Evolution in alternating environments with tunable interlandscape correlations

Natural populations are often exposed to temporally varying environments. Evolutionary dynamics in varying environments have been extensively studied, although understanding the effects of varying selection pressures remains challenging. Here, we investigate how cycling between a pair of statistically related fitness landscapes affects the evolved fitness of an asexually reproducing population. We construct pairs of fitness landscapes that share global fitness features but are correlated with one another in a tunable way, resulting in landscape pairs with specific correlations. We find that switching between these landscape pairs, depending on the ruggedness of the landscape and the interlandscape correlation, can either increase or decrease steady‐state fitness relative to evolution in single environments. In addition, we show that switching between rugged landscapes often selects for increased fitness in both landscapes, even in situations where the landscapes themselves are anticorrelated. We demonstrate that positively correlated landscapes often possess a shared maximum in both landscapes that allows the population to step through sub‐optimal local fitness maxima that often trap single landscape evolution trajectories. Finally, we demonstrate that switching between anticorrelated paired landscapes leads to ergodic‐like dynamics where each genotype is populated with nonzero probability, dramatically lowering the steady‐state fitness in comparison to single landscape evolution.     

Dynamic RNA Fitness Landscapes of a Group I Ribozyme during Changes to the Experimental Environment

Fitness landscapes of protein and RNA molecules can be studied experimentally using high-throughput techniques to measure the functional effects of numerous combinations of mutations. The rugged topography of these molecular fitness landscapes is important for understanding and predicting natural and experimental evolution. Mutational effects are also dependent upon environmental conditions, but the effects of environmental changes on fitness landscapes remains poorly understood. Here, we investigate the changes to the fitness landscape of a catalytic RNA molecule while changing a single environmental variable that is critical for RNA structure and function. Using high-throughput sequencing of in vitro selections, we mapped a fitness landscape of the Azoarcus group I ribozyme under eight different concentrations of magnesium ions (1–48 mM MgCl₂). The data revealed the magnesium dependence of 16,384 mutational neighbors, and from this, we investigated the magnesium induced changes to the topography of the fitness landscape. The results showed that increasing magnesium concentration improved the relative fitness of sequences at higher mutational distances while also reducing the ruggedness of the mutational trajectories on the landscape. As a result, as magnesium concentration was increased, simulated populations evolved toward higher fitness faster. Curve-fitting of the magnesium dependence of individual ribozymes demonstrated that deep sequencing of in vitro reactions can be used to evaluate the structural stability of thousands of sequences in parallel. Overall, the results highlight how environmental changes that stabilize structures can also alter the ruggedness of fitness landscapes and alter evolutionary processes.     

Size scaling of mutation avalanches in a model for protein evolution

The tunably rugged NK-model is used to study avalanche-like events that occur when environmental change causes fitness optima to disappear. The probability of an event with Delta substitutions scales as exp(-c Delta) for smooth landscapes, and as exp(-c Delta(2)) for rugged landscapes. Increasing the ruggedness leads to two competing effects: (1) more possible routes by which single mutations can increase the fitness, which dominates at low ruggedness and acts to increase Delta; and (2) a higher density of fitness optima, which dominates at high ruggedness and acts to decrease Delta. Due to these competing effects, the largest average values of Delta occur at intermediate ruggedness. The effects of system size on the avalanche events are examined, and average values of Delta increase logarithmically with system size. The variance to mean ratios for the number of substitutions per unit time are consistent with experimental results for protein evolution.     

Adaptive landscapes in evolving populations of Pseudomonas fluorescens

The repeatability of adaptive evolution depends on the ruggedness of the underlying adaptive landscape. We contrasted the relative ruggedness of two adaptive landscapes by measuring the variance in fitness and metabolic phenotype within and among genetically distinct strains of Pseudomonas fluorescens in two environments differing only in the carbon source provided (glucose vs. xylose). Fitness increased in all lines, plateauing in one environment but not the other. The pattern of variance in fitness among replicate lines was unique to the selection environment; it increased over the course of the experiment in xylose but not in glucose. Metabolic phenotypes displayed two results: (1) populations adapted via changes that were distinctive to their selection environment, and (2) endpoint phenotypes were less variable in glucose than in xylose. These results indicate that although the response to selection is highly repeatable at the level of fitness, the underlying genetic routes taken were different for each environment and more variable in xylose. We suggest that this reflects a more rugged adaptive landscape in xylose compared to glucose. Our study demonstrates the utility of using replicate selection lines with different evolutionary starting points to try and quantify the relative ruggedness of adaptive landscapes.     

