Pleiotropic Models of Quantitative Variation

It is widely held that each gene typically affects many characters, and that each character is affected by many genes. Moreover, strong stabilizing selection cannot act on an indefinitely large number of independent traits. This makes it likely that heritable variation in any one trait is maintained as a side effect of polymorphisms which have nothing to do with selection on that trait. This paper examines the idea that variation is maintained as the pleiotropic side effect of either deleterious mutation, or balancing selection. If mutation is responsible, it must produce alleles which are only mildly deleterious (s approximately 10(-3)), but nevertheless have significant effects on the trait. Balancing selection can readily maintain high heritabilities; however, selection must be spread over many weakly selected polymorphisms if large responses to artificial selection are to be possible. In both classes of pleiotropic model, extreme phenotypes are less fit, giving the appearance of stabilizing selection on the trait. However, it is shown that this effect is weak (of the same order as the selection on each gene): the strong stabilizing selection which is often observed is likely to be caused by correlations with a limited number of directly selected traits. Possible experiments for distinguishing the alternatives are discussed.     

A Model for Transgenerational Imprinting Variation in Complex Traits

Despite the fact that genetic imprinting, i.e., differential expression of the same allele due to its different parental origins, plays a pivotal role in controlling complex traits or diseases, the origin, action and transmission mode of imprinted genes have still remained largely unexplored. We present a new strategy for studying these properties of genetic imprinting with a two-stage reciprocal F mating design, initiated with two contrasting inbred lines. This strategy maps quantitative trait loci that are imprinted (i.e., iQTLs) based on their segregation and transmission across different generations. By incorporating the allelic configuration of an iQTL genotype into a mixture model framework, this strategy provides a path to trace the parental origin of alleles from previous generations. The imprinting effects of iQTLs and their interactions with other traditionally defined genetic effects, expressed in different generations, are estimated and tested by implementing the EM algorithm. The strategy was used to map iQTLs responsible for survival time with four reciprocal F populations and test whether and how the detected iQTLs inherit their imprinting effects into the next generation. The new strategy will provide a tool for quantifying the role of imprinting effects in the creation and maintenance of phenotypic diversity and elucidating a comprehensive picture of the genetic architecture of complex traits and diseases.     

Likelihood Under the Mixed Model for Quantitative Traits

Mathematical details of obtaining the likelihood functions for testing hypotheses under the mixed model for quantitative traits are given. Since families are assumed to be chosen by the value of the trait of a particular family member, conditional distributions are required. Algorithms for efficient computation of the likelihood are given.     

Multivariate Extensions of the Mixed Model for Quantitative Traits

The mixed model for complex segregation analysis of quantitative data from three-generational nuclear families is extended to the multivariate case. Likelihood functions for hypothesis testing are derived for two types of conditional analysis of multiple traits: first when entry to the study depends on the index case's values of all the quantitative traits that are of interest, and second when entry depends on only one trait, but other correlated traits are to be studied simultaneously. Using direct products of covariance matrices, these functions are seen to be direct multivariate equivalence of the univariate functions.     

High Stressful Temperature and Genetic Variation of Five Quantitative Traits in Drosophila Melanogaster

Variation of five quantitative traits (thorax length, wing length, sternopleural bristle number, developmental time and larva-to-adult viability) was studied in Drosophila melanogaster reared at standard (25°C) and high stressful (32°C) temperatures using half-sib analysis. In all traits, both phenotypic and environmental variances increased at 32°C. For genetic variances, only two statistically significant differences between temperature treatments were found: the among-sire variance of viability and the among-dam variance of developmental time were higher under stress. Among-sire genetic variances and evolvabilities were generally higher at 32°C but narrow sense heritabilities were not. The results of the present work considered in the context of other studies in D. melanogaster indicate different patterns of genetic variation between stressful and nonstressful environments for the traits examined. Data on thorax length and viability agree with the hypothesis that genetic variance can be increased under extreme environmental conditions. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Expression of Additive and Nonadditive Genetic Variation under Stress

Experimental lines of Drosophila melanogaster derived from a natural population, which had been isolated in the laboratory for ~70 generations, were crossed to determine if the expression of additive, dominance and epistatic genetic variation in development time and viability was associated with the environment. No association was found between the level of additive genetic effects and environmental value for either trait, but nonadditive genetic effects increased at both extremes of the environmental range for development time. The expression of high levels of dominance and epistatic genetic variation at environmental extremes may be a general expectation for some traits. The disruption of the epistatic gene complexes in the parental lines resulted in hybrid breakdown toward faster development and there was some indication of hybrid breakdown toward higher viability. A combination of genetic drift and natural selection had therefore resulted in different epistatic gene complexes being selected after ~70 generations from a common genetic base. After crossing, the hybrid populations were observed for 10 generations. Epistasis contributed on average 12 hr in development time. Fluctuating asymmetry in sternopleural bristle number also evolved in the hybrid populations, decreasing by >18% in the first seven generations after hybridization.     

