A general population genetic theory for the evolution of developmental interactions

Utilizing developmental dynamics for evolutionary prediction and control

Understanding, predicting, and controlling the phenotypic consequences of genetic and environmental change is essential to many areas of fundamental and applied biology. In evolutionary biology, the generative process of development is a major source of organismal evolvability that constrains or facilitates adaptive change by shaping the distribution of phenotypic variation that selection can act upon. While the complex interactions between genetic and environmental factors during development may appear to make it impossible to infer the consequences of perturbations, the persistent observation that many perturbations result in similar phenotypes indicates that there is a logic to what variation is generated. Here, we show that a general representation of development as a dynamical system can reveal this logic. We build a framework that allows predicting the phenotypic effects of perturbations, and conditions for when the effects of perturbations of different origins are concordant. We find that this concordance is explained by two generic features of development, namely the dynamical dependence of the phenotype on itself and the fact that all perturbations must affect the developmental process to have an effect on the phenotype. We apply our theoretical framework to classical models of development and show that it can be used to predict the evolutionary response to selection using information of plasticity and to accelerate evolution in a desired direction. The framework we introduce provides a way to quantitatively interchange perturbations, opening an avenue of perturbation design to control the generation of variation.

A mathematical framework for evo-devo dynamics

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in "geno-phenotype" space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where "total genotypic selection" vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.

Selection on modifiers of genetic architecture under migration load

Gene flow between populations adapting to differing local environmental conditions might be costly because individuals can disperse to habitats where their survival is low or because they can reproduce with locally maladapted individuals. The amount by which the mean relative population fitness is kept below one creates an opportunity for modifiers of the genetic architecture to spread due to selection. Prior work that separately considered modifiers changing dispersal, recombination rates, or altering dominance or epistasis, has typically focused on the direction of selection rather than its absolute magnitude. We here develop methods to determine the strength of selection on modifiers of the genetic architecture, including modifiers of the dispersal rate, in populations that have previously evolved local adaptation. We consider scenarios with up to five loci contributing to local adaptation and derive a new model for the deterministic spread of modifiers. We find that selection for modifiers of epistasis and dominance is stronger than selection for decreased recombination, and that selection for partial reductions in recombination are extremely weak, regardless of the number of loci contributing to local adaptation. The spread of modifiers that reduce dispersal depends on the number of loci, epistasis and extent of local adaptation in the ancestral population. We identify a novel effect, that modifiers of dominance are more strongly selected when they are unlinked to the locus that they modify. These findings help explain population differentiation and reproductive isolation and provide a benchmark to compare selection on modifiers under finite population sizes and demographic stochasticity.

When populations of a species are spread over different habitats the populations can adapt to their local conditions, provided dispersal between habitats is low enough. Natural selection allows the populations to maintain local adaptation, but dispersal and gene flow create a cost called the migration load. The migration load measures how much fitness is lost because of dispersal between different habitats, and also creates an opportunity for selection to act on the arrangement and interaction between genes that are involved in local adaptation. Modifier genes can spread in these linked populations and cause functional, local adaptation genes, to become more closely linked on a chromosome, or change the way that these genes are expressed so that the locally adapted gene copy becomes dominant. We modeled this process and found that selection on modifiers that create tighter linkage between locally adapted genes is generally weak, and modifiers that cause gene interactions are more strongly selected. Even after these gene interactions have begun to evolve, further selection for increased gene interaction is still strong. Our results show that populations are more likely to adapt to local conditions by evolving new gene interactions than by evolving tightly linked gene clusters.

Directional selection and the evolution of breeding date in birds, revisited: Hard selection and the evolution of plasticity

The mismatch between when individuals breed and when we think they should breed has been a long-standing problem in evolutionary ecology. Price et al. is a classic theory paper in this field and is mainly cited for its most obvious result: if individuals with high nutritional condition breed early, then the advantage of breeding early may be overestimated when information on nutritional condition is absent. Price at al.'s less obvious result is that individuals, on average, are expected to breed later than the optimum. Here, we provide an explanation of their non-intuitive result in terms of hard selection, and go on to show that neither of their results are expected to hold if the relationship between breeding date and nutrition is allowed to evolve. By introducing the assumption that the advantage of breeding early is greater for individuals in high nutritional condition, we show that their most cited result can be salvaged. However, individuals, on average, are expected to breed earlier than the optimum, not later. More generally, we also show that the hard selection mechanisms that underpin these results have major implications for the evolution of plasticity: when environmental heterogeneity becomes too great, plasticity is selected against, prohibiting the evolution of generalists.

Steering ecological-evolutionary dynamics to improve artificial selection of microbial communities

Microbial communities often perform important functions that depend on inter-species interactions. To improve community function via artificial selection, one can repeatedly grow many communities to allow mutations to arise, and "reproduce" the highest-functioning communities by partitioning each into multiple offspring communities for the next cycle. Since improvement is often unimpressive in experiments, we study how to design effective selection strategies in silico. Specifically, we simulate community selection to improve a function that requires two species. With a "community function landscape", we visualize how community function depends on species and genotype compositions. Due to ecological interactions that promote species coexistence, the evolutionary trajectory of communities is restricted to a path on the landscape. This restriction can generate counter-intuitive evolutionary dynamics, prevent the attainment of maximal function, and importantly, hinder selection by trapping communities in locations of low community function heritability. We devise experimentally-implementable manipulations to shift the path to higher heritability, which speeds up community function improvement even when landscapes are high dimensional or unknown. Video walkthroughs: https://go.nature.com/3GWwS6j ; https://online.kitp.ucsb.edu/online/ecoevo21/shou2/ .

Quantifying Glucocorticoid Plasticity Using Reaction Norm Approaches: There Still is So Much to Discover!