Exploring the complexity of the HIV-1 fitness landscape

Although fitness landscapes are central to evolutionary theory, so far no biologically realistic examples for large-scale fitness landscapes have been described. Most currently available biological examples are restricted to very few loci or alleles and therefore do not capture the high dimensionality characteristic of real fitness landscapes. Here we analyze large-scale fitness landscapes that are based on predictive models for in vitro replicative fitness of HIV-1. We find that these landscapes are characterized by large correlation lengths, considerable neutrality, and high ruggedness and that these properties depend only weakly on whether fitness is measured in the absence or presence of different antiretrovirals. Accordingly, adaptive processes on these landscapes depend sensitively on the initial conditions. While the relative extent to which mutations affect fitness on their own (main effects) or in combination with other mutations (epistasis) is a strong determinant of these properties, the fitness landscape of HIV-1 is considerably less rugged, less neutral, and more correlated than expected from the distribution of main effects and epistatic interactions alone. Overall this study confirms theoretical conjectures about the complexity of biological fitness landscapes and the importance of the high dimensionality of the genetic space in which adaptation takes place.     

Natural selection fails to optimize mutation rates for long-term adaptation on rugged fitness landscapes

The rate of mutation is central to evolution. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. Here, we used digital organisms to investigate the ability of natural selection to adjust and optimize mutation rates. We assessed the optimal mutation rate by empirically determining what mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve, and we evaluated the proximity to the optimum. Although we chose conditions favorable for mutation rate optimization, the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings. We hypothesized that the reason that mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates. In contrast, when fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost. We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation. This finding has important implications for applied evolutionary research in both biological and computational realms.     

The population genetics of adaptation on correlated fitness landscapes: the block model

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.     

Coevolution and maladaptation

Many of the most commonly cited examples of exquisite adaptationare of coevolved symbioses. As we learn more about the coevolutionaryprocess, however, it is becoming increasingly evident that coevolutionmay also keep populations moderately maladapted much of thetime. As a result, coevolving populations may only rarely occupyadaptive peaks, because the selective landscape is under continualchange through reciprocal selection on the species themselves.These shifting patterns of coadaptation are further shaped bythe geographic structure of most species. Selection mosaicsacross landscapes and coevolutionary hotspots can favor differentevolutionary trajectories in different populations. The combinedaction of gene flow, random genetic drift, and local extinctionof populations may then continually remold these local patterns,creating a geographic mosaic in the degrees of maladaptationfound within local interactions. Recent mathematical modelsof the geographic mosaic of coevolution suggest that complexmosaics of maladaptation are a likely consequence of spatiallystructured species interactions. These models indicate thatthe spatial structure of maladaptation may depend upon the typeof coevolutionary interaction, the underlying selection mosaic,and patterns of gene flow across landscapes. By maintaininglocal polymorphisms and driving the divergence of populations,coevolution may produce spatial patterns of maladaptation thatare a source of ongoing innovation and diversification in speciesinteractions.     

The NK model of rugged fitness landscapes and its application to maturation of the immune response

