Towards a general theory of adaptive walks on rugged landscapes

The role of epistasis in evolutionary rescue

The process by which adaptive evolution preserves a population threatened with extinction due to environmental changes is known as evolutionary rescue. Several factors determine the fate of those populations, including demography and genetic factors, such as standing genetic variation, gene flow, availability of de novo mutations, and so on. Despite the extensive debate about evolutionary rescue in the current literature, a study about the role of epistasis and the topography of the fitness landscape on the fate of dwindling populations is missing. In the current work, we aim to fill this gap and study the influence of epistasis on the probability of extinction of populations. We present simulation results, and analytical approximations are derived. Counterintuitively, we show that the likelihood of extinction is smaller when the degree of epistasis is higher. The reason underneath is twofold: first, higher epistasis can promote mutations of more significant phenotypic effects, but also, the incongruence between the maps genotype-phenotype and phenotype-fitness turns the fitness landscape at low epistasis more rugged, thus curbing some of its advantages.

Fisher's Geometric Model as a Tool to Study Speciation

Interactions between alleles and across environments play an important role in the fitness of hybrids and are at the heart of the speciation process. Fitness landscapes capture these interactions and can be used to model hybrid fitness, helping us to interpret empirical observations and clarify verbal models. Here, we review recent progress in understanding hybridization outcomes through Fisher's geometric model, an intuitive and analytically tractable fitness landscape that captures many fitness patterns observed across taxa. We use case studies to show how the model parameters can be estimated from different types of data and discuss how these estimates can be used to make inferences about the divergence history and genetic architecture. We also highlight some areas where the model's predictions differ from alternative incompatibility-based models, such as the snowball effect and outlier patterns in genome scans.

Epistasis facilitates functional evolution in an ancient transcription factor

A protein's genetic architecture - the set of causal rules by which its sequence produces its functions - also determines its possible evolutionary trajectories. Prior research has proposed that the genetic architecture of proteins is very complex, with pervasive epistatic interactions that constrain evolution and make function difficult to predict from sequence. Most of this work has analyzed only the direct paths between two proteins of interest - excluding the vast majority of possible genotypes and evolutionary trajectories - and has considered only a single protein function, leaving unaddressed the genetic architecture of functional specificity and its impact on the evolution of new functions. Here, we develop a new method based on ordinal logistic regression to directly characterize the global genetic determinants of multiple protein functions from 20-state combinatorial deep mutational scanning (DMS) experiments. We use it to dissect the genetic architecture and evolution of a transcription factor's specificity for DNA, using data from a combinatorial DMS of an ancient steroid hormone receptor's capacity to activate transcription from two biologically relevant DNA elements. We show that the genetic architecture of DNA recognition consists of a dense set of main and pairwise effects that involve virtually every possible amino acid state in the protein-DNA interface, but higher-order epistasis plays only a tiny role. Pairwise interactions enlarge the set of functional sequences and are the primary determinants of specificity for different DNA elements. They also massively expand the number of opportunities for single-residue mutations to switch specificity from one DNA target to another. By bringing variants with different functions close together in sequence space, pairwise epistasis therefore facilitates rather than constrains the evolution of new functions.

Genotype sampling for deep-learning assisted experimental mapping of a combinatorially complete fitness landscape

MOTIVATION

Experimental characterization of fitness landscapes, which map genotypes onto fitness, is important for both evolutionary biology and protein engineering. It faces a fundamental obstacle in the astronomical number of genotypes whose fitness needs to be measured for any one protein. Deep learning may help to predict the fitness of many genotypes from a smaller neural network training sample of genotypes with experimentally measured fitness. Here I use a recently published experimentally mapped fitness landscape of more than 260 000 protein genotypes to ask how such sampling is best performed.

RESULTS

I show that multilayer perceptrons, recurrent neural networks, convolutional networks, and transformers, can explain more than 90% of fitness variance in the data. In addition, 90% of this performance is reached with a training sample comprising merely ≈103 sequences. Generalization to unseen test data is best when training data is sampled randomly and uniformly, or sampled to minimize the number of synonymous sequences. In contrast, sampling to maximize sequence diversity or codon usage bias reduces performance substantially. These observations hold for more than one network architecture. Simple sampling strategies may perform best when training deep learning neural networks to map fitness landscapes from experimental data.

AVAILABILITY AND IMPLEMENTATION

The fitness landscape data analyzed here is publicly available as described previously (Papkou et al. 2023). All code used to analyze this landscape is publicly available at https://github.com/andreas-wagner-uzh/fitness_landscape_sampling.

Robust genetic codes enhance protein evolvability

The standard genetic code defines the rules of translation for nearly every life form on Earth. It also determines the amino acid changes accessible via single-nucleotide mutations, thus influencing protein evolvability-the ability of mutation to bring forth adaptive variation in protein function. One of the most striking features of the standard genetic code is its robustness to mutation, yet it remains an open question whether such robustness facilitates or frustrates protein evolvability. To answer this question, we use data from massively parallel sequence-to-function assays to construct and analyze 6 empirical adaptive landscapes under hundreds of thousands of rewired genetic codes, including those of codon compression schemes relevant to protein engineering and synthetic biology. We find that robust genetic codes tend to enhance protein evolvability by rendering smooth adaptive landscapes with few peaks, which are readily accessible from throughout sequence space. However, the standard genetic code is rarely exceptional in this regard, because many alternative codes render smoother landscapes than the standard code. By constructing low-dimensional visualizations of these landscapes, which each comprise more than 16 million mRNA sequences, we show that such alternative codes radically alter the topological features of the network of high-fitness genotypes. Whereas the genetic codes that optimize evolvability depend to some extent on the detailed relationship between amino acid sequence and protein function, we also uncover general design principles for engineering nonstandard genetic codes for enhanced and diminished evolvability, which may facilitate directed protein evolution experiments and the bio-containment of synthetic organisms, respectively.

