Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

Recombination Rate and Selection Strength in HIV Intra-patient Evolution

The evolutionary dynamics of HIV during the chronic phase of infection is driven by the host immune response and by selective pressures exerted through drug treatment. To understand and model the evolution of HIV quantitatively, the parameters governing genetic diversification and the strength of selection need to be known. While mutation rates can be measured in single replication cycles, the relevant effective recombination rate depends on the probability of coinfection of a cell with more than one virus and can only be inferred from population data. However, most population genetic estimators for recombination rates assume absence of selection and are hence of limited applicability to HIV, since positive and purifying selection are important in HIV evolution. Yet, little is known about the distribution of selection differentials between individual viruses and the impact of single polymorphisms on viral fitness. Here, we estimate the rate of recombination and the distribution of selection coefficients from time series sequence data tracking the evolution of HIV within single patients. By examining temporal changes in the genetic composition of the population, we estimate the effective recombination to be ρ = 1.4±0.6×10⁻⁵ recombinations per site and generation. Furthermore, we provide evidence that the selection coefficients of at least 15% of the observed non-synonymous polymorphisms exceed 0.8% per generation. These results provide a basis for a more detailed understanding of the evolution of HIV. A particularly interesting case is evolution in response to drug treatment, where recombination can facilitate the rapid acquisition of multiple resistance mutations. With the methods developed here, more precise and more detailed studies will be possible as soon as data with higher time resolution and greater sample sizes are available.     

Fixation probabilities depend on life history: fecundity, generation time and survival in a burst-death model

The burst-death model has been developed to describe the life history of organisms with variable generation times and a burst of a fixed number of offspring. The model also includes an optional constant clearance rate, such as washout from a chemostat, and the possibility of sustained periods of population growth followed by severe bottlenecks, as in serial passaging. In this model, a beneficial mutation can either increase the burst rate or the burst size, or reduce the clearance rate, thus increasing survival. In this article we examine the effects of these three possible mechanisms on both the Malthusian fitness and the fixation probability of the lineage. We find that equivalent relative increases in the burst rate or burst size confer equivalent increases in the Malthusian fitness of a lineage, whereas increasing survival typically has a more moderate effect on Malthusian fitness. In contrast, for beneficial mutations that confer the same increase in fitness, mutations that increase survival are the most likely to fix, followed by mutations that increase the burst rate. Mutations that increase the burst size are the least likely to fix. These results imply that mutant lineages with the highest Malthusian fitness are not, in many cases, the most likely to escape extinction.     

Persistence of Common Alleles in Two Related Populations or Species

Mathematical studies are conducted on three problems that arise in molecular population genetics. (1) The time required for a particular allele to become extinct in a population under the effects of mutation, selection, and random genetic drift is studied. In the absence of selection, the mean extinction time of an allele with an initial frequency close to 1 is of the order of the reciprocal of the mutation rate when 4Nv << 1, where N is the effective population size and v is the mutation rate per generation. Advantageous mutations reduce the extinction time considerably, whereas deleterious mutations increase it tremendously even if the effect on fitness is very slight. (2) Mathematical formulae are derived for the distribution and the moments of extinction time of a particular allele from one or both of two related populations or species under the assumption of no selection. When 4Nv << 1, the mean extinction time is about half that for a single population, if the two populations are descended from a common original stock. (3) The expected number as well as the proportion of common neutral alleles shared by two related species at the tth generation after their separation are studied. It is shown that if 4Nv is small, the two species are expected to share a high proportion of common alleles even 4N generations after separation. In addition to the above mathematical studies, the implications of our results for the common alleles at protein loci in related Drosophila species and for the degeneration of unused characters in cave animals are discussed.     