Adaptive evolution is, to a large extent, a complex combinatorial optimization process. Such processes can be characterized as "uphill walks on rugged fitness landscapes". Concrete examples of fitness landscapes include the distribution of any specific functional property such as the capacity to catalyze a specific reaction, or bind a specific ligand, in "protein space". In particular, the property might be the affinity of all possible antibody molecules for a specific antigenic determinant. That affinity landscape presumably plays a critical role in maturation of the immune response. In this process, hypermutation and clonal selection act to select antibody V region mutant variants with successively higher affinity for the immunizing antigen. The actual statistical structure of affinity landscapes, although knowable, is currently unknown. Here, we analyze a class of mathematical models we call NK models. We show that these models capture significant features of the maturation of the immune response, which is currently thought to share features with general protein evolution. The NK models have the important property that, as the parameter K increases, the "ruggedness" of the NK landscape varies from a single peaked "Fujiyama" landscape to a multi-peaked "badlands" landscape. Walks to local optima on such landscapes become shorter as K increases. This fact allows us to choose a value of K that corresponds to the experimentally observed number of mutational "steps", 6-8, taken as an antibody sequence matures. If the mature antibody is taken to correspond to a local optimum in the model, tuning the model requires that K be about 40, implying that the functional contribution of each amino acid in the V region is affected by about 40 others. Given this value of K, the model then predicts several features of "antibody space" that are in qualitative agreement with experiment: (1) The fraction of fitter variants of an initial "roughed in" germ line antibody amplified by clonal selection is about 1-2%. (2) Mutations at some sites of the mature antibody hardly affect antibody function at all, but mutations at other sites dramatically decrease function. (3) The same "roughed in" antibody sequence can "walk" to many mature antibody sequences. (4) Many adaptive walks can end on the same local optimum. (5) Comparison of different mature sequences derived from the same initial V region shows evolutionary hot spots and parallel mutations. All these predictions are open to detailed testing by obtaining monoclonal antibodies early in the immune response and carrying out in vitro mutagenesis and adaptive hill climbing with respect to affinity for the immunizing antigen.     

Hot Spots, Cold Spots, and the Geographic Mosaic Theory of Coevolution

Species interactions commonly coevolve as complex geographic mosaics of populations shaped by differences in local selection and gene flow. We use a haploid matching-alleles model for coevolution to evaluate how a pair of species coevolves when fitness interactions are reciprocal in some locations ("hot spots") but not in others ("cold spots"). Our analyses consider mutualistic and antagonistic interspecific interactions and a variety of gene flow patterns between hot and cold spots. We found that hot and cold spots together with gene flow influence coevolutionary dynamics in four important ways. First, hot spots need not be ubiquitous to have a global influence on evolution, although rare hot spots will not have a disproportionate impact unless selection is relatively strong there. Second, asymmetries in gene flow can influence local adaptation, sometimes creating stable equilibria at which species experience minimal fitness in hot spots and maximal fitness in cold spots, or vice versa. Third, asymmetries in gene flow are no more important than asymmetries in population regulation for determining the maintenance of local polymorphisms through coevolution. Fourth, intraspecific allele frequency differences among hot and cold spot populations evolve under some, but not all, conditions. That is, selection mosaics are indeed capable of producing spatially variable coevolutionary outcomes across the landscapes over which species interact. Altogether, our analyses indicate that coevolutionary trajectories can be strongly shaped by the geographic distribution of coevolutionary hot and cold spots, and by the pattern of gene flow among populations.     

Adaptation in Tunably Rugged Fitness Landscapes: The Rough Mount Fuji Model

Much of the current theory of adaptation is based on Gillespie’s mutational landscape model (MLM), which assumes that the fitness values of genotypes linked by single mutational steps are independent random variables. On the other hand, a growing body of empirical evidence shows that real fitness landscapes, while possessing a considerable amount of ruggedness, are smoother than predicted by the MLM. In the present article we propose and analyze a simple fitness landscape model with tunable ruggedness based on the rough Mount Fuji (RMF) model originally introduced by Aita et al. in the context of protein evolution. We provide a comprehensive collection of results pertaining to the topographical structure of RMF landscapes, including explicit formulas for the expected number of local fitness maxima, the location of the global peak, and the fitness correlation function. The statistics of single and multiple adaptive steps on the RMF landscape are explored mainly through simulations, and the results are compared to the known behavior in the MLM model. Finally, we show that the RMF model can explain the large number of second-step mutations observed on a highly fit first-step background in a recent evolution experiment with a microvirid bacteriophage.     

The Structural Determinants of Intra-Protein Compensatory Substitutions

Compensatory substitutions happen when one mutation is advantageously selected because it restores the loss of fitness induced by a previous deleterious mutation. How frequent such mutations occur in evolution and what is the structural and functional context permitting their emergence remain open questions. We built an atlas of intra-protein compensatory substitutions using a phylogenetic approach and a dataset of 1,630 bacterial protein families for which high-quality sequence alignments and experimentally derived protein structures were available. We identified more than 51,000 positions coevolving by the mean of predicted compensatory mutations. Using the evolutionary and structural properties of the analyzed positions, we demonstrate that compensatory mutations are scarce (typically only a few in the protein history) but widespread (the majority of proteins experienced at least one). Typical coevolving residues are evolving slowly, are located in the protein core outside secondary structure motifs, and are more often in contact than expected by chance, even after accounting for their evolutionary rate and solvent exposure. An exception to this general scheme is residues coevolving for charge compensation, which are evolving faster than noncoevolving sites, in contradiction with predictions from simple coevolutionary models, but similar to stem pairs in RNA. While sites with a significant pattern of coevolution by compensatory mutations are rare, the comparative analysis of hundreds of structures ultimately permits a better understanding of the link between the three-dimensional structure of a protein and its fitness landscape.     

