Genotype Space Research Articles

Constraint and contingency in multifunctional gene regulatory circuits.

Gene regulatory circuits drive the development, physiology, and behavior of organisms from bacteria to humans. The phenotypes or functions of such circuits are embodied in the gene expression patterns they form. Regulatory circuits are typically multifunctional, forming distinct gene expression patterns in different embryonic stages, tissues, or physiological states. Any one circuit with a single function can be realized by many different regulatory genotypes. Multifunctionality presumably constrains this number, but we do not know to what extent. We here exhaustively characterize a genotype space harboring millions of model regulatory circuits and all their possible functions. As a circuit's number of functions increases, the number of genotypes with a given number of functions decreases exponentially but can remain very large for a modest number of functions. However, the sets of circuits that can form any one set of functions becomes increasingly fragmented. As a result, historical contingency becomes widespread in circuits with many functions. Whether a circuit can acquire an additional function in the course of its evolution becomes increasingly dependent on the function it already has. Circuits with many functions also become increasingly brittle and sensitive to mutation. These observations are generic properties of a broad class of circuits and independent of any one circuit genotype or phenotype.

Evolvability is inevitable: increasing evolvability without the pressure to adapt.

Why evolvability appears to have increased over evolutionary time is an important unresolved biological question. Unlike most candidate explanations, this paper proposes that increasing evolvability can result without any pressure to adapt. The insight is that if evolvability is heritable, then an unbiased drifting process across genotypes can still create a distribution of phenotypes biased towards evolvability, because evolvable organisms diffuse more quickly through the space of possible phenotypes. Furthermore, because phenotypic divergence often correlates with founding niches, niche founders may on average be more evolvable, which through population growth provides a genotypic bias towards evolvability. Interestingly, the combination of these two mechanisms can lead to increasing evolvability without any pressure to out-compete other organisms, as demonstrated through experiments with a series of simulated models. Thus rather than from pressure to adapt, evolvability may inevitably result from any drift through genotypic space combined with evolution's passive tendency to accumulate niches.

An Efficient Genetic Algorithm for Maximum Coverage Deployment in Wireless Sensor Networks

Sensor networks have a lot of applications such as battlefield surveillance, environmental monitoring, and industrial diagnostics. Coverage is one of the most important performance metrics for sensor networks since it reflects how well a sensor field is monitored. In this paper, we introduce the maximum coverage deployment problem in wireless sensor networks and analyze the properties of the problem and its solution space. Random deployment is the simplest way to deploy sensor nodes but may cause unbalanced deployment and therefore, we need a more intelligent way for sensor deployment. We found that the phenotype space of the problem is a quotient space of the genotype space in a mathematical view. Based on this property, we propose an efficient genetic algorithm using a novel normalization method. A Monte Carlo method is adopted to design an efficient evaluation function, and its computation time is decreased without loss of solution quality using a method that starts from a small number of random samples and gradually increases the number for subsequent generations. The proposed genetic algorithms could be further improved by combining with a well-designed local search. The performance of the proposed genetic algorithm is shown by a comparative experimental study. When compared with random deployment and existing methods, our genetic algorithm was not only about twice faster, but also showed significant performance improvement in quality.

Compensatory Evolution and the Origins of Innovations

Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to adaptation when co-opted--e.g., following a mutation increasing expression from a low, attenuated baseline. This view is described, for example, by the metaphor of the spread of a population across a neutral network in genotype space. As an alternative view, consider the fact that most phenotypic traits are affected by multiple sequences, including cryptic ones. Even in a strictly clonal population, the co-option of cryptic sequences at different loci may have different phenotypic effects and offer the population multiple adaptive possibilities. Here, we model the evolution of quantitative phenotypic characters encoded by cryptic sequences and compare the relative contributions of genetic diversity and of variation across sites to the phenotypic potential of a population. We show that most of the phenotypic variation accessible through co-option would exist even in populations with no polymorphism. This is made possible by a history of compensatory evolution, whereby the phenotypic effect of a cryptic mutation at one site was balanced by mutations elsewhere in the genome, leading to a diversity of cryptic effect sizes across sites rather than across individuals. Cryptic sequences might accelerate adaptation and facilitate large phenotypic changes even in the absence of genetic diversity, as traditionally defined in terms of alternative alleles.