The distribution of fitness effects during adaptive walks using a simple genetic network

The tempo and mode of adaptation depends on the availability of beneficial alleles. Genetic interactions arising from gene networks can restrict this availability. However, the extent to which networks affect adaptation remains largely unknown. Current models of evolution consider additive genotype-phenotype relationships while often ignoring the contribution of gene interactions to phenotypic variance. In this study, we model a quantitative trait as the product of a simple gene regulatory network, the negative autoregulation motif. Using forward-time genetic simulations, we measure adaptive walks towards a phenotypic optimum in both additive and network models. A key expectation from adaptive walk theory is that the distribution of fitness effects of new beneficial mutations is exponential. We found that both models instead harbored distributions with fewer large-effect beneficial alleles than expected. The network model also had a complex and bimodal distribution of fitness effects among all mutations, with a considerable density at deleterious selection coefficients. This behavior is reminiscent of the cost of complexity, where correlations among traits constrain adaptation. Our results suggest that the interactions emerging from genetic networks can generate complex and multimodal distributions of fitness effects.

Maintaining Transient Diversity Is a General Principle for Improving Collective Problem Solving

Humans regularly solve complex problems in cooperative teams. A wide range of mechanisms have been identified that improve the quality of solutions achieved by those teams on reaching consensus. We argue that many of these mechanisms work via increasing the transient diversity of solutions while the group attempts to reach a consensus. These mechanisms can operate at the level of individual psychology (e.g., behavioral inertia), interpersonal communication (e.g., transmission noise), or group structure (e.g., sparse social networks). Transient diversity can be increased by widening the search space of possible solutions or by slowing the diffusion of information and delaying consensus. All of these mechanisms increase the quality of the solution at the cost of increased time to reach it. We review specific mechanisms that facilitate transient diversity and synthesize evidence from both empirical studies and diverse formal models-including multiarmed bandits, NK landscapes, cumulative-innovation models, and evolutionary-transmission models. Apparent exceptions to this principle occur primarily when problems are sufficiently simple that they can be solved by mere trial and error or when the incentives of team members are insufficiently aligned. This work has implications for our understanding of collective intelligence, problem solving, innovation, and cumulative cultural evolution.

How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution

The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population's mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.

Moderating the neutralist-selectionist debate: exactly which propositions are we debating, and which arguments are valid?

Half a century after its foundation, the neutral theory of molecular evolution continues to attract controversy. The debate has been hampered by the coexistence of different interpretations of the core proposition of the neutral theory, the 'neutral mutation-random drift' hypothesis. In this review, we trace the origins of these ambiguities and suggest potential solutions. We highlight the difference between the original, the revised and the nearly neutral hypothesis, and re-emphasise that none of them equates to the null hypothesis of strict neutrality. We distinguish the neutral hypothesis of protein evolution, the main focus of the ongoing debate, from the neutral hypotheses of genomic and functional DNA evolution, which for many species are generally accepted. We advocate a further distinction between a narrow and an extended neutral hypothesis (of which the latter posits that random non-conservative amino acid substitutions can cause non-ecological phenotypic divergence), and we discuss the implications for evolutionary biology beyond the domain of molecular evolution. We furthermore point out that the debate has widened from its initial focus on point mutations, and also concerns the fitness effects of large-scale mutations, which can alter the dosage of genes and regulatory sequences. We evaluate the validity of neutralist and selectionist arguments and find that the tested predictions, apart from being sensitive to violation of underlying assumptions, are often derived from the null hypothesis of strict neutrality, or equally consistent with the opposing selectionist hypothesis, except when assuming molecular panselectionism. Our review aims to facilitate a constructive neutralist-selectionist debate, and thereby to contribute to answering a key question of evolutionary biology: what proportions of amino acid and nucleotide substitutions and polymorphisms are adaptive?

Network structure shapes the impact of diversity in collective learning

It is widely believed that diversity arising from different skills enhances the performance of teams, and in particular, their ability to learn and innovate. However, diversity has also been associated with negative effects on the communication and coordination within collectives. Yet, despite the importance of diversity as a concept, we still lack a mechanistic understanding of how its impact is shaped by the underlying social network. To fill this gap, we model skill diversity within a simple model of collective learning and show that its effect on collective performance differs depending on the complexity of the task and the network density. In particular, we find that diversity consistently impairs performance in simple tasks. In contrast, in complex tasks, link density modifies the effect of diversity: while homogeneous populations outperform diverse ones in sparse networks, the opposite is true in dense networks, where diversity boosts collective performance. Our findings also provide insight on how to forge teams in an increasingly interconnected world: the more we are connected, the more we can benefit from diversity to solve complex problems.

Slow closure of Earth's carbon cycle

Carbon near the Earth's surface cycles between the production and consumption of organic carbon; the former sequesters carbon dioxide while the latter releases it. Microbes attempt to close the loop, but the longer organic matter survives, the slower microbial degradation becomes. This aging effect leaves observable quantitative signatures: Organic matter decays at rates that are inversely proportional to its age, while microbial populations and concentrations of organic carbon in ocean sediments decrease at distinct powers of age. Yet mechanisms that predict this collective organization remain unknown. Here, I show that these and other observations follow from the assumption that the decay of organic matter is limited by progressively rare extreme fluctuations in the energy available to microbes for decomposition. The theory successfully predicts not only observed scaling exponents but also a previously unobserved scaling regime that emerges when microbes subsist on the minimum energy flux required for survival. The resulting picture suggests that the carbon cycle's age-dependent dynamics are analogous to the slow approach to equilibrium in disordered systems. The impact of these slow dynamics is profound: They preclude complete oxidation of organic carbon in sediments, thereby freeing molecular oxygen to accumulate in the atmosphere.