Male competition fitness landscapes predict both forward and reverse speciation

Speciation is facilitated when selection generates a rugged fitness landscape such that populations occupy different peaks separated by valleys. Competition for food resources is a strong ecological force that can generate such divergent selection. However, it is unclear whether intrasexual competition over resources that provide mating opportunities can generate rugged fitness landscapes that foster speciation. Here we use highly variable male F2 hybrids of benthic and limnetic threespine sticklebacks, Gasterosteus aculeatus Linnaeus, 1758, to quantify the male competition fitness landscape. We find that disruptive sexual selection generates two fitness peaks corresponding closely to the male phenotypes of the two parental species, favouring divergence. Most surprisingly, an additional region of high fitness favours novel hybrid phenotypes that correspond to those observed in a recent case of reverse speciation after anthropogenic disturbance. Our results reveal that sexual selection through male competition plays an integral role in both forward and reverse speciation.     

Coevolutionary interactions between a haploid species and a diploid species

We investigate a general model describing coevolutionary interaction between a haploid population and a diploid population, each with two alleles at a single locus. Both species are allowed to evolve, with the fitness of the genotypes of each species assumed to depend linearly on the frequencies of the genotypes of the other species. We explore the resulting outcomes of these interactions, in particular determining the location of equilibria under various conditions. The coevolution here is much more complex than that between two haploid populations and allows for the possibility of two polymorphic equilibria. To allow for further analysis, we construct a semi-symmetric model. The variety of outcomes possible even in this second model provides support for the geographic mosaic theory of coevolution by suggesting the possibility of small local populations coevolving to very different outcomes, leading to a shifting geographic mosaic as neighboring populations interact with each other through migration.     

Density dependence, lifespan and the evolutionary dynamics of longevity

Longevity is a life-history trait that is shaped by natural selection. Evolution will shape mortality trajectories and lifespans, but until now the evolutionary analysis of longevity is based principally on a density-independent (Euler-Lotka) framework. The effects of density dependence on the evolution of lifespan and mortality remain largely unexplored. We investigate the influence of different population demographies on the evolution of longevity, and show how these can be linked to adaptive radiations. We present a range of models to explore the intraspecific and interspecific density effects on longevity and, consequently, diversification. We show how the magnitude, type, and timing of mutation can also affect fitness, invasion and diversification. We argue that fitness of alternative strategies under a range of different demographic structures leads to flat, as opposed to rugged, landscapes and that these flat fitness surfaces are important in the evolution of lifespan and senescence.     

Interaction cutoff effect on ruggedness of protein-protein energy landscape

The concept of the energy landscape is important for better understanding of protein-protein interactions and for designing adequate docking procedures. The intermolecular landscape has a rugged terrain that impedes search procedures. Its inherent ruggedness is related to the conformational characteristics of the molecules and to the form of the potential function--more rugged for short-range potentials and less rugged for "soft," typically long-range potentials. Our study determined that the landscape ruggedness is further substantially exacerbated by truncation of the potentials. This additional ruggedness appears below certain critical interaction ranges that depend on the form of the potential. The theoretical model describing the cutoff effect on the landscape ruggedness is confirmed by the energy calculation on a dataset of protein-protein complexes. The negative effect of the potentials cutoff is well known. However, revealing its physical basis in terms of the energy landscape is important for better understanding of intermolecular interactions.     