Hormones are highly responsive internal signals that help organisms adjust their phenotype to fluctuations in environmental and internal conditions. Our knowledge of the causes and consequences of variation in circulating hormone concentrations has improved greatly in the past. However, this knowledge often comes from population-level studies, which generally tend to make the flawed assumption that all individuals respond in the same way to environmental changes. Here, we advocate that we can vastly expand our understanding of the ecology and evolution of hormonal traits once we acknowledge the existence of individual differences by quantifying hormonal plasticity at the individual level, where selection acts. In this review, we use glucocorticoid (GC) hormones as examples of highly plastic endocrine traits that interact intimately with energy metabolism but also with other organismal traits like behavior and physiology. First, we highlight the insights gained by repeatedly assessing an individual's GC concentrations along a gradient of environmental or internal conditions using a “reaction norm approach.” This study design should be followed by a hierarchical statistical partitioning of the total endocrine variance into the among-individual component (individual differences in average hormone concentrations, i.e., in the intercept of the reaction norm) and the residual (within-individual) component. The latter is ideally further partitioned by estimating more precisely hormonal plasticity (i.e., the slope of the reaction norm), which allows to test whether individuals differ in the degree of hormonal change along the gradient. Second, we critically review the published evidence for GC variation, focusing mostly on among- and within-individual levels, finding only a good handful of studies that used repeated-measures designs and random regression statistics to investigate GC plasticity. These studies indicate that individuals can differ in both the intercept and the slope of their GC reaction norm to a known gradient. Third, we suggest rewarding avenues for future work on hormonal reaction norms, for example to uncover potential costs and trade-offs associated with GC plasticity, to test whether GC plasticity varies when an individual's reaction norm is repeatedly assessed along the same gradient, whether reaction norms in GCs covary with those in other traits like behavior and fitness (generating multivariate plasticity), or to quantify GC reaction norms along multiple external and internal gradients that act simultaneously (leading to multidimensional plasticity). Throughout this review, we emphasize the power that reaction norm approaches offer for resolving unanswered questions in ecological and evolutionary endocrinology.

Using phenotypic plasticity to understand the structure and evolution of the genotype-phenotype map

Deciphering the genotype-phenotype map necessitates relating variation at the genetic level to variation at the phenotypic level. This endeavour is inherently limited by the availability of standing genetic variation, the rate of spontaneous mutation to novo genetic variants, and possible biases associated with induced mutagenesis. An interesting alternative is to instead rely on the environment as a source of variation. Many phenotypic traits change plastically in response to the environment, and these changes are generally underlain by changes in gene expression. Relating gene expression plasticity to the phenotypic plasticity of more integrated organismal traits thus provides useful information about which genes influence the development and expression of which traits, even in the absence of genetic variation. We here appraise the prospects and limits of such an environment-for-gene substitution for investigating the genotype-phenotype map. We review models of gene regulatory networks, and discuss the different ways in which they can incorporate the environment to mechanistically model phenotypic plasticity and its evolution. We suggest that substantial progress can be made in deciphering this genotype-environment-phenotype map, by connecting theory on gene regulatory network to empirical patterns of gene co-expression, and by more explicitly relating gene expression to the expression and development of phenotypes, both theoretically and empirically.

The integrative biology of genetic dominance

Dominance is a basic property of inheritance systems describing the link between a diploid genotype at a single locus and the resulting phenotype. Models for the evolution of dominance have long been framed as an opposition between the irreconcilable views of Fisher in 1928 supporting the role of largely elusive dominance modifiers and Wright in 1929, who viewed dominance as an emerging property of the structure of enzymatic pathways. Recent theoretical and empirical advances however suggest that these opposing views can be reconciled, notably using models investigating the regulation of gene expression and developmental processes. In this more comprehensive framework, phenotypic dominance emerges from departures from linearity between any levels of integration in the genotype‐to‐phenotype map. Here, we review how these different models illuminate the emergence and evolution of dominance. We then detail recent empirical studies shedding new light on the diversity of molecular and physiological mechanisms underlying dominance and its evolution. By reconciling population genetics and functional biology, we hope our review will facilitate cross‐talk among research fields in the integrative study of dominance evolution.

A model of developmental canalization, applied to human cranial form

Developmental mechanisms that canalize or compensate perturbations of organismal development (targeted or compensatory growth) are widely considered a prerequisite of individual health and the evolution of complex life, but little is known about the nature of these mechanisms. It is even unclear if and how a “target trajectory” of individual development is encoded in the organism’s genetic-developmental system or, instead, emerges as an epiphenomenon. Here we develop a statistical model of developmental canalization based on an extended autoregressive model. We show that under certain assumptions the strength of canalization and the amount of canalized variance in a population can be estimated, or at least approximated, from longitudinal phenotypic measurements, even if the target trajectories are unobserved. We extend this model to multivariate measures and discuss reifications of the ensuing parameter matrix. We apply these approaches to longitudinal geometric morphometric data on human postnatal craniofacial size and shape as well as to the size of the frontal sinuses. Craniofacial size showed strong developmental canalization during the first 5 years of life, leading to a 50% reduction of cross-sectional size variance, followed by a continual increase in variance during puberty. Frontal sinus size, by contrast, did not show any signs of canalization. Total variance of craniofacial shape decreased slightly until about 5 years of age and increased thereafter. However, different features of craniofacial shape showed very different developmental dynamics. Whereas the relative dimensions of the nasopharynx showed strong canalization and a reduction of variance throughout postnatal development, facial orientation continually increased in variance. Some of the signals of canalization may owe to independent variation in developmental timing of cranial components, but our results indicate evolved, partly mechanically induced mechanisms of canalization that ensure properly sized upper airways and facial dimensions.