Malthusian Parameters as Estimators of the Fitness of Microbes: A Cautionary Tale about the Low Side of High Throughput

The maximum exponential growth rate, the Malthusian parameter (MP), is commonly used as a measure of fitness in experimental studies of adaptive evolution and of the effects of antibiotic resistance and other genes on the fitness of planktonic microbes. Thanks to automated, multi-well optical density plate readers and computers, with little hands-on effort investigators can readily obtain hundreds of estimates of MPs in less than a day. Here we compare estimates of the relative fitness of antibiotic susceptible and resistant strains of E. coli, Pseudomonas aeruginosa and Staphylococcus aureus based on MP data obtained with automated multi-well plate readers with the results from pairwise competition experiments. This leads us to question the reliability of estimates of MP obtained with these high throughput devices and the utility of these estimates of the maximum growth rates to detect fitness differences.     

PERSPECTIVE: SPONTANEOUS DELETERIOUS MUTATION

Mildly deleterious mutation has been invoked as a leading explanation for a diverse array of observations in evolutionary genetics and molecular evolution and is thought to be a significant risk of extinction for small populations. However, much of the empirical evidence for the deleterious-mutation process derives from studies of Drosophila melanogaster, some of which have been called into question. We review a broad array of data that collectively support the hypothesis that deleterious mutations arise in flies at rate of about one per individual per generation, with the average mutation decreasing fitness by about only 2% in the heterozygous state. Empirical evidence from microbes, plants, and several other animal species provide further support for the idea that most mutations have only mildly deleterious effects on fitness, and several other species appear to have genomic mutation rates that are of the order of magnitude observed in Drosophila. However, there is mounting evidence that some organisms have genomic deleterious mutation rates that are substantially lower than one per individual per generation. These lower rates may be at least partially reconciled with the Drosophila data by taking into consideration the number of germline cell divisions per generation. To fully resolve the existing controversy over the properties of spontaneous mutations, a number of issues need to be clarified. These include the form of the distribution of mutational effects and the extent to which this is modified by the environmental and genetic background and the contribution of basic biological features such as generation length and genome size to interspecific differences in the genomic mutation rate. Once such information is available, it should be possible to make a refined statement about the long-term impact of mutation on the genetic integrity of human populations subject to relaxed selection resulting from modern medical procedures.     

Mutational bias for body size in rhabditid nematodes

Mutational bias is a potentially important agent of evolution, but it is difficult to disentangle the effects of mutation from those of natural selection. Mutation-accumulation experiments, in which mutations are allowed to accumulate at very small population size, thus minimizing the efficiency of natural selection, are the best way to separate the effects of mutation from those of selection. Body size varies greatly among species of nematode in the family rhabditidae; mutational biases are both a potential cause and a consequence of that variation. We report data on the cumulative effects of mutations that affect body size in three species of rhabditid nematode that vary fivefold in adult size. Results are very consistent with previous studies of mutations underlying fitness in the same strains: two strains of Caenorhabditis briggsae decline in body size about twice as fast as two strains of C. elegans, with a concomitant higher point estimate of the genomic mutation rate; the confamilial Oscheius myriophila is intermediate. There is an overall mutational bias, such that mutations reduce size on average, but the bias appears consistent between species. The genetic correlation between mutations that affect size and those underlying fitness is large and positive, on average.     

Mutation accumulation in <Emphasis Type="Italic">Tetrahymena</Emphasis>

Background  

The rate and fitness effects of mutations are key in understanding the evolution of every species. Traditionally, these parameters are estimated in mutation accumulation experiments where replicate lines are propagated in conditions that allow mutations to randomly accumulate without the purging effect of natural selection. These experiments have been performed with many model organisms but we still lack empirical estimates of the rate and effects of mutation in the protists.     

Mortality plateaus and directionality theory

Recent large scale studies of senescence in animals and humans have revealed mortality rates that levelled off at advanced ages. These empirical findings are now known to be inconsistent with evolutionary theories of senescence based on the Malthusian parameter as a measure of fitness. This article analyses the incidence of mortality plateaus in terms of directionality theory, a new class of models based on evolutionary entropy as a measure of fitness. We show that the intensity of selection, in the context of directionality theory, is a convex function of age, and we invoke this property to predict that in populations evolving under bounded growth constraints, evolutionarily stable mortality patterns will be described by rates which abate with age at extreme ages. The explanatory power of directionality theory, in contrast with the limitations of the Malthusian model, accords with the claim that evolutionary entropy, rather than the Malthusian parameter, constitutes the operationally valid measure of Darwinian fitness.     

