Valleys Of Fitness Research Articles

The Runtime of the Compact Genetic Algorithm on Jump Functions

In the first and so far only mathematical runtime analysis of an estimation-of-distribution algorithm (EDA) on a multimodal problem, Hasen\"ohrl and Sutton (GECCO 2018) showed for any $k = o(n)$ that the compact genetic algorithm (cGA) with any hypothetical population size $\mu = \Omega(ne^{4k} + n^{3.5+\varepsilon})$ with high probability finds the optimum of the $n$-dimensional jump function with jump size $k$ in time $O(\mu n^{1.5} \log n)$. We significantly improve this result for small jump sizes $k \le \frac 1 {20} \ln n -1$. In this case, already for $\mu = \Omega(\sqrt n \log n) \cap \text{poly}(n)$ the runtime of the cGA with high probability is only $O(\mu \sqrt n)$. For the smallest admissible values of $\mu$, our result gives a runtime of $O(n \log n)$, whereas the previous one only shows $O(n^{5+\varepsilon})$. Since it is known that the cGA with high probability needs at least $\Omega(\mu \sqrt n)$ iterations to optimize the unimodal OneMx function, our result shows that the cGA in contrast to most classic evolutionary algorithms here is able to cross moderate-sized valleys of low fitness at no extra cost. For large $k$, we show that the exponential (in $k$) runtime guarantee of Hasen\"ohrl and Sutton is tight and cannot be improved, also not by using a smaller hypothetical population size. We prove that any choice of the hypothetical population size leads to a runtime that, with high probability, is at least exponential in the jump size $k$. This result might be the first non-trivial exponential lower bound for EDAs that holds for arbitrary parameter settings.

Computer Simulation of the Evolution of Microbial Population: Overcoming Local Minima When Reaching a Peak on the Fitness Landscape

The study focuses on the mechanisms of crossing the valleys of fitness by a population of haploid microorganisms, whose fitness depends on allelic values at two different loci and is determined by a complex landscape, the shape of which corresponds to the pattern “a mountain in the field surrounded by a trench”; these mechanisms are analyzed using computer modeling. We have studied the influence of various biological factors on the evolutionary perspective of microbial colonies, the reproduction rate of which is controlled by a protein consisting of two subunits encoded at different loci. Molecular genetic (mutation rate, affinity of subunits), population (fitness function landscape and population density), and ecological (concentration of available substrate in the habitat, flow intensity) factors have been considered. Our results demonstrate that the difference in fitness for various allelic combinations, while determining the shape of the fitness landscape, sets the optimal mutation rates to overcome its valleys and opens a window of opportunity for the evolution of the population toward the state of the highest average fitness. Moreover, depending on the fitness landscape type, either gradual or saltational evolutionary regimes are optimal for reaching the peak.

How Often Do Protein Genes Navigate Valleys of Low Fitness?

To escape from local fitness peaks, a population must navigate across valleys of low fitness. How these transitions occur, and what role they play in adaptation, have been subjects of active interest in evolutionary genetics for almost a century. However, to our knowledge, this problem has never been addressed directly by considering the evolution of a gene, or group of genes, as a whole, including the complex effects of fitness interactions among multiple loci. Here, we use a precise model of protein fitness to compute the probability that an allele, randomly sampled from a population at time t, has crossed a fitness valley of depth s during an interval in the immediate past. We study populations of model genes evolving under equilibrium conditions consistent with those in mammalian mitochondria. From this data, we estimate that genes encoding small protein motifs navigate fitness valleys of depth with probability on a time scale of human evolution, where N is the (mitochondrial) effective population size. The results are consistent with recent findings for Watson–Crick switching in mammalian mitochondrial tRNA molecules.

Gene Conversion Facilitates Adaptive Evolution on Rugged Fitness Landscapes.

Gene conversion is a ubiquitous phenomenon that leads to the exchange of genetic information between homologous DNA regions and maintains coevolving multi-gene families in most prokaryotic and eukaryotic organisms. In this paper, we study its implications for the evolution of a single functional gene with a silenced duplicate, using two different models of evolution on rugged fitness landscapes. Our analytical and numerical results show that, by helping to circumvent valleys of low fitness, gene conversion with a passive duplicate gene can cause a significant speedup of adaptation, which depends nontrivially on the frequency of gene conversion and the structure of the landscape. We find that stochastic effects due to finite population sizes further increase the likelihood of exploiting this evolutionary pathway. A universal feature appearing in both deterministic and stochastic analysis of our models is the existence of an optimal gene conversion rate, which maximizes the speed of adaptation. Our results reveal the potential for duplicate genes to act as a "scratch paper" that frees evolution from being limited to strictly beneficial mutations in strongly selective environments.