Developmental mechanisms that canalize or compensate perturbations of organismal development are a prerequisite of individual health and the evolution of complex life. However, surprisingly little is known about these mechanisms, partly because the “target trajectories” of individual development cannot be directly observed. Here we develop a statistical model of developmental canalization that allows one to estimate the strength of canalization and the amount of canalized variance in a population even if the target trajectories are unobserved. We applied these approaches to data on human postnatal craniofacial growth. Whereas overall craniofacial size was strongly canalized during the first 5 years of age, frontal sinus size did not show any signs of canalization. The relative dimensions of the nasopharynx showed strong canalization and a reduction of variance throughout postnatal development, whereas other shape features, such as facial orientation, continually increased in variance. Our results indicate evolved, partly mechanically induced mechanisms of canalization that ensure properly sized upper airways and facial dimensions.

Evolutionary branching in distorted trait spaces

Biological communities are thought to have been evolving in trait spaces that are not only multi-dimensional, but also distorted in a sense that mutational covariance matrices among traits depend on the parental phenotypes of mutants. Such a distortion may affect diversifying evolution as well as directional evolution. In adaptive dynamics theory, diversifying evolution through ecological interaction is called evolutionary branching. This study analytically develops conditions for evolutionary branching in distorted trait spaces of arbitrary dimensions, by a local nonlinear coordinate transformation so that the mutational covariance matrix becomes locally constant in the neighborhood of a focal point. The developed evolutionary branching conditions can be affected by the distortion when mutational step sizes have significant magnitude difference among directions, i.e., the eigenvalues of the mutational covariance matrix have significant magnitude difference.

Developmental integration and evolution of labile plasticity in a complex quantitative character in a multiperiodic environment

Labile plasticity in a complex quantitative character is modeled, with multiple components contributing to net plasticity in the character. Each component has a specific development rate, norm of reaction, and cost of plasticity. For example, thermal adaptation in mammals includes seasonal fat deposition and fur growth, short-term shivering and sweating or panting, and movement between warm and cold sites. Norms of reaction do not reveal patterns of developmental integration, which must be investigated by studies of developmental dynamics in a changing environment. In a periodic environment, a labile character with a single component of plasticity is constrained by filtering environmental frequencies above the development rate and by the cost of plasticity. With multiple components of plasticity, some patterns of integration can alleviate these constraints to greatly improve fidelity of the mean phenotype tracking multiperiodic cycles in the optimum phenotype. This occurs by environmental signal amplification or inhibition through developmental integration among components and by an augmented development rate of net plasticity in the character that reduces environmental frequency filtering. When development of a component with high cost of plasticity is regulated partly by the norm of reaction of another component, evolution can diminish the reaction norm slope of the costly component without curtailing its development, thereby reducing the loss of fitness from its cost of plasticity. Apparent maladaptation in a component of plasticity may be an integral part of an adaptive pattern of developmental integration by mutual inhibition between components and compensatory evolution of a negative component reaction norm slope.

Evolutionary dynamics models in biometrical genetics supports QTL × environment interactions

The process of development of quantitative trait locus (QTL) involves interactions between many factors, both environmental and genetic, in which many genes interact often in no additive pathways together and with environment. Integration of the mathematical, statistical and biological aspects of these subjects has made important and interesting results. In this review, mathematical methods offered to study the QTL × environment interactions. The topic is circumscribed, going from basic selection equations to models of evolution of QTLs. Discrete and continuous time mathematical models and subsequently, QTL modelling were introduced with and without environmental interactions. The mathematical models derived here showed that the gradients of mean fitness which have revealed in studies by many researchers had a basic role in mathematical genetics, evolutionary aspects of biometrical genetics and QTL analysis. QTL × environment interactions were studied mathematically including fitness components too. It was revealed that QTL × environment interactions in fitness could generate a balancing selection. Also, QTL analysis could be used to calculate the geometry of the phenotype landscape. In this paper, models applied in biometrical genetics corresponds to QTL analysis and matched with results from other researchers. The originality of this synthesis is the evolutionary modelling of QTL × environment interactions which can be used to investigate the extinction or stability of a population. Also to emphasize that although some scientific subjects like Brownian motion, quantum mechanics, general relativity, differential geometry, and evolutionarybiometrical genetics were apparently different subjects, but the mathematical models were the backbone of these branches of science. This implies that such matters in nature have probably common and elegant basis. The perspective of the subject of this paper in future will be a new and interesting branch of interdisciplinary science.

The developmental-genetics of canalization

Canalization, or robustness to genetic or environmental perturbations, is fundamental to complex organisms. While there is strong evidence for canalization as an evolved property that varies among genotypes, the developmental and genetic mechanisms that produce this phenomenon are very poorly understood. For evolutionary biology, understanding how canalization arises is important because, by modulating the phenotypic variation that arises in response to genetic differences, canalization is a determinant of evolvability. For genetics of disease in humans and for economically important traits in agriculture, this subject is important because canalization is a potentially significant cause of missing heritability that confounds genomic prediction of phenotypes. We review the major lines of thought on the developmental-genetic basis for canalization. These fall into two groups. One proposes specific evolved molecular mechanisms while the other deals with robustness or canalization as a more general feature of development. These explanations for canalization are not mutually exclusive and they overlap in several ways. General explanations for canalization are more likely to involve emergent features of development than specific molecular mechanisms. Disentangling these explanations is also complicated by differences in perspectives between genetics and developmental biology. Understanding canalization at a mechanistic level will require conceptual and methodological approaches that integrate quantitative genetics and developmental biology.

Developmental nonlinearity drives phenotypic robustness

Robustness to perturbation is a fundamental feature of complex organisms. Mutations are the raw material for evolution, yet robustness to their effects is required for species survival. The mechanisms that produce robustness are poorly understood. Nonlinearities are a ubiquitous feature of development that may link variation in development to phenotypic robustness. Here, we manipulate the gene dosage of a signaling molecule, Fgf8, a critical regulator of vertebrate development. We demonstrate that variation in Fgf8 expression has a nonlinear relationship to phenotypic variation, predicting levels of robustness among genotypes. Differences in robustness are not due to gene expression variance or dysregulation, but emerge from the nonlinearity of the genotype–phenotype curve. In this instance, embedded features of development explain robustness differences. How such features vary in natural populations and relate to genetic variation are key questions for unraveling the origin and evolvability of this feature of organismal development.

