Population and quantitative genetics of regulatory networks

Evolvability and robustness: A paradox restored

Evolvability and robustness are crucial for the origin and maintenance of complex organisms, but may not be simultaneously achievable as robust traits are also hard to change. Andreas Wagner has proposed a solution to this paradox by arguing that the many-to-few aspect of genotype-phenotype maps creates neutral networks of genotypes coding for the same phenotype. Phenotypes with large networks are genetically robust, but they may also have more neighboring phenotypes and thus higher evolvability. In this paper, we explore the generality of this idea by sampling large numbers of random genotype-phenotype maps for Boolean genotypes and phenotypes. We show that there is indeed a preponderance of positive correlations between the evolvability and robustness of phenotypes within a genotype-phenotype map, but also that there are negative correlations between average evolvability and robustness across maps. We interpret this as predicting a positive correlation across the phenotypic states of a character, but a negative correlation across characters. We also argue that evolvability and robustness tend to be negatively correlated when phenotypes are measured on ordinal or higher scale types. We conclude that Wagner's conjecture of a positive relation between robustness and evolvability is based on strict and somewhat unrealistic biological assumptions.

Bridging the genotype-phenotype gap: what does it take?

The genotype-phenotype map (GP map) concept applies to any time point in the ontogeny of a living system. It is the outcome of very complex dynamics that include environmental effects, and bridging the genotype-phenotype gap is synonymous with understanding these dynamics. The context for this understanding is physiology, and the disciplinary goals of physiology do indeed demand the physiological community to seek this understanding. We claim that this task is beyond reach without use of mathematical models that bind together genetic and phenotypic data in a causally cohesive way. We provide illustrations of such causally cohesive genotype-phenotype models where the phenotypes span from gene expression profiles to development of whole organs. Bridging the genotype-phenotype gap also demands that large-scale biological ('omics') data and associated bioinformatics resources be more effectively integrated with computational physiology than is currently the case. A third major element is the need for developing a phenomics technology way beyond current state of the art, and we advocate the establishment of a Human Phenome Programme solidly grounded on biophysically based mathematical descriptions of human physiology.

Parameters in dynamic models of complex traits are containers of missing heritability

Polymorphisms identified in genome-wide association studies of human traits rarely explain more than a small proportion of the heritable variation, and improving this situation within the current paradigm appears daunting. Given a well-validated dynamic model of a complex physiological trait, a substantial part of the underlying genetic variation must manifest as variation in model parameters. These parameters are themselves phenotypic traits. By linking whole-cell phenotypic variation to genetic variation in a computational model of a single heart cell, incorporating genotype-to-parameter maps, we show that genome-wide association studies on parameters reveal much more genetic variation than when using higher-level cellular phenotypes. The results suggest that letting such studies be guided by computational physiology may facilitate a causal understanding of the genotype-to-phenotype map of complex traits, with strong implications for the development of phenomics technology.

Despite an ever-increasing number of genome locations reported to be associated with complex human diseases or quantitative traits, only a small proportion of phenotypic variations in a typical quantitative trait can be explained by the discovered variants. We argue that this problem can partly be resolved by combining the statistical methods of quantitative genetics with computational biology. We demonstrate this for the in silico genotype-to-phenotype map of a model heart cell in conjunction with publically accessible genomic data. We show that genome wide association studies (GWAS) on model parameters identify more causal variants and can build better prediction models for the higher-level phenotypes than by performing GWAS on the higher-level phenotypes themselves. Since model parameters are in principle measurable physiological phenotypes, our findings suggest that development of future phenotyping technologies could be guided by mathematical models of the biological systems being targeted.

Gene networks and metacommunities: dispersal differences can override adaptive advantage

Dispersal is an important mechanism contributing to both ecological and evolutionary dynamics. In metapopulation and metacommunity ecology, dispersal enables new patches to be colonized; in evolution, dispersal counter-acts local selection, leading to regional homogenization. Here, I consider a three-patch metacommunity in which two species, each with a limiting quantitative trait underlain by gene networks of 16 to 256 genes, compete with one another and disperse among patches. Incorporating dispersal among heterogeneous patches introduces a tradeoff not observed in single-patch simulations: if the difference between gene network size of the two species is greater than the difference in dispersal ability (e.g., if the ratio of network sizes is larger than the ratio of dispersal abilities), then genetic architecture drives community outcome. However, if the difference in dispersal abilities is greater than gene network differences, then any adaptive advantages afforded by genetic architecture are over-ridden by dispersal. Thus, in addition to the selective pressures imposed by competition that shape the genetic architecture of quantitative traits, dispersal among patches creates an escape that may further alter the effects of different genetic architectures. These results provide a theoretical expectation for what we may observe as the field of ecological genomics develops.

