Quantitative Genetic Models Research Articles

Local Adaptation by Alleles of Small Effect.

Population genetic models predict that alleles with small selection coefficients may be swamped by migration and will not contribute to local adaptation. But if most alleles contributing to standing variation are of small effect, how does local adaptation proceed? Here I review predictions of population and quantitative genetic models and use individual-based simulations to illustrate how the architecture of local adaptation depends on the genetic redundancy of the trait, the maintenance of standing genetic variation (V(G)), and the susceptibility of alleles to swamping. Even when population genetic models predict swamping for individual alleles, considerable local adaptation can evolve at the phenotypic level if there is sufficient V(G). However, in such cases the underlying architecture of divergence is transient: F(ST) is low across all loci, and no locus makes an important contribution for very long. Because this kind of local adaptation is mainly due to transient frequency changes and allelic covariances, these architectures will be difficult--if not impossible--to detect using current approaches to studying the genomic basis of adaptation. Even when alleles are large and resistant to swamping, architectures can be highly transient if genetic redundancy and mutation rates are high. These results suggest that drift can play a critical role in shaping the architecture of local adaptation, both through eroding V(G) and affecting the rate of turnover of polymorphisms with redundant phenotypic effects.

Overlapping genetic and child-specific nonshared environmental influences on listening comprehension, reading motivation, and reading comprehension

This study investigated the genetic and environmental influences on observed associations between listening comprehension, reading motivation, and reading comprehension. Univariate and multivariate quantitative genetic models were conducted in a sample of 284 pairs of twins at a mean age of 9.81 years. Genetic and nonshared environmental factors accounted for statistically significant variance in listening and reading comprehension, and nonshared environmental factors accounted for variance in reading motivation. Furthermore, listening comprehension demonstrated unique genetic and nonshared environmental influences but also had overlapping genetic influences with reading comprehension. Reading motivation and reading comprehension each had unique and overlapping nonshared environmental contributions. Therefore, listening comprehension appears to be related to reading primarily due to genetic factors whereas motivation appears to affect reading via child-specific, nonshared environmental effects.

A genome-wide analysis of putative functional and exonic variation associated with extremely high intelligence.

Although individual differences in intelligence (general cognitive ability) are highly heritable, molecular genetic analyses to date have had limited success in identifying specific loci responsible for its heritability. This study is the first to investigate exome variation in individuals of extremely high intelligence. Under the quantitative genetic model, sampling from the high extreme of the distribution should provide increased power to detect associations. We therefore performed a case–control association analysis with 1409 individuals drawn from the top 0.0003 (IQ >170) of the population distribution of intelligence and 3253 unselected population-based controls. Our analysis focused on putative functional exonic variants assayed on the Illumina HumanExome BeadChip. We did not observe any individual protein-altering variants that are reproducibly associated with extremely high intelligence and within the entire distribution of intelligence. Moreover, no significant associations were found for multiple rare alleles within individual genes. However, analyses using genome-wide similarity between unrelated individuals (genome-wide complex trait analysis) indicate that the genotyped functional protein-altering variation yields a heritability estimate of 17.4% (s.e. 1.7%) based on a liability model. In addition, investigation of nominally significant associations revealed fewer rare alleles associated with extremely high intelligence than would be expected under the null hypothesis. This observation is consistent with the hypothesis that rare functional alleles are more frequently detrimental than beneficial to intelligence.

Genetic evolution, plasticity, and bet-hedging as adaptive responses to temporally autocorrelated fluctuating selection: A quantitative genetic model.

Adaptive responses to autocorrelated environmental fluctuations through evolution in mean reaction norm elevation and slope and an independent component of the phenotypic variance are analyzed using a quantitative genetic model. Analytic approximations expressing the mutual dependencies between all three response modes are derived and solved for the joint evolutionary outcome. Both genetic evolution in reaction norm elevation and plasticity are favored by slow temporal fluctuations, with plasticity, in the absence of microenvironmental variability, being the dominant evolutionary outcome for reasonable parameter values. For fast fluctuations, tracking of the optimal phenotype through genetic evolution and plasticity is limited. If residual fluctuations in the optimal phenotype are large and stabilizing selection is strong, selection then acts to increase the phenotypic variance (bet-hedging adaptive). Otherwise, canalizing selection occurs. If the phenotypic variance increases with plasticity through the effect of microenvironmental variability, this shifts the joint evolutionary balance away from plasticity in favor of genetic evolution. If microenvironmental deviations experienced by each individual at the time of development and selection are correlated, however, more plasticity evolves. The adaptive significance of evolutionary fluctuations in plasticity and the phenotypic variance, transient evolution, and the validity of the analytic approximations are investigated using simulations.