Developmental processes often involve nonlinearities, but the consequences for translating genotype to phenotype are not well characterized. Here, Green et al. vary Fgf8 signaling across allelic series of mice and show that phenotypic robustness in craniofacial shape is explained by a nonlinear effect of Fgf8 expression.

The importance of mechanisms for the evolution of cooperation

Studies aimed at explaining the evolution of phenotypic traits have often solely focused on fitness considerations, ignoring underlying mechanisms. In recent years, there has been an increasing call for integrating mechanistic perspectives in evolutionary considerations, but it is not clear whether and how mechanisms affect the course and outcome of evolution. To study this, we compare four mechanistic implementations of two well-studied models for the evolution of cooperation, the Iterated Prisoner's Dilemma (IPD) game and the Iterated Snowdrift (ISD) game. Behavioural strategies are either implemented by a 1 : 1 genotype-phenotype mapping or by a simple neural network. Moreover, we consider two different scenarios for the effect of mutations. The same set of strategies is feasible in all four implementations, but the probability that a given strategy arises owing to mutation is largely dependent on the behavioural and genetic architecture. Our individual-based simulations show that this has major implications for the evolutionary outcome. In the ISD, different evolutionarily stable strategies are predominant in the four implementations, while in the IPD each implementation creates a characteristic dynamical pattern. As a consequence, the evolved average level of cooperation is also strongly dependent on the underlying mechanism. We argue that our findings are of general relevance for the evolution of social behaviour, pleading for the integration of a mechanistic perspective in models of social evolution.

Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.

Evolution of Quantitative Traits under a Migration-Selection Balance: When Does Skew Matter?

Quantitative-genetic models of differentiation under migration-selection balance often rely on the assumption of normally distributed genotypic and phenotypic values. When a population is subdivided into demes with selection toward different local optima, migration between demes may result in asymmetric, or skewed, local distributions. Using a simplified two-habitat model, we derive formulas without a priori assuming a Gaussian distribution of genotypic values, and we find expressions that naturally incorporate higher moments, such as skew. These formulas yield predictions of the expected divergence under migration-selection balance that are more accurate than models assuming Gaussian distributions, which illustrates the importance of incorporating these higher moments to assess the response to selection in heterogeneous environments. We further show with simulations that traits with loci of large effect display the largest skew in their distribution at migration-selection balance.

Mapping complex traits as a dynamic system

Despite increasing emphasis on the genetic study of quantitative traits, we are still far from being able to chart a clear picture of their genetic architecture, given an inherent complexity involved in trait formation. A competing theory for studying such complex traits has emerged by viewing their phenotypic formation as a "system" in which a high-dimensional group of interconnected components act and interact across different levels of biological organization from molecules through cells to whole organisms. This system is initiated by a machinery of DNA sequences that regulate a cascade of biochemical pathways to synthesize endophenotypes and further assemble these endophenotypes toward the end-point phenotype in virtue of various developmental changes. This review focuses on a conceptual framework for genetic mapping of complex traits by which to delineate the underlying components, interactions and mechanisms that govern the system according to biological principles and understand how these components function synergistically under the control of quantitative trait loci (QTLs) to comprise a unified whole. This framework is built by a system of differential equations that quantifies how alterations of different components lead to the global change of trait development and function, and provides a quantitative and testable platform for assessing the multiscale interplay between QTLs and development. The method will enable geneticists to shed light on the genetic complexity of any biological system and predict, alter or engineer its physiological and pathological states.

Testing for beneficial reversal of dominance during salinity shifts in the invasive copepod Eurytemora affinis, and implications for the maintenance of genetic variation

Maintenance of genetic variation at loci under selection has profound implications for adaptation under environmental change. In temporally and spatially varying habitats, non-neutral polymorphism could be maintained by heterozygote advantage across environments (marginal overdominance), which could be greatly increased by beneficial reversal of dominance across conditions. We tested for reversal of dominance and marginal overdominance in salinity tolerance in the saltwater-to-freshwater invading copepod Eurytemora affinis. We compared survival of F1 offspring generated by crossing saline and freshwater inbred lines (between-salinity F1 crosses) relative to within-salinity F1 crosses, across three salinities. We found evidence for both beneficial reversal of dominance and marginal overdominance in salinity tolerance. In support of reversal of dominance, survival of between-salinity F1 crosses was not different from that of freshwater F1 crosses under freshwater conditions and saltwater F1 crosses under saltwater conditions. In support of marginal overdominance, between-salinity F1 crosses exhibited significantly higher survival across salinities relative to both freshwater and saltwater F1 crosses. Our study provides a rare empirical example of complete beneficial reversal of dominance associated with environmental change. This mechanism might be crucial for maintaining genetic variation in salinity tolerance in E. affinis populations, allowing rapid adaptation to salinity changes during habitat invasions.

Multidimensional (co)evolutionary stability

The complexity of biotic and abiotic environmental conditions is such that the fitness of individuals is likely to depend on multiple traits. Using a synthetic framework of phenotypic evolution that draws from adaptive dynamics and quantitative genetics approaches, we explore how the number of traits under selection influences convergence stability and evolutionary stability in models for coevolution in multidimensional phenotype spaces. Our results allow us to identify three different effects of trait dimensionality on stability. First are (i) a "combinatorial effect": without epistasis and genetic correlations, a higher number of trait dimensions offers more opportunities for equilibria to be unstable; and (ii) epistatic interactions, that is, fitness interactions between traits, which tend to destabilize evolutionary equilibria; this effect increases with the dimension of phenotype space. These first two effects influence both convergence stability and evolutionary stability, while (iii) genetic correlations (due, e.g., to pleiotropy or linkage disequilibrium) can affect only convergence stability. We illustrate the general prediction that increased dimensionality destabilizes evolutionary equilibria using examples drawn from well-studied classical models of frequency-dependent competition for resources, adaptation to a spatially heterogeneous environment, and antagonistic coevolution. In addition, our analyses show that increased dimensionality can favor diversification, for example, in the form of local adaptation, as well as evolutionary escape.