Laboratory Evolution of Antimicrobial Resistance in Bacteria to Develop Rational Treatment Strategies

Laboratory evolution studies, particularly with Escherichia coli, have yielded invaluable insights into the mechanisms of antimicrobial resistance (AMR). Recent investigations have illuminated that, with repetitive antibiotic exposures, bacterial populations will adapt and eventually become tolerant and resistant to the drugs. Through intensive analyses, these inquiries have unveiled instances of convergent evolution across diverse antibiotics, the pleiotropic effects of resistance mutations, and the role played by loss-of-function mutations in the evolutionary landscape. Moreover, a quantitative analysis of multidrug combinations has shed light on collateral sensitivity, revealing specific drug combinations capable of suppressing the acquisition of resistance. This review article introduces the methodologies employed in the laboratory evolution of AMR in bacteria and presents recent discoveries concerning AMR mechanisms derived from laboratory evolution. Additionally, the review outlines the application of laboratory evolution in endeavors to formulate rational treatment strategies.

Using design of experiments to guide genetic optimization of engineered metabolic pathways

Design of experiments (DoE) is a term used to describe the application of statistical approaches to interrogate the impact of many variables on the performance of a multivariate system. It is commonly used for process optimization in fields such as chemical engineering and material science. Recent advances in the ability to quantitatively control the expression of genes in biological systems open up the possibility to apply DoE for genetic optimization. In this review targeted to genetic and metabolic engineers, we introduce several approaches in DoE at a high level and describe instances wherein these were applied to interrogate or optimize engineered genetic systems. We discuss the challenges of applying DoE and propose strategies to mitigate these challenges.

ONE-SENTENCE SUMMARY

This is a review of literature related to applying Design of Experiments for genetic optimization.

Drift on holey landscapes as a dominant evolutionary process

An organism's phenotype has been shaped by evolution but the specific processes have to be indirectly inferred for most species. For example, correlations among traits imply the historical action of correlated selection and, more generally, the expression and distribution of traits is expected to be reflective of the adaptive landscapes that have shaped a population. However, our expectations about how quantitative traits-like most behaviors, physiological processes, and life-history traits-should be distributed under different evolutionary processes are not clear. Here, we show that genetic variation in quantitative traits is not distributed as would be expected under dominant evolutionary models. Instead, we found that genetic variation in quantitative traits across six phyla and 60 species (including both Plantae and Animalia) is consistent with evolution across high-dimensional "holey landscapes." This suggests that the leading conceptualizations and modeling of the evolution of trait integration fail to capture how phenotypes are shaped and that traits are integrated in a manner contrary to predictions of dominant evolutionary theory. Our results demonstrate that our understanding of how evolution has shaped phenotypes remains incomplete and these results provide a starting point for reassessing the relevance of existing evolutionary models.

Master regulators of biological systems in higher dimensions

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present, generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g., the rbs locus and pykF) and species (e.g., Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide a method and mathematical justification for exploration of biological networks in higher dimensions.

A rugged yet easily navigable fitness landscape

Fitness landscape theory predicts that rugged landscapes with multiple peaks impair Darwinian evolution, but experimental evidence is limited. In this study, we used genome editing to map the fitness of >260,000 genotypes of the key metabolic enzyme dihydrofolate reductase in the presence of the antibiotic trimethoprim, which targets this enzyme. The resulting landscape is highly rugged and harbors 514 fitness peaks. However, its highest peaks are accessible to evolving populations via abundant fitness-increasing paths. Different peaks share large basins of attraction that render the outcome of adaptive evolution highly contingent on chance events. Our work shows that ruggedness need not be an obstacle to Darwinian evolution but can reduce its predictability. If true in general, the complexity of optimization problems on realistic landscapes may require reappraisal.

Statistically learning the functional landscape of microbial communities

Microbial consortia exhibit complex functional properties in contexts ranging from soils to bioreactors to human hosts. Understanding how community composition determines function is a major goal of microbial ecology. Here we address this challenge using the concept of community-function landscapes-analogues to fitness landscapes-that capture how changes in community composition alter collective function. Using datasets that represent a broad set of community functions, from production/degradation of specific compounds to biomass generation, we show that statistically inferred landscapes quantitatively predict community functions from knowledge of species presence or absence. Crucially, community-function landscapes allow prediction without explicit knowledge of abundance dynamics or interactions between species and can be accurately trained using measurements from a small subset of all possible community compositions. The success of our approach arises from the fact that empirical community-function landscapes appear to be not rugged, meaning that they largely lack high-order epistatic contributions that would be difficult to fit with limited data. Finally, we show that this observation holds across a wide class of ecological models, suggesting community-function landscapes can be efficiently inferred across a broad range of ecological regimes. Our results open the door to the rational design of consortia without detailed knowledge of abundance dynamics or interactions.

Phenotype switching of the mutation rate facilitates adaptive evolution

The mutation rate plays an important role in adaptive evolution. It can be modified by mutator and anti-mutator alleles. Recent empirical evidence hints that the mutation rate may vary among genetically identical individuals: evidence from bacteria suggests that the mutation rate can be affected by expression noise of a DNA repair protein and potentially also by translation errors in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to a mutator phenotype that is independent from mutator alleles. Here, we investigate mathematically how the rate of adaptive evolution is affected by the rate of mutation rate phenotype switching. We model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. We find that switching rates that correspond to so-far empirically described non-genetic systems of inheritance of the mutation rate lead to higher rates of adaptation on both artificial and natural fitness landscapes. These switching rates can maintain within the same individuals both a mutator phenotype and intermediary mutations, a combination that facilitates adaptation. Moreover, non-genetic inheritance increases the proportion of mutators in the population, which in turn increases the probability of hitchhiking of the mutator phenotype with adaptive mutations. This in turns facilitates the acquisition of additional adaptive mutations. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.