Ancient Evolutionary Trade-Offs between Yeast Ploidy States

The number of chromosome sets contained within the nucleus of eukaryotic organisms is a fundamental yet evolutionarily poorly characterized genetic variable of life. Here, we mapped the impact of ploidy on the mitotic fitness of baker's yeast and its never domesticated relative Saccharomyces paradoxus across wide swaths of their natural genotypic and phenotypic space. Surprisingly, environment-specific influences of ploidy on reproduction were found to be the rule rather than the exception. These ploidy–environment interactions were well conserved across the 2 billion generations separating the two species, suggesting that they are the products of strong selection. Previous hypotheses of generalizable advantages of haploidy or diploidy in ecological contexts imposing nutrient restriction, toxin exposure, and elevated mutational loads were rejected in favor of more fine-grained models of the interplay between ecology and ploidy. On a molecular level, cell size and mating type locus composition had equal, but limited, explanatory power, each explaining 12.5%–17% of ploidy–environment interactions. The mechanism of the cell size–based superior reproductive efficiency of haploids during Li+ exposure was traced to the Li+ exporter ENA. Removal of the Ena transporters, forcing dependence on the Nha1 extrusion system, completely altered the effects of ploidy on Li+ tolerance and evoked a strong diploid superiority, demonstrating how genetic variation at a single locus can completely reverse the relative merits of haploidy and diploidy. Taken together, our findings unmasked a dynamic interplay between ploidy and ecology that was of unpredicted evolutionary importance and had multiple molecular roots.

Multiple scales of selection influence the evolutionary emergence of novel pathogens

When pathogens encounter a novel environment, such as a new host species or treatment with an antimicrobial drug, their fitness may be reduced so that adaptation is necessary to avoid extinction. Evolutionary emergence is the process by which new pathogen strains arise in response to such selective pressures. Theoretical studies over the last decade have clarified some determinants of emergence risk, but have neglected the influence of fitness on evolutionary rates and have not accounted for the multiple scales at which pathogens must compete successfully. We present a cross-scale theory for evolutionary emergence, which embeds a mechanistic model of within-host selection into a stochastic model for emergence at the population scale. We explore how fitness landscapes at within-host and between-host scales can interact to influence the probability that a pathogen lineage will emerge successfully. Results show that positive correlations between fitnesses across scales can greatly facilitate emergence, while cross-scale conflicts in selection can lead to evolutionary dead ends. The local genotype space of the initial strain of a pathogen can have disproportionate influence on emergence probability. Our cross-scale model represents a step towards integrating laboratory experiments with field surveillance data to create a rational framework to assess emergence risk.

Evolutionary adaptive eye tracking for low-cost human computer interaction applications

We present an evolutionary adaptive eye-tracking framework aiming for low-cost human computer interaction. The main focus is to guarantee eye-tracking performance without using high-cost devices and strongly controlled situations. The performance optimization of eye tracking is formulated into the dynamic control problem of deciding on an eye tracking algorithm structure and associated thresholds/parameters, where the dynamic control space is denoted by genotype and phenotype spaces. The evolutionary algorithm is responsible for exploring the genotype control space, and the reinforcement learning algorithm organizes the evolved genotype into a reactive phenotype. The evolutionary algorithm encodes an eye-tracking scheme as a genetic code based on image variation analysis. Then, the reinforcement learning algorithm defines internal states in a phenotype control space limited by the perceived genetic code and carries out interactive adaptations. The proposed method can achieve optimal performance by compromising the difficulty in the real-time performance of the evolutionary algorithm and the drawback of the huge search space of the reinforcement learning algorithm. Extensive experiments were carried out using webcam image sequences and yielded very encouraging results. The framework can be readily applied to other low-cost vision-based human computer interactions in solving their intrinsic brittleness in unstable operational environments.