Signatures of positive selection: from selective sweeps at individual loci to subtle allele frequency changes in polygenic adaptation.

In the past 15 years, numerous methods have been developed to detect selective sweeps underlying adaptations. These methods are based on relatively simple population genetic models, including one or two loci at which positive directional selection occurs, and one or two marker loci at which the impact of selection on linked neutral variation is quantified. Information about the phenotype under selection is not included in these models (except for fitness). In contrast, in the quantitative genetic models of adaptation, selection acts on one or more phenotypic traits, such that a genotype-phenotype map is required to bridge the gap to population genetics theory. Here I describe the range of population genetic models from selective sweeps in a panmictic population of constant size to evolutionary traffic when simultaneous sweeps at multiple loci interfere, and I also consider the case of polygenic selection characterized by subtle allele frequency shifts at many loci. Furthermore, I present an overview of the statistical tests that have been proposed based on these population genetics models to detect evidence for positive selection in the genome.

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.

Complex and changing patterns of natural selection explain the evolution of the human hip

Causal explanations for the dramatic changes that occurred during the evolution of the human hip focus largely on selection for bipedal function and locomotor efficiency. These hypotheses rest on two critical assumptions. The first—that these anatomical changes served functional roles in bipedalism—has been supported in numerous analyses showing how postcranial changes likely affected locomotion. The second—that morphological changes that did play functional roles in bipedalism were the result of selection for that behavior—has not been previously explored and represents a major gap in our understanding of hominin hip evolution. Here we use evolutionary quantitative genetic models to test the hypothesis that strong directional selection on many individual aspects of morphology was responsible for the large differences observed across a sample of fossil hominin hips spanning the Plio-Pleistocene. Our approach uses covariance among traits and the differences between relatively complete fossils to estimate the net selection pressures that drove the major transitions in hominin hip evolution. Our findings show a complex and changing pattern of natural selection drove hominin hip evolution, and that many, but not all, traits hypothesized to play functional roles in bipedalism evolved as a direct result of natural selection. While the rate of evolutionary change for all transitions explored here does not exceed the amount expected if evolution was occurring solely through neutral processes, it was far above rates of evolution for morphological traits in other mammalian groups. Given that stasis is the norm in the mammalian fossil record, our results suggest that large shifts in the adaptive landscape drove hominin evolution.

Genetics of Educational Attainment and the Persistence of Privilege at the Turn of the 21st Century

We use structural equations methodology with data on 1,576 pairs of variously related young adult siblings (MZ twins, DZ twins, full siblings, half siblings, cousins, and nonrelated siblings) to distinguish the roles of genetic and environmental influences on educational attainment. Using quantitative genetic (ACE) models, we find that the role of genes in educational attainment is relatively weaker (23 percent of the variance) and the role of the shared family environment stronger (41 percent of the variance for twins and 30 percent of the variance for non-twin siblings) than is typically found for cognitive outcomes in young adults. The pattern of high shared environmentality, especially for twins, is not accounted for by the strong degree of assortative mating in the data (parental correlation r = .629), nor by direct effects of educational attainment of the siblings on each other. The low heritability-high environmentality pattern indicates a high level of inequality of opportunity for educational attainment in American society at the turn of the twenty-first century, perhaps linked to a greater role of family financial resources in attainment. Comparative evidence suggests that inequality of opportunity has increased in the United States over past decades, and is higher there today than in other industrial societies.

Heritability of thyroid peroxidase autoantibody levels in type 1 diabetes: evidence from discordant twin pairs.

The discordance status of (autoimmune) type 1 diabetes within monozygotic twin pairs points to the importance of environmental factors. The aim of this study was to investigate whether the environmental events causing type 1 diabetes influence thyroid autoimmunity. Monozygotic and dizygotic twins discordant for type 1 diabetes from the UK and USA were tested for thyroid peroxidase autoantibodies (TPOA) by radioimmunoassay. Using quantitative genetic model fitting of a liability-threshold model we estimated the contribution of genetic (heritability) and environmental factors to TPOA. TPOA positivity was higher in females than in males in both cohorts and was associated with later age at diagnosis in the UK and combined cohorts (p < 0.01). TPOA did not specifically segregate with type 1 diabetes in the twin pairs (p > 0.2 in all groups). The best-fitting models showed heritability (95% CI) estimates for TPOA of 63% (37%, 80%) for the UK and 80% (51%, 92%) for US twins, while the best-fitting meta-analysis model of the two twin cohorts combined included additive genetic and unique environmental factors with a heritability estimate of 69% (50%, 82%). Risk of thyroid autoimmunity, defined by TPOA, in the context of autoimmune diabetes is, substantially, genetically determined in discordant twin pairs. Environmental factors leading to type 1 diabetes were not the same as those involved with thyroid autoimmunity. It follows that it is as important to investigate for thyroid autoimmunity in relatives of type 1 diabetes patients as it is in the patients themselves.