Selection and evolution of causally covarying traits

When traits cause variation in fitness, the distribution of phenotype, weighted by fitness, necessarily changes. The degree to which traits cause fitness variation is therefore of central importance to evolutionary biology. Multivariate selection gradients are the main quantity used to describe components of trait-fitness covariation, but they quantify the direct effects of traits on (relative) fitness, which are not necessarily the total effects of traits on fitness. Despite considerable use in evolutionary ecology, path analytic characterizations of the total effects of traits on fitness have not been formally incorporated into quantitative genetic theory. By formally defining "extended" selection gradients, which are the total effects of traits on fitness, as opposed to the existing definition of selection gradients, a more intuitive scheme for characterizing selection is obtained. Extended selection gradients are distinct quantities, differing from the standard definition of selection gradients not only in the statistical means by which they may be assessed and the assumptions required for their estimation from observational data, but also in their fundamental biological meaning. Like direct selection gradients, extended selection gradients can be combined with genetic inference of multivariate phenotypic variation to provide quantitative prediction of microevolutionary trajectories.

Nonlinear effects of temperature on body form and developmental canalization in the threespine stickleback

Theoretical models predict that nonlinear environmental effects on the phenotype also affect developmental canalization, which in turn can influence the tempo and course of organismal evolution. Here, we used an oceanic population of threespine stickleback (Gasterosteus aculeatus) to investigate temperature-induced phenotypic plasticity of body size and shape using a paternal half-sibling, split-clutch experimental design and rearing offspring under three different temperature regimes (13, 17 and 21 °C). Body size and shape of 466 stickleback individuals were assessed by a set of 53 landmarks and analysed using geometric morphometric methods. At approximately 100 days, individuals differed significantly in both size and shape across the temperature groups. However, the temperature-induced differences between 13 and 17 °C (mainly comprising relative head and eye size) deviated considerably from those between 17 and 21 °C (involving the relative size of the ectocoracoid, the operculum and the ventral process of the pelvic girdle). Body size was largest at 17 °C. For both size and shape, phenotypic variance was significantly smaller at 17 °C than at 13 and 21 °C, indicating that development is most stable at the intermediate temperature matching the conditions encountered in the wild. Higher additive genetic variance at 13 and 21 °C indicates that the plastic response to temperature had a heritable basis. Understanding nonlinear effects of temperature on development and the underlying genetics are important for modelling evolution and for predicting outcomes of global warming, which can lead not only to shifts in average morphology but also to destabilization of development.

Evolution of discrete phenotypes from continuous norms of reaction

Discrete phenotypic variation often involves threshold expression of a trait with polygenic inheritance. How such discrete polyphenisms evolve starting from continuously varying phenotypes has received little theoretical attention. We model the evolution of sigmoid norms of reaction in response to variation in an underlying trait or in a continuous environment to identify conditions for the evolution of discontinuity. For traits with expression depending on a randomly varying underlying factor, such as developmental noise, polyphenism is unstable under constant phenotypic selection for two selective peaks, and reaction norm evolution results in a phenotypic distribution concentrated at only one peak. But with frequency-dependent selection between two adaptive peaks, a steep threshold maintaining polyphenism can evolve. For inducible plastic traits with expression conditioned on an environmental variable that also affects phenotypic selection, the steepness of the evolved reaction norm depends both on the differentiation of the environment in time or space and on its predictability between development and selection. Together with recent measurements of genetic variance of threshold steepness, these predictions suggest that quasi-discrete phenotypic variation may often evolve from continuous norms of reactions rather than being an intrinsic property of development.

Why epistasis is important for selection and adaptation

Organisms are built from thousands of genes that interact in complex ways. Still, the mathematical theory of evolution is dominated by a gene-by-gene perspective in which genes are assumed to have the same effects regardless of genetic background. Gene interaction, or epistasis, plays a role in some theoretical developments such as the evolution of recombination, reproductive isolation, and canalization, but is strikingly missing from our standard accounts of phenotypic adaptation. This absence is most puzzling within the field of quantitative genetics, which, despite its polygenic perspective and elaborate statistical representation of epistasis, has not found a single important role for gene interaction in evolution. To the contrary, there is a widespread consensus that epistasis is evolutionary inert, and that all we need to know to predict evolutionary dynamics is the additive component of the genetic variance. This view may have roots in convenience, but also in theoretical results showing that the response to selection derived from epistatic variance components is not permanent and will decay when selection is relaxed. I show that these results are tied to a conceptual confusion, and are misleading as general statements about the significance of epistasis for the selection response and adaptation.

The Developmental Basis of Quantitative Craniofacial Variation in Humans and Mice

The human skull is a complex and highly integrated structure that has long held the fascination of anthropologists and evolutionary biologists. Recent studies of the genetics of craniofacial variation reveal a very complex and multifactorial picture. These findings contrast with older ideas that posit much simpler developmental bases for variation in cranial morphology such as the growth of the brain or the growth of the chondrocranium relative to the dermatocranium. Such processes have been shown to have major effects on cranial morphology in mice. It is not known, however, whether they are relevant to explaining normal phenotypic variation in humans. To answer this question, we obtained vectors of shape change from mutant mouse models in which the developmental basis for the craniofacial phenotype is known to varying degrees, and compared these to a homologous dataset constructed from human crania obtained from a single population with a known genealogy. Our results show that the shape vectors associated with perturbations to chondrocranial growth, brain growth, and body size in mice do largely correspond to axes of covariation in humans. This finding supports the view that the developmental basis for craniofacial variation funnels down to a relatively small number of key developmental processes that are similar across mice and humans. Understanding these processes and how they influence craniofacial shape provides fundamental insights into the developmental basis for evolutionary change in the human skull as well as the developmental-genetic basis for normal phenotypic variation in craniofacial form.

