Genotype-Phenotype Maps Maximizing Evolvability: Modularity Revisited

The mechanisms translating genetic to phenotypic variation determine the distribution of heritable phenotypic variance available to selection. Pleiotropy is an aspect of this structure that limits independent variation of characters. Modularization of pleiotropy has been suggested to promote evolvability by restricting genetic covariance among unrelated characters and reducing constraints due to correlated response. However, modularity may also reduce total genetic variation of characters. We study the properties of genotype-phenotype maps that maximize average conditional evolvability, measured as the amount of unconstrained genetic variation in random directions of phenotypic space. In general, maximal evolvability occurs by maximizing genetic variance and minimizing genetic covariance. This does not necessarily require modularity, only patterns of pleiotropy that cancel on average. The detailed structure of the most evolvable genotype-phenotype maps depends on the distribution of molecular variance. When molecular variance is determined by mutation-selection equilibrium either highly pleiotropic or highly modular genotype-phenotype maps can be optimal, depending on the mutation rate and the relative strengths of stabilizing selection on the characters.     

Is modularity necessary for evolvability? Remarks on the relationship between pleiotropy and evolvability

Evolvability is the ability to respond to a selective challenge. This requires the capacity to produce the right kind of variation for selection to act upon. To understand evolvability we therefore need to understand the variational properties of biological organisms. Modularity is a variational property, which has been linked to evolvability. If different characters are able to vary independently, selection will be able to optimize each character separately without interference. But although modularity seems like a good design principle for an evolvable organism, it does not therefore follow that it is the only design that can achieve evolvability. In this essay I analyze the effects of modularity and, more generally, pleiotropy on evolvability. Although, pleiotropy causes interference between the adaptation of different characters, it also increases the variational potential of those characters. The most evolvable genetic architectures may often be those with an intermediate level of integration among characters, and in particular those where pleiotropic effects are variable and able to compensate for each other's constraints.     

Coming to Grips with Evolvability

To explain the evolution of complex organisms by random mutation, drift, and selection is not a trivial task. This becomes obvious if we imagine an organism in which most genes affect most traits and all mutations are immediately expressed in the phenotype. Most of the mutations will be deleterious. Computer programmers experienced a similar problem when trying to evolve computer programs by introducing random changes to a conventional computer code, realizing that almost all random changes are “lethal.” Everyone who has done any programming knows that conventional computer languages are very brittle! Real organisms are not organized in this way but rather involve mediation between the genes and the phenotypic traits, namely development, also sometimes called the genotype–phenotype map. This map of genetic effects is structured in a way that enables evolvability, that is, enhances the probability that mutations will improve the performance of the organism. Here we outline two properties of organismal development, namely modularity and robustness. Modularity refers to the situation in which genes affect a restricted number of functionally related phenotypic characters. Robustness describes a situation in which cryptic mutations can accumulate without effect on fitness but can become visible to selection in a new environment or genetic background. We discuss recent empirical evidence in support of both phenomena and their effect on evolvability and also briefly address their evolution.     

Plasticity, evolvability, and modularity in RNA

RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype-phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneous and profoundly non-independent effects of natural selection. Molecular plasticity is viewed here as the capacity of an RNA sequence to assume a variety of energetically favorable shapes by equilibrating among them at constant temperature. Through simulations based on experimental designs, we study the dynamics of a population of RNA molecules that evolve toward a predefined target shape in a constant environment. Each shape in the plastic repertoire of a sequence contributes to the overall fitness of the sequence in proportion to the time the sequence spends in that shape. Plasticity is costly, since the more shapes a sequence can assume, the less time it spends in any one of them. Unsurprisingly, selection leads to a reduction of plasticity (environmental canalization). The most striking observation, however, is the simultaneous slow-down and eventual halting of the evolutionary process. The reduction of plasticity entails genetic canalization, that is, a dramatic loss of variability (and hence a loss of evolvability) to the point of lock-in. The causal bridge between environmental canalization and genetic canalization is provided by a correlation between the set of shapes in the plastic repertoire of a sequence and the set of dominant (minimum free energy) shapes in its genetic neighborhood. This statistical property of the RNA genotype-phenotype map, which we call plastogenetic congruence, traps populations in regions where most genetic variation is phenotypically neutral. We call this phenomenon neutral confinement. Analytical models of neutral confinement, made tractable by the assumption of perfect plastogenetic congruence, formally connect mutation rate, the topography of phenotype space, and evolvability. These models identify three mutational regimes: that corresponding to neutral confinement, an exploration threshold corresponding to a breakdown of neutral confinement with the simultaneous persistence of the dominant phenotype, and a classic error threshold corresponding to the loss of the dominant phenotype. In a final step, we analyze the structural properties of canalized phenotypes. The reduction of plasticity leads to extreme modularity, which we analyze from several perspectives: thermophysical (melting--the RNA version of a norm of reaction), kinetic (folding pathways--the RNA version of development), and genetic (transposability--the insensitivity to genetic context). The model thereby suggests a possible evolutionary origin of modularity as a side effect of environmental canalization.     