Smaller gene networks permit longer persistence in fast-changing environments

The environments in which organisms live and reproduce are rarely static, and as the environment changes, populations must evolve so that phenotypes match the challenges presented. The quantitative traits that map to environmental variables are underlain by hundreds or thousands of interacting genes whose allele frequencies and epistatic relationships must change appropriately for adaptation to occur. Extending an earlier model in which individuals possess an ecologically-critical trait encoded by gene networks of 16 to 256 genes and random or scale-free topology, I test the hypothesis that smaller, scale-free networks permit longer persistence times in a constantly-changing environment. Genetic architecture interacting with the rate of environmental change accounts for 78% of the variance in trait heritability and 66% of the variance in population persistence times. When the rate of environmental change is high, the relationship between network size and heritability is apparent, with smaller and scale-free networks conferring a distinct advantage for persistence time. However, when the rate of environmental change is very slow, the relationship between network size and heritability disappears and populations persist the duration of the simulations, without regard to genetic architecture. These results provide a link between genes and population dynamics that may be tested as the -omics and bioinformatics fields mature, and as we are able to determine the genetic basis of ecologically-relevant quantitative traits.

Evolution of competitive ability: an adaptation speed vs. accuracy tradeoff rooted in gene network size

Ecologists have increasingly come to understand that evolutionary change on short time-scales can alter ecological dynamics (and vice-versa), and this idea is being incorporated into community ecology research programs. Previous research has suggested that the size and topology of the gene network underlying a quantitative trait should constrain or facilitate adaptation and thereby alter population dynamics. Here, I consider a scenario in which two species with different genetic architectures compete and evolve in fluctuating environments. An important trade-off emerges between adaptive accuracy and adaptive speed, driven by the size of the gene network underlying the ecologically-critical trait and the rate of environmental change. Smaller, scale-free networks confer a competitive advantage in rapidly-changing environments, but larger networks permit increased adaptive accuracy when environmental change is sufficiently slow to allow a species time to adapt. As the differences in network characteristics increase, the time-to-resolution of competition decreases. These results augment and refine previous conclusions about the ecological implications of the genetic architecture of quantitative traits, emphasizing a role of adaptive accuracy. Along with previous work, in particular that considering the role of gene network connectivity, these results provide a set of expectations for what we may observe as the field of ecological genomics develops.

Smaller, scale-free gene networks increase quantitative trait heritability and result in faster population recovery

One of the goals of biology is to bridge levels of organization. Recent technological advances are enabling us to span from genetic sequence to traits, and then from traits to ecological dynamics. The quantitative genetics parameter heritability describes how quickly a trait can evolve, and in turn describes how quickly a population can recover from an environmental change. Here I propose that we can link the details of the genetic architecture of a quantitative trait--i.e., the number of underlying genes and their relationships in a network--to population recovery rates by way of heritability. I test this hypothesis using a set of agent-based models in which individuals possess one of two network topologies or a linear genotype-phenotype map, 16-256 genes underlying the trait, and a variety of mutation and recombination rates and degrees of environmental change. I find that the network architectures introduce extensive directional epistasis that systematically hides and reveals additive genetic variance and affects heritability: network size, topology, and recombination explain 81% of the variance in average heritability in a stable environment. Network size and topology, the width of the fitness function, pre-change additive variance, and certain interactions account for ∼75% of the variance in population recovery times after a sudden environmental change. These results suggest that not only the amount of additive variance, but importantly the number of loci across which it is distributed, is important in regulating the rate at which a trait can evolve and populations can recover. Taken in conjunction with previous research focused on differences in degree of network connectivity, these results provide a set of theoretical expectations and testable hypotheses for biologists working to span levels of organization from the genotype to the phenotype, and from the phenotype to the environment.

