Multiple trait analysis of genetic mapping for quantitative trait loci

Genetic mapping of variation in spatial learning in the mouse

Inbred strains of mice are known to differ in their performance in the Morris water maze task, a test of spatial discrimination and place navigation in rodents, but the genetic basis of individual variation in spatial learning is unknown. We have mapped genetic effects that contribute to the difference between two strains, DBA/2 and C57BL6/J, using an F2 intercross and methods to detect quantitative trait loci (QTL). We found two QTL, one on chromosome 4 and one on chromosome 12, that influence behavior in the probe trial of the water maze (genome-wide significance p = 0.017 and 0.015, respectively). By including tests of avoidance conditioning and behavior in a novel environment, we show that the QTL on chromosomes 4 and 12 specifically influence variation in spatial learning. QTL that influence differences in fearful behavior (on chromosomes 1, 3, 7, 15, and 19) operate while mice are trained in the water maze apparatus.

Pleiotropic effects on mandibular morphology I. Developmental morphological integration and differential dominance

Pleiotropy refers to a single genetic locus that affects more than one phenotypic trait. Pleiotropic effects of genetic loci are thought to play an important role in evolution, reflecting functional and developmental relationships among phenotypes. In a previous study, we examined pleiotropic effects displayed by quantitative trait loci (QTLs) on murine mandibular morphology in relation to mandibular structure and function. In replicating most of our previous QTLs and increasing our sample size, this study strengthens and extends our earlier results. As in our previous study, we find that QTL effects tend to be restricted to developmentally or functionally related traits. In addition, we examine patterns of differential dominance for pleiotropic QTL effects. Differential dominance occurs when dominance patterns for a single locus vary among traits. We find that multivariate overdominance is a common and substantial phenomenon, and may potentially provide an explanation for the persistence of heterozygosity in natural populations.

Genetic mapping of variation in spatial learning in the mouse

Inbred strains of mice are known to differ in their performance in the Morris water maze task, a test of spatial discrimination and place navigation in rodents, but the genetic basis of individual variation in spatial learning is unknown. We have mapped genetic effects that contribute to the difference between two strains, DBA/2 and C57BL6/J, using an F2 intercross and methods to detect quantitative trait loci (QTL). We found two QTL, one on chromosome 4 and one on chromosome 12, that influence behavior in the probe trial of the water maze (genome-wide significance p = 0.017 and 0.015, respectively). By including tests of avoidance conditioning and behavior in a novel environment, we show that the QTL on chromosomes 4 and 12 specifically influence variation in spatial learning. QTL that influence differences in fearful behavior (on chromosomes 1, 3, 7, 15, and 19) operate while mice are trained in the water maze apparatus.

Search for pleiotropic QTL on chromosome BTA6 affecting yield traits of milk production

The primary aim of this study was to investigate whether previous findings of similar quantitative trait loci (QTL) positions for correlated yield traits are due to a pleiotropic QTL. We applied a multitrait variance component based QTL mapping method to a dataset involving five granddaughter families from the German Holstein dairy cattle population. The marker map contained 16 microsatellite markers, distributed across chromosome BTA6. A chromosomewise significance threshold was used, because BTA6 is known to harbor QTL for several milk traits. To evaluate the results from the multivariate, across-family analysis, we also conducted single-family analyses using the least squares method of QTL estimation. The results provided two significant QTL findings at 49 and 64 cM for milk yield in different families and putative QTL at 68 cM for fat yield and at 71 cM for protein yield in another family. The results for fat and protein yield were confirmed by a univariate, across-family variance components analysis. The multivariate analysis of three bivariate trait combinations resulted in a significant pleiotropic QTL finding at 68 cM for fat yield and protein yield, bracketed by markers TGLA37 and FBN13. The estimates of variance contribution due to this QTL were 23% and 25%, respectively.

Quantitative trait loci analysis of nitrogen use efficiency in Arabidopsis

Improving plant nitrogen (N) use efficiency or controlling soil N requires a better knowledge of the regulation of plant N metabolism. This could be achieved using Arabidopsis as a model genetic system, taking advantage of the natural variation available among ecotypes. Here, we describe an extensive study of N metabolism variation in the Bay-0 x Shahdara recombinant inbred line population, using quantitative trait locus (QTL) mapping. We mapped QTL for traits such as shoot growth, total N, nitrate, and free-amino acid contents, measured in two contrasting N environments (contrasting nitrate availability in the soil), in controlled conditions. Genetic variation and transgression were observed for all traits, and most of the genetic variation was identified through QTL and QTL x QTL epistatic interactions. The 48 significant QTL represent at least 18 loci that are polymorphic between parents; some may correspond to known genes from the N metabolic pathway, but others represent new genes controlling or interacting with N physiology. The correlations between traits are dissected through QTL colocalizations: The identification of the individual factors contributing to the regulation of different traits sheds new light on the relations among these characters. We also point out that the regulation of our traits is mostly specific to the N environment (N availability). Finally, we describe four interesting loci at which positional cloning is feasible.

Multitrait fine mapping of quantitative trait loci using combined linkage disequilibria and linkage analysis

A novel multitrait fine-mapping method is presented. The method is implemented by a model that treats QTL effects as random variables. The covariance matrix of allelic effects is proportional to the IBD matrix, where each element is the probability that a pair of alleles is identical by descent, given marker information and QTL position. These probabilities are calculated on the basis of similarities of marker haplotypes of individuals of the first generation of genotyped individuals, using "gene dropping" (linkage disequilibrium) and transmission of markers from genotyped parents to genotyped offspring (linkage). A small simulation study based on a granddaughter design was carried out to illustrate that the method provides accurate estimates of QTL position. Results from the simulation also indicate that it is possible to distinguish between a model postulating one pleiotropic QTL affecting two traits vs. one postulating two closely linked loci, each affecting one of the traits.