Quantifying the similarity of monotonic trajectories in rough and smooth fitness landscapes

When selection is strong and mutations are rare, evolution can be thought of as an uphill trajectory in a rugged fitness landscape. In this context the fitness landscape is a directed acyclic graph in which nodes are genotypes and edges lead from lower to higher fitness genotypes that differ by a single mutation. Because the space of genotypes is vastly multi-dimensional, classification of fitness landscapes is challenging. Many proposed summary characteristics of fitness landscapes attempt to quantify biologically relevant and intuitive notions such as roughness or peak accessibility in alternative ways. Here we explore, in different types of landscapes, the behavior of the recently introduced mean path divergence which quantifies the degree of similarity among evolutionary trajectories with the same endpoints. We find that monotonic trajectories in empirical and model fitness landscapes are significantly more constrained, with low median path divergence, than those in purely additive landscapes. By contrast, transcription factor sequence specificity (aptamer binding affinity) landscapes are markedly smoother and allow substantial variability in monotonic paths that can be greater than that in fully additive landscapes. We propose that the smoothness of the specificity landscapes is a consequence of the simple dependence of the transcription factor binding affinity on the aptamer sequence in contrast to the complex sequence-fitness mapping in folding landscapes.

Evolutionary potential, cross‐stress behavior and the genetic basis of acquired stress resistance in Escherichia coli

Bacterial populations have a remarkable capacity to cope with extreme environmental fluctuations in their natural environments. In certain cases, adaptation to one stressful environment provides a fitness advantage when cells are exposed to a second stressor, a phenomenon that has been coined as cross-stress protection. A tantalizing question in bacterial physiology is how the cross-stress behavior emerges during evolutionary adaptation and what the genetic basis of acquired stress resistance is. To address these questions, we evolved Escherichia coli cells over 500 generations in five environments that include four abiotic stressors. Through growth profiling and competition assays, we identified several cases of positive and negative cross-stress behavior that span all strain-stress combinations. Resequencing the genomes of the evolved strains resulted in the identification of several mutations and gene amplifications, whose fitness effect was further assessed by mutation reversal and competition assays. Transcriptional profiling of all strains under a specific stress, NaCl-induced osmotic stress, and integration with resequencing data further elucidated the regulatory responses and genes that are involved in this phenomenon. Our results suggest that cross-stress dependencies are ubiquitous, highly interconnected, and can emerge within short timeframes. The high adaptive potential that we observed argues that bacterial populations occupy a genotypic space that enables a high phenotypic plasticity during adaptation in fluctuating environments.

The advantages and limitations of trait analysis with GWAS: a review

Over the last 10 years, high-density SNP arrays and DNA re-sequencing have illuminated the majority of the genotypic space for a number of organisms, including humans, maize, rice and Arabidopsis. For any researcher willing to define and score a phenotype across many individuals, Genome Wide Association Studies (GWAS) present a powerful tool to reconnect this trait back to its underlying genetics. In this review we discuss the biological and statistical considerations that underpin a successful analysis or otherwise. The relevance of biological factors including effect size, sample size, genetic heterogeneity, genomic confounding, linkage disequilibrium and spurious association, and statistical tools to account for these are presented. GWAS can offer a valuable first insight into trait architecture or candidate loci for subsequent validation.

Preferring the fittest mates: An analytically tractable model

We develop an analytically tractable model of female preference for fit mates. Our population-genetic model allows to trace the dynamics at both the individual and the population level. The preference for fit mates links ecological adaptation and mating success is individually advantageous and causes polymorphic subpopulations. This polymorphism is a strong and stable clustering in genotype and phenotype space. The alleles coding for the mating preference spread rapidly through the population, thereby increasing the selection pressure between different habitats. The resulting polymorphism exceeds the expected selection–migration equilibrium by several orders of magnitude. The evolution of preference for fit mates can, thus, act as the trigger for parapatric speciation because it initiates prezygotic isolation and divergence.

