Robustness can evolve gradually in complex regulatory gene networks with varying topology

Body plan evolvability: The role of variability in gene regulatory networks

Recent computational modeling of early fruit fly (Drosophila) development has characterized the degree to which gene regulation networks can be robust to natural variability. In the first few hours of development, broad spatial gradients of maternally derived transcription factors activate embryonic gap genes. These gap patterns determine the subsequent segmented insect body plan through pair-rule gene expression. Gap genes are expressed with greater spatial precision than the maternal patterns. Computational modeling of the gap-gap regulatory interactions provides a mechanistic understanding for this robustness to maternal variability in wild-type (WT) patterning. A long-standing question in evolutionary biology has been how a system which is robust, such as the developmental program creating any particular species' body plan, is also evolvable, i.e. how can a system evolve or speciate, if the WT form is strongly buffered and protected? In the present work, we use the WT model to explore the breakdown of such Waddington-type 'canalization'. What levels of variability will push the system out of the WT form; are there particular pathways in the gene regulatory mechanism which are more susceptible to losing the WT form; and when robustness is lost, what types of forms are most likely to occur (i.e. what forms lie near the WT)? Manipulating maternal effects in several different pathways, we find a common gap 'peak-to-step' pattern transition in the loss of WT. We discuss these results in terms of the evolvability of insect segmentation, and in terms of experimental perturbations and mutations which could test the model predictions. We conclude by discussing the prospects for using continuum models of pattern dynamics to investigate a wider range of evo-devo problems.

Expanding evolutionary theories of ageing to better account for symbioses and interactions throughout the Web of Life

How, when, and why organisms age are fascinating issues that can only be fully addressed by adopting an evolutionary perspective. Consistently, the main evolutionary theories of ageing, namely the Mutation Accumulation theory, the Antagonistic Pleiotropy theory, and the Disposable Soma theory, have formulated stimulating hypotheses that structure current debates on both the proximal and ultimate causes of organismal ageing. However, all these theories leave a common area of biology relatively under-explored. The Mutation Accumulation theory and the Antagonistic Pleiotropy theory were developed under the traditional framework of population genetics, and therefore are logically centred on the ageing of individuals within a population. The Disposable Soma theory, based on principles of optimising physiology, mainly explains ageing within a species. Consequently, current leading evolutionary theories of ageing do not explicitly model the countless interspecific and ecological interactions, such as symbioses and host-microbiomes associations, increasingly recognized to shape organismal evolution across the Web of Life. Moreover, the development of network modelling supporting a deeper understanding on the molecular interactions associated with ageing within and between organisms is also bringing forward new questions regarding how and why molecular pathways associated with ageing evolved. Here, we take an evolutionary perspective to examine the effects of organismal interactions on ageing across different levels of biological organisation, and consider the impact of surrounding and nested systems on organismal ageing. We also apply this perspective to suggest open issues with potential to expand the standard evolutionary theories of ageing.

CastNet: a systems-level sequence evolution simulator

BACKGROUND

Simulating DNA evolution has been done through coevolution-agnostic probabilistic frameworks for the past 3 decades. The most common implementation is by using the converse of the probabilistic approach used to infer phylogenies which, in the simplest form, simulates a single sequence at a time. However, biological systems are multi-genic, and gene products can affect each other's evolutionary paths through coevolution. These crucial evolutionary dynamics still remain to be simulated, and we believe that modelling them can lead to profound insights for comparative genomics.

RESULTS

Here we present CastNet, a genome evolution simulator that assumes each genome is a collection of genes with constantly evolving regulatory interactions in between them. The regulatory interactions produce a phenotype in the form of gene expression profiles, upon which fitness is calculated. A genetic algorithm is then used to evolve a population of such entities through a user-defined phylogeny. Importantly, the regulatory mutations are a response to sequence mutations, thus making a 1-1 relationship between the rate of evolution of sequences and of regulatory parameters. This is, to our knowledge, the first time the evolution of sequences and regulation have been explicitly linked in a simulation, despite there being a multitude of sequence evolution simulators, and a handful of models to simulate Gene Regulatory Network (GRN) evolution. In our test runs, we see a coevolutionary signal among genes that are active in the GRN, and neutral evolution in genes that are not included in the network, showing that selective pressures imposed on the regulatory output of the genes are reflected in their sequences.

CONCLUSION

We believe that CastNet represents a substantial step for developing new tools to study genome evolution, and more broadly, coevolutionary webs and complex evolving systems. This simulator also provides a new framework to study molecular evolution where sequence coevolution has a leading role.

Robustness and innovation in synthetic genotype networks

Genotype networks are sets of genotypes connected by small mutational changes that share the same phenotype. They facilitate evolutionary innovation by enabling the exploration of different neighborhoods in genotype space. Genotype networks, first suggested by theoretical models, have been empirically confirmed for proteins and RNAs. Comparative studies also support their existence for gene regulatory networks (GRNs), but direct experimental evidence is lacking. Here, we report the construction of three interconnected genotype networks of synthetic GRNs producing three distinct phenotypes in Escherichia coli. Our synthetic GRNs contain three nodes regulating each other by CRISPR interference and governing the expression of fluorescent reporters. The genotype networks, composed of over twenty different synthetic GRNs, provide robustness in face of mutations while enabling transitions to innovative phenotypes. Through realistic mathematical modeling, we quantify robustness and evolvability for the complete genotype-phenotype map and link these features mechanistically to GRN motifs. Our work thereby exemplifies how GRN evolution along genotype networks might be driving evolutionary innovation.

Gene regulatory networks with binary weights

An evolutionary computation framework to learn binary threshold networks is presented. Inspired by the recent trend of binary neural networks, where weights and activation thresholds are represented using 1 and -1 such that they can be stored in 1-bit instead of full precision, we explore this approach for gene regulatory network modeling. We test our method by inferring binary threshold networks of two regulatory network models: Quorum sensing systems in bacterium Paraburkholderia phytofirmans PsJN and the fission yeast cell-cycle. We considered differential evolution and particle swarm optimization for the simulations. Results for weights having only 1 and -1 values, and different activation thresholds are presented. Full binary threshold networks were found with minimum error (2 bits), whereas when the binary restriction is relaxed for the activation thresholds, networks with 0 bit error were found. .