Genetic Architecture of Flowering Time Differs Between Populations With Contrasting Demographic and Selective Histories

Understanding the evolutionary factors that impact the genetic architecture of traits is a central goal of evolutionary genetics. Here, we investigate how quantitative trait variation accumulated over time in populations that colonized a novel environment. We compare the genetic architecture of flowering time in Arabidopsis populations from the drought-prone Cape Verde Islands and their closest outgroup population from North Africa. We find that trait polygenicity is severely reduced in the island populations compared to the continental North African population. Further, trait architectures and reconstructed allelic histories best fit a model of strong directional selection in the islands in accord with a Fisher-Orr adaptive walk. Consistent with this, we find that large-effect variants that disrupt major flowering time genes (FRI and FLC) arose first, followed by smaller effect variants, including ATX2 L125F, which is associated with a 4-day reduction in flowering time. The most recently arising flowering time-associated loci are not known to be directly involved in flowering time, consistent with an omnigenic signature developing as the population approaches its trait optimum. Surprisingly, we find no effect in the natural population of EDI-Cvi-0 (CRY2 V367M), an allele for which an effect was previously validated by introgression into a Eurasian line. Instead, our results suggest the previously observed effect of the EDI-Cvi-0 allele on flowering time likely depends on genetic background, due to an epistatic interaction. Altogether, our results provide an empirical example of the effects demographic history and selection has on trait architecture.

Impact of population size on early adaptation in rugged fitness landscapes

Owing to stochastic fluctuations arising from finite population size, known as genetic drift, the ability of a population to explore a rugged fitness landscape depends on its size. In the weak mutation regime, while the mean steady-state fitness increases with population size, we find that the height of the first fitness peak encountered when starting from a random genotype displays various behaviours versus population size, even among small and simple rugged landscapes. We show that the accessibility of the different fitness peaks is key to determining whether this height overall increases or decreases with population size. Furthermore, there is often a finite population size that maximizes the height of the first fitness peak encountered when starting from a random genotype. This holds across various classes of model rugged landscapes with sparse peaks, and in some experimental and experimentally inspired ones. Thus, early adaptation in rugged fitness landscapes can be more efficient and predictable for relatively small population sizes than in the large-size limit.

This article is part of the theme issue ‘Interdisciplinary approaches to predicting evolutionary biology’.

A Generalised Dropout Mechanism for Distributed Systems

This letter uses a modified form of the NK model introduced to explore aspects of distributed control. In particular, a previous result suggesting the use of dynamically formed subgroups within the overall system can be more effective than global control is further explored. The conditions under which the beneficial distributed control emerges are more clearly identified, and the reason for the benefit over traditional global control is suggested as a generally applicable dropout mechanism to improve learning in such systems.

Geometry of fitness landscapes: peaks, shapes and universal positive epistasis

Darwinian evolution is driven by random mutations, genetic recombination (gene shuffling) and selection that favors genotypes with high fitness. For systems where each genotype can be represented as a bitstring of length L, an overview of possible evolutionary trajectories is provided by the L-cube graph with nodes labeled by genotypes and edges directed toward the genotype with higher fitness. Peaks (sinks in the graphs) are important since a population can get stranded at a suboptimal peak. The fitness landscape is defined by the fitness values of all genotypes in the system. Some notion of curvature is necessary for a more complete analysis of the landscapes, including the effect of recombination. The shape approach uses triangulations (shapes) induced by fitness landscapes. The main topic for this work is the interplay between peak patterns and shapes. Because of constraints on the shapes for [Formula: see text] imposed by peaks, there are in total 25 possible combinations of peak patterns and shapes. Similar constraints exist for higher L. Specifically, we show that the constraints induced by the staircase triangulation can be formulated as a condition of universal positive epistasis, an order relation on the fitness effects of arbitrary sets of mutations that respects the inclusion relation between the corresponding genetic backgrounds. We apply the concept to a large protein fitness landscape for an immunoglobulin-binding protein expressed in Streptococcal bacteria.

Host heterogeneity and epistasis explain punctuated evolution of SARS-CoV-2

Identifying drivers of viral diversity is key to understanding the evolutionary as well as epidemiological dynamics of the COVID-19 pandemic. Using rich viral genomic data sets, we show that periods of steadily rising diversity have been punctuated by sudden, enormous increases followed by similarly abrupt collapses of diversity. We introduce a mechanistic model of saltational evolution with epistasis and demonstrate that these features parsimoniously account for the observed temporal dynamics of inter-genomic diversity. Our results provide support for recent proposals that saltational evolution may be a signature feature of SARS-CoV-2, allowing the pathogen to more readily evolve highly transmissible variants. These findings lend theoretical support to a heightened awareness of biological contexts where increased diversification may occur. They also underline the power of pathogen genomics and other surveillance streams in clarifying the phylodynamics of emerging and endemic infections. In public health terms, our results further underline the importance of equitable distribution of up-to-date vaccines.

Group Structure and Information Distribution on the Emergence of Collective Intelligence

More and more decision-making problems are being solved by groups. Collective intelligence is the ability of groups to perform well when solving complex problems. Thus, it is important to encourage collective intelligence to emerge from groups. In this study, we explore how two critical characteristics of groups, that is, group structure and individual knowledge in groups, influence the emergence of collective intelligence. To do this, we propose a measure for group structure using the collaboration network of a group and a measure for the distribution of individual knowledge in groups. Group structure is measured based on the intensities of links and whether the network is hierarchical or flat. The distribution of individual knowledge is measured from the perspective of whether group information is shared or unique. Social interactions among group members and individual changes in opinion are modeled based on a simulation technique. We find that unbalanced information distribution undermines group performance, whereas group structure can modify the effect of information distribution. We also find that groups with broadly distributed knowledge are good at solving complex problems.

Funding: This work was supported by the National Natural Science Foundation of China [Grants 72171158, 71771156 and 71971145].