Mutation Discovery in Regions of Segmental Cancer Genome Amplifications with CoNAn-SNV: A Mixture Model for Next Generation Sequencing of Tumors

Next generation sequencing has now enabled a cost-effective enumeration of the full mutational complement of a tumor genome—in particular single nucleotide variants (SNVs). Most current computational and statistical models for analyzing next generation sequencing data, however, do not account for cancer-specific biological properties, including somatic segmental copy number alterations (CNAs)—which require special treatment of the data. Here we present CoNAn-SNV (Copy Number Annotated SNV): a novel algorithm for the inference of single nucleotide variants (SNVs) that overlap copy number alterations. The method is based on modelling the notion that genomic regions of segmental duplication and amplification induce an extended genotype space where a subset of genotypes will exhibit heavily skewed allelic distributions in SNVs (and therefore render them undetectable by methods that assume diploidy). We introduce the concept of modelling allelic counts from sequencing data using a panel of Binomial mixture models where the number of mixtures for a given locus in the genome is informed by a discrete copy number state given as input. We applied CoNAn-SNV to a previously published whole genome shotgun data set obtained from a lobular breast cancer and show that it is able to discover 21 experimentally revalidated somatic non-synonymous mutations in a lobular breast cancer genome that were not detected using copy number insensitive SNV detection algorithms. Importantly, ROC analysis shows that the increased sensitivity of CoNAn-SNV does not result in disproportionate loss of specificity. This was also supported by analysis of a recently published lymphoma genome with a relatively quiescent karyotype, where CoNAn-SNV showed similar results to other callers except in regions of copy number gain where increased sensitivity was conferred. Our results indicate that in genomically unstable tumors, copy number annotation for SNV detection will be critical to fully characterize the mutational landscape of cancer genomes.

A Comparison of Genotype-Phenotype Maps for RNA and Proteins

The relationship between the genotype (sequence) and the phenotype (structure) of macromolecules affects their ability to evolve new structures and functions. We here compare the genotype space organization of proteins and RNA molecules to identify differences that may affect this ability. To this end, we computationally study the genotype-phenotype relationship for short RNA and lattice proteins of a reduced monomer alphabet size, to make exhaustive analysis and direct comparison of their genotype spaces feasible. We find that many fewer protein molecules than RNA molecules fold, but they fold into many more structures than RNA. In consequence, protein phenotypes have smaller genotype networks whose member genotypes tend to be more similar than for RNA phenotypes. Neighborhoods in sequence space of a given radius around an RNA molecule contain more novel structures than for protein molecules. We compare this property to evidence from natural RNA and protein molecules, and conclude that RNA genotype space may be more conducive to the evolution of new structure phenotypes.

POPULATION SUBDIVISION AND ADAPTATION IN ASEXUAL POPULATIONS OF SACCHAROMYCES CEREVISIAE

Population subdivision limits competition between individuals, which can have a profound effect on adaptation. Subdivided populations maintain more genetic diversity at any given time compared to well-mixed populations, and thus "explore" larger parts of the genotype space. At the same time, beneficial mutations take longer to spread in such populations, and thus subdivided populations do not "exploit" discovered mutations as efficiently as well-mixed populations. Whether subdivision inhibits or promotes adaptation in a given environment depends on the relative importance of exploration versus exploitation, which in turn depends on the structure of epistasis among beneficial mutations. Here we investigate the relative importance of exploration versus exploitation for adaptation by evolving 976 independent asexual populations of budding yeast with several degrees of geographic subdivision. We find that subdivision systematically inhibits adaptation: even the luckiest demes in subdivided populations on average fail to discover genotypes that are fitter than those discovered by well-mixed populations. Thus, exploitation of discovered mutations is more important for adaptation in our system than a thorough exploration of the mutational neighborhood, and increasing subdivision slows adaptation.

Pyganodon (Bivalvia: Unionoida: Unionidae) phylogenetics: A male- and female-transmitted mitochondrial DNA perspective

