Local evolvability of statistically neutral GasNet robot controllers

In this paper we introduce and apply the concept of local evolvability to investigate the behaviour of populations during evolutionary search. We focus on the evolution of GasNet neural network controllers for a robotic visual discrimination problem, showing that the evolutionary process undergoes long neutral fitness epochs. We show that the local evolvability properties of the search space surrounding a group of statistically neutral solutions do vary across the course of an evolutionary run, especially during periods of population takeover. However, once takeover is complete there is no evidence for further increase in local evolvability across fitness epochs. We also see no evidence for the neutral evolution of increased solution robustness, but show that this may be due to the ability of evolutionary algorithms to focus search on volumes of the fitness landscape with above average robustness.     

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.     

Selection for mutational robustness in finite populations

We investigate the evolutionary dynamics of a finite population of RNA sequences replicating on a neutral network. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive evolution, such as increase of mean fitness over time and punctuated-equilibrium transitions, after initial mutation-selection balance has been reached. We find that a product of population size and mutation rate of approximately 30 or larger is sufficient to generate selection pressure for mutational robustness, even if the population size is orders of magnitude smaller than the neutral network on which the population resides. Our results show that quasispecies effects and neutral drift can occur concurrently, and that the relative importance of each is determined by the product of population size and mutation rate.     

Fluctuating Environments Maintain Genetic Diversity through Neutral Fitness Effects and Balancing Selection

Genetic variation is the raw material upon which selection acts. The majority of environmental conditions change over time and therefore may result in variable selective effects. How temporally fluctuating environments impact the distribution of fitness effects and in turn population diversity is an unresolved question in evolutionary biology. Here, we employed continuous culturing using chemostats to establish environments that switch periodically between different nutrient limitations and compared the dynamics of selection to static conditions. We used the pooled Saccharomyces cerevisiae haploid gene deletion collection as a synthetic model for populations comprising thousands of unique genotypes. Using barcode sequencing, we find that static environments are uniquely characterized by a small number of high-fitness genotypes that rapidly dominate the population leading to dramatic decreases in genetic diversity. By contrast, fluctuating environments are enriched in genotypes with neutral fitness effects and an absence of extreme fitness genotypes contributing to the maintenance of genetic diversity. We also identified a unique class of genotypes whose frequencies oscillate sinusoidally with a period matching the environmental fluctuation. Oscillatory behavior corresponds to large differences in short-term fitness that are not observed across long timescales pointing to the importance of balancing selection in maintaining genetic diversity in fluctuating environments. Our results are consistent with a high degree of environmental specificity in the distribution of fitness effects and the combined effects of reduced and balancing selection in maintaining genetic diversity in the presence of variable selection.     

Interaction between directional epistasis and average mutational effects.

We investigate the relationship between the average fitness decay due to single mutations and the strength of epistatic interactions in genetic sequences. We observe that epistatic interactions between mutations are correlated to the average fitness decay, both in RNA secondary structure prediction as well as in digital organisms replicating in silico. This correlation implies that, during adaptation, epistasis and average mutational effect cannot be optimized independently. In experiments with RNA sequences evolving on a neutral network, the selective pressure to decrease the mutational load then leads to a reduction in the amount of sequences with strong antagonistic interactions between deleterious mutations in the population.     

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

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

The impact of high‐order epistasis in the within‐host fitness of a positive‐sense plant RNA virus

RNA viruses are the main source of emerging infectious diseases because of the evolutionary potential bestowed by their fast replication, large population sizes and high mutation and recombination rates. However, an equally important property, which is usually neglected, is the topography of the fitness landscape. How many fitness maxima exist and how well they are connected is especially interesting, as this determines the number of accessible evolutionary pathways. To address this question, we have reconstructed a region of the fitness landscape of tobacco etch potyvirus constituted by mutations observed during the experimental adaptation of the virus to the novel host Arabidopsis thaliana. Fitness was measured for many genotypes and showed the existence of multiple peaks and holes in the landscape. We found prevailing epistatic effects between mutations, with cases of reciprocal sign epistasis being common among pairs of mutations. We also found that high‐order epistasis was as important as pairwise epistasis in their contribution to fitness. Therefore, results suggest that the landscape was rugged due to the existence of holes caused by lethal genotypes, that a very limited number of potential neutral paths exist and that it contained a single adaptive peak.     