Supply-driven evolution: Mutation bias and trait-fitness distributions can drive macro-evolutionary dynamics

Many well-documented macro-evolutionary phenomena still challenge current evolutionary theory. Examples include long-term evolutionary trends, major transitions in evolution, conservation of certain biological features such as hox genes, and the episodic creation of new taxa. Here, we present a framework that may explain these phenomena. We do so by introducing a probabilistic relationship between trait value and reproductive fitness. This integration allows mutation bias to become a robust driver of long-term evolutionary trends against environmental bias, in a way that is consistent with all current evolutionary theories. In cases where mutation bias is strong, such as when detrimental mutations are more common than beneficial mutations, a regime called “supply-driven” evolution can arise. This regime can explain the irreversible persistence of higher structural hierarchies, which happens in the major transitions in evolution. We further generalize this result in the long-term dynamics of phenotype spaces. We show how mutations that open new phenotype spaces can become frozen in time. At the same time, new possibilities may be observed as a burst in the creation of new taxa.

Ecological landscapes guide the assembly of optimal microbial communities

Assembling optimal microbial communities is key for various applications in biofuel production, agriculture, and human health. Finding the optimal community is challenging because the number of possible communities grows exponentially with the number of species, and so an exhaustive search cannot be performed even for a dozen species. A heuristic search that improves community function by adding or removing one species at a time is more practical, but it is unknown whether this strategy can discover an optimal or nearly optimal community. Using consumer-resource models with and without cross-feeding, we investigate how the efficacy of search depends on the distribution of resources, niche overlap, cross-feeding, and other aspects of community ecology. We show that search efficacy is determined by the ruggedness of the appropriately-defined ecological landscape. We identify specific ruggedness measures that are both predictive of search performance and robust to noise and low sampling density. The feasibility of our approach is demonstrated using experimental data from a soil microbial community. Overall, our results establish the conditions necessary for the success of the heuristic search and provide concrete design principles for building high-performing microbial consortia.

Accessibility percolation on Cartesian power graphs

A fitness landscape is a mapping from a space of discrete genotypes to the real numbers. A path in a fitness landscape is a sequence of genotypes connected by single mutational steps. Such a path is said to be accessible if the fitness values of the genotypes encountered along the path increase monotonically. We study accessible paths on random fitness landscapes of the House-of-Cards type, on which fitness values are independent, identically and continuously distributed random variables. The genotype space is taken to be a Cartesian power graph [Formula: see text], where [Formula: see text] is the number of genetic loci and the allele graph [Formula: see text] encodes the possible allelic states and mutational transitions on one locus. The probability of existence of accessible paths between two genotypes at a distance linear in [Formula: see text] displays a transition from 0 to a positive value at a threshold [Formula: see text] for the fitness difference between the initial and final genotype. We derive a lower bound on [Formula: see text] for general [Formula: see text] and show that this bound is tight for a large class of allele graphs. Our results generalize previous results for accessibility percolation on the biallelic hypercube, and compare favorably to published numerical results for multiallelic Hamming graphs.

Analysis of the evolution of resistance to multiple antibiotics enables prediction of the Escherichia coli phenotype-based fitness landscape

The fitness landscape represents the complex relationship between genotype or phenotype and fitness under a given environment, the structure of which allows the explanation and prediction of evolutionary trajectories. Although previous studies have constructed fitness landscapes by comprehensively studying the mutations in specific genes, the high dimensionality of genotypic changes prevents us from developing a fitness landscape capable of predicting evolution for the whole cell. Herein, we address this problem by inferring the phenotype-based fitness landscape for antibiotic resistance evolution by quantifying the multidimensional phenotypic changes, i.e., time-series data of resistance for eight different drugs. We show that different peaks of the landscape correspond to different drug resistance mechanisms, thus supporting the validity of the inferred phenotype-fitness landscape. We further discuss how inferred phenotype-fitness landscapes could contribute to the prediction and control of evolution. This approach bridges the gap between phenotypic/genotypic changes and fitness while contributing to a better understanding of drug resistance evolution.

Rate of environmental variation impacts the predictability in evolution

In the two last decades, we have improved our understanding of the adaptive evolution of natural populations under constant and stable environments. For instance, experimental methods from evolutionary biology have allowed us to explore the structure of fitness landscapes and survey how the landscape properties can constrain the adaptation process. However, understanding how environmental changes can affect adaptation remains challenging. Very little progress has been made with respect to time-varying fitness landscapes. Using the adaptive-walk approximation, we survey the evolutionary process of populations under a scenario of environmental variation. In particular, we investigate how the rate of environmental variation influences the predictability in evolution. We observe that the rate of environmental variation not only changes the duration of adaptive walks towards fitness peaks of the fitness landscape, but also affects the degree of repeatability of both outcomes and evolutionary paths. In general, slower environmental variation increases the predictability in evolution. The accessibility of endpoints is greatly influenced by the ecological dynamics. The dependence of these quantities on the genome size and number of traits is also addressed. To our knowledge, this contribution is the first to use the predictive approach to quantify and understand the impact of the speed of environmental variation on the degree of parallelism of the evolutionary process.

Getting higher on rugged landscapes: Inversion mutations open access to fitter adaptive peaks in NK fitness landscapes

Molecular evolution is often conceptualised as adaptive walks on rugged fitness landscapes, driven by mutations and constrained by incremental fitness selection. It is well known that epistasis shapes the ruggedness of the landscape’s surface, outlining their topography (with high-fitness peaks separated by valleys of lower fitness genotypes). However, within the strong selection weak mutation (SSWM) limit, once an adaptive walk reaches a local peak, natural selection restricts passage through downstream paths and hampers any possibility of reaching higher fitness values. Here, in addition to the widely used point mutations, we introduce a minimal model of sequence inversions to simulate adaptive walks. We use the well known NK model to instantiate rugged landscapes. We show that adaptive walks can reach higher fitness values through inversion mutations, which, compared to point mutations, allows the evolutionary process to escape local fitness peaks. To elucidate the effects of this chromosomal rearrangement, we use a graph-theoretical representation of accessible mutants and show how new evolutionary paths are uncovered. The present model suggests a simple mechanistic rationale to analyse escapes from local fitness peaks in molecular evolution driven by (intragenic) structural inversions and reveals some consequences of the limits of point mutations for simulations of molecular evolution.

