Statistical Power to Detect Genetic (Co)Variance of Complex Traits Using SNP Data in Unrelated Samples

We have recently developed analysis methods (GREML) to estimate the genetic variance of a complex trait/disease and the genetic correlation between two complex traits/diseases using genome-wide single nucleotide polymorphism (SNP) data in unrelated individuals. Here we use analytical derivations and simulations to quantify the sampling variance of the estimate of the proportion of phenotypic variance captured by all SNPs for quantitative traits and case-control studies. We also derive the approximate sampling variance of the estimate of a genetic correlation in a bivariate analysis, when two complex traits are either measured on the same or different individuals. We show that the sampling variance is inversely proportional to the number of pairwise contrasts in the analysis and to the variance in SNP-derived genetic relationships. For bivariate analysis, the sampling variance of the genetic correlation additionally depends on the harmonic mean of the proportion of variance explained by the SNPs for the two traits and the genetic correlation between the traits, and depends on the phenotypic correlation when the traits are measured on the same individuals. We provide an online tool for calculating the power of detecting genetic (co)variation using genome-wide SNP data. The new theory and online tool will be helpful to plan experimental designs to estimate the missing heritability that has not yet been fully revealed through genome-wide association studies, and to estimate the genetic overlap between complex traits (diseases) in particular when the traits (diseases) are not measured on the same samples.     

The statistical treatment of correlated bilateral traits in the analysis of cranial material.

At present there is no standardized method to derive frequencies from bilateral non-metric traits. In this paper the commonly used methods are evaluated in light of statistical considerations and degree of sample preservation. In particular, we explore the question of dependence between sides for the bilateral traits. Several workers have tested for bilateral trait correlation in incorrect ways, confusing tests for differences in side frequencies with tests for independence. An easy method to test for independence, using the chi-squared test, is recommended. This test is used on 16 bilateral traits in a large sample of prehistoric carnia from Central California and significant dependence is found for all 16 of these traits. We suggest the traditional method of deriving frequencies be used. Both sides of the cranium should be considered, dividing the number of times the trait occurs by the number of sides available for observation. This method can be used even in poorly preserved samples. Side to side correlation may be compensated for by modifying the constants subtracted in the mean measure of divergence and in the expression for the approximate variance of the mean measure of divergence when the samples are drawn from identical populations.     

Mapping functional similarity of predators on the basis of trait similarities

Theoretical and empirical studies in community ecology often simplify their study system by lumping together species on the basis of trait similarities (e.g., their taxonomy, resource or microhabitat usage) and then assume species sharing similar traits are functionally similar. To date, no study has directly tested whether species more similar with respect to any of these traits are more similar in their functional effects on population or ecosystem processes. In this study, we examined the association between traits and functional effects of six different aquatic predatory vertebrates. We demonstrated that functional similarity across multiple response variables was not correlated with trait similarity, but differences in trait values were associated with significantly different effects on individual response variables. The exact relationship between species traits and functional effect of predators, however, was different for each response variable. Using traits to predict functional similarity among species may be useful when considering individual response variables, but only if it is known which traits have the greatest influence on the response variable of interest. It is doubtful that any one scheme will predict the functional similarity of species across a diverse array of response variables because each response will likely be strongly influenced by different traits.     

The evolution of indicator traits for parental quality: the role of maternal and paternal effects

In systems where individuals provide material resources to their mates or offspring, mate choice based on traits that are phenotypically correlated with the quality of resources provided is expected to be adaptive. Several models have explored the evolution of mating preference where there are direct benefits to choice, but few have addressed how a phenotypic correlation can be established between a male indicator trait and the degree of parental investment. We present a model with three quantitative traits: male and female parental investment and a potential male indicator trait. In our model, the expression of the "indicator" trait in offspring is affected by parental investment. These effects are referred to as maternal or paternal effects, or as "indirect genetic effects" when parental investment is heritable. With genetic variation for degree of parental investment, offspring harbor genes for parental investment that are unexpressed before mating but will affect the investment that they provide when expressed. Because the investment received from the parents affects the expression of the indicator trait, there will be a correlation between the genes for parental investment inherited and the degree of expression of the indicator trait in the offspring. The indicator trait is thus an "honest" signal for the degree of paternal investment.     