Translating HIV Sequences into Quantitative Fitness Landscapes Predicts Viral Vulnerabilities for Rational Immunogen Design

A prophylactic or therapeutic vaccine offers the best hope to curb the HIV-AIDS epidemic gripping sub-Saharan Africa, but it remains elusive. A major challenge is the extreme viral sequence variability among strains. Systematic means to guide immunogen design for highly variable pathogens like HIV are not available. Using computational models, we have developed an approach to translate available viral sequence data into quantitative landscapes of viral fitness as a function of the amino acid sequences of its constituent proteins. Predictions emerging from our computationally defined landscapes for the proteins of HIV-1 clade B Gag were positively tested against new invitro fitness measurements and were consistent with previously defined invitro measurements and clinical observations. These landscapes chart the peaks and valleys of viral fitness as protein sequences change and inform the design of immunogens and therapies that can target regions of the virus most vulnerable to selection pressure.

From HIV protein sequences to viral fitness landscapes: a new paradigm for in silico vaccine design

Background An inexpensive prophylactic vaccine offers the best hope to curb the HIV/AIDS epidemic gripping sub-Saharan Africa. Systematic means to guide the design of an effective immunogen for this, and other, infectious diseases are not available. What is required is a method to chart the peaks and valleys of viral fitness as a function of amino acid sequence. An efficacious vaccine would eject the virus from the high fitness peaks, and drive it into the valleys where its compromised fitness impairs its ability to replicate and inflict damage to the host. Methods Appealing to spin glass models in statistical physics, we present a novel approach to translate viral sequence databases into landscapes of viral fitness. These inferred models furnish a quantitative description of viral replicative capacity as a function of amino acid sequence. We illustrate this approach in the development of landscapes for the proteins of HIV-1 clade B Gag. Results In comparisons to experimental and clinical data, our inferred landscapes demonstrate excellent agreement with: 1) in vitro replicative fitness measurements, 2) clinically observed high-fitness circulating viral strains, 3) documented HLA associated CTL escape mutations, and 4) intrahost temporal adaptation pathways revealed by deep sequencing. These favorable comparisons support our landscapes as reflections of intrinsic viral fitness. We illustrate the value of such descriptions in the computational design of a CTL Gag immunogen. Conclusion We present a novel methodology to translate viral sequence data into quantitative landscapes of viral fitness. In an application to HIV-1 Gag, we illustrate excellent agreement of our model predictions with experimental and clinical data, and demonstrate a powerful new approach for HIV immunogen design. We anticipate that this approach may represent a heretofore unprecedented means to synthesize fitness landscapes for diverse pathogens, and may provide the basis for the design of improved prophylactic and therapeutic strategies.

Reciprocal Sign Epistasis between Frequently Experimentally Evolved Adaptive Mutations Causes a Rugged Fitness Landscape

The fitness landscape captures the relationship between genotype and evolutionary fitness and is a pervasive metaphor used to describe the possible evolutionary trajectories of adaptation. However, little is known about the actual shape of fitness landscapes, including whether valleys of low fitness create local fitness optima, acting as barriers to adaptive change. Here we provide evidence of a rugged molecular fitness landscape arising during an evolution experiment in an asexual population of Saccharomyces cerevisiae. We identify the mutations that arose during the evolution using whole-genome sequencing and use competitive fitness assays to describe the mutations individually responsible for adaptation. In addition, we find that a fitness valley between two adaptive mutations in the genes MTH1 and HXT6/HXT7 is caused by reciprocal sign epistasis, where the fitness cost of the double mutant prohibits the two mutations from being selected in the same genetic background. The constraint enforced by reciprocal sign epistasis causes the mutations to remain mutually exclusive during the experiment, even though adaptive mutations in these two genes occur several times in independent lineages during the experiment. Our results show that epistasis plays a key role during adaptation and that inter-genic interactions can act as barriers between adaptive solutions. These results also provide a new interpretation on the classic Dobzhansky-Muller model of reproductive isolation and display some surprising parallels with mutations in genes often associated with tumors.