Adaptive dynamics of regulatory networks: size matters

To accomplish adaptability, all living organisms are constructed of regulatory networks on different levels which are capable to differentially respond to a variety of environmental inputs. Structure of regulatory networks determines their phenotypical plasticity, that is, the degree of detail and appropriateness of regulatory replies to environmental or developmental challenges. This regulatory network structure is encoded within the genotype. Our conceptual simulation study investigates how network structure constrains the evolution of networks and their adaptive abilities. The focus is on the structural parameter network size. We show that small regulatory networks adapt fast, but not as good as larger networks in the longer perspective. Selection leads to an optimal network size dependent on heterogeneity of the environment and time pressure of adaptation. Optimal mutation rates are higher for smaller networks. We put special emphasis on discussing our simulation results on the background of functional observations from experimental and evolutionary biology.

Adaptive dynamics of regulatory networks: size matters

To accomplish adaptability, all living organisms are constructed of regulatory networks on different levels which are capable to differentially respond to a variety of environmental inputs. Structure of regulatory networks determines their phenotypical plasticity, that is, the degree of detail and appropriateness of regulatory replies to environmental or developmental challenges. This regulatory network structure is encoded within the genotype. Our conceptual simulation study investigates how network structure constrains the evolution of networks and their adaptive abilities. The focus is on the structural parameter network size. We show that small regulatory networks adapt fast, but not as good as larger networks in the longer perspective. Selection leads to an optimal network size dependent on heterogeneity of the environment and time pressure of adaptation. Optimal mutation rates are higher for smaller networks. We put special emphasis on discussing our simulation results on the background of functional observations from experimental and evolutionary biology.

A network model for the correlation between epistasis and genomic complexity

The study of genetic interactions (epistasis) is central to the understanding of genome organization and evolution. A general correlation between epistasis and genomic complexity has been recently shown, such that in simpler genomes epistasis is antagonistic on average (mutational effects tend to cancel each other out), whereas a transition towards synergistic epistasis occurs in more complex genomes (mutational effects strengthen each other). Here, we use a simple network model to identify basic features explaining this correlation. We show that, in small networks with multifunctional nodes, lack of redundancy, and absence of alternative pathways, epistasis is antagonistic on average. In contrast, lack of multi-functionality, high connectivity, and redundancy favor synergistic epistasis. Moreover, we confirm the previous finding that epistasis is a covariate of mutational robustness: in less robust networks it tends to be antagonistic whereas in more robust networks it tends to be synergistic. We argue that network features associated with antagonistic epistasis are typically found in simple genomes, such as those of viruses and bacteria, whereas the features associated with synergistic epistasis are more extensively exploited by higher eukaryotes.

Emergence and maintenance of functional modules in signaling pathways

Background

While detection and analysis of functional modules in biological systems have received great attention in recent years, we still lack a complete understanding of how such modules emerge. One theory is that systems must encounter a varying selection (i.e. environment) in order for modularity to emerge. Here, we provide an alternative and simpler explanation using a realistic model of biological signaling pathways and simulating their evolution.

Results

These evolutionary simulations start with a homogenous population of a minimal pathway containing two effectors coupled to two signals via a single receptor. This population is allowed to evolve under a constant selection pressure for mediating two separate responses. Results of these evolutionary simulations show that under such a selective pressure, mutational processes easily lead to the emergence of pathways with two separate sub-pathways (i.e. modules) each mediating a distinct response only to one of the signals. Such functional modules are maintained as long as mutations leading to new interactions among existing proteins in the pathway are rare.

Conclusion

While supporting a neutralistic view for the emergence of modularity in biological systems, these findings highlight the relevant rate of different mutational processes and the distribution of functional pathways in the topology space as key factors for its maintenance.

Nonlinear regulation enhances the phenotypic expression of trans-acting genetic polymorphisms

BACKGROUND

Genetic variation explains a considerable part of observed phenotypic variation in gene expression networks. This variation has been shown to be located both locally (cis) and distally (trans) to the genes being measured. Here we explore to which degree the phenotypic manifestation of local and distant polymorphisms is a dynamic feature of regulatory design.