RFLP Mapping in Soybean: Association between Marker Loci and Variation in Quantitative Traits

Quantitative trait loci (QTLs) have been mapped to small intervals along the chromosomes of tomato (Lycopersicon esculentum), by a method we call substitution mapping. The size of the interval to which a QTL can be mapped is determined primarily by the number and spacing of previously mapped genetic markers in the region surrounding the QTL. We demonstrate the method using tomato genotypes carrying chromosomal segments from Lycopersicon chmielewskii, a wild relative of tomato with high soluble solids concentration but small fruit and low yield. Different L. chmielewskii chromosomal segments carrying a common restriction fragment length polymorphism were identified, and their regions of overlap determined using all available genetic markers. The effect of these chromosomal segments on soluble solids concentration, fruit mass, yield, and pH, was determined in the field. Many overlapping chromosomal segments had very different phenotypic effects, indicating QTLs affecting the phenotype(s) to lie in intervals of as little as 3 cM by which the segments differed. Some associations between different traits were attributed to close linkage between two or more QTLs, rather than pleiotropic effects of a single QTL: in such cases, recombination should separate desirable QTLs from genes with undesirable effects. The prominence of such trait associations in wide crosses appears partly due to infrequent reciprocal recombination between heterozygous chromosomal segments flanked by homozygous regions. Substitution mapping is particularly applicable to gene introgression from wild to domestic species, and generally useful in narrowing the gap between linkage mapping and physical mapping of QTLs.     

Variation in CHI3LI in Relation to Type 2 Diabetes and Related Quantitative Traits

Background

CHI3LI encoding the inflammatory glycoprotein YKL-40 is located on chromosome 1q32.1. YKL-40 is involved in inflammatory processes and patients with Type 2 Diabetes (T2D) have elevated circulating YKL-40 levels which correlate with their level of insulin resistance. Interestingly, it has been reported that rs10399931 (−329 G/A) of CHI3LI contributes to the inter-individual plasma YKL-40 levels in patients with sarcoidosis, and that rs4950928 (−131 C/G) is a susceptibility polymorphism for asthma and a decline in lung function. We hypothesized that single nucleotide polymorphisms (SNPs) or haplotypes thereof the CHI3LI locus might influence risk of T2D. The aim of the present study was to investigate the putative association between SNPs and haplotype blocks of CHI3LI and T2D and T2D related quantitative traits.

Methods/Principal Findings

Eleven SNPs of CHI3LI were genotyped in 6514 individuals from the Inter99 cohort and 2924 individuals from the outpatient clinic at Steno Diabetes Center. In cas-control studies a total of 2345 T2D patients and 5302 individuals with a normal glucose tolerance test were examined.We found no association between rs10399931 (OR, 0.98 (CI, 0.88–1.10), p = 0.76), rs4950928 (0.98 (0.87–1.10), p = 0.68) or any of the other SNPs with T2D. Similarly, we found no significant association between any of the 11 tgSNPs and T2D related quantitative traits, all p>0.14. None of the identified haplotype blocks of CHI3LI showed any association with T2D, all p>0.16.

Conclusions/Significance

None of the examined SNPs or haplotype blocks of CHI3LI showed any association with T2D or T2D related quantitative traits. Estimates of insulin resistance and dysregulated glucose homeostasis in T2D do not seem to be accounted for by the examined variations of CHI3LI.     

Pleiotropic Overdominance and the Maintenance of Genetic Variation in Polygenic Characters

A model of selection is described in which optimizing phenotypic selection is combined with pleiotropic overdominance. Thus, the role that mutation commonly plays in models of phenotypic evolution is replaced by balancing selection. Expressions are provided for the equilibrium genetic variance in phenotype and for the heterozygosity. An approximate analysis of the transient properties of the model shows that, in certain circumstances, the behavior is quite similar to that of models based on the interaction of mutation and selection.     