Comparing the adaptive landscape across trait types: larger QTL effect size in traits under biotic selection

BackgroundIn a spatially and temporally variable adaptive landscape, mutations operating in opposite directions and mutations of large effect should be commonly fixed due to the shifting locations of phenotypic optima. Similarly, an adaptive landscape with multiple phenotypic optima and deep valleys of low fitness between peaks will favor mutations of large effect. Traits under biotic selection should experience a more spatially and temporally variable adaptive landscape with more phenotypic optima than that experienced by traits under abiotic selection. To test this hypothesis, we assemble information from QTL mapping studies conducted in plants, comparing effect directions and effect sizes of detected QTL controlling traits putatively under abiotic selection to those controlling traits putatively under biotic selection.ResultsWe find no differences in the fraction of antagonistic QTL in traits under abiotic and biotic selection, suggesting similar consistency in selection pressure on these two types of traits. However, we find that QTL controlling traits under biotic selection have a larger effect size than those under abiotic selection, supporting our hypothesis that QTL of large effect are more commonly detected in traits under biotic selection than in traits under abiotic selection. For traits under both abiotic and biotic selection, we find a large number of QTL of large effect, with 10.7% of all QTLs detected controlling more than 20% of the variance in phenotype.ConclusionThese results suggest that mutations of large effect are more common in adaptive landscapes strongly determined by biotic forces, but that these types of adaptive landscapes do not result in a higher fraction of mutations acting in opposite directions. The high number of QTL of large effect detected shows that QTL of large effect are more common than predicted by the infinitesimal model of genetic adaptation.

Compensatory evolution in mitochondrial tRNAs navigates valleys of low fitness

A long-standing controversy in evolutionary biology is whether or not evolving lineages can cross valleys on the fitness landscape that correspond to low-fitness genotypes, which can eventually enable them to reach isolated fitness peaks. Here we study the fitness landscapes traversed by switches between different AU and GC Watson-Crick nucleotide pairs at complementary sites of mitochondrial transfer RNA stem regions in 83 mammalian species. We find that such Watson-Crick switches occur 30-40 times more slowly than pairs of neutral substitutions, and that alleles corresponding to GU and AC non-Watson-Crick intermediate states segregate within human populations at low frequencies, similar to those of non-synonymous alleles. Substitutions leading to a Watson-Crick switch are strongly correlated, especially in mitochondrial tRNAs encoded on the GT-nucleotide-rich strand of the mitochondrial genome. Using these data we estimate that a typical Watson-Crick switch involves crossing a fitness valley of a depth of about 10(-3) or even about 10(-2), with AC intermediates being slightly more deleterious than GU intermediates. This compensatory evolution must proceed through rare intermediate variants that never reach fixation. The ubiquitous nature of compensatory evolution in mammalian mitochondrial tRNAs and other molecules implies that simultaneous fixation of two alleles that are individually deleterious may be a common phenomenon at the molecular level.

Radical Epistasis and the Genotype-Phenotype Relationship

Models of evolution often assume that the offspring of two genotypes, which are genetically intermediate by definition, are also phenotypically intermediate. The continuity between genotype and phenotype interferes with the process of evolution on multipeaked adaptive landscapes because the progeny of genotypes that lie on separate adaptive peaks fall into valleys of low fitness. This problem can be solved by epistasis, which disrupts the continuity between genotype and phenotype. In a five-locus sexual haploid model with maximum epistasis, natural selection in multipeak landscapes evolves a set of genotypes that a) occupy the adaptive peaks and b) give rise to each other by recombination. The epistatic genetic system therefore “molds” the phenotypic distribution to the adaptive landscape, without assortative mating or linkage disequilibrium. If the adaptive landscape is changed, a new set of genotypes quickly evolves that satisfies conditions a and b, above, for the new peaks. Our model may be relevant to a number of recalcitrant problems in biology and also stands in contrast to Kauffman's [3] NK model of evolution on rugged fitness surfaces, in which epistasis and recombination tend to constrain the evolutionary process.

Radical Epistasis and the Genotype-Phenotype Relationship

Models of evolution often assume that the offspring of two genotypes, which are genetically intermediate by definition, are also phenotypically intermediate. The continuity between genotype and phenotype interferes with the process of evolution on multipeaked adaptive landscapes because the progeny of genotypes that lie on separate adaptive peaks fall into valleys of low fitness. This problem can be solved by epistasis, which disrupts the continuity between genotype and phenotype. In a five-locus sexual haploid model with maximum epistasis, natural selection in multipeak landscapes evolves a set of genotypes that a) occupy the adaptive peaks and b) give rise to each other by recombination. The epistatic genetic system therefore “molds” the phenotypic distribution to the adaptive landscape, without assortative mating or linkage disequilibrium. If the adaptive landscape is changed, a new set of genotypes quickly evolves that satisfies conditions a and b, above, for the new peaks.Our model may be relevant to a number of recalcitrant problems in biology and also stands in contrast to Kauffman's [3] NK model of evolution on rugged fitness surfaces, in which epistasis and recombination tend to constrain the evolutionary process.