Multigenerational versus single generation studies to estimate herbicide resistance fitness cost in Arabidopsis thaliana

The evolution of resistance in response to pesticide selection is expected to be delayed if fitness costs are associated with resistance genes. The estimate of fitness costs usually involves comparing major growth traits of resistant versus susceptible individuals in the absence of pesticide. Ideally, a measure of changes in resistance allele frequency over several generations would allow the best estimate of the overall fitness cost of a resistance gene. In greenhouse conditions, we monitored the dynamics of the evolution of the frequencies of six herbicide-resistant mutations (acetolactate synthase, cellulose synthase, and auxin-induced target genes) in the model species Arabidopsis thaliana in a multigenerational study covering five to seven nonoverlapping generations. The microevolutionary dynamics in experimental populations indicated a mean fitness cost of 38%, 73%, and 94% for the ixr1-2, axr1-3, and axr2-1 resistances, respectively; no fitness cost for the csr1-1, and ixr2-1 resistances; and a transient advantage for the aux1-7 resistance. The result for the csr1-1 resistance contrasts with a cost of 37% based on total seed number in a previous study, demonstrating that single generation studies could have limitation for detecting cost. A positive frequency dependence for the fitness cost was also detected for the ixr1-2 resistance. The results are discussed in relation to the maintenance of polymorphism at resistance loci.     

Experimental adaptation of Salmonella typhimurium to mice

Experimental evolution is a powerful approach to study the dynamics and mechanisms of bacterial niche specialization. By serial passage in mice, we evolved 18 independent lineages of Salmonella typhimurium LT2 and examined the rate and extent of adaptation to a mainly reticuloendothelial host environment. Bacterial mutation rates and population sizes were varied by using wild-type and DNA repair-defective mutator (mutS) strains with normal and high mutation rates, respectively, and by varying the number of bacteria intraperitoneally injected into mice. After <200 generations of adaptation all lineages showed an increased fitness as measured by a faster growth rate in mice (selection coefficients 0.11-0.58). Using a generally applicable mathematical model we calculated the adaptive mutation rate for the wild-type bacterium to be >10(-6)/cell/generation, suggesting that the majority of adaptive mutations are not simple point mutations. For the mutator lineages, adaptation to mice was associated with a loss of fitness in secondary environments as seen by a reduced metabolic capability. During adaptation there was no indication that a high mutation rate was counterselected. These data show that S. typhimurium can rapidly and extensively increase its fitness in mice but this niche specialization is, at least in mutators, associated with a cost.     

Accumulation of Spontaneous Mutations in the Ciliate Tetrahymena thermophila

Knowledge of the rate and fitness effects of mutations is essential for understanding the process of evolution. Mutations are inherently difficult to study because they are rare and are frequently eliminated by natural selection. In the ciliate Tetrahymena thermophila, mutations can accumulate in the germline genome without being exposed to selection. We have conducted a mutation accumulation (MA) experiment in this species. Assuming that all mutations are deleterious and have the same effect, we estimate that the deleterious mutation rate per haploid germline genome per generation is U = 0.0047 (95% credible interval: 0.0015, 0.0125), and that germline mutations decrease fitness by s = 11% when expressed in a homozygous state (95% CI: 4.4%, 27%). We also estimate that deleterious mutations are partially recessive on average (h = 0.26; 95% CI: –0.022, 0.62) and that the rate of lethal mutations is <10% of the deleterious mutation rate. Comparisons between the observed evolutionary responses in the germline and somatic genomes and the results from individual-based simulations of MA suggest that the two genomes have similar mutational parameters. These are the first estimates of the deleterious mutation rate and fitness effects from the eukaryotic supergroup Chromalveolata and are within the range of those of other eukaryotes.     