INTERGENOMIC EPISTASIS AND COEVOLUTIONARY CONSTRAINT IN PLANTS AND RHIZOBIA

Studying how the fitness benefits of mutualism differ among a wide range of partner genotypes, and at multiple spatial scales, can shed light on the processes that maintain mutualism and structure coevolutionary interactions. Using legumes and rhizobia from three natural populations, I studied the symbiotic fitness benefits for both partners in 108 plant maternal family by rhizobium strain combinations. Genotype‐by‐genotype (G × G) interactions among local genotypes and among partner populations determined, in part, the benefits of mutualism for both partners; for example, the fitness effects of particular rhizobium strains ranged from uncooperative to mutualistic depending on the plant family. Correlations between plant and rhizobium fitness benefits suggest a trade off, and therefore a potential conflict, between the interests of the two partners. These results suggest that legume–rhizobium mutualisms are dynamic at multiple spatial scales, and that strictly additive models of mutualism benefits may ignore dynamics potentially important to both the maintenance of genetic variation and the generation of geographic patterns in coevolutionary interactions.     

Adaptive radiation and coevolution — pollination biology case studies

The impact of coevolutionary interaction between species on adaptive radiation processes is analysed with reference to pollination biology case studies. Occasional colonization of archipelagos can bring together coevolving partners and cause coradiation of the colonizing species, e.g. the drepanidids and the lobelioids on Hawaii. Permanent reciprocal selective pressure between pairs of coevolving species can lead to a coevolutionary race and rapid evolutionary change. This is exemplified by spurred flowers and long-tongued flower-visitors. The geographic patterning of diffuse coevolution systems can lead to dramatic changes in species interactions. In different populations, interaction between pollinating and seed-parasitizing Greya moths and their host plants varies from mutualism to commensalism and antagonism, depending on the presence of copollinators. Asymmetrical coevolution between angiosperms and oligolectic flower-visitors may facilitate rapid reproductive isolation of populations following a food-plant switch, if the oligoleges use their specific food plants as the rendezvous sites. Diffuse coevolution between angiosperm species and pollinating insects may cause frequent convergent evolution of floral traits such as nectar reward instead of pollen reward, floral guides, zygomorphic flowers, or mimicry of pollen signals, since the multiple plant species experience similar selective pressures via the coevolving partners. Patterns of angiosperm adaptive radiation are highlighted in the context of coevolution with pollinators.     

Chasing long-range evolutionary couplings in the AlphaFold era

Coevolution between protein residues is normally interpreted as direct contact. However, the evolutionary record of a protein sequence contains rich information that may include long-range functional couplings, couplings that report on homo-oligomeric states or even conformational changes. Due to the complexity of the sequence space and the lack of structural information on various members of a protein family, it has been difficult to effectively mine the additional information encoded in a multiple sequence alignment (MSA). Here, taking advantage of the recent release of the AlphaFold (AF) database we attempt to identify coevolutionary couplings that cannot be explained simply by spatial proximity. We propose a simple computational method that performs direct coupling analysis on a MSA and searches for couplings that are not satisfied in any of the AF models of members of the identified protein family. Application of this method on 2012 protein families suggests that ~12% of the total identified coevolving residue pairs are spatially distant and more likely to be disordered than their contacting counterparts. We expect that this analysis will help improve the quality of coevolutionary distance restraints used for structure determination and will be useful in identifying potentially functional/allosteric cross-talk between distant residues.     

Population Size Affects Adaptation in Complex Ways: Simulations on Empirical Adaptive Landscapes

Do large populations always outcompete smaller ones? Does increasing the mutation rate have a similar effect to increasing the population size, with respect to the adaptation of a population? How important are substitutions in determining the adaptation rate? In this study, we ask how population size and mutation rate interact to affect adaptation on empirical adaptive landscapes. Using such landscapes, we do not need to make many ad hoc assumption about landscape topography, such as about epistatic interactions among mutations or about the distribution of fitness effects. Moreover, we have a better understanding of all the mutations that occur in a population and their effects on the average fitness of the population than we can know in experimental studies. Our results show that the evolutionary dynamics of a population cannot be fully explained by the population mutation rate \(N\mu\); even at constant \(N\mu\), there can be dramatic differences in the adaptation of populations of different sizes. Moreover, the substitution rate of mutations is not always equivalent to the adaptation rate, because we observed populations adapting to high adaptive peaks without fixing any mutations. Finally, in contrast to some theoretical predictions, even on the most rugged landscapes we study, small population size is never an advantage over larger population size. These result show that complex interactions among multiple factors can affect the evolutionary dynamics of populations, and simple models should be taken with caution.