The Topological Characteristics of Biological Ratio-Sensing Networks

Ratio sensing is a fundamental biological function observed in signal transduction and decision making. In the synthetic biology context, ratio sensing presents one of the elementary functions for cellular multi-signal computation. To investigate the mechanism of the ratio-sensing behavior, we explored the topological characteristics of biological ratio-sensing networks. With exhaustive enumeration of three-node enzymatic and transcriptional regulatory networks, we found that robust ratio sensing was highly dependent on network structure rather than network complexity. Specifically, a set of seven minimal core topological structures and four motifs were deduced to be capable of robust ratio sensing. Further investigations on the evolutionary space of robust ratio-sensing networks revealed highly clustered domains surrounding the core motifs which suggested their evolutionary plausibility. Our study revealed the network topological design principles of ratio-sensing behavior and provided a design scheme for constructing regulatory circuits with ratio-sensing behavior in synthetic biology.

The ensemble of gene regulatory networks at mutation-selection balance

The evolution of diverse phenotypes both involves and is constrained by molecular interaction networks. When these networks influence patterns of expression, we refer to them as gene regulatory networks (GRNs). Here, we develop a model of GRN evolution analogous to work from quasi-species theory, which is itself essentially the mutation-selection balance model from classical population genetics extended to multiple loci. With this GRN model, we prove that-across a broad spectrum of selection pressures-the dynamics converge to a stationary distribution over GRNs. Next, we show from first principles how the frequency of GRNs at equilibrium is related to the topology of the genotype network, in particular, via a specific network centrality measure termed the eigenvector centrality. Finally, we determine the structural characteristics of GRNs that are favoured in response to a range of selective environments and mutational constraints. Our work connects GRN evolution to quasi-species theory-and thus to classical populations genetics-providing a mechanistic explanation for the observed distribution of GRNs evolving in response to various evolutionary forces, and shows how complex fitness landscapes can emerge from simple evolutionary rules.

A linear reciprocal relationship between robustness and plasticity in homeostatic biological networks

In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of core genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase to provide a plastic (sensitive) response. A feedforward structure from the non-core to core genes evolved autonomously. Negative proportionality was observed between the average changes in core and non-core genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. The proportion coefficient between those genes is represented by their number ratio, as in the "lever principle", whereas the decrease in the ratio results in a transition from perfect to partial adaptation, in which only a portion of the core genes exhibits robustness against environmental changes. This reciprocity between robustness and plasticity was satisfied throughout the evolutionary course, imposing an evolutionary constraint. This result suggests a simple macroscopic law for the adaptation characteristic in evolved complex biological networks.

Functional Resilience of Mutually Repressing Motifs Embedded in Larger Networks

Elucidating the design principles of regulatory networks driving cellular decision-making has important implications for understanding cell differentiation and guiding the design of synthetic circuits. Mutually repressing feedback loops between 'master regulators' of cell fates can exhibit multistable dynamics enabling "single-positive" phenotypes: (high A, low B) and (low A, high B) for a toggle switch, and (high A, low B, low C), (low A, high B, low C) and (low A, low B, high C) for a toggle triad. However, the dynamics of these two motifs have been interrogated in isolation in silico, but in vitro and in vivo, they often operate while embedded in larger regulatory networks. Here, we embed these motifs in complex larger networks of varying sizes and connectivity to identify hallmarks under which these motifs maintain their canonical dynamical behavior. We show that an increased number of incoming edges onto a motif leads to a decay in their canonical stand-alone behaviors. We also show that this decay can be exacerbated by adding self-inhibition but not self-activation loops on the 'master regulators'. These observations offer insights into the design principles of biological networks containing these motifs and can help devise optimal strategies for the integration of these motifs into larger synthetic networks.

Experimental evidence for the correlation between RNA structural fluctuations and the frequency of beneficial mutations

RNA has been used as a model molecule to understand the adaptive evolution process owing to the simple relationship between the structure (i.e., phenotype) and sequence (i.e., genotype). RNA usually forms multiple substructures with similar thermodynamic stabilities, called structural fluctuations. Ancel and Fontana theoretically proposed that structural fluctuation is directly related to the ease of change in structures by mutations and thus works as a source of adaptive evolution; however, experimental verification is limited. Here, we analyzed 76 RNA genotypes that appeared in our previous in vitro evolution to examine whether (i) RNA fluctuation decreases as adaptive evolution proceeds and (ii) RNAs that have larger fluctuations tend to have higher frequencies of beneficial mutations. We first computationally estimated the structural fluctuations of all RNAs and observed that they tended to decrease as their fitness increased. We next measured the frequency of beneficial mutations for 10 RNA genotypes and observed that the total number of beneficial mutations was correlated with the size of the structural fluctuations. These results consistently support the idea that the structural fluctuation of RNA, at least those evaluated in our study, works as a source of adaptive evolution.

Early effects of gene duplication on the robustness and phenotypic variability of gene regulatory networks

Background

Research on gene duplication is abundant and comes from a wide range of approaches, from high-throughput analyses and experimental evolution to bioinformatics and theoretical models. Notwithstanding, a consensus is still lacking regarding evolutionary mechanisms involved in evolution through gene duplication as well as the conditions that affect them. We argue that a better understanding of evolution through gene duplication requires considering explicitly that genes do not act in isolation. It demands studying how the perturbation that gene duplication implies percolates through the web of gene interactions. Due to evolution’s contingent nature, the paths that lead to the final fate of duplicates must depend strongly on the early stages of gene duplication, before gene copies have accumulated distinctive changes.

Methods

Here we use a widely-known model of gene regulatory networks to study how gene duplication affects network behavior in early stages. Such networks comprise sets of genes that cross-regulate. They organize gene activity creating the gene expression patterns that give cells their phenotypic properties. We focus on how duplication affects two evolutionarily relevant properties of gene regulatory networks: mitigation of the effect of new mutations and access to new phenotypic variants through mutation.

