Allele frequency distribution under recurrent selective sweeps

The allele frequency of a neutral variant in a population is pushed either upward or downward by directional selection on a linked beneficial mutation ("selective sweeps"). DNA sequences sampled after the fixation of the beneficial allele thus contain an excess of rare neutral alleles. This study investigates the allele frequency distribution under selective sweep models using analytic approximation and simulation. First, given a single selective sweep at a fixed time, I derive an expression for the sampling probabilities of neutral mutants. This solution can be used to estimate the time of the fixation of a beneficial allele from sequence data. Next, I obtain an approximation to mean allele frequencies under recurrent selective sweeps. Under recurrent sweeps, the frequency spectrum is skewed toward rare alleles. However, the excess of high-frequency derived alleles, previously shown to be a signature of single selective sweeps, disappears with recurrent sweeps. It is shown that, using this approximation and multilocus polymorphism data, genomewide parameters of directional selection can be estimated.     

Genome‐wide analysis of allele frequency change in sunflower crop–wild hybrid populations evolving under natural conditions

Crop‐wild hybridization occurs in numerous plant species and could alter the genetic structure and evolutionary dynamics of wild populations. Studying crop‐derived alleles in wild populations is also relevant to assessing/mitigating the risks associated with transgene escape. To date, crop‐wild hybridization has generally been examined via short‐term studies, typically within a single generation, focusing on few traits or genetic markers. Little is known about patterns of selection on crop‐derived alleles over multiple generations, particularly at a genome‐wide scale. Here, we documented patterns of natural selection in an experimental crop × wild sunflower population that was allowed to evolve under natural conditions for two generations at two locations. Allele frequencies at a genome‐wide collection of SNPs were tracked across generations, and a common garden experiment was conducted to compare trait means between generations. These data allowed us to identify instances of selection on crop‐derived alleles/traits and, in concert with QTL mapping results, test for congruence between our genotypic and phenotypic results. We found that natural selection overwhelmingly favours wild alleles and phenotypes. However, crop alleles in certain genomic regions can be favoured, and these changes often occurred in parallel across locations. We did not, however, consistently observe close agreement between our genotypic and phenotypic results. For example, when a trait evolved towards the wild phenotype, wild QTL alleles associated with that trait did not consistently increase in frequency. We discuss these results in the context of crop allele introgression into wild populations and implications for the management of GM crops.     

Controlling for P‐value inflation in allele frequency change in experimental evolution and artificial selection experiments

Experimental evolution studies can be used to explore genomic response to artificial and natural selection. In such studies, loci that display larger allele frequency change than expected by genetic drift alone are assumed to be directly or indirectly associated with traits under selection. However, such studies report surprisingly many loci under selection, suggesting that current tests for allele frequency change may be subject to P‐value inflation and hence be anticonservative. One factor known from genomewide association (GWA) studies to cause P‐value inflation is population stratification, such as relatedness among individuals. Here, we suggest that by treating presence of an individual in a population after selection as a binary response variable, existing GWA methods can be used to account for relatedness when estimating allele frequency change. We show that accounting for relatedness like this effectively reduces false‐positives in tests for allele frequency change in simulated data with varying levels of population structure. However, once relatedness has been accounted for, the power to detect causal loci under selection is low. Finally, we demonstrate the presence of P‐value inflation in allele frequency change in empirical data spanning multiple generations from an artificial selection experiment on tarsus length in two free‐living populations of house sparrow and correct for this using genomic control. Our results indicate that since allele frequencies in large parts of the genome may change when selection acts on a heritable trait, such selection is likely to have considerable and immediate consequences for the eco‐evolutionary dynamics of the affected populations.     