Interpreting Geographic Variation in Life-History Traits

The geographic variation in the length of the larval periodand the size at metamorphosis of the wood frog,Rana sylvatica,is examined for populations in the tundra of Canada, the mountainsof Virginia, and the lowlands of Maryland. We argue that theobserved differences in developmental plasticity, heriisbilitiesand genetic covariances of traits among localities result fromdifferential selection pressures in each environment, and arerelated to the physiological constraints inherent in developmentand to the degree of compromise between the timing and sizeat metamorphosis allowed in each environment. In Maryland populationsfitness has been maximized by evolutionary changes in size alone;body size in this population is canalized, has low heritabilityand is highly correlated with juvenile survival relative todevelopmental time. In Canada, minimum developmental time yieldsmaximum fitness; the length of the larval period in this populationis canalized and genetically monomorphic relative to body size.In contrast, fitness in the Virginia populations has been determinedby correlated and pleiotropic effects of genes on both developmentaltime and larval body size, and both traits are equally canalized,affect juvenile survivorship equally and display moderate heritabilities.These results stress the importance of interpreting variationin life-history traits relative to constraints inherent in developmentand those imposed by the environment. Heritability and survivorshipdata support the general notion that fitness traits should havelow levels of additive genetic variation, but also suggest thatantagonistic pleiotropy may act to preserve genetic variationin fitness traits under simultaneous selection, and cautionagainst inferring evolutionary importance of individual traitswithout considering the possible presence of pleiotropy.     

A Bayesian Nonparametric Approach for Mapping Dynamic Quantitative Traits

In biology, many quantitative traits are dynamic in nature. They can often be described by some smooth functions or curves. A joint analysis of all the repeated measurements of the dynamic traits by functional quantitative trait loci (QTL) mapping methods has the benefits to (1) understand the genetic control of the whole dynamic process of the quantitative traits and (2) improve the statistical power to detect QTL. One crucial issue in functional QTL mapping is how to correctly describe the smoothness of trajectories of functional valued traits. We develop an efficient Bayesian nonparametric multiple-loci procedure for mapping dynamic traits. The method uses the Bayesian P-splines with (nonparametric) B-spline bases to specify the functional form of a QTL trajectory and a random walk prior to automatically determine its degree of smoothness. An efficient deterministic variational Bayes algorithm is used to implement both (1) the search of an optimal subset of QTL among large marker panels and (2) estimation of the genetic effects of the selected QTL changing over time. Our method can be fast even on some large-scale data sets. The advantages of our method are illustrated on both simulated and real data sets.     

Additive Variation Maintained under Stabilizing Selection: A Two-Locus Model of Pleiotropy for Two Quantitative Characters

A model with two diallelic loci controlling two additive quantitative characters is suggested. One of the loci has a similar effect on both characters, whereas the second locus has an antagonistic effect on two characters. Both characters experience direct stabilizing selection. The model yields a stable polymorphic state, with both characters maintaining genetic variation. The genetic correlation between the characters at the equilibrium is zero, in spite of the pleiotropic effects of the loci controlling them.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

A Review for Life-history Traits Variation in Frogs Especially for Anurans in China

Environmental variation can promote differentiation in life-history traits in species of anurans. Increased environmental stress usually results in larger age at sexual maturity, older mean age, longer longevity, slower growth, larger body size, and a shift in reproductive allocation from offspring quantity to quality, and a stronger trade-off between offspring size and number. However, previous studies have suggested that there are inconsistent geographical variations in life-history traits among anuran species in China. Hence, we here review the intraspecific patterns and differences in life-history traits(i.e., egg size, clutch size, testes size, sperm length, age at sexual maturity, longevity, body size and sexual size dimorphism) among different populations within species along geographical gradients for anurans in China in recent years. We also provide future directions for studying difference in sperm performance between longer and shorter sperm within a species through transplant experiments and the relationships between metabolic rate and brain size and life-history.     