Pleiotropic mutation, modularity and evolvability

The relationship between pleiotropy and the rate of evolution of a phenotypic character (evolvability) in a population is explored using computer simulations. I present results that suggest the rate of evolution of a phenotypic character may not decline when that character is pleiotropically associated to an increasing number of other characters, provided that the characters are under pure directional selection such that they are far from their optima relative to the average magnitude of a mutation. These conditions may be relevant during adaptive radiations. Adding pleiotropic associations to a set of characters in which one is under directional selection and the other is under stabilizing selection increases the rate of adaptation of the character under directional selection provided that the new characters that come to be pleiotropically associated are under directional selection. Thus, increasing the number of pleiotropic associations under these conditions increases the rate of adaptation of a character.     

Sexual Dimorphism Increases Evolvability in a Genetic Regulatory Network

The majority of work on genetic regulatory networks has focused on environmental and mutational robustness, and much less attention has been paid to the conditions under which a network may produce an evolvable phenotype. Sexually dimorphic characters often show rapid rates of change over short evolutionary time scales and while this is thought to be due to the strength of sexual selection acting on the trait, a dimorphic character with an underlying pleiotropic architecture may also influence the evolution of the regulatory network that controls the character and affect evolvability. As evolvability indicates a capacity for phenotypic change and mutational robustness refers to a capacity for phenotypic stasis, increases in evolvability may show a negative relationship with mutational robustness. I tested this with a computational model of a genetic regulatory network and found that, contrary to expectation, sexually dimorphic characters exhibited both higher mutational robustness and higher evolvability. Decomposition of the results revealed that linkage disequilibrium within sex and linkage disequilibrium between sexes, two of the three primary components of additive genetic variance and evolvability in quantitative genetics models, contributed to the differences in evolvability between sexually dimorphic and monomorphic populations. These results indicate that producing two pleiotropically linked characters did not constrain either the production of a robust phenotype or adaptive potential. Instead, the genetic system evolved to maximize both quantities.     

The role of epistatic gene interactions in the response to selection and the evolution of evolvability

It has been argued that the architecture of the genotype-phenotype map determines evolvability, but few studies have attempted to quantify these effects. In this article we use the multilinear epistatic model to study the effects of different forms of epistasis on the response to directional selection. We derive an analytical prediction for the change in the additive genetic variance, and use individual-based simulations to understand the dynamics of evolvability and the evolution of genetic architecture. This shows that the major determinant for the evolution of the additive variance, and thus the evolvability, is directional epistasis. Positive directional epistasis leads to an acceleration of evolvability, while negative directional epistasis leads to canalization. In contrast, pure non-directional epistasis has little effect on the response to selection. One consequence of this is that the classical epistatic variance components, which do not distinguish directional and non-directional effects, are useless as predictors of evolutionary dynamics. The build-up of linkage disequilibrium also has negligible effects. We argue that directional epistasis is likely to have major effects on evolutionary dynamics and should be the focus of empirical studies of epistasis.     