Patterns of neutral diversity under general models of selective sweeps

Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked selection). There is now good evidence that linked selection plays an important role in shaping polymorphism levels in a number of species. One of the best-investigated models of linked selection is the recurrent full-sweep model, in which newly arisen selected alleles fix rapidly. However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation. Here we develop a general model of recurrent selective sweeps in a coalescent framework, one that generalizes the recurrent full-sweep model to the case where selected alleles do not sweep to fixation. We show that in a large population, only the initial rapid increase of a selected allele affects the genealogy at partially linked sites, which under fairly general assumptions are unaffected by the subsequent fate of the selected allele. We also apply the theory to a simple model to investigate the impact of recurrent partial sweeps on levels of neutral diversity and find that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequencies rapidly achieved by the selected alleles. Consequently, recurrent sweeps of selected alleles to low frequencies can have a profound effect on levels of diversity but can leave the frequency spectrum relatively unperturbed. In fact, the limiting coalescent model under a high rate of sweeps to low frequency is identical to the standard neutral model. The general model of selective sweeps we describe goes some way toward providing a more flexible framework to describe genomic patterns of diversity than is currently available.     

ANTAGONISTIC VERSUS NONANTAGONISTIC MODELS OF BALANCING SELECTION: CHARACTERIZING THE RELATIVE TIMESCALES AND HITCHHIKING EFFECTS OF PARTIAL SELECTIVE SWEEPS

Antagonistically selected alleles‐–those with opposing fitness effects between sexes, environments, or fitness components‐–represent an important component of additive genetic variance in fitness‐related traits, with stably balanced polymorphisms often hypothesized to contribute to observed quantitative genetic variation. Balancing selection hypotheses imply that intermediate‐frequency alleles disproportionately contribute to genetic variance of life‐history traits and fitness. Such alleles may also associate with population genetic footprints of recent selection, including reduced genetic diversity and inflated linkage disequilibrium at linked, neutral sites. Here, we compare the evolutionary dynamics of different balancing selection models, and characterize the evolutionary timescale and hitchhiking effects of partial selective sweeps generated under antagonistic versus nonantagonistic (e.g., overdominant and frequency‐dependent selection) processes. We show that the evolutionary timescales of partial sweeps tend to be much longer, and hitchhiking effects are drastically weaker, under scenarios of antagonistic selection. These results predict an interesting mismatch between molecular population genetic and quantitative genetic patterns of variation. Balanced, antagonistically selected alleles are expected to contribute more to additive genetic variance for fitness than alleles maintained by classic, nonantagonistic mechanisms. Nevertheless, classical mechanisms of balancing selection are much more likely to generate strong population genetic signatures of recent balancing selection.     

MUTANT INVASIONS AND ADAPTIVE DYNAMICS IN VARIABLE ENVIRONMENTS

The evolution of natural organisms is ultimately driven by the invasion and possible fixation of mutant alleles. The invasion process is highly stochastic, however, and the probability of success is generally low, even for advantageous alleles. Additionally, all organisms live in a stochastic environment, which may have a large influence on what alleles are favorable, but also contributes to the uncertainty of the invasion process. We calculate the invasion probability of a beneficial, mutant allele in a monomorphic, large population subject to stochastic environmental fluctuations, taking into account density‐ and frequency‐dependent selection, stochastic population dynamics and temporal autocorrelation of the environment. We treat both discrete and continuous time population dynamics, and allow for overlapping generations in the continuous time case. The results can be generalized to diploid, sexually reproducing organisms embedded in communities of interacting species. We further use these results to derive an extended canonical equation of adaptive dynamics, predicting the rate of evolutionary change of a heritable trait on long evolutionary time scales.     

Estimates of natural selection due to protein tertiary structure inform the ancestry of biallelic loci

We consider the inference of which of two alleles is ancestral when the alleles have a single nonsynonymous difference and when natural selection acts via protein tertiary structure. Whereas the probability that an allele is ancestral under neutrality is equal to its frequency, under selection this probability depends on allele frequency and on the magnitude and direction of selection pressure. Although allele frequencies can be well estimated from intraspecific data, small fitness differences have a large evolutionary impact but can be difficult to estimate with only intraspecific data. Methods for predicting aspects of phenotype from genotype can supplement intraspecific sequence data. Recently developed statistical techniques can assess effects of phenotypes, such as protein tertiary structure on molecular evolution. While these techniques were initially designed for comparing protein-coding genes from different species, the resulting interspecific inferences can be assigned population genetic interpretations to assess the effect of selection pressure, and we use them here along with intraspecific allele frequency data to estimate the probability that an allele is ancestral. We focus on 140 nonsynonymous single nucleotide polymorphisms of humans that are in proteins with known tertiary structures. We find that our technique for employing protein tertiary structure information yields some biologically plausible results but that it does not substantially improve the inference of ancestral human allele types.     

