adaptive walks, the sequential substitution of beneficial mutations by selection, make two compelling predictions: adaptive walks should be short, and fitness increases should become exponentially smaller as successive mutations fix. We estimated the number and fitness effects of beneficial mutations in each of 118 replicate lineages of Aspergillus nidulans evolving for approximately 800 generations at two population sizes using a novel maximum likelihood framework, the results of which were confirmed experimentally using sexual crosses. We find that adaptive walks do indeed tend to be short, and fitness increases become smaller as successive mutations fix. Moreover, we show that these patterns are associated with a decreasing supply of beneficial mutations as the population adapts. We also provide empirical distributions of fitness effects among mutations fixed at each step. Our results provide a first glimpse into the properties of multiple steps in an adaptive walk in asexual populations and lend empirical support to models of adaptation involving selection towards a single optimum phenotype. In practical terms, our results suggest that the bulk of adaptation is likely to be accomplished within the first few steps.     

The nearly neutral and selection theories of molecular evolution under the fisher geometrical framework: substitution rate, population size, and complexity

The general theories of molecular evolution depend on relatively arbitrary assumptions about the relative distribution and rate of advantageous, deleterious, neutral, and nearly neutral mutations. The Fisher geometrical model (FGM) has been used to make distributions of mutations biologically interpretable. We explored an FGM-based molecular model to represent molecular evolutionary processes typically studied by nearly neutral and selection models, but in which distributions and relative rates of mutations with different selection coefficients are a consequence of biologically interpretable parameters, such as the average size of the phenotypic effect of mutations and the number of traits (complexity) of organisms. A variant of the FGM-based model that we called the static regime (SR) represents evolution as a nearly neutral process in which substitution rates are determined by a dynamic substitution process in which the population's phenotype remains around a suboptimum equilibrium fitness produced by a balance between slightly deleterious and slightly advantageous compensatory substitutions. As in previous nearly neutral models, the SR predicts a negative relationship between molecular evolutionary rate and population size; however, SR does not have the unrealistic properties of previous nearly neutral models such as the narrow window of selection strengths in which they work. In addition, the SR suggests that compensatory mutations cannot explain the high rate of fixations driven by positive selection currently found in DNA sequences, contrary to what has been previously suggested. We also developed a generalization of SR in which the optimum phenotype can change stochastically due to environmental or physiological shifts, which we called the variable regime (VR). VR models evolution as an interplay between adaptive processes and nearly neutral steady-state processes. When strong environmental fluctuations are incorporated, the process becomes a selection model in which evolutionary rate does not depend on population size, but is critically dependent on the complexity of organisms and mutation size. For SR as well as VR we found that key parameters of molecular evolution are linked by biological factors, and we showed that they cannot be fixed independently by arbitrary criteria, as has usually been assumed in previous molecular evolutionary models.     

A resolution of the mutation load paradox in humans

Current information on the rate of mutation and the fraction of sites in the genome that are subject to selection suggests that each human has received, on average, at least two new harmful mutations from its parents. These mutations were subsequently removed by natural selection through reduced survival or fertility. It has been argued that the mutation load, the proportional reduction in population mean fitness relative to the fitness of an idealized mutation-free individual, allows a theoretical prediction of the proportion of individuals in the population that fail to reproduce as a consequence of these harmful mutations. Application of this theory to humans implies that at least 88% of individuals should fail to reproduce and that each female would need to have more than 16 offspring to maintain population size. This prediction is clearly at odds with the low reproductive excess of human populations. Here, we derive expressions for the fraction of individuals that fail to reproduce as a consequence of recurrent deleterious mutation () for a model in which selection occurs via differences in relative fitness, such as would occur through competition between individuals. We show that is much smaller than the value predicted by comparing fitness to that of a mutation-free genotype. Under the relative fitness model, we show that depends jointly on U and the selective effects of new deleterious mutations and that a species could tolerate 10's or even 100's of new deleterious mutations per genome each generation.     

Inbreeding depression due to mildly deleterious mutations in finite populations: size does matter

We studied the effects of population size on the inbreeding depression and genetic load caused by deleterious mutations at a single locus. Analysis shows how the inbreeding depression decreases as population size becomes smaller and/or the rate of inbreeding increases. This pattern contrasts with that for the load, which increases as population size becomes smaller but decreases as inbreeding rate goes up. The depression and load both approach asymptotic limits when the population size becomes very large or very small. Numerical results show that the transition between the small and the large population regimes is quite rapid, and occurs largely over a range of population sizes that vary by a factor of 10. The effects of drift on inbreeding depression may bias some estimates of the genomic rate of deleterious mutation. These effects could also be important in the evolution of breeding systems in hermaphroditic organisms and in the conservation of endangered populations.     

Mutational effects on the clonal interference phenomenon

We study the process of fixation of beneficial mutations in an asexual population by means of a theoretical model. Particularly, we wish to investigate how the supply of deleterious and beneficial mutations influences the dynamics of the adaptive process of an evolving population. It is well known that the deleterious mutations drastically affect the fate of beneficial mutations. In addition, an increasing supply of favorable mutations, to compensate the decay of the fitness due to the accumulation of deleterious mutations, produces the clonal interference phenomenon where advantageous mutations in distinct lineages compete to reach fixation. This competition imposes a limit to the speed of adaptation of the population. Intuitively, we would expect that the interplay of the two mechanisms would conspire to ensure fixation of only large-effect beneficial mutations. Our results, however, show that beneficial mutations of small effect have an increased probability of fixation when both beneficial and deleterious mutations rates are increased.     