Genetic fatalism and social policy: the implications of behavior genetics research.

Recent advances in molecular genetics methods have provided new means of determining the genetic bases of human behavioral traits. The impetus for the use of these approaches for specific behaviors depends, in large part, on previous familial studies on inheritance of such traits. In the past, a finding of a genetic basis for a trait was often accompanied with the idea that that trait is unchangeable. We discuss the definition of "genetic trait" and heritability and examine the relationship between these concepts and the malleability of traits for both molecular and nonmolecular approaches to behavioral genetics. We argue that the malleability of traits is as much a social and political question as it is a biological one and that whether or not a trait is genetic has little relevance to questions concerning determinism, free will, and individual responsibility for actions. We conclude by noting that "scientific objectivity" should not be used to conceal the social perspectives that underlie proposals regarding social change.     

A critique of life history approaches to human trait covariation

Covariation of life history traits across species may be organised on a ‘fast-slow’ continuum. A burgeoning literature in psychology and social science argues that trait covariation should be similarly organised across individuals within human populations. Here we describe why extrapolating from inter-species to inter-individual trait covariation is not generally appropriate. The process that genetically tailors species to their environments (i.e. Darwinian evolution) is fundamentally different from processes that tailor individuals to their environments (e.g. developmental plasticity), so their outcomes in terms of trait covariation need not be parallel or even related. We discuss why correlational selection, physical linkage, pleiotropy, and non-random mating do not substantively affect this claim in the context of complex human traits. We also discuss life history trade-offs and their relation to inter-individual trait covariation. We conclude that researchers should avoid hypotheses and explanations that assume trait covariation will correspond across and within species, unless they can mount a theoretically coherent argument to support this claim in the context of their research question.     

Covariation among floral traits in Spergularia marina (Caryophyllaceae): geographic and temporal variation in phenotypic and among-family correlations

Strong covariation among traits suggests the presence of constraints on their independent evolution due to pleiotropy, to linkage, or to selective forces that maintain particular trait combinations. We examined floral trait covariation among individuals, among maternal families within and across populations, and over time, in greenhouse-raised plants of the autogamous Spergularia marina. We had three aims. First, since the phenotype of traits expressed by modular organs often changes as individuals age, estimates of the degree of genetic covariation between such traits may also change over time. To seek evidence for this, we measured weekly (for five weeks) an array of floral traits among plants representing ～ 10 maternal families from each of four populations. The statistical significance of the phenotypic and among-family correlations among traits changed over time. Second, we compared populations with respect to trait covariation to determine whether populations or traits appear to be evolving independently of one another. Differences observed among populations suggest that they have diverged genetically. Third, we sought correlations that might reflect constraints on the independent evolution of floral traits. Investment in another and ovule production per flower vary independently among maternal families; there was no evidence for a “trade-off” between male and female investment. We propose that in autogamous taxa one should not find a negative correlation between pollen and ovule production per flower, as such taxa cannot evolve sexual specialization and should be under strong selection to maintain an efficient pollen:ovule ratio, preventing the evolution of male-biased or female-biased genotypes. We found that other pairs of floral traits, however, expressed highly signficant correlation coefficients, suggesting the presence of some evolutionary constraints, at least within some populations, although their strength depended on exactly when flowers were sampled.     

Genotype?��?environment interaction is weaker in genitalia than in mating signals and body traits in Enchenopa treehoppers (Hemiptera: Membracidae)

Theory predicts that selection acting across environments should erode genetic variation in reaction norms; i.e., selection should weaken genotype × environment interaction (G × E). In spite of this expectation, G × E is often detected in fitness-related traits. It thus appears that G × E is at least sometimes sustained under selection, a possibility that highlights the need for theory that can account for variation in the presence and strength of G × E. We tested the hypothesis that trait differences in developmental architecture contribute to variation in the expression of G × E. Specifically, we assessed the influence of canalization (robustness to genetic or environmental perturbations) and condition-dependence (association between trait expression and prior resource acquisition or vital cellular processes). We compared G × E across three trait types expected to differ in canalization and condition-dependence: mating signals, body size-related traits, and genitalia. Because genitalia are expected to show the least condition-dependence and the most canalization, they should express weaker G × E than the other trait types. Our study species was a member of the Enchenopa binotata species complex of treehoppers. We found significant G × E in most traits; G × E was strongest in signals and body traits, and weakest in genitalia. These results support the hypothesis that trait differences in developmental architecture (canalization and condition-dependence) contribute to variation in the expression of G × E. We discuss implications for the dynamics of sexual selection on different trait types.     