Visualizing fitness landscapes

Fitness landscapes are a classical concept for thinking about the relationship between genotype and fitness. However, because the space of genotypes is typically high-dimensional, the structure of fitness landscapes can be difficult to understand and the heuristic approach of thinking about fitness landscapes as low-dimensional, continuous surfaces may be misleading. Here, I present a rigorous method for creating low-dimensional representations of fitness landscapes. The basic idea is to plot the genotypes in a manner that reflects the ease or difficulty of evolving from one genotype to another. Such a layout can be constructed using the eigenvectors of the transition matrix describing the evolution of a population on the fitness landscape when mutation is weak. In addition, the eigendecomposition of this transition matrix provides a new, high-level view of evolution on a fitness landscape. I demonstrate these techniques by visualizing the fitness landscape for selection for the amino acid serine and by visualizing a neutral network derived from the RNA secondary structure genotype-phenotype map.     

Natural selection drives altitudinal divergence at the albumin locus in deer mice, Peromyscus maniculatus

In populations that are distributed across steep environmental gradients, the potential for local adaptation is largely determined by the spatial scale of fitness variation relative to dispersal distance. Since altitudinal gradients are generally characterized by dramatic ecological transitions over relatively short linear distances, adaptive divergence across such gradients will typically require especially strong selection to counterbalance the homogenizing effect of gene flow. Here we report the results of a study that was designed to test for evidence of adaptive divergence across an altitudinal gradient in a natural population of deer mice, Peromyscus maniculatus. We conducted a multilocus survey of allozyme variation across a steep altitudinal gradient in the southern Rocky Mountains that spanned several distinct biomes, from prairie grassland to alpine tundra. As a control for the effects of altitude, we also surveyed the same loci in mice sampled along a latitudinal transect through the prairie grassland that ran perpendicular to the east-west altitudinal transect. We used a coalescent-based simulation model to identify loci that deviated from neutral expectations, and we then assessed whether locus-specific patterns of variation were nonrandom with respect to altitude. Results indicated that the albumin locus (Alb) reflects a history of diversifying selection across the altitudinal gradient. This conclusion is supported by two main lines of evidence: (1) Alb was characterized by levels of divergence across the altitudinal transect that exceeded neutral expectations in two consecutive years of sampling (in contrast to the spatial pattern of variation across the latitudinal transect), and (2) levels of divergence at the Alb locus exhibited a positive association with altitudinal distance in both years (in contrast to the pattern observed at unlinked loci). We conclude that clinal variation at the Alb locus reflects a balance between gene flow and diversifying selection that results from elevational changes in fitness rankings among alternative genotypes.     

The effect of host heterogeneity and parasite intragenomic interactions on parasite population structure

Understanding the processes that shape the genetic structure of parasite populations and the functional consequences of different parasite genotypes is critical for our ability to predict how an infection can spread through a host population and for the design of effective vaccines to combat infection and disease. Here, we examine how the genetic structure of parasite populations responds to host genetic heterogeneity. We consider the well-characterized molecular specificity of major histocompatibility complex binding of antigenic peptides to derive deterministic and stochastic models. We use these models to ask, firstly, what conditions favour the evolution of generalist parasite genotypes versus specialist parasite genotypes? Secondly, can parasite genotypes coexist in a population? We find that intragenomic interactions between parasite loci encoding antigenic peptides are pivotal in determining the outcome of evolution. Where parasite loci interact synergistically (i.e. the recognition of additional antigenic peptides has a disproportionately large effect on parasite fitness), generalist parasite genotypes are favoured. Where parasite loci act multiplicatively (have independent effects on fitness) or antagonistically (have diminishing effects on parasite fitness), specialist parasite genotypes are favoured. A key finding is that polymorphism is not stable and that, with respect to functionally important antigenic peptides, parasite populations are dominated by a single genotype.     