Mitochondrial-nuclear interactions and accelerated compensatory evolution: evidence from the primate cytochrome C oxidase complex

Accelerated rates of mitochondrial protein evolution have been proposed to reflect Darwinian coadaptation for efficient energy production for mammalian flight and brain activity. However, several features of mammalian mtDNA (absence of recombination, small effective population size, and high mutation rate) promote genome degradation through the accumulation of weakly deleterious mutations. Here, we present evidence for "compensatory" adaptive substitutions in nuclear DNA- (nDNA) encoded mitochondrial proteins to prevent fitness decline in primate mitochondrial protein complexes. We show that high mutation rate and small effective population size, key features of primate mitochondrial genomes, can accelerate compensatory adaptive evolution in nDNA-encoded genes. We combine phylogenetic information and the 3D structure of the cytochrome c oxidase (COX) complex to test for accelerated compensatory changes among interacting sites. Physical interactions among mtDNA- and nDNA-encoded components are critical in COX evolution; amino acids in close physical proximity in the 3D structure show a strong tendency for correlated evolution among lineages. Only nuclear-encoded components of COX show evidence for positive selection and adaptive nDNA-encoded changes tend to follow mtDNA-encoded amino acid changes at nearby sites in the 3D structure. This bias in the temporal order of substitutions supports compensatory weak selection as a major factor in accelerated primate COX evolution.     

An explicit model for the inbreeding load in the evolutionary analysis of selfing

I present analytical predictions for the equilibrium inbreeding load expected in a population under mutation, selection, and a regular mating system for any population size and for any magnitude and recessivity of the deleterious effects. Using this prediction, I deduce the relative fitness of mutant alleles with small effect on selfing to explore the situations where selfing or outcrossing are expected to evolve. The results obtained are in agreement with previous literature, showing that natural selection is expected to lead to stable equilibria where populations show either complete outcrossing or complete selfing, and that selfing is promoted by large deleterious mutation rates. I find that the evolution of selfing is favored by a large recessivity of deleterious effects, while the magnitude of homozygous deleterious effects only becomes relevant in relatively small populations. This result contradicts the standard assumption that purging in large populations will only promote selfing when homozygous deleterious effects are large, and implies that previously published results obtained assuming lethal mutations in large populations can be extrapolated to nonlethal alleles of similar recessivity. This conclusion and the general approach used in this analysis can be useful in the study of the evolution of mating systems.     

Modeling viral genome fitness evolution associated with serial bottleneck events: evidence of stationary states of fitness

Evolution of fitness values upon replication of viral populations is strongly influenced by the size of the virus population that participates in the infections. While large population passages often result in fitness gains, repeated plaque-to-plaque transfers result in average fitness losses. Here we develop a numerical model that describes fitness evolution of viral clones subjected to serial bottleneck events. The model predicts a biphasic evolution of fitness values in that a period of exponential decrease is followed by a stationary state in which fitness values display large fluctuations around an average constant value. This biphasic evolution is in agreement with experimental results of serial plaque-to-plaque transfers carried out with foot-and-mouth disease virus (FMDV) in cell culture. The existence of a stationary phase of fitness values has been further documented by serial plaque-to-plaque transfers of FMDV clones that had reached very low relative fitness values. The statistical properties of the stationary state depend on several parameters of the model, such as the probability of advantageous versus deleterious mutations, initial fitness, and the number of replication rounds. In particular, the size of the bottleneck is critical for determining the trend of fitness evolution.     

Fitness recovery and compensatory evolution in natural mutant lines of C. elegans

Deleterious mutation accumulation plays a central role in evolutionary genetics, conservation biology, human health, and evolutionary medicine (e.g., methods of viral attenuation for live vaccines). It is therefore important to understand whether and how quickly populations with accumulated deleterious mutational loads can recover fitness through adaptive evolution. We used laboratory experimental evolution with four long-term mutation-accumulation (MA) lines of Caenorhabditis elegans nematodes to study the dynamics of such fitness evolution. We previously showed that when homozygous mutant populations are evolved in large population sizes, they can rapidly achieve wild-type fitness through the accumulation of new beneficial or compensatory epistatic mutations. Here, we expand this approach to demonstrate that when replicate lineages are initiated from the same mutant genotype, phenotypic evolution is only sometimes repeatable. MA genotypes that recovered ancestral fitness in the previous experiment did not always do so here. Further, the pattern of adaptive evolution in independently evolved replicates was contingent upon the MA genotype and varied among fitness-related traits. Our findings suggest that new beneficial mutations can drive rapid fitness evolution, but that the adaptive process is rendered somewhat unpredictable by its susceptibility to chance events and sensitivity to the evolutionary history of the starting population.     

Mutation accumulation in populations of varying size: large effect mutations cause most mutational decline in the rotifer Brachionus calyciflorus under UV‐C radiation

Theory predicts that fitness decline via mutation accumulation will depend on population size, but there are only a few direct tests of this key idea. To gain a qualitative understanding of the fitness effect of new mutations, we performed a mutation accumulation experiment with the facultative sexual rotifer Brachionus calyciflorus at six different population sizes under UV‐C radiation. Lifetime reproduction assays conducted after ten and sixteen UV‐C radiations showed that while small populations lost fitness, fitness losses diminished rapidly with increasing population size. Populations kept as low as 10 individuals were able to maintain fitness close to the nonmutagenized populations throughout the experiment indicating that selection was able to remove the majority of large effect mutations in small populations. Although our results also seem to imply that small populations are effectively immune to mutational decay, we caution against this interpretation. Given sufficient time, populations of moderate to large size can experience declines in fitness from accumulating weakly deleterious mutations as demonstrated by fitness estimates from simulations and, tentatively, from a long‐term experiment with populations of moderate size. There is mounting evidence to suggest that mutational distributions contain a heavier tail of large effects. Our results suggest that this is also true when the mutational spectrum is altered by UV radiation.