Whose trait is it anyways? Coevolution of joint phenotypes and genetic architecture in mutualisms

Evolutionary biologists typically envision a trait’s genetic basis and fitness effects occurring within a single species. However, traits can be determined by and have fitness consequences for interacting species, thus evolving in multiple genomes. This is especially likely in mutualisms, where species exchange fitness benefits and can associate over long periods of time. Partners may experience evolutionary conflict over the value of a multi-genomic trait, but such conflicts may be ameliorated by mutualism’s positive fitness feedbacks. Here, we develop a simulation model of a host–microbe mutualism to explore the evolution of a multi-genomic trait. Coevolutionary outcomes depend on whether hosts and microbes have similar or different optimal trait values, strengths of selection and fitness feedbacks. We show that genome-wide association studies can map joint traits to loci in multiple genomes and describe how fitness conflict and fitness feedback generate different multi-genomic architectures with distinct signals around segregating loci. Partner fitnesses can be positively correlated even when partners are in conflict over the value of a multi-genomic trait, and conflict can generate strong mutualistic dependency. While fitness alignment facilitates rapid adaptation to a new optimum, conflict maintains genetic variation and evolvability, with implications for applied microbiome science.     

Rate of deleterious mutation and the distribution of its effects on fitness in vesicular stomatitis virus

Despite their importance, the parameters describing the spontaneous deleterious mutation process have not been well described in many organisms. If mutations are important for the evolution of every living organism, their importance becomes critical in the case of RNA-based viruses, in which the frequency of mutation is orders of magnitude larger than in DNA-based organisms. The present work reports minimum estimates of the deleterious mutation rate, as well as the characterization of the distribution of deleterious mutational effects on the total fitness of the vesicular stomatitis virus (VSV). The estimates are based on mutation-accumulation experiments in which selection against deleterious mutations was minimized by recurrently imposing genetic bottlenecks of size one. The estimated deleterious mutation rate was 1.2 mutations per genome and generation, with a mean fitness effect of –0.39% per generation. At the end of the mutation-accumulation experiment, the average reduction in fitness was 38% and the distribution of accumulated deleterious effects was, on average, left-skewed. The magnitude of the skewness depends on the initial fitness of the clone analysed. The implications of our findings for the evolutionary biology of RNA viruses are discussed.     

Adaptive topography of fluctuating selection in a Mendelian population

An adaptive topography is derived for a large randomly mating diploid population under weak density-independent selection in a fluctuating environment. Assuming a stationary distribution of environmental states with no temporal autocorrelation, a diffusion approximation for population size and allele frequency, p, reveals that the expected change in p involves the gradient with respect to p of the stochastic intrinsic rate of increase (the density-independent long-run growth rate), r = r - sigma 2 e/2, where r is the mean Malthusian fitness in the average environment and is the environmental variance in population growth rate. The expected relative fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its fitness with population growth rate. The influence of fitness correlation between genotypes is illustrated by an analysis of the Haldane-Jayakar model of fluctuating selection on a single diallelic locus, and on two loci with additive effects on a quantitative character.     

Measuring selection coefficients below 10(-3): method, questions, and prospects

Measuring fitness with precision is a key issue in evolutionary biology, particularly in studying mutations of small effects. It is usually thought that sampling error and drift prevent precise measurement of very small fitness effects. We circumvented these limits by using a new combined approach to measuring and analyzing fitness. We estimated the mutational fitness effect (MFE) of three independent mini-Tn10 transposon insertion mutations by conducting competition experiments in large populations of Escherichia coli under controlled laboratory conditions. Using flow cytometry to assess genotype frequencies from very large samples alleviated the problem of sampling error, while the effect of drift was controlled by using large populations and massive replication of fitness measures. Furthermore, with a set of four competition experiments between ancestral and mutant genotypes, we were able to decompose fitness measures into four estimated parameters that account for fitness effects of our fluorescent marker (α), the mutation (β), epistasis between the mutation and the marker (γ), and departure from transitivity (τ). Our method allowed us to estimate mean selection coefficients to a precision of 2 × 10(-4). We also found small, but significant, epistatic interactions between the allelic effects of mutations and markers and confirmed that fitness effects were transitive in most cases. Unexpectedly, we also detected variation in measures of s that were significantly bigger than expected due to drift alone, indicating the existence of cryptic variation, even in fully controlled experiments. Overall our results indicate that selection coefficients are best understood as being distributed, representing a limit on the precision with which selection can be measured, even under controlled laboratory conditions.     