The Developmental Basis of Variational Modularity: Insights from Quantitative Genetics,Morphometrics, and Developmental Biology

Groups of correlated characters (variational modules) often are considered to be the result of dissociated local developmental factors, i.e., of a modular genotype–phenotype map. But certain sets of pleiotropic factors can equally well induce modular phenotypic variation—no local developmental factors are necessary for a modular covariance structure. It is thus not possible to infer genetic or developmental modularity from standing variation alone. Yet, only for approximately linear genotype–phenotype maps is the induced covariance structure stable over changes of the phenotypic mean. For larger genetic and phenotypic variation, such as on a macroevolutionary level, developmental effects often are nonlinear and variational modularity remains stable only when it is realized by local dissociated developmental factors with no overlap of pleiotropic ranges. The evo-devo concept of modularity concurs only at this macroevolutionary level with the quantitative notion of variational modularity. Empirical evidence on the genetic and developmental architecture underlying phenotypic variation is inconclusive and partly subject to methodological problems. Many studies seem to indicate modularized phenotypic variation and local clusters of QTL effects, whereas other studies find support for several alternative models of modularity and report continuous distributions of QTL effects. This inconsistency partly results from the neglect of spatial relationships among the measured traits. Given the complex development of higher organisms, a combination of pleiotropic factors and more local developmental effects with a hierarchical, overlapping, and more or less continuous distribution appears most likely.     

On the pleiotropic structure of the genotype-phenotype map and the evolvability of complex organisms

Analyses of effects of mutants on many traits have enabled estimates to be obtained of the magnitude of pleiotropy, and in reviews of such data others have concluded that the degree of pleiotropy is highly restricted, with implications on the evolvability of complex organisms. We show that these conclusions are highly dependent on statistical assumptions, for example significance levels. We analyze models with pleiotropic effects on all traits at all loci but by variable amounts, considering distributions of numbers of traits declared significant, overall pleiotropic effects, and extent of apparent modularity of effects. We demonstrate that these highly pleiotropic models can give results similar to those obtained in analyses of experimental data and that conclusions on limits to evolvability through pleiotropy are not robust.     

Evolution of networks for body plan patterning; interplay of modularity, robustness and evolvability

A major goal of evolutionary developmental biology (evo-devo) is to understand how multicellular body plans of increasing complexity have evolved, and how the corresponding developmental programs are genetically encoded. It has been repeatedly argued that key to the evolution of increased body plan complexity is the modularity of the underlying developmental gene regulatory networks (GRNs). This modularity is considered essential for network robustness and evolvability. In our opinion, these ideas, appealing as they may sound, have not been sufficiently tested. Here we use computer simulations to study the evolution of GRNs' underlying body plan patterning. We select for body plan segmentation and differentiation, as these are considered to be major innovations in metazoan evolution. To allow modular networks to evolve, we independently select for segmentation and differentiation. We study both the occurrence and relation of robustness, evolvability and modularity of evolved networks. Interestingly, we observed two distinct evolutionary strategies to evolve a segmented, differentiated body plan. In the first strategy, first segments and then differentiation domains evolve (SF strategy). In the second scenario segments and domains evolve simultaneously (SS strategy). We demonstrate that under indirect selection for robustness the SF strategy becomes dominant. In addition, as a byproduct of this larger robustness, the SF strategy is also more evolvable. Finally, using a combined functional and architectural approach, we determine network modularity. We find that while SS networks generate segments and domains in an integrated manner, SF networks use largely independent modules to produce segments and domains. Surprisingly, we find that widely used, purely architectural methods for determining network modularity completely fail to establish this higher modularity of SF networks. Finally, we observe that, as a free side effect of evolving segmentation and differentiation in combination, we obtained in-silico developmental mechanisms resembling mechanisms used in vertebrate development.     

以发育模块重复征用和整合为基础的进化创新机制

进化新征的起源和分化是进化发育生物学研究的核心问题。通过对多细胞生物早期发育调控机制的比较分析,发现亲缘关系较远的生物所共有的一些形态特征受保守的发育调控程序调节（深同源性）。许多创新性状的发生是基于对预先存在的基因或发育调控模块的重复利用和整合。发育基因调控网络在结构和功能上高度模块化,因此不仅可以通过模块拆分和重复征用改变发育程式,而且也增强了调控网络自身的进化力。研究基因调控网络和发育系统的进化动态将有助于更深入地认识生物演化过程中创新性状发生和表型进化的分子机制。     

The evolutionary dynamics of evolvability in a gene network model

Evolvability, the ability of populations to adapt, has recently emerged as a major unifying concept in biology. Although the study of evolvability offers new insights into many important biological questions, the conceptual bases of evolvability, and the mechanisms of its evolution, remain controversial. We used simulated evolution of a model of gene network dynamics to test the contentious hypothesis that natural selection can favour high evolvability, in particular in sexual populations. Our results conclusively demonstrate that fluctuating natural selection can increase the capacity of model gene networks to adapt to new environments. Detailed studies of the evolutionary dynamics of these networks establish a broad range of validity for this result and quantify the evolutionary forces responsible for changes in evolvability. Analysis of the genotype–phenotype map of these networks also reveals mechanisms connecting evolvability, genetic architecture and robustness. Our results suggest that the evolution of evolvability can have a pervasive influence on many aspects of organisms.     