RESULTS

By combining mathematical models of gene expression networks with genetic maps and linkage analysis we find that very different network structures and regulatory motifs give similar cis/trans linkage patterns. However, when the shape of the cis-regulatory input functions is more nonlinear or threshold-like, we observe for all networks a dramatic increase in the phenotypic expression of distant compared to local polymorphisms under otherwise equal conditions.

CONCLUSION

Our findings indicate that genetic variation affecting the form of cis-regulatory input functions may reshape the genotype-phenotype map by changing the relative importance of cis and trans variation. Our approach combining nonlinear dynamic models with statistical genetics opens up for a systematic investigation of how functional genetic variation is translated into phenotypic variation under various systemic conditions.

A CENTENNIAL CELEBRATION FOR QUANTITATIVE GENETICS

Quantitative genetics is at or is fast approaching its centennial. In this perspective I consider five current issues pertinent to the application of quantitative genetics to evolutionary theory. First, I discuss the utility of a quantitative genetic perspective in describing genetic variation at two very different levels of resolution, (1) in natural, free-ranging populations and (2) to describe variation at the level of DNA transcription. Whereas quantitative genetics can serve as a very useful descriptor of genetic variation, its greater usefulness is in predicting evolutionary change, particularly when used in the first instance (wild populations). Second, I review the contributions of Quantitative trait loci (QLT) analysis in determining the number of loci and distribution of their genetic effects, the possible importance of identifying specific genes, and the ability of the multivariate breeder's equation to predict the results of bivariate selection experiments. QLT analyses appear to indicate that genetic effects are skewed, that at least 20 loci are generally involved, with an unknown number of alleles, and that a few loci have major effects. However, epistatic effects are common, which means that such loci might not have population-wide major effects: this question waits upon (QTL) analyses conducted on more than a few inbred lines. Third, I examine the importance of research into the action of specific genes on traits. Although great progress has been made in identifying specific genes contributing to trait variation, the high level of gene interactions underlying quantitative traits makes it unlikely that in the near future we will have mechanistic models for such traits, or that these would have greater predictive power than quantitative genetic models. In the fourth section I present evidence that the results of bivariate selection experiments when selection is antagonistic to the genetic covariance are frequently not well predicted by the multivariate breeder's equation. Bivariate experiments that combine both selection and functional analyses are urgently needed. Finally, I discuss the importance of gaining more insight, both theoretical and empirical, on the evolution of the G and P matrices.

Statistical epistasis is a generic feature of gene regulatory networks

Functional dependencies between genes are a defining characteristic of gene networks underlying quantitative traits. However, recent studies show that the proportion of the genetic variation that can be attributed to statistical epistasis varies from almost zero to very high. It is thus of fundamental as well as instrumental importance to better understand whether different functional dependency patterns among polymorphic genes give rise to distinct statistical interaction patterns or not. Here we address this issue by combining a quantitative genetic model approach with genotype-phenotype models capable of translating allelic variation and regulatory principles into phenotypic variation at the level of gene expression. We show that gene regulatory networks with and without feedback motifs can exhibit a wide range of possible statistical genetic architectures with regard to both type of effect explaining phenotypic variance and number of apparent loci underlying the observed phenotypic effect. Although all motifs are capable of harboring significant interactions, positive feedback gives rise to higher amounts and more types of statistical epistasis. The results also suggest that the inclusion of statistical interaction terms in genetic models will increase the chance to detect additional QTL as well as functional dependencies between genetic loci over a broad range of regulatory regimes. This article illustrates how statistical genetic methods can fruitfully be combined with nonlinear systems dynamics to elucidate biological issues beyond reach of each methodology in isolation.

Evolution of branched regulatory genetic pathways: directional selection on pleiotropic loci accelerates developmental system drift

Developmental systems are regulated by a web of interacting loci. One common and useful approach in studying the evolution of development is to focus on classes of interacting elements within these systems. Here, we use individual-based simulations to study the evolution of traits controlled by branched developmental pathways involving three loci, where one locus regulates two different traits. We examined the system under a variety of selective regimes. In the case where one branch was under stabilizing selection and the other under directional selection, we observed "developmental system drift": the trait under stabilizing selection showed little phenotypic change even though the loci underlying that trait showed considerable evolutionary divergence. This occurs because the pleiotropic locus responds to directional selection and compensatory mutants are then favored in the pathway under stabilizing selection. Though developmental system drift may be caused by other mechanisms, it seems likely that it is accelerated by the same underlying genetic mechanism as that producing the Dobzhansky-Muller incompatibilities that lead to speciation in both linear and branched pathways. We also discuss predictions of our model for developmental system drift and how different selective regimes affect probabilities of speciation in the branched pathway system.