The genetic architecture of Drosophila sensory bristle number

We have mapped quantitative trait loci (QTL) for Drosophila mechanosensory bristle number in six recombinant isogenic line (RIL) mapping populations, each of which was derived from an isogenic chromosome extracted from a line selected for high or low, sternopleural or abdominal bristle number and an isogenic wild-type chromosome. All RILs were evaluated as male and female F(1) progeny of crosses to both the selected and the wild-type parental chromosomes at three developmental temperatures (18 degrees, 25 degrees, and 28 degrees ). QTL for bristle number were mapped separately for each chromosome, trait, and environment by linkage to roo transposable element marker loci, using composite interval mapping. A total of 53 QTL were detected, of which 33 affected sternopleural bristle number, 31 affected abdominal bristle number, and 11 affected both traits. The effects of most QTL were conditional on sex (27%), temperature (14%), or both sex and temperature (30%). Epistatic interactions between QTL were also common. While many QTL mapped to the same location as candidate bristle development loci, several QTL regions did not encompass obvious candidate genes. These features are germane to evolutionary models for the maintenance of genetic variation for quantitative traits, but complicate efforts to understand the molecular genetic basis of variation for complex traits.

Detection of pleiotropic effects of quantitative trait loci in outbred populations using regression analysis

In this paper a method is presented to determine pleiotropic quantitative trait loci (QTL) or closely linked QTL in an outbred population. The method is based on results from single-trait analyses for different traits and is derived for a granddaughter design. The covariance between estimated contrasts of grandsires obtained in single-trait regression analysis is computed. When there is no pleiotropic QTL, the covariance between contrasts depends on the heritabilities of the traits involved, the polygenic and environmental correlation between the traits, the phenotypic standard deviations, the number of sires per grandsire, and the number of daughters per sire. A pleiotropic QTL results in a covariance that deviates from this expected covariance. The deviation depends on the size of the effects on both traits and on the fraction of grandsires heterozygous for the QTL. When analyzing experimental data, the expected covariance and the confidence interval for the expected covariance can be determined by permutation of the data. A covariance outside the confidence interval suggests the presence of a pleiotropic QTL or a closely linked QTL. The method is verified by simulation and illustrated by analyzing an experimental data set on chromosome 6 in dairy cattle.

Minor quantitative trait loci underlie floral traits associated with mating system divergence in Mimulus

The genetic basis of species differences provides insight into the mode and tempo of phenotypic divergence. We investigate the genetic basis of floral differences between two closely related plant taxa with highly divergent mating systems, Mimulus guttatus (large-flowered outcrosser) and M. nasutus (small-flowered selfer). We had previously constructed a framework genetic linkage map of the hybrid genome containing 174 markers spanning approximately 1800 cM on 14 linkage groups. In this study, we analyze the genetics of 16 floral, reproductive, and vegetative characters measured in a large segregating M. nasutus x M. guttatus F2 population (N = 526) and in replicates of the parental lines and F1 hybrids. Phenotypic analyses reveal strong genetic correlations among floral traits and epistatic breakdown of male and female fertility traits in the F2 hybrids. We use multitrait composite interval mapping to jointly locate and characterize quantitative trait loci (QTLs) underlying interspecific differences in seven floral traits. We identified 24 floral QTLs, most of which affected multiple traits. The large number of QTLs affecting each trait (mean = 13, range = 11-15) indicates a strikingly polygenic basis for floral divergence in this system. In general, QTL effects are small relative to both interspecific differences and environmental variation within genotypes, ruling out QTLs of major effect as contributors to floral divergence between M. guttatus and M. nasutus. QTLs show no pattern of directional dominance. Floral characters associated with pollinator attraction (corolla width) and self-pollen deposition (stigma-anther distance) share several pleiotropic or linked QTLs, but unshared QTLs may have allowed selfing to evolve independently from flower size. We discuss the polygenic nature of divergence between M. nasutus and M. guttatus in light of theoretical work on the evolution of selfing, genetics of adaptation, and maintenance of variation within populations.

The complex genetic architecture of Drosophila life span

Continuous phenotypic variation in life span results from segregating genetic variation at multiple loci, the environmental sensitivity of expression of these loci, and the history of environmental variation experienced by the organism throughout its life. We have mapped quantitative trait loci (QTL) that produce variation in the life span of mated Drosophila melanogaster using a panel of recombinant inbred lines (RIL) that were backcrossed to the parental strains from which they were derived. Five QTL were identified that influence mated life span, three were male-specific, one was female-specific, and one affected life span in both sexes. The additive allelic effects and dominance of QTL were highly sex-specific. One pair of QTL also exhibited significant epistatic effects on life span. We summarize all of the QTL mapping data for Drosophila life span, and outline future prospects for disentangling the genetic and environmental influences on this trait.