Evolutionary vestigialization of sex in a clonal plant: selection versus neutral mutation in geographically peripheral populations

The loss of traits that no longer contribute to fitness is widespread; however, the causative evolutionary mechanisms are poorly understood. Vestigialization could proceed through the fixation of selectively neutral degenerative mutations via genetic drift. Alternatively, selection may facilitate vestigialization if trait loss results in enhanced fitness. We tested these hypotheses using Decodon verticillatus, a clonal plant in which sexual sterility has arisen repeatedly in populations across the northern geographical range limit. We compared growth and survival of replicated genotypes from 7 sexually fertile and 18 sterile populations, over 3 years in a common environment. Survival of sterile genotypes was 53% greater than for fertile genotypes, but there was no difference in biomass accumulation. Almost all mortality, and hence increased performance of sterile genotypes, occurred during simulated overwinter dormancy. These observations suggest that selection has facilitated the vestigialization of sex, and thus do not support the neutral mutation hypothesis. The selective mechanism probably involves the relaxation of a genetic trade-off between sexual reproduction and survival: alleles that increase vegetative performance at the expense of sexual fertility are selected in geographically peripheral populations where sexual reproduction is suppressed by adverse environmental conditions.     

The effect of recombination on the neutral evolution of genetic robustness

Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure only through neutral mutations can evolve mutational robustness [E. van Nimwegen, J.P. Crutchfield, M. Huynen, Neutral evolution of mutational robustness, Proc. Natl. Acad. Sci. USA 96(17), 9716-9720 (1999)], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.     

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.     

LONG-TERM EXPERIMENTAL EVOLUTION IN ESCHERICHIA COLI. VII. MECHANISMS MAINTAINING GENETIC VARIABILITY WITHIN POPULATIONS

Six replicate populations of the bacterium Escherichia coli were propagated for more than 10,000 generations in a defined environment. We sought to quantify the variation among clones within these populations with respect to their relative fitness, and to evaluate the roles of three distinct population genetic processes in maintaining this variation. On average, a pair of clones from the same population differed from one another in their relative fitness by approximately 4%. This within-population variation was small compared with the average fitness gain relative to the common ancestor, but it was statistically significant. According to one hypothesis, the variation in fitness is transient and reflects the ongoing substitution of beneficial alleles. We used Fisher's fundamental theorem to compare the observed rate of each population's change in mean fitness with the extent of variation for fitness within that population, but we failed to discern any correspondence between these quantities. A second hypothesis supposes that the variation in fitness is maintained by recurrent deleterious mutations that give rise to a mutation-selection balance. To test this hypothesis, we made use of the fact that two of the six replicate populations had evolved mutator phenotypes, which gave them a genomic mutation rate approximately 100-fold higher than that of the other populations. There was a marginally significant correlation between a population's mutation rate and the extent of its within-population variance for fitness, but this correlation was driven by only one population (whereas two of the populations had elevated mutation rates). Under a third hypothesis, this variation is maintained by frequency-dependent selection, whereby genotypes have an advantage when they are rare relative to when they are common. In all six populations, clones were more fit, on average, when they were rare than when they were common, although the magnitude of the advantage when rare was usually small (~1% in five populations and ~5% in the other). These three hypotheses are not mutually exclusive, but frequency-dependent selection appears to be the primary force maintaining the fitness variation within these experimental populations.     

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.     

Evolutionary dynamics, epistatic interactions, and biological information

We investigate a definition of biological information that connects population genetics with the tools of information theory by focusing on the distribution of genotypes found in a population. Previous research has treated loci as non-interacting by making specific approximations in the calculation of information-theoretic quantities. We expand earlier mathematical forms to include epistasis, or interactions between mutations at all pairs of loci. Application of our improved measure of biological information to evolution on two-locus, two-allele fitness landscapes demonstrates that mutual information between loci reflects epistatic interaction of mutations. Finally, we consider four-locus, two-allele fitness landscapes with modular structure. As modular interactions are inherently epistatic, we demonstrate that our refined approximation provides insight into the underlying structure of these non-trivial fitness landscapes.     