Results

Among other observations, we find that those networks that are better at maintaining the original phenotype after duplication are usually also better at buffering the effect of single interaction mutations and that duplication tends to enhance further this ability. Moreover, the effect of mutations after duplication depends on both the kind of mutation and genes involved in it. We also found that those phenotypes that had easier access through mutation before duplication had higher chances of remaining accessible through new mutations after duplication.

Conclusion

Our results support that gene duplication often mitigates the impact of new mutations and that this effect is not merely due to changes in the number of genes. The work that we put forward helps to identify conditions under which gene duplication may enhance evolvability and robustness to mutations.

Resolving Anomalies in the Behaviour of a Modularity-Inducing Problem Domain with Distributional Fitness Evaluation

Discrete gene regulatory networks (GRNs) play a vital role in the study of robustness and modularity. A common method of evaluating the robustness of GRNs is to measure their ability to regulate a set of perturbed gene activation patterns back to their unperturbed forms. Usually, perturbations are obtained by collecting random samples produced by a predefined distribution of gene activation patterns. This sampling method introduces stochasticity, in turn inducing dynamicity. This dynamicity is imposed on top of an already complex fitness landscape. So where sampling is used, it is important to understand which effects arise from the structure of the fitness landscape, and which arise from the dynamicity imposed on it. Stochasticity of the fitness function also causes difficulties in reproducibility and in post-experimental analyses. We develop a deterministic distributional fitness evaluation by considering the complete distribution of gene activity patterns, so as to avoid stochasticity in fitness assessment. This fitness evaluation facilitates repeatability. Its determinism permits us to ascertain theoretical bounds on the fitness, and thus to identify whether the algorithm has reached a global optimum. It enables us to differentiate the effects of the problem domain from those of the noisy fitness evaluation, and thus to resolve two remaining anomalies in the behaviour of the problem domain of Espinosa-Soto and A. Wagner (2010). We also reveal some properties of solution GRNs that lead them to be robust and modular, leading to a deeper understanding of the nature of the problem domain. We conclude by discussing potential directions toward simulating and understanding the emergence of modularity in larger, more complex domains, which is key both to generating more useful modular solutions, and to understanding the ubiquity of modularity in biological systems.

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 effects of the modularity of gene regulatory networks on phenotypic variability and its association with robustness

Biological adaptations depend on natural selection sorting out those individuals that exhibit characters fit to their environment. Selection, in turn, depends on the phenotypic variation present in a population. Thus, evolutionary outcomes depend, to a certain extent, on the kind of variation that organisms can produce through random genetic perturbation, that is, their phenotypic variability. Moreover, the properties of developmental mechanisms that produce the organisms affect their phenotypic variability. Two of these properties are modularity and robustness. Modularity is the degree to which interactions occur mostly within groups of the system's elements and scarcely between elements in different groups. Robustness is the propensity of a system to endure perturbations while preserving its phenotype. In this paper, we used a model of gene regulatory networks (GRNs) to study the relationship between modularity and robustness in developmental processes and how modularity affects the variation that random genetic mutations produce in the expression patterns of GRNs. Our results show that modularity and robustness are correlated in multifunctional GRNs and that selection for one of these properties affects the other as well. We contend that these observations may help to understand why modularity and robustness are widespread in biological systems. Additionally, we found that modular networks tend to produce new expression patterns with subtle changes localized in the expression of a few groups of genes. This effect in the phenotypic variability of modular GRNs may bear important consequences for adaptive evolution: it may help to adjust the expression of one group of genes at a time, with few alterations on other previously evolved expression patterns.

A computational exploration of resilience and evolvability of protein-protein interaction networks

Protein-protein interaction (PPI) networks represent complex intra-cellular protein interactions, and the presence or absence of such interactions can lead to biological changes in an organism. Recent network-based approaches have shown that a phenotype's PPI network's resilience to environmental perturbations is related to its placement in the tree of life; though we still do not know how or why certain intra-cellular factors can bring about this resilience. Here, we explore the influence of gene expression and network properties on PPI networks' resilience. We use publicly available data of PPIs for E. coli, S. cerevisiae, and H. sapiens, where we compute changes in network resilience as new nodes (proteins) are added to the networks under three node addition mechanisms-random, degree-based, and gene-expression-based attachments. By calculating the resilience of the resulting networks, we estimate the effectiveness of these node addition mechanisms. We demonstrate that adding nodes with gene-expression-based preferential attachment (as opposed to random or degree-based) preserves and can increase the original resilience of PPI network in all three species, regardless of gene expression distribution or network structure. These findings introduce a general notion of prospective resilience, which highlights the key role of network structures in understanding the evolvability of phenotypic traits.

Evolution of phenotypic fluctuation under host-parasite interactions

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important “environmental” factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness. Then, the robustness of the corresponding phenotype will be increased by reducing phenotypic fluctuations. Conversely, plasticity tends to evolve to avoid certain phenotypes that are attacked by parasites. By using a dynamic model of gene expression for the host, we investigate the evolution of the genotype-phenotype map and of phenotypic variances. If the host–parasite interaction is weak, the fittest phenotype of the host evolves to reduce phenotypic variances. In contrast, if there exists a sufficient degree of interaction, the phenotypic variances of hosts increase to escape parasite attacks. For the latter case, we found two strategies: if the noise in the stochastic gene expression is below a certain threshold, the phenotypic variance increases via genetic diversification, whereas above this threshold, it is increased mediated by noise-induced phenotypic fluctuation. We examine how the increase in the phenotypic variances caused by parasite interactions influences the growth rate of a single host, and observed a trade-off between the two. Our results help elucidate the roles played by noise and genetic mutations in the evolution of phenotypic fluctuation and robustness in response to host–parasite interactions.