Genetic modifiers of otocephalic phenotypes inOtx2heterozygous mutant mice

Mice heterozygous for the Otx2 mutation display a craniofacial malformation, known as otocephaly or agnathia-holoprosencephaly complex. The severity of the phenotype is dependent on the genetic background of a C57BL/6 (B6) strain; most of the offspring of Otx2 knock-out chimeras, which are equivalent to the F1 of CBA and B6 strains, backcrossed with B6 females display reduction or loss of mandible, whereas those backcrossed with CBA females do not show noticeable phenotype at birth. The availability of phenotypically disparate strains renders identification of Otx2 modifier loci possible. In this study, a backcross of chimera with B6 was generated and genome-wide scans were conducted with polymorphic markers for non-mendelian distribution of alleles in Otx2 heterozygous mutant mice displaying abnormalities in the lower jaw. We identified one significant locus, Otmf18, between D18Mit68 and D18Mit120 on chromosomes 18, linked to the mandibular phenotype (LOD score 3.33). A similar replication experiment using a second backcross (N3) mouse demonstrated the presence of another significant locus, Otmf2 between D2Mit164 and D2Mit282 on chromosome 2, linked to the mandibular phenotype (LOD score 3.93). These two modifiers account for the distribution of the craniofacial malformations by the genetic effect between B6 and CBA strains. Moreover, Otmf2 contain a candidate gene for several diseases in mice and humans. These genetic studies involving an otocephalic mouse model appear to provide new insights into mechanistic pathways of craniofacial development. Furthermore, these experiments offer a powerful approach with respect to identification and characterization of candidate genes that may contribute to human agnathia-holoprosencephaly complex diseases.

Functional mapping of quantitative trait loci underlying the character process: a theoretical framework

Unlike a character measured at a finite set of landmark points, function-valued traits are those that change as a function of some independent and continuous variable. These traits, also called infinite-dimensional characters, can be described as the character process and include a number of biologically, economically, or biomedically important features, such as growth trajectories, allometric scalings, and norms of reaction. Here we present a new statistical infrastructure for mapping quantitative trait loci (QTL) underlying the character process. This strategy, termed functional mapping, integrates mathematical relationships of different traits or variables within the genetic mapping framework. Logistic mapping proposed in this article can be viewed as an example of functional mapping. Logistic mapping is based on a universal biological law that for each and every living organism growth over time follows an exponential growth curve (e.g., logistic or S-shaped). A maximum-likelihood approach based on a logistic-mixture model, implemented with the EM algorithm, is developed to provide the estimates of QTL positions, QTL effects, and other model parameters responsible for growth trajectories. Logistic mapping displays a tremendous potential to increase the power of QTL detection, the precision of parameter estimation, and the resolution of QTL localization due to the small number of parameters to be estimated, the pleiotropic effect of a QTL on growth, and/or residual correlations of growth at different ages. More importantly, logistic mapping allows for testing numerous biologically important hypotheses concerning the genetic basis of quantitative variation, thus gaining an insight into the critical role of development in shaping plant and animal evolution and domestication. The power of logistic mapping is demonstrated by an example of a forest tree, in which one QTL affecting stem growth processes is detected on a linkage group using our method, whereas it cannot be detected using current methods. The advantages of functional mapping are also discussed.

Polymorphism in the bovine growth hormone gene affects endocrine release in dairy calves

The objective was to test whether calves with the Leu/Leu genotype release more growth hormone (GH) than calves with Leu/Val and Val/Val genotypes. Danish Holstein (n = 286), Danish Red (n = 68), and Danish Jersey (n = 61) calves were genotyped for the Leu/Val polymorphism in the GH gene and assessed for GH release following inducement by the growth hormone releasing hormone (GHRH). Three GH traits were assessed for each calf: BASELINE, PEAK, and RATE. BASELINE and PEAK are the mean concentration of GH in blood sampled before and after GHRH inducement. RATE is the disappearance rate of GH in blood sampled after GHRH inducement. Danish Jersey calves with Leu/Leu genotype had a higher PEAK and RATE than calves with the Val/Val genotype, whereas the Leu/Val genotype had an intermediate response. The contribution of the Leu/Val polymorphism to the total genetic variation of the BASELINE, PEAK, and RATE traits was 5, 30, and 27%, respectively. By contrast, the amount of GH released by the Danish Holstein and Danish Red calves was not influenced by their GH genotype. Further studies involving calves with all three genotypes are required to further elucidate whether this polymorphism has a functional role or whether it works through a linked-gene effect specific to certain cattle breeds.

Complex-trait genetics: emergence of multivariate strategies

Complex traits, including many disease-related traits, are influenced by multiple genes. Bivariate approaches that associate one gene with one trait are yielding to multivariate methods to synthesize the effects of multiple genes, integrate results across independent studies, and aid in the identification of coordinated pathways and interactions between loci.

Quantitative trait locus mapping of genes that regulate HDL cholesterol in SM/J and NZB/B1NJ inbred mice

To investigate the quantitative trait loci (QTL) regulating plasma cholesterol, the female progeny of an (SMxNZB/ B1NJ)xNZB/B1NJ backcross were fed an atherogenic diet. After 18 wk, plasma total cholesterol and high-density lipoprotein cholesterol (HDL-C) was measured. HDL-C concentrations were greater in NZB than in SM mice. For standard chow-fed mice, QTL were found near D5Mit370 and D18Mit34. For mice fed an atherogenic diet, a QTL was found near D5Mit239. The QTL for chow-fed and atherogenic-fed mice on chromosome 5 seem to be two different loci. We used a multitrait analysis to rule out pleiotropy in favor of a two-QTL hypothesis. Furthermore, the HDL-C in these strains was induced by the high-fat diet. For inducible HDL-C, one significant locus was found near D15Mit39. The gene for an HDL receptor, Srb1, maps close to the HDL-C QTL at D5Mit370, but the concentrations of Srb1 mRNA and SR-B1 protein and the gene sequence of NZB/B1NJ and SM/J did not support Srb1 as a candidate gene. With these QTL, we have identified chromosomal regions that affect lipoprotein profiles in these strains.