Genotype by environment interactions in winter survival in red deer

1. The extent to which environmental heterogeneity interacts with genetic hetero geneity to affect individual fitness within populations has the potential to affect the dynamics of natural populations and the amount of genetic variation maintained in natural populations, yet is a relatively poorly investigated topic in either ecology or evolutionary biology.
2. Many individual-based studies are precluded from such investigations by the practical problems of measuring heritability of traits affecting fitness and the difficulties of experimental manipulation of the study population. One way of demonstrating how commonly genotype by environmental interactions affect fitness, though not their overall importance in determining fitness, is to investigate fitness in a population subdivided by genotype at one or more marker loci.
3. We analyse data on calf winter survival from a population of red deer from the Isle of Rum, Scotland. Data on individual survival, environmental fluctuations and genotype at 13 loci were collected from 1982 to 1994.
4. We found associations between survival over the first winter of life and calf genotype at two out of three allozyme loci and five out of 10 microsatellite loci. All of the results remained significant under randomization tests. Other genotypes that initially appeared to have an association with survival were rejected when bootstrapped, usually due to insufficient data or anomalies in the data.
5. Our results suggest that associations between fitness and genotype are common. Five out of the seven associations found involved interactions with environmental variables. Four of these showed density-dependent selection with different genotypes showing high survival at high population size compared to low population size and one interacted with autumn rainfall. In a sixth case, genotype interacted with sex.     

Growing with siblings: a common ground for cooperation or for fiercer competition among plants?

Recent work has shown that certain plants can identify their kin in competitive settings through root recognition, and react by decreasing root growth when competing with relatives. Although this may be a necessary step in kin selection, no clear associated improvement in individual or group fitness has been reported to qualify as such. We designed an experiment to address whether genetic relatedness between neighbouring plants affects individual or group fitness in artificial populations. Seeds of Lupinus angustifolius were sown in groups of siblings, groups of different genotypes from the same population and groups of genotypes from different populations. Both plants surrounded by siblings and by genotypes from the same population had lower individual fitness and produced fewer flowers and less vegetative biomass as a group. We conclude that genetic relatedness entails decreased individual and group fitness in L. angustifolius. This, together with earlier work, precludes the generalization that kin recognition may act as a widespread, major microevolutionary mechanism in plants.     

HETEROZYGOSITY-FITNESS CORRELATIONS REVEALED BY NEUTRAL AND CANDIDATE GENE MARKERS IN ROE DEER FROM A LONG-TERM STUDY

Heterozygosity-fitness correlations (HFCs) are increasingly reported but the underlying mechanisms causing HFCs are generally poorly understood. Here, we test for HFCs in roe deer ( Capreolus capreolus ) using 22 neutral microsatellites widely distributed in the genome and four microsatellites in genes that are potentially under selection. Juvenile survival was used as a proxy for individual fitness in a population that has been intensively studied for 30 years in northeastern France. For 222 juveniles, we computed two measures of genetic diversity: individual heterozygosity ( H ), and mean d ² (relatedness of parental genomes). We found a relationship between genetic diversity and fitness both for the 22 neutral markers and two candidate genes: IGF1 (Insulin-like Growth Factor I) and NRAMP (natural resistance-associated macrophage protein). Statistical evidence and the size of genetic effects on juvenile survival were comparable to those reported for early development and cohort variation, suggesting a substantial influence of genetic components on fitness in this roe deer population. For the 22 neutral microsatellites, a correlation with fitness was revealed for mean d ², but not for H , suggesting a possible outbreeding advantage. This heterosis effect could have been favored by introduction of genetically distant (Hungarian) roe deer to the population in recent times and, possibly, by the structuring of the population into distinct clans. The locus-specific correlations with fitness may be driven by growth rate advantages and resistance to diseases known to exist in the studied population. Our analyses of neutral and candidate gene markers both suggest that the observed HFCs are likely mainly due to linkage with dominant or overdominant loci that affect fitness ("local" effect) rather than to a genome-wide relationship with homozygosity due to inbreeding ("general" effect).