Signatures of environmental genetic adaptation pinpoint pathogens as the main selective pressure through human evolution

Previous genome-wide scans of positive natural selection in humans have identified a number of non-neutrally evolving genes that play important roles in skin pigmentation, metabolism, or immune function. Recent studies have also shown that a genome-wide pattern of local adaptation can be detected by identifying correlations between patterns of allele frequencies and environmental variables. Despite these observations, the degree to which natural selection is primarily driven by adaptation to local environments, and the role of pathogens or other ecological factors as selective agents, is still under debate. To address this issue, we correlated the spatial allele frequency distribution of a large sample of SNPs from 55 distinct human populations to a set of environmental factors that describe local geographical features such as climate, diet regimes, and pathogen loads. In concordance with previous studies, we detected a significant enrichment of genic SNPs, and particularly non-synonymous SNPs associated with local adaptation. Furthermore, we show that the diversity of the local pathogenic environment is the predominant driver of local adaptation, and that climate, at least as measured here, only plays a relatively minor role. While background demography by far makes the strongest contribution in explaining the genetic variance among populations, we detected about 100 genes which show an unexpectedly strong correlation between allele frequencies and pathogenic environment, after correcting for demography. Conversely, for diet regimes and climatic conditions, no genes show a similar correlation between the environmental factor and allele frequencies. This result is validated using low-coverage sequencing data for multiple populations. Among the loci targeted by pathogen-driven selection, we found an enrichment of genes associated to autoimmune diseases, such as celiac disease, type 1 diabetes, and multiples sclerosis, which lends credence to the hypothesis that some susceptibility alleles for autoimmune diseases may be maintained in human population due to past selective processes.     

Components of Selection in the Evolution of the Influenza Virus: Linkage Effects Beat Inherent Selection

The influenza virus is an important human pathogen, with a rapid rate of evolution in the human population. The rate of homologous recombination within genes of influenza is essentially zero. As such, where two alleles within the same gene are in linkage disequilibrium, interference between alleles will occur, whereby selection acting upon one allele has an influence upon the frequency of the other. We here measured the relative importance of selection and interference effects upon the evolution of influenza. We considered time-resolved allele frequency data from the global evolutionary history of the haemagglutinin gene of human influenza A/H3N2, conducting an in-depth analysis of sequences collected since 1996. Using a model that accounts for selection-caused interference between alleles in linkage disequilibrium, we estimated the inherent selective benefit of individual polymorphisms in the viral population. These inherent selection coefficients were in turn used to calculate the total selective effect of interference acting upon each polymorphism, considering the effect of the initial background upon which a mutation arose, and the subsequent effect of interference from other alleles that were under selection. Viewing events in retrospect, we estimated the influence of each of these components in determining whether a mutant allele eventually fixed or died in the global viral population. Our inherent selection coefficients, when combined across different regions of the protein, were consistent with previous measurements of dN/dS for the same system. Alleles going on to fix in the global population tended to be under more positive selection, to arise on more beneficial backgrounds, and to avoid strong negative interference from other alleles under selection. However, on average, the fate of a polymorphism was determined more by the combined influence of interference effects than by its inherent selection coefficient.     