Ninety years ago, Wright translated Darwin’s core idea of survival of the fittest into rugged landscapes—a highly influential metaphor—with peaks representing high values of fitness separated by valleys of lower fitness. In this picture, once a population has reached a local peak, the adaptive dynamics may stall as further adaptation requires crossing a valley. At the DNA level, adaptation is often modelled as a space of genotypes that is explored through point mutations. Therefore, once a local peak is reached, any genotype fitter than that of the peak will be away from the neighbourhood of genotypes accessible through point mutations. Here we present a simple computational model for inversion mutations, one of the most frequent structural variations, and show that adaptive processes in rugged landscapes can escape from local peaks through intragenic inversion mutations. This new escape mechanism reveals the innovative role of inversions at the DNA level and provides a step towards more realistic models of adaptive dynamics, beyond the dominance of point mutations in theories of molecular evolution.

Intragenic compensation through the lens of deep mutational scanning

A significant fraction of mutations in proteins are deleterious and result in adverse consequences for protein function, stability, or interaction with other molecules. Intragenic compensation is a specific case of positive epistasis when a neutral missense mutation cancels effect of a deleterious mutation in the same protein. Permissive compensatory mutations facilitate protein evolution, since without them all sequences would be extremely conserved. Understanding compensatory mechanisms is an important scientific challenge at the intersection of protein biophysics and evolution. In human genetics, intragenic compensatory interactions are important since they may result in variable penetrance of pathogenic mutations or fixation of pathogenic human alleles in orthologous proteins from related species. The latter phenomenon complicates computational and clinical inference of an allele's pathogenicity. Deep mutational scanning is a relatively new technique that enables experimental studies of functional effects of thousands of mutations in proteins. We review the important aspects of the field and discuss existing limitations of current datasets. We reviewed ten published DMS datasets with quantified functional effects of single and double mutations and described rates and patterns of intragenic compensation in eight of them.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12551-022-01005-w.

Rebiasing: Managing automatic biases over time

Automatic preferences can influence a decision maker's choice before any relevant or meaningful information is available. We account for this element of human cognition in a computational model of problem solving that involves active trial and error and show that automatic biases are not just a beneficial or detrimental property: they are a tool that, if properly managed over time, can give rise to superior performance. In particular, automatic preferences are beneficial early on and detrimental at later stages. What is more, additional value can be generated by a timely rebiasing, i.e., a calculated reversal of the initial automatic preference. Remarkably, rebiasing can dominate not only debiasing (i.e., eliminating the bias) but also continuously unbiased decision making. This research contributes to the debate on the adaptiveness of automatic and intuitive biases, which has centered primarily on one-shot controlled laboratory experiments, by simulating outcomes across extended time spans. We also illustrate the value of the novel intervention of adopting the opposite automatic preference-something organizations can readily achieve by changing key decision makers-as opposed to attempting to correct for or simply accepting the ubiquity of such biases.

The structure of genotype-phenotype maps makes fitness landscapes navigable

Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution.

Fitness landscape analysis of a tRNA gene reveals that the wild type allele is sub-optimal, yet mutationally robust

Fitness landscape mapping and the prediction of evolutionary trajectories on these landscapes are major tasks in evolutionary biology research. Evolutionary dynamics is tightly linked to the landscape topography, but this relation is not straightforward. Here, we analyze a fitness landscape of a yeast tRNA gene, previously measured under four different conditions. We find that the wild type allele is sub-optimal, and 8–10% of its variants are fitter. We rule out the possibilities that the wild type is fittest on average on these four conditions or located on a local fitness maximum. Notwithstanding, we cannot exclude the possibility that the wild type might be fittest in some of the many conditions in the complex ecology that yeast lives at. Instead, we find that the wild type is mutationally robust (“flat”), while more fit variants are typically mutationally fragile. Similar observations of mutational robustness or flatness have been so far made in very few cases, predominantly in viral genomes.

Immune Heterogeneity and Epistasis Explain Punctuated Evolution of SARS-CoV-2

Identifying drivers of viral diversity is key to understanding the evolutionary as well as epidemiological dynamics of the COVID-19 pandemic. Using rich viral genomic data sets, we show that periods of steadily rising diversity have been punctuated by sudden, enormous increases followed by similarly abrupt collapses of diversity. We introduce a mechanistic model of saltational evolution with epistasis and demonstrate that these features parsimoniously account for the observed temporal dynamics of inter-genomic diversity. Our results provide support for recent proposals that saltational evolution may be a signature feature of SARS-CoV-2, allowing the pathogen to more readily evolve highly transmissible variants. These findings lend theoretical support to a heightened awareness of biological contexts where increased diversification may occur. They also underline the power of pathogen genomics and other surveillance streams in clarifying the phylodynamics of emerging and endemic infections. In public health terms, our results further underline the importance of equitable distribution of up-to-date vaccines.

From vesicles toward protocells and minimal cells

In contrast to ordinary condensed matter systems, "living systems" are unique. They are based on molecular compartments that reproduce themselves through (i) an uptake of ingredients and energy from the environment, and (ii) spatially and timely coordinated internal chemical transformations. These occur on the basis of instructions encoded in information molecules (DNAs). Life originated on Earth about 4 billion years ago as self-organised systems of inorganic compounds and organic molecules including macromolecules (e.g. nucleic acids and proteins) and low molar mass amphiphiles (lipids). Before the first living systems emerged from non-living forms of matter, functional molecules and dynamic molecular assemblies must have been formed as prebiotic soft matter systems. These hypothetical cell-like compartment systems often are called "protocells". Other systems that are considered as bridging units between non-living and living systems are called "minimal cells". They are synthetic, autonomous and sustainable reproducing compartment systems, but their constituents are not limited to prebiotic substances. In this review, we focus on both membrane-bounded (vesicular) protocells and minimal cells, and provide a membrane physics background which helps to understand how morphological transformations of vesicle systems might have happened and how vesicle reproduction might be coupled with metabolic reactions and information molecules. This research, which bridges matter and life, is a great challenge in which soft matter physics, systems chemistry, and synthetic biology must take joined efforts to better understand how the transformation of protocells into living systems might have occurred at the origin of life.