Functional and evolutionary inference in gene networks: does topology matter?

The relationship between the topology of a biological network and its functional or evolutionary properties has attracted much recent interest. It has been suggested that most, if not all, biological networks are 'scale free.' That is, their connections follow power-law distributions, such that there are very few nodes with very many connections and vice versa. The number of target genes of known transcriptional regulators in the yeast, Saccharomyces cerevisiae, appears to follow such a distribution, as do other networks, such as the yeast network of protein-protein interactions. These findings have inspired attempts to draw biological inferences from general properties associated with scale-free network topology. One often cited general property is that, when compromised, highly connected nodes will tend to have a larger effect on network function than sparsely connected nodes. For example, more highly connected proteins are more likely to be lethal when knocked out. However, the correlation between lethality and connectivity is relatively weak, and some highly connected proteins can be removed without noticeable phenotypic effect. Similarly, network topology only weakly predicts the response of gene expression to environmental perturbations. Evolutionary simulations of gene-regulatory networks, presented here, suggest that such weak or non-existent correlations are to be expected, and are likely not due to inadequacy of experimental data. We argue that 'top-down' inferences of biological properties based on simple measures of network topology are of limited utility, and we present simulation results suggesting that much more detailed information about a gene's location in a regulatory network, as well as dynamic gene-expression data, are needed to make more meaningful functional and evolutionary predictions. Specifically, we find in our simulations that: (1) the relationship between a gene's connectivity and its fitness effect upon knockout depends on its equilibrium expression level; (2) correlation between connectivity and genetic variation is virtually non-existent, yet upon independent evolution of networks with identical topologies, some nodes exhibit consistently low or high polymorphism; and (3) certain genes show low polymorphism yet high divergence among independent evolutionary runs. This latter pattern is generally taken as a signature of positive selection, but in our simulations its cause is often neutral coevolution of regulatory inputs to the same gene.

A computational method to detect epistatic effects contributing to a quantitative trait

We develop a new computational method to detect epistatic effects that contribute to a complex quantitative trait. Rather than looking for epistatic effects that show statistical significance when considered in isolation, we search for a close approximation to the quantitative trait by a sum of epistatic effects. Our search algorithm consists of a sequence of random walks around the space of sums of epistatic effects. An important feature of our approach is that there is learning between random walks, i.e. the control mechanism that chooses steps in our random walks adapts to the experiences of earlier random walks. We test the effectiveness of our algorithms by applying them to synthetic datasets where the phenotype is a sum of epistatic effects plus normally distributed noise. Our test statistic is the rate of success that our methods achieve in identifying the underlying epistatic effects. We report on the effectiveness of our methods as we vary parameters that are intrinsic to the computation (length of random walks and degree of learning) as well as parameters that are extrinsic to the computation (number of markers, number of individuals, noise level, architecture of the epistatic effects).

The Evolutionary Genetics of Canalization

Evolutionary genetics has recently made enormous progress in understanding how genetic variation maps into phenotypic variation. However why some traits are phenotypically invariant despite apparent genetic and environmental changes has remained a major puzzle. In the 1940s, Conrad Hal Waddington coined the concept and term "canalization" to describe the robustness of phenotypes to perturbation; a similar concept was proposed by Waddington's contemporary Ivan Ivanovich Schmalhausen. This paper reviews what has been learned about canalization since Waddington. Canalization implies that a genotype's phenotype remains relatively invariant when individuals of a particular genotype are exposed to different environments (environmental canalization) or when individuals of the same single- or multilocus genotype differ in their genetic background (genetic canalization). Consequently, genetic canalization can be viewed as a particular kind of epistasis, and environmental canalization and phenotypic plasticity are two aspects of the same phenomenon. Canalization results in the accumulation of phenotypically cryptic genetic variation, which can be released after a "decanalizing" event. Thus, canalized genotypes maintain a cryptic potential for expressing particular phenotypes, which are only uncovered under particular decanalizing environmental or genetic conditions. Selection may then act on this newly released genetic variation. The accumulation of cryptic genetic variation by canalization may therefore increase evolvability at the population level by leading to phenotypic diversification under decanalizing conditions. On the other hand, under canalizing conditions, a major part of the segregating genetic variation may remain phenotypically cryptic; canalization may therefore, at least temporarily, constrain phenotypic evolution. Mechanistically, canalization can be understood in terms of transmission patterns, such as epistasis, pleiotropy, and genotype by environment interactions, and in terms of genetic redundancy, modularity, and emergent properties of gene networks and biochemical pathways. While different forms of selection can favor canalization, the requirements for its evolution are typically rather restrictive. Although there are several methods to detect canalization, there are still serious problems with unambiguously demonstrating canalization, particularly its adaptive value.