ASSORTATIVE MATE CHOICE AND DOMINANCE MODIFICATION: ALTERNATIVE WAYS OF REMOVING HETEROZYGOTE DISADVANTAGE

In genetic polymorphisms of two alleles, heterozygous individuals may contribute to the next generation on average more or fewer descendants than the homozygotes. Two different evolutionary responses that remove a disadvantageous heterozygote phenotype from the population are the evolution of strictly assortative mate choice, and that of a modifier making one of the two alleles completely dominant. We derive invasion fitness of mutants introducing dominance or assortative mate choice in a randomly mating population with a genetic polymorphism for an ecological trait. Mutations with small effects as well as mutants introducing complete dominance or perfect assorting are considered. Using adaptive dynamics techniques, we are able to calculate the ratio of fitness gradients for the effects of a dominance modifier and a mate choice locus, near evolutionary branching points. With equal resident allele frequencies, selection for mate choice is always stronger. Dominance is more strongly selected than assortative mating when the resident (common) alleles have very unequal frequencies at equilibrium. With female mate choice the difference in frequencies where dominance is more strongly selected is smaller than when mutants of both sexes can choose without costs. A symmetric resource-competition model illustrates the results.     

FREQ-Seq: A Rapid,Cost-Effective,Sequencing-Based Method to Determine Allele Frequencies Directly from Mixed Populations

Understanding evolutionary dynamics within microbial populations requires the ability to accurately follow allele frequencies through time. Here we present a rapid, cost-effective method (FREQ-Seq) that leverages Illumina next-generation sequencing for localized, quantitative allele frequency detection. Analogous to RNA-Seq, FREQ-Seq relies upon counts from the >10⁵ reads generated per locus per time-point to determine allele frequencies. Loci of interest are directly amplified from a mixed population via two rounds of PCR using inexpensive, user-designed oligonucleotides and a bar-coded bridging primer system that can be regenerated in-house. The resulting bar-coded PCR products contain the adapters needed for Illumina sequencing, eliminating further library preparation. We demonstrate the utility of FREQ-Seq by determining the order and dynamics of beneficial alleles that arose as a microbial population, founded with an engineered strain of Methylobacterium, evolved to grow on methanol. Quantifying allele frequencies with minimal bias down to 1% abundance allowed effective analysis of SNPs, small in-dels and insertions of transposable elements. Our data reveal large-scale clonal interference during the early stages of adaptation and illustrate the utility of FREQ-Seq as a cost-effective tool for tracking allele frequencies in populations.     

Adaptations to new environments in humans: the role of subtle allele frequency shifts

Humans show tremendous phenotypic diversity across geographically distributed populations, and much of this diversity undoubtedly results from genetic adaptations to different environmental pressures. The availability of genome-wide genetic variation data from densely sampled populations offers unprecedented opportunities for identifying the loci responsible for these adaptations and for elucidating the genetic architecture of human adaptive traits. Several approaches have been used to detect signals of selection in human populations, and these approaches differ in the assumptions they make about the underlying mode of selection. We contrast the results of approaches based on haplotype structure and differentiation of allele frequencies to those from a method for identifying single nucleotide polymorphisms strongly correlated with environmental variables. Although the first group of approaches tends to detect new beneficial alleles that were driven to high frequencies by selection, the environmental correlation approach has power to identify alleles that experienced small shifts in frequency owing to selection. We suggest that the first group of approaches tends to identify only variants with relatively strong phenotypic effects, whereas the environmental correlation methods can detect variants that make smaller contributions to an adaptive trait.     

What paths do advantageous alleles take during short‐term evolutionary change?

Combining experimental evolution with whole‐genome resequencing is a promising new strategy for investigating the dynamics of evolutionary change. Published studies that have resequenced laboratory‐selected populations of sexual organisms have typically focused on populations sampled at the end of an evolution experiment. These studies have attempted to associate particular alleles with phenotypic change and attempted to distinguish between different theoretical models of adaptation. However, neither the population used to initiate the experiment nor multiple time points sampled during the evolutionary trajectory are generally available for examination. In this issue of Molecular Ecology, Orozco‐terWengel et al. (2012) take a significant step forward by estimating genome‐wide allele frequencies at the start, 15 generations into and at the end of a 37‐generation Drosophila experimental evolution study. The authors identify regions of the genome that have responded to laboratory selection and describe the temporal dynamics of allele frequency change. They identify two common trajectories for putatively adaptive alleles: alleles either gradually increase in frequency throughout the entire 37 generations or alleles plateau at a new frequency by generation 15. The identification of complex trajectories of alleles under selection contributes to a growing body of literature suggesting that simple models of adaptation, whereby beneficial alleles arise and increase in frequency unimpeded until they become fixed, may not adequately describe short‐term response to selection.     