Plasticity and phenotypic variability induced by internal or external perturbations are common features of biological systems. However, under evolution for given environmental conditions, phenotypic variability is not advantageous, because it leads to the deviation from the fittest state. This has been demonstrated by previous laboratory and computer experiments. As a possible origin for the remnant phenotypic variance, we investigated the role of host–parasite interactions such as those between bacteria and phages. Different parasite-types attack hosts of certain phenotypes. Through numerical simulations of the evolution of the host genotype–phenotype mapping, we found that hosts increase phenotypic variation by increasing phenotypic fluctuations if the interaction is sufficiently strong. Depending on the degree of noise in gene expression dynamics, there are two distinct strategies for increasing phenotypic variances: stochasticity in gene expression or genetic variances. The former strategy, which can work over a faster time scale, leads to a decline in fitness, whereas the latter reduces the robustness of the fitted state. Our results provide insights into how phenotypic variances are preserved and how hosts can escape being attacked by parasites whose genes mutate to adapt to changes in parasites. These two host strategies, which depend on internal and external conditions, can be verified experimentally via the transcriptome analysis of microorganisms.

Chromatin Network Analyses: Towards Structure-Function Relationships in Epigenomics

Recent technological advances have allowed us to map chromatin conformation and uncover the genome’s spatial organization of the genome inside the nucleus. These experiments have revealed the complexities of genome folding, characterized by the presence of loops and domains at different scales, which can change across development and in different cell types. There is strong evidence for a relationship between the topological properties of chromatin contacts and cellular phenotype. Chromatin can be represented as a network, in which genomic fragments are the nodes and connections represent experimentally observed spatial proximity of two genomically distant regions in a specific cell type or biological condition. With this approach we can consider a variety of chromatin features in association with the 3D structure, investigating how nuclear chromatin organization can be related to gene regulation, replication, malignancy, phenotypic variability and plasticity. We briefly review the results obtained on genome architecture through network theoretic approaches. As previously observed in protein-protein interaction networks and many types of non-biological networks, external conditions could shape network topology through a yet unidentified structure-function relationship. Similar to scientists studying the brain, we are confronted with a duality between a spatially embedded network of physical contacts, a related network of correlation in the dynamics of network nodes and, finally, an abstract definition of function of this network, related to phenotype. We summarise major developments in the study of networks in other fields, which we think can suggest a path towards better understanding how 3D genome configuration can impact biological function and adaptation to the environment.

A Framework for Investigating Rules of Life by Establishing Zones of Influence

The incredible complexity of biological processes across temporal and spatial scales hampers defining common underlying mechanisms driving the patterns of life. However, recent advances in sequencing, big data analysis, machine learning, and molecular dynamics simulation have renewed the hope and urgency of finding potential hidden rules of life. There currently exists no framework to develop such synoptic investigations. Some efforts aim to identify unifying rules of life across hierarchical levels of time, space, and biological organization, but not all phenomena occur across all the levels of these hierarchies. Instead of identifying the same parameters and rules across levels, we posit that each level of a temporal and spatial scale and each level of biological organization has unique parameters and rules that may or may not predict outcomes in neighboring levels. We define this neighborhood, or the set of levels, across which a rule functions as the zone of influence. Here, we introduce the zone of influence framework and explain using three examples: (Smocovitis, 1992) randomness in biology, where we use a Poisson process to describe processes from protein dynamics to DNA mutations to gene expressions, (Leroi, 2014) island biogeography, and (Gropp, 2016) animal coloration. The zone of influence framework may enable researchers to identify which levels are worth investigating for a particular phenomenon and reframe the narrative of searching for a unifying rule of life to the investigation of how, when, and where various rules of life operate.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Neutral quasispecies evolution and the maximal entropy random walk

Even if they have no impact on phenotype, neutral mutations are not equivalent in the eyes of evolution: A robust neutral variant-one which remains functional after further mutations-is more likely to spread in a large, diverse population than a fragile one. Quasispecies theory shows that the equilibrium frequency of a genotype is proportional to its eigenvector centrality in the neutral network. This paper explores the link between the selection for mutational robustness and the navigability of neutral networks. I show that sequences of neutral mutations follow a "maximal entropy random walk," a canonical Markov chain on graphs with nonlocal, nondiffusive dynamics. I revisit M. Smith's word-game model of evolution in this light, finding that the likelihood of certain sequences of substitutions can decrease with the population size. These counterintuitive results underscore the fertility of the interface between evolutionary dynamics, information theory, and physics.

Dynamical systems approach to evolution-development congruence: Revisiting Haeckel's recapitulation theory

It is acknowledged that embryonic development has a tendency to proceed from common toward specific. Ernst Haeckel raised the question of why that tendency prevailed through evolution, and the question remains unsolved. Here, we revisit Haeckel's recapitulation theory, that is, the parallelism between evolution and development through numerical evolution and dynamical systems theory. By using intracellular gene expression dynamics with cell‐to‐cell interaction over spatially aligned cells to represent the developmental process, gene regulation networks (GRN) that govern these dynamics evolve under the selection pressure to achieve a prescribed spatial gene expression pattern. For most numerical evolutionary experiments, the evolutionary pattern changes over generations, as well as the developmental pattern changes governed by the evolved GRN exhibit remarkable similarity. Changes in both patterns consisted of several epochs where stripes are formed in a short time, whereas for other temporal regimes, the pattern hardly changes. In evolution, these quasi‐stationary generations are needed to achieve relevant mutations, whereas, in development, they are due to some gene expressions that vary slowly and control the pattern change. These successive epochal changes in development and evolution are represented as common bifurcations in dynamical systems theory, regulating working network structure from feedforward subnetwork to those containing feedback loops. The congruence is the correspondence between successive acquisitions of subnetworks through evolution and changes in working subnetworks in development. Consistency of the theory with the segmentation gene‐expression dynamics is discussed. Novel outlook on recapitulation and heterochrony are provided, testable experimentally by the transcriptome and network analysis.

We confirmed recapitulation, parallelism between evolution and development, by evolutionary simulation of pattern formation. Its origin is analyzed in terms of bifurcation in dynamical systems theory, slow‐mode control, and network structures.