Catch Me if You Can: Adaptation from Standing Genetic Variation to a Moving Phenotypic Optimum.

Adaptation lies at the heart of Darwinian evolution. Accordingly, numerous studies have tried to provide a formal framework for the description of the adaptive process. Of these, two complementary modeling approaches have emerged: While so-called adaptive-walk models consider adaptation from the successive fixation of de novo mutations only, quantitative genetic models assume that adaptation proceeds exclusively from preexisting standing genetic variation. The latter approach, however, has focused on short-term evolution of population means and variances rather than on the statistical properties of adaptive substitutions. Our aim is to combine these two approaches by describing the ecological and genetic factors that determine the genetic basis of adaptation from standing genetic variation in terms of the effect-size distribution of individual alleles. Specifically, we consider the evolution of a quantitative trait to a gradually changing environment. By means of analytical approximations, we derive the distribution of adaptive substitutions from standing genetic variation, that is, the distribution of the phenotypic effects of those alleles from the standing variation that become fixed during adaptation. Our results are checked against individual-based simulations. We find that, compared to adaptation from de novo mutations, (i) adaptation from standing variation proceeds by the fixation of more alleles of small effect and (ii) populations that adapt from standing genetic variation can traverse larger distances in phenotype space and, thus, have a higher potential for adaptation if the rate of environmental change is fast rather than slow.

Rapid evolution of a consumer stoichiometric trait destabilizes consumer–producer dynamics

Recent studies have shown that adaptive evolution can be rapid enough to affect contemporary ecological dynamics in nature (i.e. ‘rapid evolution’). These studies tend to focus on trait functions relating to interspecific interactions; however, the importance of rapid evolution of stoichiometric traits has been relatively overlooked. Various traits can affect the balance of elements (carbon, nitrogen, and phosphorus) of organisms, and rapid evolution of such stoichiometric traits will not only alter population and community dynamics but also influence ecosystem functions such as nutrient cycling. Multiple environmental changes may exert a selection pressure leading to adaptation of stoichiometrically important traits, such as an organism's growth rate. In this paper, we use theoretical approaches to explore the connections between rapid evolution and ecological stoichiometry at both the population and ecosystem level. First, we incorporate rapid evolution into an ecological stoichiometry model to investigate the effects of rapid evolution of a consumer's stoichiometric phosphorus:carbon ratio on consumer–producer population dynamics. We took two complementary approaches, an asexual clonal genotype model and a quantitative genetic model. Next, we extended these models to explicitly track nutrients in order to evaluate the effect of rapid evolution at the ecosystem level. Our model results indicate rapid evolution of the consumer stoichiometric trait can cause complex dynamics where rapid evolution destabilizes population dynamics and rescues the consumer population from extinction (evolutionary rescue). The model results also show that rapid evolution may influence the level of nutrients available in the environment and the flux of nutrients across trophic levels. Our study represents an important step for theoretical integration of rapid evolution and ecological stoichiometry.

Developmental changes in genetic and environmental influences on rule-breaking and aggression: age and pubertal development.

Antisocial behavior (ASB) can be meaningfully divided into nonaggressive rule-breaking versus aggressive dimensions, which differ in developmental course and etiology. Previous research has found that genetic influences on rule-breaking, but not aggression, increase from late childhood to mid-adolescence. This study tested the extent to which the developmental increase in genetic influence on rule-breaking was associated with pubertal development compared to chronological age. Child and adolescent twins (n=1,031), ranging in age from 8 to 20years (M age=13.5years), were recruited from public schools as part of the Texas Twin Project. Participants reported on their pubertal development using the Pubertal Development Scale and on their involvement in ASB on items from the Child Behavior Checklist. Measurement invariance of ASB subtypes across age groups (≤12years vs. >12years old) was tested using confirmatory factor analyses. Quantitative genetic modeling was used to test whether the genetic and environmental influences on aggression and rule-breaking were moderated by age, pubertal status, or both. Quantitative genetic modeling indicated that genetic influences specific to rule-breaking increased as a function of pubertal development controlling for age (a gene×puberty interaction), but did not vary as a function of age controlling for pubertal status. There were no developmental differences in the genetic etiology of aggression. Family-level environmental influences common to aggression and rule-breaking decreased with age, further contributing to the differentiation between these subtypes of ASB from childhood to adolescence. Future research should discriminate between alternative possible mechanisms underlying gene×puberty interactions on rule-breaking forms of antisocial behavior, including possible effects of pubertal hormones on gene expression.