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nμ > 1). We show how the method can be modified for small mutation rates (4Nμ → 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.     

The timing of human adaptation from Neanderthal introgression

Admixture has the potential to facilitate adaptation by providing alleles that are immediately adaptive in a new environment or by simply increasing the long-term reservoir of genetic diversity for future adaptation. A growing number of cases of adaptive introgression are being identified in species across the tree of life, however the timing of selection, and therefore the importance of the different evolutionary roles of admixture, is typically unknown. Here, we investigate the spatio-temporal history of selection favoring Neanderthal-introgressed alleles in modern human populations. Using both ancient and present-day samples of modern humans, we integrate the known demographic history of populations, namely population divergence and migration, with tests for selection. We model how a sweep placed along different branches of an admixture graph acts to modify the variance and covariance in neutral allele frequencies among populations at linked loci. Using a method based on this model of allele frequencies, we study previously identified cases of adaptive Neanderthal introgression. From these, we identify cases in which Neanderthal-introgressed alleles were quickly beneficial and other cases in which they persisted at low frequency for some time. For some of the alleles that persisted at low frequency, we show that selection likely independently favored them later on in geographically separated populations. Our work highlights how admixture with ancient hominins has contributed to modern human adaptation and contextualizes observed levels of Neanderthal ancestry in present-day and ancient samples.     

How does adaptation sweep through the genome? Insights from long-term selection experiments

A major goal in evolutionary biology is to understand the origins and fates of adaptive mutations. Natural selection may act to increase the frequency of de novo beneficial mutations, or those already present in the population as standing genetic variation. These beneficial mutations may ultimately reach fixation in a population, or they may stop increasing in frequency once a particular phenotypic state has been achieved. It is not yet well understood how different features of population biology, and/or different environmental circumstances affect these adaptive processes. Experimental evolution is a promising technique for studying the dynamics of beneficial alleles, as populations evolving in the laboratory experience natural selection in a replicated, controlled manner. Whole-genome sequencing, regularly obtained over the course of sustained laboratory selection, could potentially reveal insights into the mutational dynamics that most likely occur in natural populations under similar circumstances. To date, only a few evolution experiments for which whole-genome data are available exist. This review describes results from these resequenced laboratory-selected populations, in systems with and without sexual recombination. In asexual systems, adaptation from new mutations can be studied, and results to date suggest that the complete, unimpeded fixation of these mutations is not always observed. In sexual systems, adaptation from standing genetic variation can be studied, and in the admittedly few examples we have, the complete fixation of standing variants is not always observed. To date, the relative frequency of adaptation from new mutations versus standing variation has not been tested using a single experimental system, but recent studies using Caenorhabditis elegans and Saccharomyces cerevisiae suggest that this a realistic future goal.     

Evolution of balanced genetic polymorphism

Extreme genetic polymorphism maintained by balancing selection (so called because many alleles are maintained in a balance by a mechanism of rare allele advantage) is intimately associated with the important task of self/non-self-discrimination. Widely disparate self-recognition systems of plants, animals and fungi share several general features, including the maintenance of large numbers of alleles at relatively even frequency, and persistence of this variation over very long time periods. Because the evolutionary dynamics of balanced polymorphism are very different from those of neutral genetic variation, data on balanced polymorphism have been used as a novel source for inference of the history of populations. This review highlights the unique evolutionary properties of balanced genetic polymorphism, and the use of theoretical understanding in analysis and application of empirical data for inference of population history. However, a second goal of this review is to point out where current theory is incomplete. Recent observations suggest that entirely novel selective forces may act in concert with balancing selection, and these novel forces may be extremely potent in shaping genetic variation at self-recognition loci.     

DOES FREQUENCY‐DEPENDENT SELECTION WITH COMPLEX DOMINANCE INTERACTIONS ACCURATELY PREDICT ALLELIC FREQUENCIES AT THE SELF‐INCOMPATIBILITY LOCUS IN ARABIDOPSIS HALLERI?