Age-specific fitness components and their temporal variation in the barn owl

Theory predicts that temporal variability plays an important role in the evolution of life histories, but empirical studies evaluating this prediction are rare. In constant environments, fitness can be measured by the population growth rate lambda, and the sensitivity of lambda to changes in fitness components estimates selection on these traits. In variable environments, fitness is measured by the stochastic growth rate lambda(S), and stochastic sensitivities estimate selection pressure. Here we examine age-specific schedules for reproduction and survival in a barn owl population (Tyto alba). We estimated how temporal variability affected fitness and selection, accounting for sampling variance. Despite large sample sizes of old individuals, we found no strong evidence for senescence. The most variable fitness components were associated with reproduction. Survival was less variable. Stochastic simulations showed that the observed variation decreased fitness by about 30%, but the sensitivities of lambda and lambda(S) to changes in all fitness components were almost equal, suggesting that temporal variation had negligible effects on selection. We obtained these results despite high observed variability in the fitness components and relatively short generation time of the study organism, a situation in which temporal variability should be particularly important for natural selection and early senescence is expected.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

Fitness effects of mutation accumulation in a natural outbred population of wild radish (Raphanus raphanistrum): comparison of field and greenhouse environments

Spontaneous deleterious mutation has been measured in a handful of organisms, always under laboratory conditions and usually employing inbred species or genotypes. We report the results of a mutation accumulation experiment with an outbred annual plant, Raphanus raphanistrum, with lifetime fitness measured in both the field and the greenhouse. This is the first study to report the effects of spontaneous mutation measured under field conditions. Two large replicate populations (N(e) approximately 600) were maintained with random mating in the greenhouse under relaxed selection for nine generations before the field assay was performed and ten generations before the greenhouse assay. Each generation, every individual was mated twice, once as a pollen donor and once as a pollen recipient, and a single seed from each plant was chosen randomly to create the next generation. The ancestral population was maintained as seeds at 4 degrees C. Declines in lifetime fitness were observed in both the field (1.7% per generation; P= 0.27) and the greenhouse (0.6% per generation; P= 0.07). Significant increases in additive genetic variance for fitness were found for stems per day, flowers per stem, fruits per flower and seeds per fruit in the field as well as for fruits per flower in the greenhouse. Lack of significance of the fitness decline may be due to the short period of mutation accumulation, the use of outbred populations, or both. The percent declines in fitness are at the high end of the range observed in other mutation accumulation experiments and give some support to the idea that mutational effects may be magnified under harsher field conditions. Thus, measurement of mutational parameters under laboratory conditions may underestimate the effects of mutations in natural populations.     

A method to infer positive selection from marker dynamics in an asexual population

MOTIVATION: The observation of positive selection acting on a mutant indicates that the corresponding mutation has some form of functional relevance. Determining the fitness effects of mutations thus has relevance to many interesting biological questions. One means of identifying beneficial mutations in an asexual population is to observe changes in the frequency of marked subsets of the population. We here describe a method to estimate the establishment times and fitnesses of beneficial mutations from neutral marker frequency data. RESULTS: The method accurately reproduces complex marker frequency trajectories. In simulations for which positive selection is close to 5% per generation, we obtain correlations upwards of 0.91 between correct and inferred haplotype establishment times. Where mutation selection coefficients are exponentially distributed, the inferred distribution of haplotype fitnesses is close to being correct. Applied to data from a bacterial evolution experiment, our method reproduces an observed correlation between evolvability and initial fitness defect.