Canalisation in the wild: effects of developmental conditions on physiological traits are inversely linked to their association with fitness

Ecological conditions affect fitness, but mechanisms causing such effects are not well known, while evolved responses to environmental variation may depend on the underlying mechanisms. Consequences of environmental conditions vary strongly between traits, but a framework to interpret such variation is lacking. We propose that variation in trait response may be explained by differential canalisation, with traits with larger fitness effects showing weaker responses to environmental perturbations due to preferential resource allocation to such traits. We tested the canalisation hypothesis using brood size manipulation in wild jackdaw nestlings in which we measured eight physiological traits (mainly oxidative stress markers), and two feather traits. For each trait, we estimated manipulation response and association with fitness (over‐winter survival). As predicted, a strong negative correlation emerged between manipulation response and association with fitness (r =?0.76). We discuss the consequences of differential trait canalisation for the study of mechanisms mediating environmental effects on fitness.     

Sexually selected traits and adult survival: a meta-analysis

Traits correlated with male mating success are likely to be subject to sexual selection. Sexually selected characters are thought to be costly to develop and maintain. If males do not vary their investment in sexual traits in relation to their ability to bear the costs, there should be a negative relationship between male longevity or survival and the expression of sexual traits. In particular, a negative relationship is predicted by pure Fisherian models for the evolution of sexual ornaments. The same should also be true for traits that evolve via pleiotropy (e.g., due to sensory exploitation or bias) with no subsequent evolution of condition dependent modification. We collected information on the relationship between traits correlated with male mating rate and estimates of adult male survivorship or life span. In total we obtained 122 samples from 69 studies of 40 species of bird, spider, insect, and fish. In a meta-analysis we calculated the average sample size weighted correlation between trait expression and adult survival. Analyses at the level of samples, studies, and species revealed significant positive relationships (r = 0.08, 0.10, and 0.13, respectively; all P < 0.001). The unweighted correlation at the species level was r = 0.24. In general, males with larger ornaments or weapons, greater body size, or higher rates of courtship showed greater survivorship or longevity. This finding is inconsistent with pure Fisherian models or other models that do not incorporate condition or quality dependent trait expression. It suggests that male investment in sexually selected traits is not fixed but varies in relation to the ability to pay the underlying costs of expressing these characters. Hence, many secondary sexual characters are likely to be condition dependent in their expression.     

Functional association between malting quality trait components and cDNA array based expression patterns in barley (Hordeum vulgare L.)

We developed an approach for relating differences in gene expression to the phenotypic variation of a trait of interest. This allows the identification of candidate genes for traits that display quantitative variation. To validate the principle, gene expression was monitored on a cDNA array with 1400 ESTs to identify genes involved in the variation of the complex trait malting quality in barley. RNA profiles were monitored during grain germination in a set of 10 barley genotypes that had been characterized for 6 quality-associated trait components. The selection of the candidate genes was achieved via a correlation of dissimilarity matrices that were based on (i) trait variation and (ii) gene expression data. As expected, a comparison based on the complete set of differentially-expressed genes did not reveal any correlation between the matrices, because not all genes that show differential expression between the 10 cultivars are responsible for the observed differences in malting quality. However, by iteratively taking out one gene (with replacement) and re-computing the correlation, those genes that are positively contributing to the correlation could be identified. Using this procedure between 17 and 30 candidate genes were identified for each of the six malting parameters analysed. In addition to genes of unknown function, the list of candidates contains well-known malting-related genes. Five out of eight mapped candidate genes display linkage to known QTLs for malting quality traits. The described functional association strategy may provide an efficient link between functional genomics and plant breeding.     

Selection strategies for linkage studies using twins.