Modelling the fitness landscapes of a SCRaMbLEd yeast genome

The use of microorganisms for the production of industrially important compounds and enzymes is becoming increasingly important. Eukaryotes have been less widely used than prokaryotes in biotechnology, because of the complexity of their genomic structure and biology. The Yeast2.0 project is an international effort to engineer the yeast Saccharomyces cerevisiae to make it easy to manipulate, and to generate random variants using a system called SCRaMbLE. SCRaMbLE relies on artificial evolution in vitro to identify useful variants, an approach which is time consuming and expensive. We developed an in silico simulator for the SCRaMbLE system, using an evolutionary computing approach, which can be used to investigate and optimize the fitness landscape of the system. We applied the system to the investigation of the fitness landscape of one of the S. saccharomyces chromosomes, and found that our results fitted well with those previously published. We then simulated directed evolution with or without manipulation of SCRaMbLE, and revealed that controlling the SCRaMbLE process could effectively impact directed evolution. Our simulator can be applied to the analysis of the fitness landscapes of any organism for which SCRaMbLE has been implemented.

Hybridization alters the shape of the genotypic fitness landscape, increasing access to novel fitness peaks during adaptive radiation

Estimating the complex relationship between fitness and genotype or phenotype (i.e. the adaptive landscape) is one of the central goals of evolutionary biology. However, adaptive walks connecting genotypes to organismal fitness, speciation, and novel ecological niches are still poorly understood and processes for surmounting fitness valleys remain controversial. One outstanding system for addressing these connections is a recent adaptive radiation of ecologically and morphologically novel pupfishes (a generalist, molluscivore, and scale-eater) endemic to San Salvador Island, Bahamas. We leveraged whole-genome sequencing of 139 hybrids from two independent field fitness experiments to identify the genomic basis of fitness, estimate genotypic fitness networks, and measure the accessibility of adaptive walks on the fitness landscape. We identified 132 single nucleotide polymorphisms (SNPs) that were significantly associated with fitness in field enclosures. Six out of the 13 regions most strongly associated with fitness contained differentially expressed genes and fixed SNPs between trophic specialists; one gene (mettl21e) was also misexpressed in lab-reared hybrids, suggesting a potential intrinsic genetic incompatibility. We then constructed genotypic fitness networks from adaptive alleles and show that scale-eating specialists are the most isolated of the three species on these networks. Intriguingly, introgressed and de novo variants reduced fitness landscape ruggedness as compared to standing variation, increasing the accessibility of genotypic fitness paths from generalist to specialists. Our results suggest that adaptive introgression and de novo mutations alter the shape of the fitness landscape, providing key connections in adaptive walks circumventing fitness valleys and triggering the evolution of novelty during adaptive radiation.

A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and "ruggedness". As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population's evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.

The new paradigm of economic complexity

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Economic complexity offers a potentially powerful paradigm to understand key societal issues and challenges of our time.

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This brief introduction to economic complexity summarizes key theoretical foundations and principles of economic complexity.

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It also reviews the tools and metrics developed in the economic complexity literature that exploit information encoded in the structure of the economy to find new empirical patterns.

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It finally aims is to highlight the insights from economic complexity to improve political decision-making.

Economic complexity offers a potentially powerful paradigm to understand key societal issues and challenges of our time. The underlying idea is that growth, development, technological change, income inequality, spatial disparities, and resilience are the visible outcomes of hidden systemic interactions. The study of economic complexity seeks to understand the structure of these interactions and how they shape various socioeconomic processes. This emerging field relies heavily on big data and machine learning techniques. This brief introduction to economic complexity has three aims. The first is to summarize key theoretical foundations and principles of economic complexity. The second is to briefly review the tools and metrics developed in the economic complexity literature that exploit information encoded in the structure of the economy to find new empirical patterns. The final aim is to highlight the insights from economic complexity to improve prediction and political decision-making. Institutions including the World Bank, the European Commission, the World Economic Forum, the OECD, and a range of national and regional organizations have begun to embrace the principles of economic complexity and its analytical framework. We discuss policy implications of this field, in particular the usefulness of building recommendation systems for major public investment decisions in a complex world.

Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution

The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.

Living systems are products of evolution, and their present forms reflect their evolutionary history. Thus, to investigate the particularity of the evolutionary process by computer simulations, an appropriate reference system is needed for comparison with the outcomes of evolutionary simulations. In this study, we considered a model of gene regulatory networks (GRNs). Our idea was to construct a reference ensemble comprising randomly generated GRNs. To produce GRNs with high fitness values, which are rare, we employed a “rare event sampling” method developed in statistical physics. In particular, we focused on the evolution of mutational robustness. Living systems do not lose viability readily, even when some genes are mutated. This trait, called mutational robustness, has developed throughout evolution, along with functionality. Using the abovementioned method, we found that mutational robustness resulting from evolution exceeded that of the reference set. Therefore, mutational robustness is enhanced by evolution. We also found that the emergence of a new phenotype was significantly delayed in evolution. Our results suggest that this delay is a consequence of the fact that mutationally robust GRNs are favored by evolution.