On the origin of modular variation

We study the dynamics of modularization in a minimal substrate. A module is a functional unit relatively separable from its surrounding structure. Although it is known that modularity is useful both for robustness and for evolvability (Wagner 1996), there is no quantitative model describing how such modularity might originally emerge. Here we suggest, using simple computer simulations, that modularity arises spontaneously in evolutionary systems in response to variation, and that the amount of modular separation is logarithmically proportional to the rate of variation. Consequently, we predict that modular architectures would appear in correlation with high environmental change rates. Because this quantitative model does not require any special substrate to occur, it may also shed light on the origin of modular variation in nature. This observed relationship also indicates that modular design is a generic phenomenon that might be applicable to other fields, such as engineering: Engineering design methods based on evolutionary simulation would benefit from evolving to variable, rather than stationary, fitness criteria, as a weak and problem-independent method for inducing modularity.     

The Evolutionary Origins of Hierarchy

Hierarchical organization—the recursive composition of sub-modules—is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments). Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force–the cost of connections–promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics.     

Mosaic evolution,preadaptation, and the evolution of evolvability in apes

A major goal in postsynthesis evolutionary biology has been to better understand how complex interactions between traits drive movement along and facilitate the formation of distinct evolutionary pathways. I present analyses of a character matrix sampled across the haplorrhine skeleton that revealed several modules of characters displaying distinct patterns in macroevolutionary disparity. Comparison of these patterns to those in neurological development showed that early ape evolution was characterized by an intense regime of evolutionary and developmental flexibility. Shifting and reduced constraint in apes was met with episodic bursts in phenotypic innovation that built a wide array of functional diversity over a foundation of shared developmental and anatomical structure. Shifts in modularity drove dramatic evolutionary changes across the ape body plan in two distinct ways: (1) an episode of relaxed integration early in hominoid evolution coincided with bursts in evolutionary rate across multiple character suites; (2) the formation of two new trait modules along the branch leading to chimps and humans preceded rapid and dramatic evolutionary shifts in the carpus and pelvis. Changes to the structure of evolutionary mosaicism may correspond to enhanced evolvability that has a “preadaptive” effect by catalyzing later episodes of dramatic morphological remodeling.     

Sexual reproduction reshapes the genetic architecture of digital organisms

Modularity and epistasis, as well as other aspects of genetic architecture, have emerged as central themes in evolutionary biology. Theory suggests that modularity promotes evolvability, and that aggravating (synergistic) epistasis among deleterious mutations facilitates the evolution of sex. Here, by contrast, we investigate the evolution of different genetic architectures using digital organisms, which are computer programs that self-replicate, mutate, compete and evolve. Specifically, we investigate how genetic architecture is shaped by reproductive mode. We allowed 200 populations of digital organisms to evolve for over 10 000 generations while reproducing either asexually or sexually. For 10 randomly chosen organisms from each population, we constructed and analysed all possible single mutants as well as one million mutants at each mutational distance from 2 to 10. The genomes of sexual organisms were more modular than asexual ones; sites encoding different functional traits had less overlap and sites encoding a particular trait were more tightly clustered. Net directional epistasis was alleviating (antagonistic) in both groups, although the overall strength of this epistasis was weaker in sexual than in asexual organisms. Our results show that sexual reproduction profoundly influences the evolution of the genetic architecture.     