Towards more biological mutation operators in gene regulation studies

Genetic regulation is often viewed as a complex system whose properties emerge from the interaction of regulatory genes. One major paradigm for studying the complex dynamics of gene regulation uses directed graphs to explore structure, behaviour and evolvability. Mutation operators used in such studies typically involve the insertion and deletion of nodes, and the insertion, deletion and rewiring of links at the network level. These network-level mutational operators are sufficient to allow the statistical analysis of network structure, but impose limitations on the way networks are evolved. There are a wide variety of mutations in DNA sequences that have yet to be analysed for their network-level effects. By modelling an artificial genome at the level of nucleotide sequences and mapping it to a regulatory network, biologically grounded mutation operators can be mapped to network-level mutations. This paper analyses five such sequence level mutations (single-point mutation, transposition, inversion, deletion and gene duplication) for their effects at the network level. Using analytic and simulation techniques, we show that it is rarely the case that nodes and links are cleanly added or deleted, with even the simplest point mutation causing a wide variety of network-level modifications. As expected, the vast majority of simple (single-point) mutations are neutral, resulting in a neutral plateau from which a range of functional behaviours can be reached. By analysing the effects of sequence-level mutations at the network level of gene regulation, we aim to stimulate more careful consideration of mutation operators in gene regulation models than has previously been given.

Flowering time control: gene network modelling and the link to quantitative genetics

Flowering is a key stage in plant development that initiates grain production and is vulnerable to stress. The genes controlling flowering time in the model plant Arabidopsis thaliana are reviewed. Interactions between these genes have been described previously by qualitative network diagrams. We mathematically relate environmentally dependent transcription, RNA processing, translation, and protein–protein interaction rates to resultant phenotypes. We have developed models (reported elsewhere) based on these concepts that simulate flowering times for novel A. thaliana genotype–environment combinations. Here we draw 12 contrasts between genetic network (GN) models of this type and quantitative genetics (QG), showing that both have equal contributions to make to an ideal theory. Physiological dominance and additivity are examined as emergent properties in the context of feed-forwards networks, an instance of which is the signal-integration portion of the A. thaliana flowering time network. Additivity is seen to be a complex, multi-gene property with contributions from mass balance in transcript production, the feed-forwards structure itself, and downstream promoter reaction thermodynamics. Higher level emergent properties are exemplified by critical short daylength (CSDL), which we relate to gene expression dynamics in rice (Oryza sativa). Next to be discussed are synergies between QG and GN relating to the quantitative trait locus (QTL) mapping of model coefficients. This suggests a new verification test useful in GN model development and in identifying needed updates to existing crop models. Finally, the utility of simple models is evinced by 80 years of QG theory and mathematical ecology.

The evolution of molecular genetic pathways and networks

There is growing interest in the evolutionary dynamics of molecular genetic pathways and networks, and the extent to which the molecular evolution of a gene depends on its position within a pathway or network, as well as over-all network topology. Investigations on the relationships between network organization, topological architecture and evolutionary dynamics provide intriguing hints as to how networks evolve. Recent studies also suggest that genetic pathway and network structures may influence the action of evolutionary forces, and may play a role in maintaining phenotypic robustness in organisms.