Genetic linkage analysis for complex diseases offers a major challenge to geneticists. In these complex diseases multiple genetic loci are responsible for the disease and they may vary in the size of their contribution; the effect of any single one of them is likely to be small. In many situations, like in extensive twin registries, trait values have been recorded for a large number of individuals, and preliminary studies have revealed summary measures for those traits, like mean, variance and components of variance, including heritability. Given the small effect size, a random sample of twins will require a prohibitively large sample size. It is well known that selective sampling is far more efficient in terms of genotyping effort. In this paper we derive easy expressions for the information contributed by sib pairs for the detection of linkage to a quantitative trait locus (QTL). We consider random samples as well as samples of sib pairs selected on the basis of their trait values. These expressions can be rapidly computed and do not involve simulation. We extend our results for quantitative traits to dichotomous traits using the concept of a liability threshold model. We present tables with required sample sizes for height, insulin levels and migraine, three of the traits studied in the GenomEUtwin project.     

Why are rare traits unilaterally expressed?: Trait frequency and unilateral expression for cranial nonmetric traits in humans

Based on an analysis of nonmetric trait databases from several large skeletal series in Northern Europe and South America, representing 27 bilateral traits, we report a predictable relationship between the frequency of nonmetric traits and the probability that they are expressed bilaterally. In a wider sampling of traits and populations, this study thus confirms the findings of an earlier study by Ossenberg ([1981] Am. J. Phys. Anthropol. 54:471-479), which reported the same relationship for two mandibular traits. This trend was previously explained by extending the multifactorial threshold model for discontinuous traits to incorporate either separate thresholds for unilateral or bilateral expression, or by a fuzzy threshold in which the probability of bilateral expression increases away from the median threshold value. We show that the trend is produced under the standard multifactorial threshold model for discontinuous traits simply if the within-individual or developmental instability variance remains relatively constant across the range of liability. Under this assumption, the number of individuals in which one side but not the other is pushed over the threshold for trait formation will be a larger proportion of the number of individuals expressing the trait when the trait frequency is low. As trait frequency increases, the significance of within-individual variance as a determinant of trait formation decreases relative to the genetic and among-individual environmental variance. These results have implications for interpreting nonmetric trait data as well as for understanding the prevalence of unilateral vs. bilateral expression of a wide variety of discontinuous traits, including dysmorphologies in humans.     

Condition dependence and trade-offs of sexual versus non-sexual traits in an insect

Sexual traits often communicate male condition and so are known to be highly condition-dependent. Thus, it is expected that, under restricted environments, sexual traits will be more heavily impacted than non-sexual traits, and so a negative covariation will be expected between sexual traits and non-sexual traits as only high-quality males will sustain the costs of producing both trait types. Such covariation will not necessarily appear in non-restricted environments. We tested these predictions using males of the American rubyspot, Hetaerina americana. First, fully mature males from different seasons were collected and their sexual [a wing red spot and body size (this corrected for body mass using residuals)], and condition-indicating, non-sexual (phenoloxidase and protein concentration) traits were measured. Second, larvae were reared under different food quantities and the same traits plus another non-sexual trait [pro-phenoloxidase (proPO)], were measured in recently emerged males. Contrary to expected, non-sexual traits showed larger expression variance than sexual traits. We found a significant covariation between body size and proPO for experimental males. Both rich and poor diet groups showed a negative slope for body size and proPO. This supposes a resource allocation trade-off between these two traits for recently emerged animals. On the other hand, the presumed signaling function between sexual traits, such as spot size, and physiological indicators of condition in this species, is not supported.     

Congruency analysis of species ranking based on leaf traits: which traits are the more reliable?

Nine leaf traits (area, fresh weight, dry weight, volume, density, thickness, specific leaf area (SLA), dry matter content (LDMC), leaf nitrogen content (LNC)) from ten plant species at eight sites in southern mediterranean France were investigated in order to assess their variability along a climatic gradient and their ranking congruency power. After examination of trait correlation patterns, we reduced the nine initial leaf traits to four traits, representative of three correlation groups: allometric traits (dry weight), functional traits (SLA and dry matter percentage) and Leaf Thickness. We analysed the variability of these four leaf traits at species and site level. We observed that between species variation (between 64.5 for SLA and 91% for LDMC) is higher than within species variation. Allowing a good congruency of species ranking assessed by spearman rank correlation () and a good reallocation of individuals to species by discriminant analysis. A site level variability (between 0.7% for Dry weight and 6.9% for SLA) was identified and environmental parameters (altitude, temperature, precipitation, nitrogen, pH) were considered as probable control factors. We found significant correlation between SLA, LDMC and the average minimum temperature (respectively r=0.87 and r=-0,9) and no correlation for the other traits or environmental parameters. Furthermore, we conclude that two leaf traits appear to be central in describing species: specific leaf area (SLA), percentage of dry matter (LDMC. While, SLA and LDMC are strongly correlated, LDMC appears to be less variable than SLA. According to our results the Dry Matter Content (or its reversal Leaf Water Content) appears the best leaf trait to be quantified for plant functional screening. Leaf thickness appeared to be rather uncorrelated with other leaf traits and show no environmental contingency; its variability could not have been explained in this study. Further studies should focus on this trait. This revised version was published online in June 2006 with corrections to the Cover Date.     