On the sparsity of fitness functions and implications for learning

The properties of proteins and other biological molecules are encoded in large part in the sequence of amino acids or nucleotides that defines them. Increasingly, researchers estimate functions that map sequences to a particular property using machine learning and related statistical approaches. However, an important question remains unanswered: How many experimental measurements are needed in order to accurately learn these “fitness” functions? We leverage perspectives from the fields of biophysics, evolutionary biology, and signal processing to develop a theoretical framework that enables us to make progress on answering this question. We demonstrate that this framework can be used to make useful calculations on real-world data and suggest how these calculations may be used to guide experiments.

Fitness functions map biological sequences to a scalar property of interest. Accurate estimation of these functions yields biological insight and sets the foundation for model-based sequence design. However, the fitness datasets available to learn these functions are typically small relative to the large combinatorial space of sequences; characterizing how much data are needed for accurate estimation remains an open problem. There is a growing body of evidence demonstrating that empirical fitness functions display substantial sparsity when represented in terms of epistatic interactions. Moreover, the theory of Compressed Sensing provides scaling laws for the number of samples required to exactly recover a sparse function. Motivated by these results, we develop a framework to study the sparsity of fitness functions sampled from a generalization of the NK model, a widely used random field model of fitness functions. In particular, we present results that allow us to test the effect of the Generalized NK (GNK) model’s interpretable parameters—sequence length, alphabet size, and assumed interactions between sequence positions—on the sparsity of fitness functions sampled from the model and, consequently, the number of measurements required to exactly recover these functions. We validate our framework by demonstrating that GNK models with parameters set according to structural considerations can be used to accurately approximate the number of samples required to recover two empirical protein fitness functions and an RNA fitness function. In addition, we show that these GNK models identify important higher-order epistatic interactions in the empirical fitness functions using only structural information.

When to Be Critical? Performance and Evolvability in Different Regimes of Neural Ising Agents

It has long been hypothesized that operating close to the critical state is beneficial for natural and artificial evolutionary systems. We put this hypothesis to test in a system of evolving foraging agents controlled by neural networks that can adapt the agents' dynamical regime throughout evolution. Surprisingly, we find that all populations that discover solutions evolve to be subcritical. By a resilience analysis, we find that there are still benefits of starting the evolution in the critical regime. Namely, initially critical agents maintain their fitness level under environmental changes (for example, in the lifespan) and degrade gracefully when their genome is perturbed. At the same time, initially subcritical agents, even when evolved to the same fitness, are often inadequate to withstand the changes in the lifespan and degrade catastrophically with genetic perturbations. Furthermore, we find the optimal distance to criticality depends on the task complexity. To test it we introduce a hard task and a simple task: For the hard task, agents evolve closer to criticality, whereas more subcritical solutions are found for the simple task. We verify that our results are independent of the selected evolutionary mechanisms by testing them on two principally different approaches: a genetic algorithm and an evolutionary strategy. In summary, our study suggests that although optimal behaviour in the simple task is obtained in a subcritical regime, initializing near criticality is important to be efficient at finding optimal solutions for new tasks of unknown complexity.

On the Fourier transform of a quantitative trait: Implications for compressive sensing

This paper explores the genotype-phenotype relationship. It outlines conditions under which the dependence of a quantitative trait on the genome might be predictable, based on measurement of a limited subset of genotypes. It uses the theory of real-valued Boolean functions in a systematic way to translate trait data into the Fourier domain. Important trait features, such as the roughness of the trait landscape or the modularity of a trait have a simple Fourier interpretation. Roughness at a gene location corresponds to high sensitivity to mutation, while a modular organization of gene activity reduces such sensitivity. Traits where rugged loci are rare will naturally compress gene data in the Fourier domain, leading to a sparse representation of trait data, concentrated in identifiable, low-level coefficients. This Fourier representation of a trait organizes epistasis in a form which is isometric to the trait data. As Fourier matrices are known to be maximally incoherent with the standard basis, this permits employing compressive sensing techniques to work from data sets that are relatively small-sometimes even of polynomial size-compared to the exponentially large sets of possible genomes. This theory provides a theoretical underpinning for systematic use of Boolean function machinery to dissect the dependency of a trait on the genome and environment.

Both Binding Strength and Evolutionary Accessibility Affect the Population Frequency of Transcription Factor Binding Sequences in Arabidopsis thaliana

Mutations in DNA sequences that bind transcription factors and thus modulate gene expression are a source of adaptive variation in gene expression. To understand how transcription factor binding sequences evolve in natural populations of the thale cress Arabidopsis thaliana, we integrated genomic polymorphism data for loci bound by transcription factors with in vitro data on binding affinity for these transcription factors. Specifically, we studied 19 different transcription factors, and the allele frequencies of 8,333 genomic loci bound in vivo by these transcription factors in 1,135 A. thaliana accessions. We find that transcription factor binding sequences show very low genetic diversity, suggesting that they are subject to purifying selection. High frequency alleles of such binding sequences tend to bind transcription factors strongly. Conversely, alleles that are absent from the population tend to bind them weakly. In addition, alleles with high frequencies also tend to be the endpoints of many accessible evolutionary paths leading to these alleles. We show that both high affinity and high evolutionary accessibility contribute to high allele frequency for at least some transcription factors. Although binding sequences with stronger affinity are more frequent, we did not find them to be associated with higher gene expression levels. Epistatic interactions among individual mutations that alter binding affinity are pervasive and can help explain variation in accessibility among binding sequences. In summary, combining in vitro binding affinity data with in vivo binding sequence data can help understand the forces that affect the evolution of transcription factor binding sequences in natural populations.

Are Artificial Dendrites Useful in Neuro-Evolution?

The significant role of dendritic processing within neuronal networks has become increasingly clear. This letter explores the effects of including a simple dendrite-inspired mechanism into neuro-evolution. The phenomenon of separate dendrite activation thresholds on connections is allowed to emerge under an evolutionary process. It is shown how such processing can be positively selected for, particularly for connections between the hidden and output layers, and increases performance.