A Multiparent Advanced Generation Inter-Cross to Fine-Map Quantitative Traits in Arabidopsis thaliana

Identifying natural allelic variation that underlies quantitative trait variation remains a fundamental problem in genetics. Most studies have employed either simple synthetic populations with restricted allelic variation or performed association mapping on a sample of naturally occurring haplotypes. Both of these approaches have some limitations, therefore alternative resources for the genetic dissection of complex traits continue to be sought. Here we describe one such alternative, the Multiparent Advanced Generation Inter-Cross (MAGIC). This approach is expected to improve the precision with which QTL can be mapped, improving the outlook for QTL cloning. Here, we present the first panel of MAGIC lines developed: a set of 527 recombinant inbred lines (RILs) descended from a heterogeneous stock of 19 intermated accessions of the plant Arabidopsis thaliana. These lines and the 19 founders were genotyped with 1,260 single nucleotide polymorphisms and phenotyped for development-related traits. Analytical methods were developed to fine-map quantitative trait loci (QTL) in the MAGIC lines by reconstructing the genome of each line as a mosaic of the founders. We show by simulation that QTL explaining 10% of the phenotypic variance will be detected in most situations with an average mapping error of about 300 kb, and that if the number of lines were doubled the mapping error would be under 200 kb. We also show how the power to detect a QTL and the mapping accuracy vary, depending on QTL location. We demonstrate the utility of this new mapping population by mapping several known QTL with high precision and by finding novel QTL for germination data and bolting time. Our results provide strong support for similar ongoing efforts to produce MAGIC lines in other organisms.     

Genetic Distances Based on Quantitative Traits

Morphological data showing continuous distributions, polygenically controlled, may be particularly useful in intergroup classification below the species level; an appropriate distance analysis based on these traits is an important tool in evolutionary biology and in plant and animal breeding.--The interpretation of morphological distances in genetic terms is not easy because simple phenotypic data may lead to biased estimates of genetic distances. Convenient estimates can be obtained whenever it is possible to breed populations according to a suitable crossing design and to derive information from genetic parameters.--A general method for determining genetic distances is proposed. The procedure of multivariate analysis of variance is extended to estimate appropriate genetic parameters (genetic effects). Not only are optimal statistical estimates of parameters obtained but also the procedure allows the measurement of genetic distances between populations as linear functions of the estimated parameters, providing an appropriate distance matrix that can be defined in terms of these parameters. The use of the T2 statistic, defined in terms of the vector of contrasts specifying the distance, permits the testing of the significance of any distance between any pair of populations that may be of interest from a genetic point of view.--A numerical example from maize diallel data is reported in order to illustrate the procedure. In particular, heterosis effects are used as the basis for estimates of genetic divergence between populations.     

Geographical Variation in a Quantitative Character

A model for the evolution of the local averages of a quantitative character under migration, selection, and random genetic drift in a subdivided population is formulated and investigated. Generations are discrete and nonoverlapping; the monoecious, diploid population mates at random in each deme. All three evolutionary forces are weak, but the migration pattern and the local population numbers are otherwise arbitrary. The character is determined by purely additive gene action and a stochastically independent environment; its distribution is Gaussian with a constant variance; and it is under Gaussian stabilizing selection with the same parameters in every deme. Linkage disequilibrium is neglected. Most of the results concern the covariances of the local averages. For a finite number of demes, explicit formulas are derived for (i) the asymptotic rate and pattern of convergence to equilibrium, (ii) the variance of a suitably weighted average of the local averages, and (iii) the equilibrium covariances when selection and random drift are much weaker than migration. Essentially complete analyses of equilibrium and convergence are presented for random outbreeding and site homing, the Levene and island models, the circular habitat and the unbounded linear stepping-stone model in the diffusion approximation, and the exact unbounded stepping-stone model in one and two dimensions.     

Comparing Evolvability and Variability of Quantitative Traits

There are two distinct reasons for making comparisons of genetic variation for quantitative characters. The first is to compare evolvabilities, or ability to respond to selection, and the second is to make inferences about the forces that maintain genetic variability. Measures of variation that are standardized by the trait mean, such as the additive genetic coefficient of variation, are appropriate for both purposes. Variation has usually been compared as narrow sense heritabilities, but this is almost always an inappropriate comparative measure of evolvability and variability. Coefficients of variation were calculated from 842 estimates of trait means, variances and heritabilities in the literature. Traits closely related to fitness have higher additive genetic and nongenetic variability by the coefficient of variation criterion than characters under weak selection. This is the reverse of the accepted conclusion based on comparisons of heritability. The low heritability of fitness components is best explained by their high residual variation. The high additive genetic and residual variability of fitness traits might be explained by the great number of genetic and environmental events they are affected by, or by a lack of stabilizing selection to reduce their phenotypic variance. Over one-third of the quantitative genetics papers reviewed did not report trait means or variances. Researchers should always report these statistics, so that measures of variation appropriate to a variety of situations may be calculated.