Information Theory Can Help Quantify the Potential of New Phenotypes to Originate as Exaptations

Exaptations are adaptive traits that do not originate de novo but from other adaptive traits. They include complex macroscopic traits, such as the middle ear bones of mammals, which originated from reptile jaw bones, but also molecular traits, such as new binding sites of transcriptional regulators. What determines whether a trait originates de novo or as an exaptation is unknown. I here use simple information theoretic concepts to quantify a molecular phenotype’s potential to give rise to new phenotypes. These quantities rely on the amount of genetic information needed to encode a phenotype. I use these quantities to estimate the propensity of new transcription factor binding phenotypes to emerge de novo or exaptively, and do so for 187 mouse transcription factors. I also use them to quantify whether an organism’s viability in one of 10 different chemical environment is likely to arise exaptively. I show that informationally expensive traits are more likely to originate exaptively. Exaptive evolution is only sometimes favored for new transcription factor binding, but it is always favored for the informationally complex metabolic phenotypes I consider. As our ability to genotype evolving populations increases, so will our ability to understand how phenotypes of ever-increasing informational complexity originate in evolution.

Quantum aspects of evolution: a contribution towards evolutionary explorations of genotype networks via quantum walks

Quantum biology seeks to explain biological phenomena via quantum mechanisms, such as enzyme reaction rates via tunnelling and photosynthesis energy efficiency via coherent superposition of states. However, less effort has been devoted to study the role of quantum mechanisms in biological evolution. In this paper, we used transcription factor networks with two and four different phenotypes, and used classical random walks (CRW) and quantum walks (QW) to compare network search behaviour and efficiency at finding novel phenotypes between CRW and QW. In the network with two phenotypes, at temporal scales comparable to decoherence time TD, QW are as efficient as CRW at finding new phenotypes. In the case of the network with four phenotypes, the QW had a higher probability of mutating to a novel phenotype than the CRW, regardless of the number of mutational steps (i.e. 1, 2 or 3) away from the new phenotype. Before quantum decoherence, the QW probabilities become higher turning the QW effectively more efficient than CRW at finding novel phenotypes under different starting conditions. Thus, our results warrant further exploration of the QW under more realistic network scenarios (i.e. larger genotype networks) in both closed and open systems (e.g. by considering Lindblad terms).

Predictive features of gene expression variation reveal mechanistic link with differential expression

For most biological processes, organisms must respond to extrinsic cues, while maintaining essential gene expression programmes. Although studied extensively in single cells, it is still unclear how variation is controlled in multicellular organisms. Here, we used a machine-learning approach to identify genomic features that are predictive of genes with high versus low variation in their expression across individuals, using bulk data to remove stochastic cell-to-cell variation. Using embryonic gene expression across 75 Drosophila isogenic lines, we identify features predictive of expression variation (controlling for expression level), many of which are promoter-related. Genes with low variation fall into two classes reflecting different mechanisms to maintain robust expression, while genes with high variation seem to lack both types of stabilizing mechanisms. Applying this framework to humans revealed similar predictive features, indicating that promoter architecture is an ancient mechanism to control expression variation. Remarkably, expression variation features could also partially predict differential expression after diverse perturbations in both Drosophila and humans. Differential gene expression signatures may therefore be partially explained by genetically encoded gene-specific features, unrelated to the studied treatment.

Emergence of cooperative bistability and robustness of gene regulatory networks

Gene regulatory networks (GRNs) are complex systems in which many genes regulate mutually to adapt the cell state to environmental conditions. In addition to function, the GRNs possess several kinds of robustness. This robustness means that systems do not lose their functionality when exposed to disturbances such as mutations or noise, and is widely observed at many levels in living systems. Both function and robustness have been acquired through evolution. In this respect, GRNs utilized in living systems are rare among all possible GRNs. In this study, we explored the fitness landscape of GRNs and investigated how robustness emerged in highly-fit GRNs. We considered a toy model of GRNs with one input gene and one output gene. The difference in the expression level of the output gene between two input states, "on" and "off", was considered as fitness. Thus, the determination of the fitness of a GRN was based on how sensitively it responded to the input. We employed the multicanonical Monte Carlo method, which can sample GRNs randomly in a wide range of fitness levels, and classified the GRNs according to their fitness. As a result, the following properties were found: (1) Highly-fit GRNs exhibited bistability for intermediate input between "on" and "off". This means that such GRNs responded to two input states by using different fixed points of dynamics. This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. In other words, noise robustness is a byproduct of high fitness. (3) GRNs that were robust against mutations were not extremely rare among the highly-fit GRNs. This implies that mutational robustness is readily acquired through the evolutionary process. These properties are universal irrespective of the evolutionary pathway, because the results do not rely on evolutionary simulation.

Random Parametric Perturbations of Gene Regulatory Circuit Uncover State Transitions in Cell Cycle

Many biological processes involve precise cellular state transitions controlled by complex gene regulation. Here, we use budding yeast cell cycle as a model system and explore how a gene regulatory circuit encodes essential information of state transitions. We present a generalized random circuit perturbation method for circuits containing heterogeneous regulation types and its usage to analyze both steady and oscillatory states from an ensemble of circuit models with random kinetic parameters. The stable steady states form robust clusters with a circular structure that are associated with cell cycle phases. This circular structure in the clusters is consistent with single-cell RNA sequencing data. The oscillatory states specify the irreversible state transitions along cell cycle progression. Furthermore, we identify possible mechanisms to understand the irreversible state transitions from the steady states. We expect this approach to be robust and generally applicable to unbiasedly predict dynamical transitions of a gene regulatory circuit.

Predicting Evolutionary Constraints by Identifying Conflicting Demands in Regulatory Networks

Gene regulation networks allow organisms to adapt to diverse environmental niches. However, the constraints underlying the evolution of gene regulation remain ill defined. Here, we show that partial order-a concept that ranks network output levels as a function of different input signals-identifies such constraints. We tested our predictions by experimentally evolving an engineered signal-integrating network in multiple environments. We find that populations: (1) expand in fitness space along the Pareto-optimal front associated with conflicts in regulatory demands, by fine-tuning binding affinities within the network, and (2) expand beyond the Pareto-optimal front through changes in the network structure. Our constraint predictions are based only on partial order and do not require information on the network architecture or underlying genetics. Overall, our findings show that limited knowledge of current regulatory phenotypes can provide predictions on future evolutionary constraints.

Dimensional Reduction in Evolving Spin-Glass Model: Correlation of Phenotypic Responses to Environmental and Mutational Changes

The evolution of high-dimensional phenotypes is investigated using a statistical physics model consisting of interacting spins, in which phenotypes, genotypes, and environments are represented by spin configurations, interaction matrices, and external fields, respectively. We found that phenotypic changes upon diverse environmental change and genetic variation are highly correlated across all spins, consistent with recent experimental observations of biological systems. The dimension reduction in phenotypic changes is shown to be a result of the evolution of the robustness to thermal noise, achieved at the replica symmetric phase.

Adding levels of complexity enhances robustness and evolvability in a multilevel genotype-phenotype map

Robustness and evolvability are the main properties that account for the stability and accessibility of phenotypes. They have been studied in a number of computational genotype-phenotype maps. In this paper, we study a metabolic genotype-phenotype map defined in toyLIFE, a multilevel computational model that represents a simplified cellular biology. toyLIFE includes several levels of phenotypic expression, from proteins to regulatory networks to metabolism. Our results show that toyLIFE shares many similarities with other seemingly unrelated computational genotype-phenotype maps. Thus, toyLIFE shows a high degeneracy in the mapping from genotypes to phenotypes, as well as a highly skewed distribution of phenotypic abundances. The neutral networks associated with abundant phenotypes are highly navigable, and common phenotypes are close to each other in genotype space. All of these properties are remarkable, as toyLIFE is built on a version of the HP protein-folding model that is neither robust nor evolvable: phenotypes cannot be mutually accessed through point mutations. In addition, both robustness and evolvability increase with the number of genes in a genotype. Therefore, our results suggest that adding levels of complexity to the mapping of genotypes to phenotypes and increasing genome size enhances both these properties.

Evolution of embryonic cis-regulatory landscapes between divergent Phallusia and Ciona ascidians

Ascidian species of the Phallusia and Ciona genera are distantly related, their last common ancestor dating several hundred million years ago. Although their genome sequences have extensively diverged since this radiation, Phallusia and Ciona species share almost identical early morphogenesis and stereotyped cell lineages. Here, we explored the evolution of transcriptional control between P. mammillata and C. robusta. We combined genome-wide mapping of open chromatin regions in both species with a comparative analysis of the regulatory sequences of a test set of 10 pairs of orthologous early regulatory genes with conserved expression patterns. We find that ascidian chromatin accessibility landscapes obey similar rules as in other metazoa. Open-chromatin regions are short, highly conserved within each genus and cluster around regulatory genes. The dynamics of chromatin accessibility and closest-gene expression are strongly correlated during early embryogenesis. Open-chromatin regions are highly enriched in cis-regulatory elements: 73% of 49 open chromatin regions around our test genes behaved as either distal enhancers or proximal enhancer/promoters following electroporation in Phallusia eggs. Analysis of this datasets suggests a pervasive use in ascidians of "shadow" enhancers with partially overlapping activities. Cross-species electroporations point to a deep conservation of both the trans-regulatory logic between these distantly-related ascidians and the cis-regulatory activities of individual enhancers. Finally, we found that the relative order and approximate distance to the transcription start site of open chromatin regions can be conserved between Ciona and Phallusia species despite extensive sequence divergence, a property that can be used to identify orthologous enhancers, whose regulatory activity can partially diverge.

Alternative Biochemistries for Alien Life: Basic Concepts and Requirements for the Design of a Robust Biocontainment System in Genetic Isolation

The universal genetic code, which is the foundation of cellular organization for almost all organisms, has fostered the exchange of genetic information from very different paths of evolution. The result of this communication network of potentially beneficial traits can be observed as modern biodiversity. Today, the genetic modification techniques of synthetic biology allow for the design of specialized organisms and their employment as tools, creating an artificial biodiversity based on the same universal genetic code. As there is no natural barrier towards the proliferation of genetic information which confers an advantage for a certain species, the naturally evolved genetic pool could be irreversibly altered if modified genetic information is exchanged. We argue that an alien genetic code which is incompatible with nature is likely to assure the inhibition of all mechanisms of genetic information transfer in an open environment. The two conceivable routes to synthetic life are either de novo cellular design or the successive alienation of a complex biological organism through laboratory evolution. Here, we present the strategies that have been utilized to fundamentally alter the genetic code in its decoding rules or its molecular representation and anticipate future avenues in the pursuit of robust biocontainment.

Formation of dominant mode by evolution in biological systems

A reduction in high-dimensional phenotypic states to a few degrees of freedom is essential to understand biological systems. Here, we show evolutionary robustness causes such reduction which restricts possible phenotypic changes in response to a variety of environmental conditions. First, global protein expression changes in Escherichia coli after various environmental perturbations were shown to be proportional across components, across different types of environmental conditions. To examine if such dimension reduction is a result of evolution, we analyzed a cell model-with a huge number of components, that reproduces itself via a catalytic reaction network-and confirmed that common proportionality in the concentrations of all components is shaped through evolutionary processes. We found that the changes in concentration across all components in response to environmental and evolutionary changes are constrained to the changes along a one-dimensional major axis, within a huge-dimensional state space. On the basis of these observations, we propose a theory in which such constraints in phenotypic changes are achieved both by evolutionary robustness and plasticity and formulate this proposition in terms of dynamical systems. Accordingly, broad experimental and numerical results on phenotypic changes caused by evolution and adaptation are coherently explained.

Synthetic circuits reveal how mechanisms of gene regulatory networks constrain evolution

Phenotypic variation is the raw material of adaptive Darwinian evolution. The phenotypic variation found in organismal development is biased towards certain phenotypes, but the molecular mechanisms behind such biases are still poorly understood. Gene regulatory networks have been proposed as one cause of constrained phenotypic variation. However, most pertinent evidence is theoretical rather than experimental. Here, we study evolutionary biases in two synthetic gene regulatory circuits expressed in Escherichia coli that produce a gene expression stripe-a pivotal pattern in embryonic development. The two parental circuits produce the same phenotype, but create it through different regulatory mechanisms. We show that mutations cause distinct novel phenotypes in the two networks and use a combination of experimental measurements, mathematical modelling and DNA sequencing to understand why mutations bring forth only some but not other novel gene expression phenotypes. Our results reveal that the regulatory mechanisms of networks restrict the possible phenotypic variation upon mutation. Consequently, seemingly equivalent networks can indeed be distinct in how they constrain the outcome of further evolution.

Hierarchical closeness-based properties reveal cancer survivability and biomarker genes in molecular signaling networks

Specific molecular signaling networks underlie different cancer types and quantitative analyses on those cancer networks can provide useful information about cancer treatments. Their structural metrics can reveal survivability of cancer patients and be used to identify biomarker genes for early cancer detection. In this study, we devised a novel structural metric called hierarchical closeness (HC) entropy and found that it was negatively correlated with 5-year survival rates. We also made an interesting observation that a network of higher HC entropy was likely to be more robust against mutations. This finding suggested that cancers of high HC entropy tend to be incurable because their signaling networks are robust to perturbations caused by treatment. We also proposed a novel core identification method based on the reachability factor in the HC measure. The cores were permitted to decompose such that the negative relationship between HC entropy and cancer survival rate was consistently conserved in every core level. Interestingly, we observed that many promising biomarker genes for early cancer detection reside in the innermost core of a signaling network. Taken together, the proposed analyses of the hierarchical structure of cancer signaling networks may be useful in developing future novel cancer treatments.

Asymmetry in indegree and outdegree distributions of gene regulatory networks arising from dynamical robustness

Although outdegree distributions of gene regulatory networks have scale-free characteristics similar to other biological networks, indegree distributions have single-scale characteristics with significantly lower variance than that of outdegree distributions. In this study, we mathematically explain that such asymmetric characteristics arise from dynamical robustness, which is the property of maintaining an equilibrium state of gene expressions against inevitable perturbations to the networks, such as gene dysfunction and mutation of promoters. We reveal that the expression of a single gene is robust to a perturbation for a large number of inputs and a small number of outputs. Applying these results to the networks, we also show that an equilibrium state of the networks is robust if the variance of the indegree distribution is low (i.e., single-scale characteristics) and that of the outdegree distribution is high (i.e., scale-free characteristics). These asymmetric characteristics are conserved across a wide range of species, from bacteria to humans.

Macroscopic Theory for Evolving Biological Systems Akin to Thermodynamics

We present a macroscopic theory to characterize the plasticity, robustness, and evolvability of biological responses and their fluctuations. First, linear approximation in intracellular reaction dynamics is used to demonstrate proportional changes in the expression of all cellular components in response to a given environmental stress, with the proportion coefficient determined by the change in growth rate as a consequence of the steady growth of cells. We further demonstrate that this relationship is supported through adaptation experiments of bacteria, perhaps too well as this proportionality is held even across cultures of different types of conditions. On the basis of simulations of cell models, we further show that this global proportionality is a consequence of evolution in which expression changes in response to environmental or genetic perturbations are constrained along a unique one-dimensional curve, which is a result of evolutionary robustness. It then follows that the expression changes induced by environmental changes are proportionally reduced across different components of a cell by evolution, which is akin to the Le Chatelier thermodynamics principle. Finally, with the aid of a fluctuation-response relationship, this proportionality is shown to hold between fluctuations caused by genetic changes and those caused by noise. Overall, these results and support from the theoretical and experimental literature suggest a formulation of cellular systems akin to thermodynamics, in which a macroscopic potential is given by the growth rate (or fitness) represented as a function of environmental and evolutionary changes.

On the role of sparseness in the evolution of modularity in gene regulatory networks

Modularity is a widespread property in biological systems. It implies that interactions occur mainly within groups of system elements. A modular arrangement facilitates adjustment of one module without perturbing the rest of the system. Therefore, modularity of developmental mechanisms is a major factor for evolvability, the potential to produce beneficial variation from random genetic change. Understanding how modularity evolves in gene regulatory networks, that create the distinct gene activity patterns that characterize different parts of an organism, is key to developmental and evolutionary biology. One hypothesis for the evolution of modules suggests that interactions between some sets of genes become maladaptive when selection favours additional gene activity patterns. The removal of such interactions by selection would result in the formation of modules. A second hypothesis suggests that modularity evolves in response to sparseness, the scarcity of interactions within a system. Here I simulate the evolution of gene regulatory networks and analyse diverse experimentally sustained networks to study the relationship between sparseness and modularity. My results suggest that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, sparseness amplifies the effects of forms of selection that, like selection for additional gene activity patterns, already produce an increase in modularity. That evolution of new gene activity patterns is frequent across evolution also supports that it is a major factor in the evolution of modularity. That sparseness is widespread across gene regulatory networks indicates that it may have facilitated the evolution of modules in a wide variety of cases.

Modular systems have performance and design advantages over non-modular systems. Thus, modularity is very important for the development of a wide range of new technological or clinical applications. Moreover, modularity is paramount to evolutionary biology since it allows adjusting one organismal function without disturbing other previously evolved functions. But how does modularity itself evolve? Here I analyse the structure of regulatory networks and follow simulations of network evolution to study two hypotheses for the origin of modules in gene regulatory networks. The first hypothesis considers that sparseness, a low number of interactions among the network genes, could be responsible for the evolution of modular networks. The second, that modules evolve when selection favours the production of additional gene activity patterns. I found that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, it enhances the effects of selection for multiple gene activity patterns. While selection for multiple patterns may be decisive in the evolution of modularity, that sparseness is widespread across gene regulatory networks suggests that its contributions should not be neglected.

Gene regulatory and signaling networks exhibit distinct topological distributions of motifs

The biological processes of cellular decision making and differentiation involve a plethora of signaling pathways and gene regulatory circuits. These networks in turn exhibit a multitude of motifs playing crucial parts in regulating network activity. Here we compare the topological placement of motifs in gene regulatory and signaling networks and observe that it suggests different evolutionary strategies in motif distribution for distinct cellular subnetworks.

Structural properties of genotype-phenotype maps

The map between genotype and phenotype is fundamental to biology. Biological information is stored and passed on in the form of genotypes, and expressed in the form of phenotypes. A growing body of literature has examined a wide range of genotype-phenotype (GP) maps and has established a number of properties that appear to be shared by many GP maps. These properties are 'structural' in the sense that they are properties of the distribution of phenotypes across the point-mutation network of genotypes. They include: a redundancy of genotypes, meaning that many genotypes map to the same phenotypes, a highly non-uniform distribution of the number of genotypes per phenotype, a high robustness of phenotypes and the ability to reach a large number of new phenotypes within a small number of mutational steps. A further important property is that the robustness and evolvability of phenotypes are positively correlated. In this review, I give an overview of the study of GP maps with particular emphasis on these structural properties, and discuss a model that attempts to explain why these properties arise, as well as some of the fundamental ways in which the structure of GP maps can affect evolutionary outcomes.

Modelling the influence of parental effects on gene-network evolution

Understanding the importance of nongenetic heredity in the evolutionary process is a major topic in modern evolutionary biology. We modified a classical gene-network model by allowing parental transmission of gene expression and studied its evolutionary properties through individual-based simulations. We identified ontogenetic time (i.e. the time gene networks have to stabilize before being submitted to natural selection) as a crucial factor in determining the evolutionary impact of this phenotypic inheritance. Indeed, fast-developing organisms display enhanced adaptation and greater robustness to mutations when evolving in presence of nongenetic inheritance (NGI). In contrast, in our model, long development reduces the influence of the inherited state of the gene network. NGI thus had a negligible effect on the evolution of gene networks when the speed at which transcription levels reach equilibrium is not constrained. Nevertheless, simulations show that intergenerational transmission of the gene-network state negatively affects the evolution of robustness to environmental disturbances for either fast- or slow-developing organisms. Therefore, these results suggest that the evolutionary consequences of NGI might not be sought only in the way species respond to selection, but also on the evolution of emergent properties (such as environmental and genetic canalization) in complex genetic architectures.

How transcription circuits explore alternative architectures while maintaining overall circuit output

This review by Dalal and Johnson focuses on the evolutionary rewiring of transcription regulators and the conservation of patterns of gene expression. They describe how preservation of gene expression patterns in the wake of extensive rewiring is a general feature of transcription circuit evolution.

Transcription regulators bind to cis-regulatory sequences and thereby control the expression of target genes. While transcription regulators and the target genes that they regulate are often deeply conserved across species, the connections between the two change extensively over evolutionary timescales. In this review, we discuss case studies where, despite this extensive evolutionary rewiring, the resulting patterns of gene expression are preserved. We also discuss in silico models that reach the same general conclusions and provide additional insights into how this process occurs. Together, these approaches make a strong case that the preservation of gene expression patterns in the wake of extensive rewiring is a general feature of transcription circuit evolution.

Robustness versus evolvability analysis for regulatory feed-forward loops

From the definition, it appears that phenotypic robustness and evolvability of an organism are inversely related to each other. However, a number of studies exploring this question have found conflicting evidences in this regard. This question motivated the current work where we explore the relationship between robustness and evolvability. As a model system, we pick the Feed Forward Loops (FFLs), and develop a framework to characterize their performance in terms of their ability to resist changes to steady state expression (robustness), and their ability to evolve towards novel phenotypes (evolvability). We demonstrate that robustness and evolvability are positively correlated in some FFL topologies. We compare this against other small regulatory topologies, and show that the same trend does not hold among them. We postulate that the ability to positively link robustness and evolvability could be an additional reason for over-representation of FFLs in living organisms, as compared to other regulatory topologies.

The space of genotypes is a network of networks: implications for evolutionary and extinction dynamics

The forcing that environmental variation exerts on populations causes continuous changes with only two possible evolutionary outcomes: adaptation or extinction. Here we address this topic by studying the transient dynamics of populations on complex fitness landscapes. There are three important features of realistic landscapes of relevance in the evolutionary process: fitness landscapes are rough but correlated, their fitness values depend on the current environment, and many (often most) genotypes do not yield viable phenotypes. We capture these properties by defining time-varying, holey, NK fitness landscapes. We show that the structure of the space of genotypes so generated is that of a network of networks: in a sufficiently holey landscape, populations are temporarily stuck in local networks of genotypes. Sudden jumps to neighbouring networks through narrow adaptive pathways (connector links) are possible, though strong enough local trapping may also cause decays in population growth and eventual extinction. A combination of analytical and numerical techniques to characterize complex networks and population dynamics on such networks permits to derive several quantitative relationships between the topology of the space of genotypes and the fate of evolving populations.

Genetic variation in adaptability and pleiotropy in budding yeast

Evolution can favor organisms that are more adaptable, provided that genetic variation in adaptability exists. Here, we quantify this variation among 230 offspring of a cross between diverged yeast strains. We measure the adaptability of each offspring genotype, defined as its average rate of adaptation in a specific environmental condition, and analyze the heritability, predictability, and genetic basis of this trait. We find that initial genotype strongly affects adaptability and can alter the genetic basis of future evolution. Initial genotype also affects the pleiotropic consequences of adaptation for fitness in a different environment. This genetic variation in adaptability and pleiotropy is largely determined by initial fitness, according to a rule of declining adaptability with increasing initial fitness, but several individual QTLs also have a significant idiosyncratic role. Our results demonstrate that both adaptability and pleiotropy are complex traits, with extensive heritable differences arising from naturally occurring variation.