Genetic analysis of quantitative traits in highly ascertained samples: total serum IgE in families with asthma

The objective of this study was to compare the effect of an approximate ascertainment correction using proband phenotypes with heuristic corrections based on sample trait means and on published "standard" population values. Data were from the Collaborative Study on the Genetics of Asthma, which comprises 225 families ascertained through sib pairs affected with asthma. In variance component linkage analysis of IgE no lod scores greater than 3.0 were observed, either with or without several attempted corrections for ascertainment. The ascertained nature of the sample may have compromised the power to detect linkage to a quantitative trait (IgE) associated with the focal phenotype (asthma).

Statistical methods for QTL mapping in cereals

This paper gives an overview of the statistical theory suitable for mapping quantitative trait loci in experimental populations derived from inbred parents, with a particular emphasis on methodology for cereal crops. The basic theory is described, and some new areas of statistical research appropriate for mapping in cereal crops are discussed.

Mapping epigenetic quantitative trait loci (QTL) altering a developmental trajectory

Genetic variation in a quantitative trait that changes with age is important to both evolutionary biologists and breeders. A traditional analysis of the dynamics of genetic variation is based on the genetic variance-covariance matrix among different ages estimated from a quantitative genetic model. Such an analysis, however, cannot reveal the mechanistic basis of the genetic variation for a growth trait during ontogeny. Age-specific genetic variance at time t conditional on the causal genetic effect at time t - 1 implies the generation of episodes of new genetic variation arising during the interval t - 1 to t. In the present paper, the conditional genetic variance estimated from Zhu's (1995) conditional model was partitioned into its underlying individual quantitative trait loci (QTL) using molecular markers in an F2 progeny of poplars (Populus trichocarpa and Populus deltoides). These QTL, defined as epigenetic QTL, govern the alterations of growth trajectory in a population. Three epigenetic QTL were detected to contribute significantly to variation in growth trajectory during the period from the establishment year to the subsequent year in the field. It is suggested that the activation and expression of epigenetic QTL are influenced by the developmental status of trees and the environment in which they are grown.

Quantitative trait loci controlling light and hormone response in two accessions of Arabidopsis thaliana

We have mapped quantitative trait loci (QTL) responsible for natural variation in light and hormone response between the Cape Verde Islands (Cvi) and Landsberg erecta (Ler) accessions of Arabidopsis thaliana using recombinant inbred lines (RILs). Hypocotyl length was measured in four light environments: white, blue, red, and far-red light and in the dark. In addition, white light plus gibberellin (GA) and dark plus the brassinosteroid biosynthesis inhibitor brassinazole (BRZ) were used to detect hormone effects. Twelve QTL were identified that map to loci not previously known to affect light response, as well as loci where candidate genes have been identified from known mutations. Some QTL act in all environments while others show genotype-by-environment interaction. A global threshold was established to identify a significant epistatic interaction between two loci that have few main effects of their own. LIGHT1, a major QTL, has been confirmed in a near isogenic line (NIL) and maps to a new locus with effects in all light environments. The erecta mutation can explain the effect of the HYP2 QTL in the blue, BRZ, and dark environments, but not in far-red. LIGHT2, also confirmed in an NIL, has effects in white and red light and shows interaction with GA. The phenotype and map position of LIGHT2 suggest the photoreceptor PHYB as a candidate gene. Natural variation in light and hormone response thus defines both new genes and known genes that control light response in wild accessions.

The genetic architecture of quantitative traits

Phenotypic variation for quantitative traits results from the segregation of alleles at multiple quantitative trait loci (QTL) with effects that are sensitive to the genetic, sexual, and external environments. Major challenges for biology in the post-genome era are to map the molecular polymorphisms responsible for variation in medically, agriculturally, and evolutionarily important complex traits; and to determine their gene frequencies and their homozygous, heterozygous, epistatic, and pleiotropic effects in multiple environments. The ease with which QTL can be mapped to genomic intervals bounded by molecular markers belies the difficulty in matching the QTL to a genetic locus. The latter requires high-resolution recombination or linkage disequilibrium mapping to nominate putative candidate genes, followed by genetic and/or functional complementation and gene expression analyses. Complete genome sequences and improved technologies for polymorphism detection will greatly advance the genetic dissection of quantitative traits in model organisms, which will open avenues for exploration of homologous QTL in related taxa.

Mapping and analysis of quantitative trait loci in experimental populations

Simple statistical methods for the study of quantitative trait loci (QTL), such as analysis of variance, have given way to methods that involve several markers and high-resolution genetic maps. As a result, the mapping community has been provided with statistical and computational tools that have much greater power than ever before for studying and locating multiple and interacting QTL. Apart from their immediate practical applications, the lessons learnt from this evolution of QTL methodology might also be generally relevant to other types of functional genomics approach that are aimed at the dissection of complex phenotypes, such as microarray assessment of gene expression.

The nature of quantitative genetic variation for Drosophila longevity

Longevity is a typical quantitative trait: the continuous variation in life span observed in natural populations is attributable to genetic variation at multiple quantitative trait loci (QTL), environmental sensitivity of QTL alleles, and truly continuous environmental variation. To begin to understand the genetic architecture of longevity at the level of individual QTL, we have mapped QTL for Drosophila life span that segregate between two inbred strains that were not selected for longevity. A mapping population of 98 recombinant inbred lines (RIL) was derived from these strains, and life span of virgin male and female flies measured under control culture conditions, chronic heat and cold stress, heat shock and starvation stress, and high and low density larval environments. The genotypes of the RIL were determined for polymorphic roo transposable element insertion sites, and life span QTL were mapped using composite interval mapping methods. A minimum of 19 life span QTL were detected by recombination mapping. The life span QTL exhibited strong genotype by sex, genotype by environment, and genotype by genotype (epistatic) interactions. These interactions complicate mapping efforts, but evolutionary theory predicts such properties of segregating QTL alleles. Quantitative deficiency mapping of four longevity QTL detected in the control environment by recombination mapping revealed a minimum of 11 QTL in these regions. Clearly, longevity is a complex quantitative trait. In the future, linkage disequilibrium mapping can be used to determine which candidate genes in a QTL region correspond to the genetic loci affecting variation in life span, and define the QTL alleles at the molecular level.