On testing an unspecified function through a linear mixed effects model with multiple variance components

We examine a generalized F-test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedure can be used to test a nonparametric function or varying-coefficient with clustered data, compare two spline functions, test the significance of an unspecified function in an additive model with multiple components, and test a row or a column effect in a two-way analysis of variance model. Through a spectral decomposition of the residual sum of squares, we provide a fast algorithm for computing the null distribution of the test, which significantly improves the computational efficiency over bootstrap. The spectral representation reveals a connection between the likelihood ratio test (LRT) in a multiple variance components model and a single component model. We examine our methods through simulations, where we show that the power of the generalized F-test may be higher than the LRT, depending on the hypothesis of interest and the true model under the alternative. We apply these methods to compute the genome-wide critical value and p-value of a genetic association test in a genome-wide association study (GWAS), where the usual bootstrap is computationally intensive (up to 10(8) simulations) and asymptotic approximation may be unreliable and conservative.

Flexible semiparametric analysis of longitudinal genetic studies by reduced rank smoothing

In family-based longitudinal genetic studies, investigators collect repeated measurements on a trait that changes with time along with genetic markers. Since repeated measurements are nested within subjects and subjects are nested within families, both the subject-level and measurement-level correlations must be taken into account in the statistical analysis to achieve more accurate estimation. In such studies, the primary interests include to test for quantitative trait locus (QTL) effect, and to estimate age-specific QTL effect and residual polygenic heritability function. We propose flexible semiparametric models along with their statistical estimation and hypothesis testing procedures for longitudinal genetic designs. We employ penalized splines to estimate nonparametric functions in the models. We find that misspecifying the baseline function or the genetic effect function in a parametric analysis may lead to substantially inflated or highly conservative type I error rate on testing and large mean squared error on estimation. We apply the proposed approaches to examine age-specific effects of genetic variants reported in a recent genome-wide association study of blood pressure collected in the Framingham Heart Study.

Natural selection. II. Developmental variability and evolutionary rate

In classical evolutionary theory, genetic variation provides the source of heritable phenotypic variation on which natural selection acts. Against this classical view, several theories have emphasized that developmental variability and learning enhance nonheritable phenotypic variation, which in turn can accelerate evolutionary response. In this paper, I show how developmental variability alters evolutionary dynamics by smoothing the landscape that relates genotype to fitness. In a fitness landscape with multiple peaks and valleys, developmental variability can smooth the landscape to provide a directly increasing path of fitness to the highest peak. Developmental variability also allows initial survival of a genotype in response to novel or extreme environmental challenge, providing an opportunity for subsequent adaptation. This initial survival advantage arises from the way in which developmental variability smooths and broadens the fitness landscape. Ultimately, the synergism between developmental processes and genetic variation sets evolutionary rate.

Genomics of environmentally induced phenotypes in 2 extremely plastic arthropods

Understanding how genes and the environment interact to shape phenotypes is of fundamental importance for resolving important issues in adaptive evolution. Yet, for most model species with mature genetics and accessible genomic resources, we know little about the natural environmental factors that shape their evolution. By contrast, animal species with deeply understood ecologies and well characterized responses to environmental cues are rarely subjects of genomic investigations. Here, we preview advances in genomics in aphids and waterfleas that may help transform research on the regulatory mechanisms of phenotypic plasticity. This insect and crustacean duo has the capacity to produce extremely divergent phenotypes in response to environmental stimuli. Sexual fate and reproductive mode are condition-dependent in both groups, which are also capable of altering morphology, physiology and behavior in response to biotic and abiotic cues. Recently, the genome sequences for the pea aphid Acyrthosiphon pisum and the waterflea Daphnia pulex were described by their respective research communities. We propose that an integrative study of genome biology focused on the condition-dependent transcriptional basis of their shared plastic traits and specialized mode of reproduction will provide broad insight into adaptive plasticity and genome by environment interactions. We highlight recent advances in understanding the genome regulation of alternative phenotypes and environmental cue processing, and we propose future research avenues to discover gene networks and epigenetic mechanisms underlying phenotypic plasticity.

A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms

For structured populations in equilibrium with everybody born equal, ln(R (0)) is a useful fitness proxy for evolutionarily steady strategy (ESS) and most adaptive dynamics calculations, with R (0) the average lifetime number of offspring in the clonal and haploid cases, and half the average lifetime number of offspring fathered or mothered for Mendelian diploids. When individuals have variable birth states, as is, for example, the case in spatial models, R (0) is itself an eigenvalue, which usually cannot be expressed explicitly in the trait vectors under consideration. In that case, Q(Y| X):=-det (I-L(Y| X)) can often be used as fitness proxy, with L the next-generation matrix for a potential mutant characterized by the trait vector Y in the (constant) environment engendered by a resident characterized by X. If the trait space is connected, global uninvadability can be determined from it. Moreover, it can be used in all the usual local calculations like the determination of evolutionarily singular trait vectors and their local invadability and attractivity. We conclude with three extended case studies demonstrating the usefulness of Q: the calculation of ESSs under haplo-diploid genetics (I), of evolutionarily steady genetic dimorphisms (ESDs) with a priori proportionality of macro- and micro-gametic outputs (an assumption that is generally made but the fulfilment of which is a priori highly exceptional) (II), and of ESDs without such proportionality (III). These case studies should also have some interest in their own right for the spelled out calculation recipes and their underlying modelling methodology.