The Selective Values of Alleles in a Molecular Network Model Are Context Dependent

Classical quantitative genetics has applied linear modeling to the problem of mapping genotypic to phenotypic variation. Much of this theory was developed prior to the availability of molecular biology. The current understanding of the mechanisms of gene expression indicates the importance of nonlinear effects resulting from gene interactions. We provide a bridge between genetics and gene network theories by relating key concepts from quantitative genetics to the parameters, variables, and performance functions of genetic networks. We illustrate this methodology by simulating the genetic switch controlling galactose metabolism in yeast and its response to selection for a population of individuals. Results indicate that genes have heterogeneous contributions to phenotypes and that additive and nonadditive effects are context dependent. Early cycles of selection suggest strong additive effects attributed to some genes. Later cycles suggest the presence of strong context-dependent nonadditive effects that are conditional on the outcomes of earlier selection cycles. A single favorable allele cannot be consistently identified for most loci. These results highlight the complications that can arise with the presence of nonlinear effects associated with genes acting in networks when selection is conducted on a population of individuals segregating for the genes contributing to the network.

Waddington's canalization revisited: developmental stability and evolution

Most species maintain abundant genetic variation and experience a range of environmental conditions, yet phenotypic variation is low. That is, development is robust to changes in genotype and environment. It has been claimed that this robustness, termed canalization, evolves because of long-term natural selection for optimal phenotypes. We show that the developmental process, here modeled as a network of interacting transcriptional regulators, constrains the genetic system to produce canalization, even without selection toward an optimum. The extent of canalization, measured as the insensitivity to mutation of a network's equilibrium state, depends on the complexity of the network, such that more highly connected networks evolve to be more canalized. We argue that canalization may be an inevitable consequence of complex developmental-genetic processes and thus requires no explanation in terms of evolution to suppress phenotypic variation.

Rapid speciation via parallel, directional selection on regulatory genetic pathways

Regulatory genetic pathways are ubiquitous in organisms and play a central role in the realization of the phenotype during development. We explored the proposition that these pathways can provide a plausible source of the epistatic variation that has been implicated in the evolution of postzygotic reproductive isolation. We modeled gene regulation as a matching function between the product of one locus and the promoter site of the next locus in the pathway, with binding strength determining the amount of product. When the phenotype is subject to parallel selection in a pair of independent populations, we find that the fitnesses of F(1)and F(2)hybrids often drop to very low values as the populations respond in genetically different and incompatible ways. The simulations support the predictions of the analytical models. Hybrid fitness reduction occurs more often as the number of loci in the pathway increases, and as the binding site interactions become more complex. Less hybrid fitness reduction is seen when the populations start with imperfect binding in the pathway. In contrast, when we constructed the phenotype without gene regulation using multiplicative rules, isomorphic to the additive phenotype commonly assumed in evolutionary models, we found no appreciable F(1)fitness reduction and only slight F(2)fitness reduction. The interaction of genetic drift and mutation, even at very high rates, did not reduce hybrid fitness at all on the time-scales we considered. Clearly, the evolution of regulatory genetic pathways can play an important role in speciation, but much more empirical information is needed on the effect of allelic variability in regulatory site interactions before this role is fully understood.

Emergence of homeostasis and "noise imprinting" in an evolution model

Homeostasis, the creation of a stabilized internal milieu, is ubiquitous in biological evolution, despite the entropic cost of excluding noise information from a region. The advantages of stability seem self evident, but the alternatives are not so clear. This issue was studied by means of numerical experiments on a simple evolution model: a population of Boolean network "organisms" selected for performance of a curve-fitting task while subjected to noise. During evolution, noise sensitivity increased with fitness. Noise exclusion evolved spontaneously, but only if the noise was sufficiently unpredictable. Noise that was limited to one or a few stereotyped patterns caused symmetry breaking that prevented noise exclusion. Instead, the organisms incorporated the noise into their function at little cost in ultimate fitness and became totally noise dependent. This "noise imprinting" suggests caution when interpreting apparent adaptations seen in nature. If the noise was totally random from generation to generation, noise exclusion evolved reliably and irreversibly, but if the noise was correlated over several generations, maladaptive selection of noise-dependent traits could reverse noise exclusion, with catastrophic effect on population fitness. Noise entering the selection process rather than the organism had a different effect: adaptive evolution was totally abolished above a critical noise amplitude, in a manner resembling a thermodynamic phase transition. Evolutionary adaptation to noise involves the creation of a subsystem screened from noise information but increasingly vulnerable to its effects. Similar considerations may apply to information channeling in human cultural evolution.