Linkage analysis of human systemic lupus erythematosus-related traits: a principal component approach

OBJECTIVE

To identify chromosomal regions containing genes involved in the susceptibility to human systemic lupus erythematosus (SLE)-related traits.

METHODS

In the context of a genome scan, we analyzed 101 SLE-affected sibpairs with respect to dermatologic, renal, immunologic, hematologic, neurologic, cardiopulmonary, and arthritic characteristics. Phenotypes were redefined in terms of principal components, which are synthetic variables composed of linear combinations of the original traits. Using 9 principal components obtained from these 7 traits plus age at SLE onset and race, we analyzed genome scan data with the multivariate version of the new Haseman-Elston regression model.

RESULTS

The largest linkage for an individual trait was on chromosome 2 at 228 cM (immunologic; P = 0.00048). The most significant linkage to an individual principal component was on chromosome 4 at 208 cM (P = 0.00007). The largest multivariate linkage was on chromosome 7 at 69 cM (P = 0.0001). Of the individual organ systems, dermatologic involvement had the largest effect (P = 0.0083) at this peak at 7p13 on chromosome 7. Further analyses revealed that malar rash, a subtype of dermatologic involvement, was linked significantly (P = 0.00458) to this location.

CONCLUSION

These results provide evidence of the presence and locations of genes that are involved in the genetic susceptibility to SLE-related traits in humans.

Mapping quantitative trait Loci using generalized estimating equations

A number of statistical methods are now available to map quantitative trait loci (QTL) relative to markers. However, no existing methodology can simultaneously map QTL for multiple nonnormal traits. In this article we rectify this deficiency by developing a QTL-mapping approach based on generalized estimating equations (GEE). Simulation experiments are used to illustrate the application of the GEE-based approach.

A statistical framework for quantitative trait mapping

We describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.

EH. The biological basis of epistasis between quantitative trait loci for flavone and 3-deoxyanthocyanin synthesis in maize (Zea mays L.)

A major weakness in our understanding of the genetic basis of complex traits has been that of defining the extent and biological basis of epistasis. Our research group has been studying the genetic control of the accumulation of maysin, a C-glycosyl flavone, in maize, Zea mays (L.), silks. Previously, we demonstrated the importance of the p1 locus as a QTL for maysin synthesis. The p1 locus often exhibits significant epistatic interactions with other loci. We developed a mapping population, (W23a1 × GT119)F2, specifically designed to test whether genes in an intersecting pathway might be detected as QTLs for maysin synthesis and result in epistatic interaction effects. The a1 gene is not required for the synthesis of flavones but is required for the synthesis of 3-deoxyanthocyanins, an intersecting pathway, in maize silks. The p1 locus (P < 0.0001) was a QTL for both flavones and 3-deoxyanthocyanins. The a1 locus was also highly significant (P < 0.0001) for both traits, as was the p1 × a1 epistatic interaction (P < 0.0001). Our results demonstrate that altering the flux of biochemical intermediates between pathways may be the biological basis of major QTL effects and epistatic interactions.Key words: maysin, epistasis, QTL, insect resistance.

Genetic control of the mouse cerebellum: identification of quantitative trait loci modulating size and architecture

To discover genes influencing cerebellum development, we conducted a complex trait analysis of variation in the size of the adult mouse cerebellum. We analyzed two sets of recombinant inbred BXD strains and an F2 intercross of the common inbred strains, C57BL/6J and DBA/2J. We measured cerebellar size as the weight or volume of fixed or histologically processed tissue. Among BXD recombinant inbred strains, the cerebellum averages 52 mg (12.4% of the brain) and ranges 18 mg in size. In F2 mice, the cerebellum averages 62 mg (12.9% of the brain) and ranges approximately 20 mg in size. Five quantitative trait loci (QTLs) that significantly control variation in cerebellar size were mapped to chromosomes 1 (Cbs1a), 8 (Cbs8a), 14 (Cbs14a), and 19 (Cbs19a, Cbs19b). In combination, these QTLs can shift cerebellar size an appreciable 35% of the observed range. To assess regional genetic control of the cerebellum, we also measured the volume of the cell-rich, internal granule layer (IGL) in a set of BXD strains. The IGL ranges from 34 to 43% of total cerebellar volume. The QTL Cbs8a is significantly linked to variation in IGL volume and is suggestively linked to variation in the number of cerebellar folia. The QTLs we have discovered are among the first loci shown to modulate the size and architecture of the adult mouse cerebellum.