Epistasis contributes to the genetic buffering of plasma HDL cholesterol in mice

Stressful environmental factors, such as a high-fat diet, can induce responses in the expression of genes that act to maintain physiological homeostasis. We observed variation in plasma concentrations of high-density lipoprotein (HDL) cholesterol across inbred mouse strains in response to high dietary fat intake. Several strains, including C57BL/6J, have stable levels of plasma HDL independent of diet, whereas other strains, including DBA2/J, show marked changes in plasma HDL. To explore this phenomenon further, we used publicly available data from a C57BL/6J × DBA/2J intercross to identify genetic factors that associate with HDL under high-fat diet conditions. Our analysis identified an epistatic interaction that plays a role in the buffering of HDL levels in C57BL/6J mice, and we have identified Arl4d as a candidate gene that mediates this effect. Structural modeling further elucidates the interaction of genetic factors that contribute to the robustness of HDL in response to high-fat diet in the C57BL/6J strain.

Complex genotype interactions influence social fitness during the developmental phase of the social amoeba Dictyostelium discoideum

When individuals interact, phenotypic variation can be partitioned into direct genetic effects (DGEs) of the individuals' own genotypes, indirect genetic effects (IGEs) of their social partners' genotypes and epistatic interactions between the genotypes of interacting individuals ('genotype-by-genotype (GxG) epistasis'). These components can all play important roles in evolutionary processes, but few empirical studies have examined their importance. The social amoeba Dictyostelium discoideum provides an ideal system to measure these effects during social interactions and development. When starved, free-living amoebae aggregate and differentiate into a multicellular fruiting body with a dead stalk that holds aloft viable spores. By measuring interactions among a set of natural strains, we quantify DGEs, IGEs and GxG epistasis affecting spore formation. We find that DGEs explain most of the phenotypic variance (57.6%) whereas IGEs explain a smaller (13.3%) but highly significant component. Interestingly, GxG epistasis explains nearly a quarter of the variance (23.0%), highlighting the complex nature of genotype interactions. These results demonstrate the large impact that social interactions can have on development and suggest that social effects should play an important role in developmental evolution in this system.

Conflicting processes in the evolution of body size and development time

Body size and development time of Manduca sexta are both determined by the same set of three developmental-physiological factors. These define a parameter space within which it is possible to analyse and explain how phenotypic change is associated with changes in the underlying factors. Body size and development time are determined by the identical set of underlying factors, so they are not independent, but because the mechanisms by which these factors produce each phenotype are different, the two phenotypes are only weakly correlated, and the correlation is context dependent. We use a mathematical model of this mechanism to explore the association between body size and development time and show that the correlation between these two life-history traits can be positive, zero or negative, depending entirely on where in parameter space a population is located, and on which of the underlying factors has a greater variation. The gradient within this parameter space predicts the unconstrained evolutionary trajectory under directional selection on each trait. Calculations of the gradients for body size and development time revealed that these are nearly orthogonal through much of the parameter space. Therefore, simultaneous directional selection on body size and development time can be neither synergistic nor antagonistic but leads to conflicting selection on the underlying developmental parameters.

Phenotypic plasticity facilitates recurrent rapid adaptation to introduced predators

A central role for phenotypic plasticity in adaptive evolution is often posited yet lacks empirical support. Selection for the stable production of an induced phenotype is hypothesized to modify the regulation of preexisting developmental pathways, producing rapid adaptive change. We examined the role of plasticity in rapid adaptation of the zooplankton Daphnia melanica to novel fish predators. Here we show that plastic up-regulation of the arthropod melanin gene dopa decarboxylase (Ddc) in the absence of UV radiation is associated with reduced pigmentation in D. melanica. Daphnia populations coexisting with recently introduced fish exhibit environmentally invariant up-regulation of Ddc, accompanied by constitutive up-regulation of the interacting arthropod melanin gene ebony. Both changes in regulation are associated with adaptive reduction in the plasticity and mean expression of melanin. Our results provide evidence that the developmental mechanism underlying ancestral plasticity in response to an environmental factor has been repeatedly co-opted to facilitate rapid adaptation to an introduced predator.

Genetic architecture and postzygotic reproductive isolation: evolution of Bateson-Dobzhansky-Muller incompatibilities in a polygenic model

The Bateson-Dobzhansky-Muller model predicts that postzygotic isolation evolves due to the accumulation of incompatible epistatic interactions, but few studies have quantified the relationship between genetic architecture and patterns of reproductive divergence. We examined how the direction and magnitude of epistatic interactions in a polygenic trait under stabilizing selection influenced the evolution of hybrid incompatibilities. We found that populations evolving independently under stabilizing selection experienced suites of compensatory allelic changes that resulted in genetic divergence between populations despite the maintenance of a stable, high-fitness phenotype. A small number of loci were then incompatible with multiple alleles in the genetic background of the hybrid and the identity of these incompatibility loci changed over the evolution of the populations. For F(1) hybrids, reduced fitness evolved in a window of intermediate strengths of epistatic interactions, but F(2) and backcross hybrids evolved reduced fitness across weak and moderate strengths of epistasis due to segregation variance. Strong epistatic interactions constrained the allelic divergence of parental populations and prevented the development of reproductive isolation. Because many traits with varying genetic architectures must be under stabilizing selection, our results indicate that polygenetic drift is a plausible hypothesis for the evolution of postzygotic reproductive isolation.