Genetic interference reduces the evolvability of modular and non-modular visual neural networks

The aim of this paper is to propose an interdisciplinary evolutionary connectionism approach for the study of the evolution of modularity. It is argued that neural networks as a model of the nervous system and genetic algorithms as simulative models of biological evolution would allow us to formulate a clear and operative definition of module and to simulate the different evolutionary scenarios proposed for the origin of modularity. I will present a recent model in which the evolution of primate cortical visual streams is possible starting from non-modular neural networks. Simulation results not only confirm the existence of the phenomenon of neural interference in non-modular network architectures but also, for the first time, reveal the existence of another kind of interference at the genetic level, i.e. genetic interference, a new population genetic mechanism that is independent from the network architecture. Our simulations clearly show that genetic interference reduces the evolvability of visual neural networks and sexual reproduction can at least partially solve the problem of genetic interference. Finally, it is shown that entrusting the task of finding the neural network architecture to evolution and that of finding the network connection weights to learning is a way to completely avoid the problem of genetic interference. On the basis of this evidence, it is possible to formulate a new hypothesis on the origin of structural modularity, and thus to overcome the traditional dichotomy between innatist and empiricist theories of mind.     

Is the genotype-phenotype map modular? A statistical approach using mouse quantitative trait loci data.

Various theories about the evolution of complex characters make predictions about the statistical distribution of genetic effects on phenotypic characters, also called the genotype-phenotype map. With the advent of QTL technology, data about these distributions are becoming available. In this article, we propose simple tests for the prediction that functionally integrated characters have a modular genotype-phenotype map. The test is applied to QTL data on the mouse mandible. The results provide statistical support for the notion that the ascending ramus region of the mandible is modularized. A data set comprising the effects of QTL on a more extensive portion of the phenotype is required to determine if the alveolar region of the mandible is also modularized.     

Evolvability and genetic constraint in Dalechampia blossoms: genetic correlations and conditional evolvability

The short-term evolvability of a character is closely related to its level of additive genetic variation. However, a large component of the variation in any one character may be pleiotropically linked to other characters under the influence of different selective factors. Therefore, the organization of the organism into quasi-independent modules may be an important prerequisite for evolvability. In this paper we propose to study character evolvability in terms of conditional genetic variation. By estimating the amount of genetic variation in a character, y, that is independent of other characters, x, we can assess the evolvability of y when there is stabilizing selection on x. We suggest that systematic use of conditioning may help build a picture of modular organization and quasi-independent evolvability. As an illustration, we use this approach to assess the evolvability of floral characters in Dalechampia scandens (Euphorbiaceae). Although our study population had relatively low levels of genetic variation at the outset, we find evidence that conditioning may lead to substantial further reduction in the genetic variation available for independent adaptation. This provides additional evidence that the D. scandens blossom is constrained in its short-term evolvability.     

Macroevolutionary Freezing and the Janusian Nature of Evolvability: Is the Evolution (of Profound Biological Novelty) Going to End?

In a macroevolutionary timescale, evolvability itself evolves. Lineages are sorted based on their ability to generate adaptive novelties, which leads to the optimization of their genotype-phenotype map. The system of translation of genetic or epigenetic changes to the phenotype may reach significant horizontal and vertical complexity, and may even exhibit certain aspects of learning behaviour. This continuously evolving semiotic system probably enables the origin of complex yet functional and internally compatible adaptations. However, it also has a second, “darker”, side. As was pointed out by several authors, the same process gradually reduces the probability of the origination of significant evolutionary novelties. In a similar way to the evolution of societies, teachings, or languages, in which the growing number of internal linkages gradually solidifies their overall structure and the structure or interpretation of their constitutive elements, the evolutionary potential of lineages decreases during biological evolution. Possible adaptations become limited to small “peripheral” modifications. According to the Frozen Evolution theory, some of the proximate causes of this “macroevolutionary freezing” are more pronounced or present exclusively in sexual lineages. Sorting based on the highest (remaining) evolvability probably leads to the establishment of certain structural features of complex organisms, e.g. the modular character of their development and morphology. However, modules also “macroevolutionary freeze” whereas the hypothetical “thawing” of modules or their novel adaptive combinations becomes rarer and rarer. Some possible ways out of this dead end include the rearrangement of individual development, e.g. neoteny, radical simplification, i.e. sacculinization, and transition to a higher level of organization, e.g. symbiosis or symbiogenesis. The evolution of evolvability is essentially a biosemiotic process situated at the intersection of the genocentric modern synthesis and the evo-devo-centric extended synthesis. Therefore, evolvability may eventually connect these three not necessarily contradictory approaches.