Genetic control of the mouse cerebellum: identification of quantitative trait loci modulating size and architecture

To discover genes influencing cerebellum development, we conducted a complex trait analysis of variation in the size of the adult mouse cerebellum. We analyzed two sets of recombinant inbred BXD strains and an F2 intercross of the common inbred strains, C57BL/6J and DBA/2J. We measured cerebellar size as the weight or volume of fixed or histologically processed tissue. Among BXD recombinant inbred strains, the cerebellum averages 52 mg (12.4% of the brain) and ranges 18 mg in size. In F2 mice, the cerebellum averages 62 mg (12.9% of the brain) and ranges approximately 20 mg in size. Five quantitative trait loci (QTLs) that significantly control variation in cerebellar size were mapped to chromosomes 1 (Cbs1a), 8 (Cbs8a), 14 (Cbs14a), and 19 (Cbs19a, Cbs19b). In combination, these QTLs can shift cerebellar size an appreciable 35% of the observed range. To assess regional genetic control of the cerebellum, we also measured the volume of the cell-rich, internal granule layer (IGL) in a set of BXD strains. The IGL ranges from 34 to 43% of total cerebellar volume. The QTL Cbs8a is significantly linked to variation in IGL volume and is suggestively linked to variation in the number of cerebellar folia. The QTLs we have discovered are among the first loci shown to modulate the size and architecture of the adult mouse cerebellum.

Quantitative trait locus mapping in laboratory mice derived from a replicated selection experiment for open-field activity

Bidirectional selection in rodents has been used to derive animal models of human behavior. An important question is whether selection for behavior operates on a limited number of QTL or whether the number and individual contribution of QTL varies between selection experiments. To address this question, we mapped QTL in two large F2 intercrosses (N = 815 and 821) from the four lines derived from a replicated selection experiment for open-field activity, an animal model for susceptibility to anxiety. Our analyses indicate that selection operated on the same relatively small number of loci in both crosses. Haplotype information and the direction of effect of each QTL allele were used to confirm that the QTL mapped in the two crosses lie in the same chromosomal regions, although we were unable to determine whether QTL in the two crosses represent the same genes. We conclude that the genetic architecture of the selected strains is similar and relatively simple.

A simple correction for multiple comparisons in interval mapping genome scans

Several approaches have been proposed to correct point-wise significance thresholds used in interval-mapping genome scans. A method for significance threshold correction based on the Bonferroni test is presented. This test involves calculating the effective number of independent comparisons performed in a genome scan from the variance of the eigenvalues of the observed marker correlation matrix. The more highly correlated the markers, the higher the variance of the eigenvalues and the lower the number of independent tests performed on a chromosome. This approach was evaluated by mapping 1000 normally distributed phenotypes along chromosomes of varying length and marker density in a population size of 500. Experiment-wise significance thresholds obtained from the simulation are compared to those calculated using the Bonferroni criterion and the newly developed measure of the effective number of independent tests in a genome scan. The Bonferroni calculation produced significance thresholds very similar to those obtained by simulation. The threshold levels for both Bonferroni and simulation analysis depended strongly on the marker density and size of chromosomes. There was a slight bias of about 1% in the thresholds obtained at the 5% and 10% point-wise significance levels. The method introduced here provides a relatively simple correction for multiple comparisons that can be easily calculated using standard statistics packages.

Detection of closely linked multiple quantitative trait loci using a genetic algorithm

The existence of a quantitative trait locus (QTL) is usually tested using the likelihood of the quantitative trait on the basis of phenotypic character data plus the recombination fraction between QTL and flanking markers. When doing this, the likelihood is calculated for all possible locations on the linkage map. When multiple QTL are suspected close by, it is impractical to calculate the likelihood for all possible combinations of numbers and locations of QTL. Here, we propose a genetic algorithm (GA) for the heuristic solution of this problem. GA can globally search the optimum by improving the "genotype" with alterations called "recombination" and "mutation." The "genotype" of our GA is the number and location of QTL. The "fitness" is a function based on the likelihood plus Akaike's information criterion (AIC), which helps avoid false-positive QTL. A simulation study comparing the new method with existing QTL mapping packages shows the advantage of the new GA. The GA reliably distinguishes multiple QTL located in a single marker interval.

Genetic loci determining bone density in mice with diet-induced atherosclerosis

This study investigates the phenotypic and genetic relationships among bone-density-related traits and those of adipose tissue and plasma lipids in mice with diet-induced atherosclerosis. Sixteen-month-old female F2 progeny of a C57BL/6J and DBA/2J intercross, which had received an atherogenic diet for 4 mo, were examined for multiple measures of femoral bone mass, density, and biomechanical properties using both computerized tomographic and radiographic methods. In addition, body weight and length, adipose tissue mass, plasma lipids and insulin, and aortic fatty lesions were assessed. Bone mass was inversely correlated with extent of atherosclerosis and with a prooxidant lipid profile and directly correlated with body weight, length, and, most strongly, adipose tissue mass. Quantitative trait locus (QTL) analysis, using composite interval mapping (CIM) and multi-trait analysis, identified six loci with multi-trait CIM LOD scores > 5. Three of these coincided with loci linked with adipose tissue and plasma high-density lipoprotein. Application of statistical tests for distinguishing close linkage vs. pleiotropy supported the presence of a potential pleiotropic effect of two of the loci on these traits. This study shows that bone mass in older female mice with atherosclerosis has multiple genetic determinants and provides phenotypic and genetic evidence linking the regulation of bone density with adipose tissue and plasma lipids.