Gene Expression Evolves under a House-of-Cards Model of Stabilizing Selection.

Divergence in gene regulation is hypothesized to underlie much of phenotypic evolution, but the role of natural selection in shaping the molecular phenotype of gene expression continues to be debated. To resolve the mode of gene expression, evolution requires accessible theoretical predictions for the effect of selection over long timescales. Evolutionary quantitative genetic models of phenotypic evolution can provide such predictions, yet those predictions depend on the underlying hypotheses about the distributions of mutational and selective effects that are notoriously difficult to disentangle. Here, we draw on diverse genomic data sets including expression profiles of natural genetic variation and mutation accumulation lines, empirical estimates of genomic mutation rates, and inferences of genetic architecture to differentiate contrasting hypotheses for the roles of stabilizing selection and mutation in shaping natural expression variation. Our analysis suggests that gene expression evolves in a domain of phenotype space well fit by the House-of-Cards (HC) model. Although the strength of selection inferred is sensitive to the number of loci controlling gene expression, the model is not. The consistency of these results across evolutionary time from budding yeast through fruit fly implies that this model is general and that mutational effects on gene expression are relatively large. Empirical estimates of the genetic architecture of gene expression traits imply that selection provides modest constraints on gene expression levels for most genes, but that the potential for regulatory evolution is high. Our prediction using data from laboratory environments should encourage the collection of additional data sets allowing for more nuanced parameterizations of HC models for gene expression.

Modest genetic influence on bronchodilator response: a study in healthy twins.

AimTo determine the reasons for large standard deviation of bronchodilator response (BDR) and establish whether there is a potential heritable component in healthy subjects.Methods67 monozygotic and 42 dizygotic adult twin pairs were assessed for bronchodilator response (%change in FEV1 after inhaling 400 µg salbutamol). Univariate quantitative genetic modeling was performed.ResultsMultiple regression modeling showed a significant association between BDR and sex and baseline FEV1 (P < 0.05), while no association was found with smoking habits, body mass index, or age. Within pair correlation in monozygotic twins was modest (0.332), but higher than in dizygotic twins (0.258). Age-, sex-, and baseline FEV1-adjusted genetic effect accounted for 14.9% (95% confidence interval, CI 0%-53.1%) of the variance of BDR, shared environmental effect for 18.4% (95% CI 0%-46.8%), and unshared environmental effect for 66.8% (95% CI 46.8%-88.7%).ConclusionOur twin study showed that individual differences in BDR can be mostly explained by unshared environmental effects. In addition, it is the first study to show low, insignificant hereditary influences, independently from sex, age, and baseline FEV1.

Evolutionary processes make invasion speed difficult to predict

A capacity to predict the spread rate of populations is critical for understanding the impacts of climate change and invasive species. Despite sophisticated theory describing how populations spread, the prediction of spread rate remains a formidable challenge. As well as the inherent stochasticity in the spread process, spreading populations are subject to strong evolutionary forces (operating on dispersal and reproductive rates) that can cause accelerating spread. Despite these strong evolutionary forces, serial founder events and drift on the expanding range edge mean that evolutionary trajectories in the invasion vanguard may be highly stochastic. Here I develop a model of spatial spread in continuous space that incorporates evolution of continuous traits under a quantitative genetic model of inheritance. I use this model to investigate the potential role of evolution on the variation in spread rate between replicate model realisations. Models incorporating evolution exhibited more than four times the variance in spread rate across replicate invasions compared with non-evolving scenarios. Results suggest that the majority of this increase in variation is driven by evolutionary stochasticity on the invasion front rather than initial founder events: in many cases evolutionary stochasticity on the invasion front contributed more than 90 % of the variance in spread rate over 30 generations. Our uncertainty around predicted spread rates—whether for invasive species or those shifting under climate change—may be much larger than we expect when the spreading population contains heritable variation in rates of dispersal and reproduction.