Frequency-dependent selection is a major force determining the evolutionary dynamics of alleles at the self-incompatibility locus (S-locus) in flowering plants. We introduce a general method using numerical simulations to test several alternative models of frequency-dependent selection on S-locus data from sporophytic systems, taking into account both genetic drift and observed patterns of dominance interactions among S-locus haplotypes (S-haplotypes). Using a molecular typing method, we estimated S-haplotype frequencies in a sample of 322 adult plants and of 245 offspring obtained from seeds sampled on 22 maternal plants, collected in a single population of Arabidopsis halleri (Brassicaceae). We found eight different S-haplotypes and characterized their dominance interactions by controlled pollinations. We then compared the likelihood of different models of frequency-dependent selection: we found that the observed haplotype frequencies and observed frequency changes in one generation best fitted a model with (1) the observed dominance interactions and (2) no pollen limitation. Overall, our population genetic models of frequency-dependent selection, including patterns of dominance interactions among S-haplotypes and genetic drift, can reliably predict polymorphism at the S-locus. We discuss how these approaches allow detecting additional processes influencing the evolutionary dynamics of the S-locus, such as purifying selection on linked loci.     

Signs of selective pressure on genetic variants affecting human height

Many decades of scientific investigation have proved the role of selective pressure in Homo Sapiens at least at the level of individual genes or loci. Nevertheless, there are examples of polygenic traits that are bound to be under selection, but studies devoted to apply population genetics methods to unveil such occurrence are still lacking. Stature provides a relevant example of well-studied polygenic trait for which is now available a genome-wide association study which has identified the genes involved in this trait, and which is known to be under selection. We studied the behavior of F_ST in a simulated toy model to detect population differentiation on a generic polygenic phenotype under selection. The simulations showed that the set of alleles involved in the trait has a higher mean F_ST value than those undergoing genetic drift only. In view of this we looked for an increase in the mean F_ST value of the 180 variants associated to human height. For this set of alleles we found F_ST to be significantly higher than the genomic background (p = 0.0356). On the basis of a statistical analysis we excluded that the increase was just due to the presence of outliers. We also proved as marginal the role played by local adaptation phenomena, even on different phenotypes in linkage disequilibrium with genetic variants involved in height. The increase of F_ST for the set of alleles involved in a polygenic trait seems to provide an example of symmetry breaking phenomenon concerning the population differentiation. The splitting in the allele frequencies would be driven by the initial conditions in the population dynamics which are stochastically modified by events like drift, bottlenecks, etc, and other stochastic events like the born of new mutations.     

Microsatellite null alleles and estimation of population differentiation

Microsatellite null alleles are commonly encountered in population genetics studies, yet little is known about their impact on the estimation of population differentiation. Computer simulations based on the coalescent were used to investigate the evolutionary dynamics of null alleles, their impact on F(ST) and genetic distances, and the efficiency of estimators of null allele frequency. Further, we explored how the existing method for correcting genotype data for null alleles performed in estimating F(ST) and genetic distances, and we compared this method with a new method proposed here (for F(ST) only). Null alleles were likely to be encountered in populations with a large effective size, with an unusually high mutation rate in the flanking regions, and that have diverged from the population from which the cloned allele state was drawn and the primers designed. When populations were significantly differentiated, F(ST) and genetic distances were overestimated in the presence of null alleles. Frequency of null alleles was estimated precisely with the algorithm presented in Dempster et al. (1977). The conventional method for correcting genotype data for null alleles did not provide an accurate estimate of F(ST) and genetic distances. However, the use of the genetic distance of Cavalli-Sforza and Edwards (1967) corrected by the conventional method gave better estimates than those obtained without correction. F(ST) estimation from corrected genotype frequencies performed well when restricted to visible allele sizes. Both the proposed method and the traditional correction method have been implemented in a program that is available free of charge at http://www.montpellier.inra.fr/URLB/. We used 2 published microsatellite data sets based on original and redesigned pairs of primers to empirically confirm our simulation results.