Enhanced efficiency of quantitative trait loci mapping analysis based on multivariate complexes of quantitative traits

An approach to increase the efficiency of mapping quantitative trait loci (QTL) was proposed earlier by the authors on the basis of bivariate analysis of correlated traits. The power of QTL detection using the log-likelihood ratio (LOD scores) grows proportionally to the broad sense heritability. We found that this relationship holds also for correlated traits, so that an increased bivariate heritability implicates a higher LOD score, higher detection power, and better mapping resolution. However, the increased number of parameters to be estimated complicates the application of this approach when a large number of traits are considered simultaneously. Here we present a multivariate generalization of our previous two-trait QTL analysis. The proposed multivariate analogue of QTL contribution to the broad-sense heritability based on interval-specific calculation of eigenvalues and eigenvectors of the residual covariance matrix allows prediction of the expected QTL detection power and mapping resolution for any subset of the initial multivariate trait complex. Permutation technique allows chromosome-wise testing of significance for the whole trait complex and the significance of the contribution of individual traits owing to: (a) their correlation with other traits, (b) dependence on the chromosome in question, and (c) both a and b. An example of application of the proposed method on a real data set of 11 traits from an experiment performed on an F(2)/F(3) mapping population of tetraploid wheat (Triticum durum x T. dicoccoides) is provided.

Genetic linkage methods for quantitative traits

We discuss methods for detecting genetic linkage for quantitative data. The usual LOD score method uses a pseudolikelihood formulation and has optimal power provided all parameters are correctly specified, but can lead to erroneous estimates of the location for the locus influencing a trait under misspecification of parameters describing the variance of the trait. Alternative methods, in which attention focuses upon modelling covariation among relatives as a function of genetic marker, similarity lead to unbiased estimates of the location and major gene heritability of the trait influencing locus. The Haseman-Elston approach uses a regression method to perform linkage analysis and its properties have been widely studied. This method is generally less powerful than variance components procedures, but the maximum likelihood-based variance components procedures require normality of the trait to ensure robustness of the genetic linkage tests (i.e. a correct false positive rate). When samples are non-randomly selected an ascertainment correction is generally required in order to obtain unbiased parameter estimates when applying variance components methods. For quantitative traits, ascertainment corrections usually condition either on the proband exceeding a threshold, or on the trait value of the proband. We summarize simulations that show that both approaches lead to similar efficiencies for estimating genetic effects. Finally, we discuss methods for analysing diseases that include time-to-onset information. A variety of methods are available for the linkage analysis of quantitative traits. Here, we have reviewed the most commonly used methods.

Quantitative trait loci in Drosophila

Phenotypic variation for quantitative traits results from the simultaneous segregation of alleles at multiple quantitative trait loci. Understanding the genetic architecture of quantitative traits begins with mapping quantitative trait loci to broad genomic regions and ends with the molecular definition of quantitative trait loci alleles. This has been accomplished for some quantitative trait loci in Drosophila. Drosophila quantitative trait loci have sex-, environment- and genotype-specific effects, and are often associated with molecular polymorphisms in non-coding regions of candidate genes. These observations offer valuable lessons to those seeking to understand quantitative traits in other organisms, including humans.

Quantitative trait loci for floral morphology in Arabidopsis thaliana

A central question in biology is how genes control the expression of quantitative variation. We used statistical methods to estimate genetic variation in eight Arabidopsis thaliana floral characters (fresh flower mass, petal length, petal width, sepal length, sepal width, long stamen length, short stamen length, and pistil length) in a cosmopolitan sample of 15 ecotypes. In addition, we used genome-wide quantitative trait locus (QTL) mapping to evaluate the genetic basis of variation in these same traits in the Landsberg erecta x Columbia recombinant inbred line population. There was significant genetic variation for all traits in both the sample of naturally occurring ecotypes and in the Ler x Col recombinant inbred line population. In addition, broad-sense genetic correlations among the traits were positive and high. A composite interval mapping (CIM) analysis detected 18 significant QTL affecting at least one floral character. Eleven QTL were associated with several floral traits, supporting either pleiotropy or tight linkage as major determinants of flower morphological integration. We propose several candidate genes that may underlie these QTL on the basis of positional information and functional arguments. Genome-wide QTL mapping is a promising tool for the discovery of candidate genes controlling morphological development, the detection of novel phenotypic effects for known genes, and in generating a more complete understanding of the genetic basis of floral development.

Genetic mapping of quantitative trait loci influencing left ventricular mass in rats

High blood pressure is the leading cause of left ventricular hypertrophy (LVH); however, not all hypertensive patients develop LVH. Genetic factors are important in the development of LVH. With the use of F2 male rats from spontaneously hypertensive rats and Lewis rats, we performed a study to identify the quantitative trait loci (QTL) that influence left ventricular mass (LVM). Mean arterial pressure (MAP) was measured by the direct intra-arterial method in conscious animals, and LVM was determined at 24 wk of age. QTL analysis was done using 160 microsatellite markers for a genome-wide scan. Two loci that influenced body weight-adjusted LVM with logarithm of the odds scores >3.4 were found. One locus on chromosome 17 influenced LVM independently of MAP. Another locus on chromosome 7 influenced LVM and MAP. These findings indicate not only the existence of a gene on chromosome 7 that influences LVM in a manner dependent on blood pressure but also the existence of a gene on chromosome 17 that influences LVM independently of blood pressure.

Multitrait least squares for quantitative trait loci detection

A multiple-trait QTL mapping method using least squares is described. It is presented as an extension of a single-trait method for use with three-generation, outbred pedigrees. The multiple-trait framework allows formal testing of whether the same QTL affects more than one trait (i.e., a pleiotropic QTL) or whether more than one linked QTL are segregating. Several approaches to the testing procedure are presented and their suitability discussed. The performance of the method is investigated by simulation. As previously found, multitrait analyses increase the power to detect a pleiotropic QTL and the precision of its location estimate. With enough information, discrimination between alternative genetic models is possible.

On the differences between maximum likelihood and regression interval mapping in the analysis of quantitative trait loci

The differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.