The evolution of phenotypic plasticity: Genealogy of a debate in genetics

The paper describes the context and the origin of a particular debate that concerns the evolution of phenotypic plasticity. In 1965, British biologist A. D. Bradshaw proposed a widely cited model intended to explain the evolution of norms of reaction, based on his studies of plant populations. Bradshaw's model went beyond the notion of the “adaptive norm of reaction” discussed before him by Dobzhansky and Schmalhausen by suggesting that “plasticity”—the ability of a phenotype to be modified by the environment—should be genetically determined. To prove Bradshaw's hypothesis, it became necessary for some authors to identify the pressures exerted by natural selection on phenotypic plasticity in particular traits, and thus to model its evolution. In this paper, I contrast two different views, based on quantitative genetic models, proposed in the mid-1980s: Russell Lande and Sara Via's conception of phenotypic plasticity, which assumes that the evolution of plasticity is linked to the evolution of the plastic trait itself, and Samuel Scheiner and Richard Lyman's view, which assumes that the evolution of plasticity is independent from the evolution of the trait. I show how the origin of this specific debate, and different assumptions about the evolution of phenotypic plasticity, depended on Bradshaw's definition of plasticity and the context of quantitative genetics.

Bring in the genes: genetic-ecophysiological modeling of the adaptive response of trees to environmental change. With application to the annual cycle.

The observation of strong latitudinal clines in the date of bud burst of tree species indicate that populations of these species are genetically adapted to local environmental conditions. Existing phenological models rarely address this clinal variation, so that adaptive responses of tree populations to changes in environmental conditions are not taken into account, e.g., in models on species distributions that use phenological sub-models. This omission of simulating adaptive response in tree models may over- or underestimate the effects of climate change on tree species distributions, as well as the impacts of climate change on tree growth and productivity. Here, we present an approach to model the adaptive response of traits to environmental change based on an integrated process-based eco-physiological and quantitative genetic model of adaptive traits. Thus, the parameter values of phenological traits are expressed in genetic terms (allele effects and—frequencies, number of loci) for individual trees. These individual trees thereby differ in their ability to acquire resources, grow and reproduce as described by the process-based model, leading to differential survival. Differential survival is thus the consequence of both differences in parameters values and their genetic composition. By simulating recombination and dispersal of pollen, the genetic composition of the offspring will differ from that of their parents. Over time, the distribution of both trait values and the frequency of the underlying alleles in the population change as a consequence of changes in environmental drivers leading to adaptation of trees to local environmental conditions. This approach is applied to an individual-tree growth model that includes a phenological model on the annual cycle of trees whose parameters are allowed to adapt. An example of the adaptive response of the onset of the growing season across Europe is presented.

Measures of mate choice: a comment on Dougherty &amp; Shuker

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Quantitative genetics model as the unifying model for defining genomic relationship and inbreeding coefficient.

The traditional quantitative genetics model was used as the unifying approach to derive six existing and new definitions of genomic additive and dominance relationships. The theoretical differences of these definitions were in the assumptions of equal SNP effects (equivalent to across-SNP standardization), equal SNP variances (equivalent to within-SNP standardization), and expected or sample SNP additive and dominance variances. The six definitions of genomic additive and dominance relationships on average were consistent with the pedigree relationships, but had individual genomic specificity and large variations not observed from pedigree relationships. These large variations may allow finding least related genomes even within the same family for minimizing genomic relatedness among breeding individuals. The six definitions of genomic relationships generally had similar numerical results in genomic best linear unbiased predictions of additive effects (GBLUP) and similar genomic REML (GREML) estimates of additive heritability. Predicted SNP dominance effects and GREML estimates of dominance heritability were similar within definitions assuming equal SNP effects or within definitions assuming equal SNP variance, but had differences between these two groups of definitions. We proposed a new measure of genomic inbreeding coefficient based on parental genomic co-ancestry coefficient and genomic additive correlation as a genomic approach for predicting offspring inbreeding level. This genomic inbreeding coefficient had the highest correlation with pedigree inbreeding coefficient among the four methods evaluated for calculating genomic inbreeding coefficient in a Holstein sample and a swine sample.

Causal Foundations of Evolutionary Genetics

The causal nature of evolution is one of the central topics in the philosophy of biology. The issue concerns whether equations used in evolutionary genetics point to some causal processes or purely phenomenological patterns. To address this question the present article builds well-defined causal models that underlie standard equations in evolutionary genetics. These models are based on minimal and biologically plausible hypotheses about selection and reproduction, and generate statistics to predict evolutionary changes. The causal reconstruction of the evolutionary principles shows adaptive evolution as a genuine causal process, where fitness and selection are both causes of evolution. 1 Introduction 2 The Philosophical Puzzle 3 Causal Models 4 Causal Foundations of Evolutionary Genetics 4.1 Univariate quantitative genetics model 4.1.1 The causal graph 4.1.2 Structural equations 4.1.3 Deriving evolutionary transition functions 4.2 One-locus population genetics model 5 Evolution as a Causal Process 5.1 Selection as a causal process 5.2 Causes of evolutionary change 6 Conclusion