Correlated development, organism‐wide asymmetry and patterns of asymmetry in two moth species

Understanding the mechanisms that determine the development of a bilaterally symmetrical trait is crucial to the interpretation of patterns of fluctuating asymmetry (FA). Experimental and theoretical studies have indicated that feedback mechanisms both within and between developing traits, may participate in the developmental control of asymmetry. This study provides evidence that naturally occurring patterns of FA are affected by interactions between different traits. We found positive between‐trait correlations in signed FA values for tibia lengths on different legs, but not between wing and tibia FA in two moth species. Further research should investigate if trait functionality is related to this presumed correlated development. An extension of the Rashevsky–Turing model of morphogenesis further showed that correlations between the signed FA values can be generated by feedback mechanisms that regulate growth patterns between traits. We argue that such feedback mechanisms can be expected to be widespread and show that between‐trait correlations in the unsigned FA then become confounded with correlations in the signed FA. In addition, correlated development appeared to invalidate the use of the hypothetical repeatability to translate correlations between the unsigned FA values into correlations in the presumed underlying developmental instability. In conclusion, the presence of an organism‐wide asymmetry, which are most frequently found in morphologically integrated traits, may be even less common than previously thought. This revised version was published online in July 2006 with corrections to the Cover Date.     

Alternative phenotypes and sexual selection: can dichotomous handicaps honestly signal quality?

Considerable theoretical and empirical effort has been focused on the potential of continuously variable sexual traits to honestly indicate male quality, but relatively little effort has been devoted to a similar evolutionary role for dimorphic traits. Male dimorphisms, associated with conditionally expressed alternative reproductive tactics, represent extreme phenotypic plasticity. Evidence suggests that considerable heritable variation exists in the 'liability' underlying many threshold traits; if this liability is correlated with the genetic quality of males, dimorphic traits have the potential to be reliable indicators. We investigated the genetic architecture of phenotypically plastic morph expression in the context of condition-dependent signalling theory. Male morph in the mite Sancassania berlesei is condition dependent: 'fighters' armed with thickened and sharp third pairs of legs emerge from heavier nymphs than unarmoured 'scramblers'. We selected on male morph in three replicate 'fighter' and 'scrambler' lines and recorded a significant response to selection over seven generations; this was due to a shift in the threshold reaction norm but the lines showed no correlated response in condition. This is inconsistent with models predicting a substantial genetic correlation between condition and sexual trait expression. We discuss why dimorphic sexual traits may show more condition-independent genetic variance than continuous sexual traits.     

Trait variation and integration across scales: is the leaf economic spectrum present at local scales?

Trait‐based approaches have taken an increasingly dominant role in community ecology. Although trait‐based strategy dimensions such as the leaf economic spectrum (LES) have been identified primarily at global‐scales, trait variation at the community scale is often interpreted in this context. Here we argue from several lines of evidence that a research priority should be to determine whether global‐scale trait relationships hold at more local scales. We review recent literature assessing trait variation at smaller scales, and then present a case study exploring the relationship between the correlation strength of leaf traits and their similarity in variation structure across ecological scales. We find that the correlation strength between pairs of leaf traits does not predict whether the traits respond similarly to different drivers of variation. Instead, correlation strength only sets an upper bound to the dissimilarity in trait variation structure. With moderate correlation strengths, LES traits largely retain the ability to respond independently to different drivers of phenotypic variation at different scales. Recent literature and our results suggest that LES relationships may not hold at local scales. Clarifying under what conditions and at which scales the LES is consistently expressed is necessary for us to make the most of the emerging trait toolbox.