Testing causal hypotheses in multivariate linkage analysis of quantitative traits: general formulation and application to sibpair data

We provide a general framework for the development of model-free methods for the linkage analysis of multivariate phenotypic data. It is possible within this framework to test both for linkage of a set of phenotypes to one or more markers and for the presence of structural relations among the phenotypes themselves. This report presents the general model, paying special attention to the assumptions that enter its formulation, and outlines the estimation procedures that may be used.

Maximum likelihood analysis of quantitative trait loci under selective genotyping

Selective genotyping is a cost-saving strategy in mapping quantitative trait loci (QTLs). When the proportion of individuals selected for genotyping is low, the majority of the individuals are not genotyped, but their phenotypic values, if available, are still included in the data analysis to correct the bias in parameter estimation. These ungenotyped individuals do not contribute much information about linkage analysis and their inclusion can substantially increase the computational burden. For multiple trait analysis, ungenotyped individuals may not have a full array of phenotypic measurements. In this case, unbiased estimation of QTL effects using current methods seems to be impossible. In this study, we develop a maximum likelihood method of QTL mapping under selective genotyping using only the phenotypic values of genotyped individuals. Compared with the full data analysis (using all phenotypic values), the proposed method performs well. We derive an expectation-maximization (EM) algorithm that appears to be a simple modification of the existing EM algorithm for standard interval mapping. The new method can be readily incorporated into a standard QTL mapping software, e.g. MAPMAKER. A general recommendation is that whenever full data analysis is possible, the full maximum likelihood analysis should be performed. If it is impossible to analyse the full data, e.g. sample sizes are too large, phenotypic values of ungenotyped individuals are missing or composite interval mapping is to be performed, the proposed method can be applied.

A multivariate approach to the problem of QTL localization

QTL mapping with statistical likelihood-based procedures or asymptotically equivalent regression methods is usually carried out in a univariate way, even if many traits were observed in the experiment. Some proposals for multivariate QTL mapping by an extension of the maximum likelihood method for mixture models or by an application of the canonical transformation have been given in the literature. This paper describes a method of analysis of multitrait data sets, aimed at localization of QTLs contributing to many traits simultaneously, which is based on the linear model of multivariate multiple regression. A special form of the canonical analysis is employed to decompose the test statistic for the general no-QTL hypothesis into components pertaining to individual traits and individual, putative QTLs. Extended linear hypotheses are used to formulate conjectures concerning pleiotropy. A practical mapping algorithm is described. The theory is illustrated with the analysis of data from a study of maize drought resistance.

Genetic architecture of a morphological shape difference between two Drosophila species

The size and shape of the posterior lobe of the male genital arch differs dramatically between Drosophila simulans and D. mauritiana. This difference can be quantified with a morphometric descriptor (PC1) based on elliptical Fourier and principal components analyses. The genetic basis of the interspecific difference in PC1 was investigated by the application of quantitative trait locus (QTL) mapping procedures to segregating backcross populations. The parental difference (35 environmental standard deviations) and the heritability of PC1 in backcross populations (>90%) are both very large. The use of multiple interval mapping gives evidence for 19 different QTL. The greatest additive effect estimate accounts for 11. 4% of the parental difference but could represent multiple closely linked QTL. Dominance parameter estimates vary among loci from essentially no dominance to complete dominance, and mauritiana alleles tend to be dominant over simulans alleles. Epistasis appears to be relatively unimportant as a source of variation. All but one of the additive effect estimates have the same sign, which means that one species has nearly all plus alleles and the other nearly all minus alleles. This result is unexpected under many evolutionary scenarios and suggests a history of strong directional selection acting on the posterior lobe.

Genotype-environment interaction for quantitative trait loci affecting life span in Drosophila melanogaster

The nature of genetic variation for Drosophila longevity in a population of recombinant inbred lines was investigated by estimating quantitative genetic parameters and mapping quantitative trait loci (QTL) for adult life span in five environments: standard culture conditions, high and low temperature, and heat-shock and starvation stress. There was highly significant genetic variation for life span within each sex and environment. In the analysis of variance of life span pooled over sexes and environments, however, the significant genetic variation appeared in the genotype x sex and genotype x environment interaction terms. The genetic correlation of longevity across the sexes and environments was not significantly different from zero in these lines. We estimated map positions and effects of QTL affecting life span by linkage to highly polymorphic roo transposable element markers, using a multiple-trait composite interval mapping procedure. A minimum of 17 QTL were detected; all were sex and/or environment-specific. Ten of the QTL had sexually antagonistic or antagonistic pleiotropic effects in different environments. These data provide support for the pleiotropy theory of senescence and the hypothesis that variation for longevity might be maintained by opposing selection pressures in males and females and variable environments. Further work is necessary to assess the generality of these results, using different strains, to determine heterozygous effects and to map the life span QTL to the level of genetic loci.

Linkage of chromosome 1 markers to alcoholism-related phenotypes by sib pair linkage analysis of principal components

Using the Collaborative Study on the Genetics of Alcoholism data and affected-sib-pair linkage methods, Reich et al. [1998] reported linkage of alcohol dependence to a region near D1S1588 on chromosome 1. In this paper, we assessed the ability of multivariate sib-pair linkage analysis of the neurophysiologic measurements (including age and sex) to evaluate evidence for linkage to chromosome 1. Principal components of 16 neurophysiologic measurements, plus age and sex, were analyzed separately using sib-pair linkage analysis, and a cumulative sum of the resulting t2-statistics computed at each point on the chromosome. The first four principal components, which accounted for 74% of the total variation, showed little or no evidence for linkage in the D1S1588 region, while the remaining components showed substantial evidence for linkage. We conclude that potentially important linkage results can be missed if investigators limit attention only to major sources of variability.