Characterizing the evolution of genetic variance using genetic covariance tensors

Determining how genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary genetics. In the same way that understanding the availability of genetic variance within populations requires the simultaneous consideration of genetic variance in sets of functionally related traits, determining how genetic variance changes under selection in natural populations will require ascertaining how genetic variance-covariance (G) matrices evolve. Here, we develop a geometric framework using higher-order tensors, which enables the empirical characterization of how G matrices have diverged among populations. We then show how divergence among populations in genetic covariance structure can then be associated with divergence in selection acting on those traits using key equations from evolutionary theory. Using estimates of G matrices of eight male sexually selected traits from nine geographical populations of Drosophila serrata, we show that much of the divergence in genetic variance occurred in a single trait combination, a conclusion that could not have been reached by examining variation among the individual elements of the nine G matrices. Divergence in G was primarily in the direction of the major axes of genetic variance within populations, suggesting that genetic drift may be a major cause of divergence in genetic variance among these populations.

Complex interactions among temporal variables affect the plasticity of clutch size in a multi-brooded bird

Phenotypic plasticity is a widespread phenomenon and may have important influences on evolutionary processes. Multidimensional plasticity, in which multiple environmental variables affect a phenotype, is especially interesting if there are interactions among these variables. We used a long-term data set from House Sparrows (Passer domesticus), a multi-brooded passerine bird, to test several predictions from life-history theory regarding the shape of optimal reaction norms for clutch size. The best-fit model for variation in clutch size included three temporal variables (the order of attempt within a season, the date of those attempts, and the age of the female). Clutch size was also sensitive to the quadratics of date and female age, both of which had negative coefficients. Finally, we found that the relationship between date and clutch size became more negative as attempt order increased. These results suggest that female sparrows have a multidimensional reaction norm for clutch size that matches predictions of life-history theory but also implicates more complexity than can be captured by any single model. Analysis of the sources of variation in reaction norm height and slope was complicated by the additional environmental dimensions. We found significant individual variation in mean clutch size in all analyses, indicating that individuals differed in the height of their clutch size reaction norm. By contrast, we found no evidence of significant individual heterogeneity in the slopes of several dimensions. We assess the possible mechanisms producing this reaction norm and discuss their implications for understanding complex plasticity.

A framework for evolutionary systems biology

BACKGROUND

Many difficult problems in evolutionary genomics are related to mutations that have weak effects on fitness, as the consequences of mutations with large effects are often simple to predict. Current systems biology has accumulated much data on mutations with large effects and can predict the properties of knockout mutants in some systems. However experimental methods are too insensitive to observe small effects.

RESULTS

Here I propose a novel framework that brings together evolutionary theory and current systems biology approaches in order to quantify small effects of mutations and their epistatic interactions in silico. Central to this approach is the definition of fitness correlates that can be computed in some current systems biology models employing the rigorous algorithms that are at the core of much work in computational systems biology. The framework exploits synergies between the realism of such models and the need to understand real systems in evolutionary theory. This framework can address many longstanding topics in evolutionary biology by defining various 'levels' of the adaptive landscape. Addressed topics include the distribution of mutational effects on fitness, as well as the nature of advantageous mutations, epistasis and robustness. Combining corresponding parameter estimates with population genetics models raises the possibility of testing evolutionary hypotheses at a new level of realism.

CONCLUSION

EvoSysBio is expected to lead to a more detailed understanding of the fundamental principles of life by combining knowledge about well-known biological systems from several disciplines. This will benefit both evolutionary theory and current systems biology. Understanding robustness by analysing distributions of mutational effects and epistasis is pivotal for drug design, cancer research, responsible genetic engineering in synthetic biology and many other practical applications.

Effects of epistasis and the evolution of genetic architecture: exact results for a 2-locus model

We study a two-locus model of a quantitative trait with a continuum-of alleles and multilinear epistasis that evolves under mutation, selection, and genetic drift. We derive analytical results based on the so-called House of Gauss approximation for the genetic variance, the mean phenotype, and the mutational variance in the balance of the evolutionary forces. The analytical work is complemented by extensive individual-based computer simulations. We find that (1) analytical results are accurate in a large parameter space; (2) epistasis always reduces the equilibrium genetic variance, as predicted in earlier studies that exclude drift; (3) large-scale stochastic fluctuations and non-equilibrium phenomena like adaptive inertia can strongly influence the evolution of the genetic architecture of the trait.

Estimating evolutionary parameters when viability selection is operating

Some individuals die before a trait is measured or expressed (the invisible fraction), and some relevant traits are not measured in any individual (missing traits). This paper discusses how these concepts can be cast in terms of missing data problems from statistics. Using missing data theory, I show formally the conditions under which a valid evolutionary inference is possible when the invisible fraction and/or missing traits are ignored. These conditions are restrictive and unlikely to be met in even the most comprehensive long-term studies. When these conditions are not met, many selection and quantitative genetic parameters cannot be estimated accurately unless the missing data process is explicitly modelled. Surprisingly, this does not seem to have been attempted in evolutionary biology. In the case of the invisible fraction, viability selection and the missing data process are often intimately linked. In such cases, models used in survival analysis can be extended to provide a flexible and justified model of the missing data mechanism. Although missing traits pose a more difficult problem, important biological parameters can still be estimated without bias when appropriate techniques are used. This is in contrast to current methods which have large biases and poor precision. Generally, the quantitative genetic approach is shown to be superior to phenotypic studies of selection when invisible fractions or missing traits exist because part of the missing information can be recovered from relatives.

Theoretical approaches to the evolution of development and genetic architecture

Developmental evolutionary biology has, in the past decade, started to move beyond simply adapting traditional population and quantitative genetics models and has begun to develop mathematical approaches that are designed specifically to study the evolution of complex, nonadditive systems. This article first reviews some of these methods, discussing their strengths and shortcomings. The article then considers some of the principal questions to which these theoretical methods have been applied, including the evolution of canalization, modularity, and developmental associations between traits. I briefly discuss the kinds of data that could be used to test and apply the theories, as well as some consequences for other approaches to phenotypic evolution of discoveries from theoretical studies of developmental evolution.