Species boundaries, evolutionary relationships and geographic distributions of many unionoid bivalve species, like those in the genus Pyganodon, remain unresolved in Eastern North America. Because unionoid bivalves are one of the most imperiled groups of animals in the world, understanding the genetic variation within and among populations as well as among species is crucial for effective conservation planning. Conservation of unionoid species is indispensable from a freshwater habitat perspective but also because they possess a unique mitochondrial inheritance system where distinct gender-associated mitochondrial DNA lineages coexist: a female-transmitted (F) mt genome and a male-transmitted (M) mt genome that are involved in the maintenance of separate sexes (=dioecy). In this study, 42 populations of Pyganodon sp. were sampled across a large geographical range and fragments of two mitochondrial genes (cox1 and cox2) were sequenced from both the M- and F-transmitted mtDNA genomes. Our results support the recency of the divergence between P. cataracta and P. fragilis. We also found two relatively divergent F and M lineages within P. grandis. Surprisingly, the relationships among the P. grandis specimens in the F and M sequence trees are not congruent. We found that a single haplotype in P. lacustris has recently swept throughout the M genotype space leading to an unexpectedly low diversity in the M lineage in that species. Our survey put forward some challenging results that force us to rethink hybridization and species boundaries in the genus Pyganodon. As the M and F genomes do not always display the same phylogeographic story in each species, we also discuss the importance of being careful in the interpretation of molecular data based solely on maternal transmitted mtDNA genomes. The involvement of F and M genomes in unionoid bivalve sex determination likely played a role in the genesis of the unorthodox phylogeographic patterns reported herein.

Adaptive walks on correlated fitness landscapes with heterogeneous connectivities

We propose a model for studying the statistical properties of adaptive walks on correlatedfitness landscapes which are established in genotype spaces of complex structure. Thefitness distribution on the genotype space follows either the bivariate Gaussian distributionor the bivariate exponential distribution. In both cases the degree of correlation of thefitness landscape can be tuned by using a single parameter. To perform the adaptivewalks two distinct rules are applied: the random adaptation walk (RAW) and thegradient adaptation walk (GAW). While for the RAW the mean walk length, , is a monotonic increasing function of the connectivity of the genotype space, for theGAW is a one-humped function. The RAW produces longer adaptive walks compared to theGAW, though its performance is slightly poorer and thereby the local maxima reachedby the GAW algorithm are usually closer to the global optimum of the fitnesslandscape.

Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP

Many important traits in plant breeding are polygenic and therefore recalcitrant to traditional marker-assisted selection. Genomic selection addresses this complexity by including all markers in the prediction model. A key method for the genomic prediction of breeding values is ridge regression (RR), which is equivalent to best linear unbiased prediction (BLUP) when the genetic covariance between lines is proportional to their similarity in genotype space. This additive model can be broadened to include epistatic effects by using other kernels, such as the Gaussian, which represent inner products in a complex feature space. To facilitate the use of RR and nonadditive kernels in plant breeding, a new software package for R called rrBLUP has been developed. At its core is a fast maximum-likelihood algorithm for mixed models with a single variance component besides the residual error, which allows for efficient prediction with unreplicated training data. Use of the rrBLUP software is demonstrated through several examples, including the identification of optimal crosses based on superior progeny value. In cross-validation tests, the prediction accuracy with nonadditive kernels was significantly higher than RR for wheat (Triticum aestivum L.) grain yield but equivalent for several maize (Zea mays L.) traits.

Adaptive Walks and Extreme Value Theory

We study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to genotypes, we show that the mean walk length is logarithmic in the number of initially available beneficial mutations, with a prefactor determined by the tail of the fitness distribution. This result is derived analytically in a simplified setting where the mutational neighborhood is fixed during the adaptive process, and confirmed by numerical simulations.

Computational design of synthetic regulatory networks from a genetic library to characterize the designability of dynamical behaviors

The engineering of synthetic gene networks has mostly relied on the assembly of few characterized regulatory elements using rational design principles. It is of outmost importance to analyze the scalability and limits of such a design workflow. To analyze the design capabilities of libraries of regulatory elements, we have developed the first automated design approach that combines such elements to search the genotype space associated to a given phenotypic behavior. Herein, we calculated the designability of dynamical functions obtained from circuits assembled with a given genetic library. By designing circuits working as amplitude filters, pulse counters and oscillators, we could infer new mechanisms for such behaviors. We also highlighted the hierarchical design and the optimization of the interface between devices. We dissected the functional diversity of a constrained library and we found that even such libraries can provide a rich variety of behaviors. We also found that intrinsic noise slightly reduces the designability of digital circuits, but it increases the designability of oscillators. Finally, we analyzed the robust design as a strategy to counteract the evolvability and noise in gene expression of the engineered circuits within a cellular background, obtaining mechanisms for robustness through non-linear negative feedback loops.

Computability, Gödel's incompleteness theorem, and an inherent limit on the predictability of evolution

The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory.