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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. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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.

Evolvability is the ability of a biological system to produce phenotypic variation that is both heritable and adaptive. It has long been the subject of anecdotal observations and theoretical work. In recent years, however, the molecular causes of evolvability have been an increasing focus of experimental work. Here, we review recent experimental progress in areas as different as the evolution of drug resistance in cancer cells and the rewiring of transcriptional regulation circuits in vertebrates. This research reveals the importance of three major themes: multiple genetic and non-genetic mechanisms to generate phenotypic diversity, robustness in genetic systems, and adaptive landscape topography. We also discuss the mounting evidence that evolvability can evolve and the question of whether it evolves adaptively.

Much of gene regulation is carried out by proteins that bind DNA or RNA molecules at specific sequences. One class of such proteins is transcription factors, which bind short DNA sequences to regulate transcription. Another class is RNA binding proteins, which bind short RNA sequences to regulate RNA maturation, transport, and stability. Here, we study the robustness and evolvability of these regulatory mechanisms. To this end, we use experimental binding data from 172 human and fruit fly transcription factors and RNA binding proteins as well as human polymorphism data to study the evolution of binding sites in vivo. We find little difference between the robustness of regulatory protein–RNA interactions and transcription factor–DNA interactions to DNA mutations. In contrast, we find that RNA-mediated regulation is less evolvable than transcriptional regulation, because mutations are less likely to create interactions of an RNA molecule with a new RNA binding protein than they are to create interactions of a gene regulatory region with a new transcription factor. Our observations are consistent with the high level of conservation observed for interactions between RNA binding proteins and their target molecules as well as the evolutionary plasticity of regulatory regions bound by transcription factors. They may help explain why transcriptional regulation is implicated in many more evolutionary adaptations and innovations than RNA-mediated gene regulation.

The adaptive landscape is an iconic metaphor that pervades evolutionary biology. It was mostly applied in theoretical models until recent years, when empirical data began to allow partial landscape reconstructions. Here, we exhaustively analyse 1,137 complete landscapes from 129 eukaryotic species, each describing the binding affinity of a transcription factor to all possible short DNA sequences. We find that the navigability of these landscapes through single mutations is intermediate to that of additive and shuffled null models, suggesting that binding affinity—and thereby gene expression—is readily fine-tuned via mutations in transcription factor binding sites. The landscapes have few peaks that vary in their accessibility and in the number of sequences they contain. Binding sites in the mouse genome are enriched in sequences found in the peaks of especially navigable landscapes and the genetic diversity of binding sites in yeast increases with the number of sequences in a peak. Our findings suggest that landscape navigability may have contributed to the enormous success of transcriptional regulation as a source of evolutionary adaptations and innovations. An adaptive landscape is a mapping from a high-dimensional space of genotypes onto fitness or some other related quantitative phenotype, which defines the ‘elevation’ of each coordinate in genotype space 1 . Evolution can be viewed as a hill-climbing process in an adaptive landscape, where populations tend to move towards peaks as a consequence of natural selection. The ruggedness of an adaptive landscape has important evolutionary consequences, particularly for the evolution of sex, reproductive isolation and mutational robustness, and for the predictability of evolution 2 . An adaptive landscape that is smooth and single peaked does not pose any obstacle to evolutionary exploration. It is therefore highly navigable, in that it is possible to reach the global peak via positive selection through a series of sma

Gene regulatory circuits are to the cell what arithmetic logic units are to the chip: fundamental components of information processing that map an input onto an output. Gene regulatory circuits come in many different forms, distinct structural configurations that determine who regulates whom. Studies that have focused on the gene expression patterns (functions) of circuits with a given structure (form) have examined just a few structures or gene expression patterns. Here, we use a computational model to exhaustively characterize the gene expression patterns of nearly 17 million three-gene circuits in order to systematically explore the relationship between circuit form and function. Three main conclusions emerge. First, function does not follow form. A circuit of any one structure can have between twelve and nearly thirty thousand distinct gene expression patterns. Second, and conversely, form does not follow function. Most gene expression patterns can be realized by more than one circuit structure. And third, multifunctionality severely constrains circuit form. The number of circuit structures able to drive multiple gene expression patterns decreases rapidly with the number of these patterns. These results indicate that it is generally not possible to infer circuit function from circuit form, or vice versa.

Robustness is the invariance of a phenotype in the face of environmental or genetic change. The phenotypes produced by transcriptional regulatory circuits are gene expression patterns that are to some extent robust to mutations. Here we review several causes of this robustness. They include robustness of individual transcription factor binding sites, homotypic clusters of such sites, redundant enhancers, transcription factors, redundant transcription factors, and the wiring of transcriptional regulatory circuits. Such robustness can either be an adaptation by itself, a byproduct of other adaptations, or the result of biophysical principles and non-adaptive forces of genome evolution. The potential consequences of such robustness include complex regulatory network topologies that arise through neutral evolution, as well as cryptic variation, i.e., genotypic divergence without phenotypic divergence. On the longest evolutionary timescales, the robustness of transcriptional regulation has helped shape life as we know it, by facilitating evolutionary innovations that helped organisms such as flowering plants and vertebrates diversify.

In gene regulatory circuits, the expression of individual genes is commonly modulated by a set of regulating gene products, which bind to a gene's cis-regulatory region. This region encodes an input-output function, referred to as signal-integration logic, that maps a specific combination of regulatory signals (inputs) to a particular expression state (output) of a gene. The space of all possible signal-integration functions is vast and the mapping from input to output is many-to-one: For the same set of inputs, many functions (genotypes) yield the same expression output (phenotype). Here, we exhaustively enumerate the set of signal-integration functions that yield identical gene expression patterns within a computational model of gene regulatory circuits. Our goal is to characterize the relationship between robustness and evolvability in the signal-integration space of regulatory circuits, and to understand how these properties vary between the genotypic and phenotypic scales. Among other results, we find that the distributions of genotypic robustness are skewed, so that the majority of signal-integration functions are robust to perturbation. We show that the connected set of genotypes that make up a given phenotype are constrained to specific regions of the space of all possible signal-integration functions, but that as the distance between genotypes increases, so does their capacity for unique innovations. In addition, we find that robust phenotypes are (i) evolvable, (ii) easily identified by random mutation, and (iii) mutationally biased toward other robust phenotypes. We explore the implications of these latter observations for mutation-based evolution by conducting random walks between randomly chosen source and target phenotypes. We demonstrate that the time required to identify the target phenotype is independent of the properties of the source phenotype.

BACKGROUND Latent phenotypes are non-adaptive byproducts of adaptive phenotypes. They exist in biological systems as different as promiscuous enzymes and genome-scale metabolic reaction networks, and can give rise to evolutionary adaptations and innovations. We know little about their prevalence in the gene expression phenotypes of regulatory circuits, important sources of evolutionary innovations. RESULTS Here, we study a space of more than sixteen million three-gene model regulatory circuits, where each circuit is represented by a genotype, and has one or more functions embodied in one or more gene expression phenotypes. We find that the majority of circuits with single functions have latent expression phenotypes. Moreover, the set of circuits with a given spectrum of functions has a repertoire of latent phenotypes that is much larger than that of any one circuit. Most of this latent repertoire can be easily accessed through a series of small genetic changes that preserve a circuit's main functions. Both circuits and gene expression phenotypes that are robust to genetic change are associated with a greater number of latent phenotypes. CONCLUSIONS Our observations suggest that latent phenotypes are pervasive in regulatory circuits, and may thus be an important source of evolutionary adaptations and innovations involving gene regulation.

The population structure of an evolutionary algorithm influences the dissemination and mixing of advantageous alleles, and therefore affects search performance. Much recent attention has focused on the analysis of complex population structures, characterized by heterogeneous connectivity distributions, non-trivial clustering properties, and degree-degree correlations. Here, we synthesize the results of these recent studies, discuss their limitations, and highlight several open questions regarding (1) unsolved theoretical issues and (2) the practical utility of complex population structures for evolutionary search. In addition, we will discuss an alternative complex population structure that is known to significantly influence dynamical processes, but has yet to be explored for evolutionary optimization. We then shift our attention toward dynamic population structures, which have received markedly less attention than their static counterparts. We will discuss the strengths and limitations of extant techniques and present open theoretical and experimental questions and directions for future research. In particular, we will focus on the prospects of "active linking,” wherein edges are dynamically rewired according to the genotypic or phenotypic properties of individuals, or according to the success of prior inter-individual interactions

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.