Modeling extent and distribution of zygotic disequilibrium: implications for a multigenerational canine pedigree.

Unlike gametic linkage disequilibrium defined for a random-mating population, zygotic disequilibrium describes the nonrandom association between different loci in a nonequilibrium population that deviates from Hardy-Weinberg equilibrium. Zygotic disequilibrium specifies five different types of disequilibria simultaneously that are (1) Hardy-Weinberg disequilibria at each locus, (2) gametic disequilibrium (including two alleles in the same gamete, each from a different locus), (3) nongametic disequilibrium (including two alleles in different gametes, each from a different locus), (4) trigenic disequilibrium (including a zygote at one locus and an allele at the other), and (5) quadrigenic disequilibrium (including two zygotes each from a different locus). However, because of the uncertainty on the phase of the double heterozygote, gametic and nongametic disequilibria need to be combined into a composite digenic disequilibrium and further define a composite quadrigenic disequilibrium together with the quadrigenic disequilibrium. To investigate the extent and distribution of zygotic disequilibrium across the canine genome, a total of 148 dogs were genotyped at 247 microsatellite markers located on 39 pairs of chromosomes for an outbred multigenerational pedigree, initiated with a limited number of unrelated founders. A major portion of zygotic disequilibrium was contributed by the composite digenic and quadrigenic disequilibrium whose values and numbers of significant marker pairs are both greater than those of trigenic disequilibrium. All types of disequilibrium are extensive in the canine genome, although their values tend to decrease with extended map distances, but with a greater slope for trigenic disequilibrium than for the other types of disequilibrium. Considerable variation in the pattern of disequilibrium reduction was observed among different chromosomes. The results from this study provide scientific guidance about the determination of the number of markers used for whole-genome association studies.

Structured antedependence models for functional mapping of multiple longitudinal traits.

In this article, we present a statistical model for mapping quantitative trait loci (QTL) that determine growth trajectories of two correlated traits during ontogenetic development. This model is derived within the maximum likelihood context, incorporated by mathematical aspects of growth processes to model the mean vector and by structured antedependence (SAD) models to approximate time-dependent covariance matrices for longitudinal traits. It provides a quantitative framework for testing the relative importance of two mechanisms, pleiotropy and linkage, in contributing to genetic correlations during ontogeny. This model has been employed to map QTL affecting stem height and diameter growth trajectories in an interspecific hybrid progeny of Populus, leading to the successful discovery of three pleiotropic QTL on different linkage groups. The implications of this model for genetic mapping within a broader context are discussed.

Effect of administration of a controlled-release monensin capsule on incidence of calving-related disorders, fertility, and milk yield in dairy cows.

OBJECTIVE: To determine the effect of a controlled-release monensin capsule administered at cessation of lactation on incidence of calving-related disorders, fertility, and milk yield in dairy cows. ANIMALS: 290 dairy cows treated with monensin and 290 untreated control cows. PROCEDURE: Treated cows received a capsule that released monensin at 335 mg/d for 95 days. Incidence of calving-related disorders; daily milk yield up to 20 days postpartum; test-day milk yield, fat, protein, and mature-equivalent 305-day milk production; and body condition score at calving were determined. Reproductive variables were conception rate at first service, pregnancy rate, and calving-to-conception interval. RESULTS: Cows treated with monensin were 2.1 times as likely to develop dystocia and 0.8 times as likely to develop metritis as control cows. For milk yield, there was an interaction of treatment X time X parity. In multiparous cows, monensin significantly improved milk yield at test days 4 and 7. In addition, monensin increased body condition score at calving. CONCLUSIONS AND CLINICAL RELEVANCE: Despite increasing the likelihood of developing dystocia and metritis, administration of monensin improved the lactational performance of multiparous cows and may be a promising additive for use at the time of cessation of lactation.

Statistical methods for dissecting triploid endosperm traits using molecular markers. An autogamous model.

The endosperm, a result of double fertilization in flowering plants, is a triploid tissue whose genetic composition is more complex than diploid tissue. We present a new maximum-likelihood-based statistical method for mapping quantitative trait loci (QTL) underlying endosperm traits in an autogamous plant. Genetic mapping of quantitative endosperm traits is qualitatively different from traits for other plant organs because the endosperm displays complicated trisomic inheritance and represents a younger generation than its mother plant. Our endosperm mapping method is based on two different experimental designs: (1) a one-stage design in which marker information is derived from the maternal genome and (2) a two-stage hierarchical design in which marker information is derived from both the maternal and offspring genomes (embryos). Under the one-stage design, the position and additive effect of a putative QTL can be well estimated, but the estimates of the dominant and epistatic effects are upward biased and imprecise. The two-stage hierarchical design, which extracts more genetic information from the material, typically improves the accuracy and precision of the dominant and epistatic effects for an endosperm trait. We discuss the effects on the estimation of QTL parameters of different sampling strategies under the two-stage hierarchical design. Our method will be broadly useful in mapping endosperm traits for many agriculturally important crop plants and also make it possible to study the genetic significance of double fertilization in the evolution of higher plants.

A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis.

For tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.

Comparing nutrient intake from food to the estimated average requirements shows middle- to upper-income pregnant women lack iron and possibly magnesium.

OBJECTIVE: To determine whether nutrient intake from food alone was adequate across trimesters for middle- to upper-income pregnant women when compared with estimated average requirements (EAR), and to determine whether food intake exceeded the tolerable upper intake level (UL) for any nutrient. DESIGN: Observational study in which pregnant women completed 3-day diet records each month during their pregnancy. Records were analyzed for nutrient content, and usual intake distributions were determined. SUBJECTS/SETTING: Subjects were low-risk women in their first trimester of pregnancy (living in middle- to upper-income households). Ninety-four women were recruited, and sixty-three participated. STATISTICAL ANALYSIS PERFORMED: Nutrient intake data were adjusted to achieve normality by using a power transformation. A mixed model method was used to assess trends in intake over time, and to estimate mean intake and within-subjects and between-subjects variance. The usual intake distribution for each nutrient was determined and compared with the EAR and UL. RESULTS: The probabilities of usual nutrient intake from food being less than the EAR were highest for iron (.91), magnesium (.53), zinc (.31), vitamin B6 (.21), selenium (.20), and vitamin C (.12). Women were not at risk of exceeding the UL from food intake for any nutrient studied. APPLICATIONS/CONCLUSIONS: Study participants did not consume adequate amounts of iron from food to meet the needs of pregnancy, and therefore iron supplementation is warranted in this population. Intake of magnesium was suboptimal using the EAR as a cut-point for adequacy.

Gas chromatographic analysis of histamine in mahi-mahi (Coryphaena hippurus).

Several authors have studied histamine using gas chromatography (GC) as a tool for quantitation, but the methods used were not always suitable depending on the kind of food. Problems frequently cited include incomplete histamine elution from the columns and peak tailing. Histamine is of interest because it is the factor common to all cases of scombroid poisoning, it has physiological and biological activity, and it is a chemical indicator of fish quality. In this study a modified GC method was used to quantify histamine in mahi-mahi (Coryphaena hippurus). Mean recovery was 67% for the GC method, compared with 90% for the AOAC fluorometric method. There was a 0.96 correlation of the GC histamine values with those of the AOAC fluorometric method. A temperature program, splitless/split injection, and analyte cleanup were essential for GC properties. Histamine retention time was 8.2 min. The method allowed peak height to be used for quantitation and simultaneous analysis of cadaverine and putrescine.

Modelling epistatic effects of embryo and endosperm QTL on seed quality traits.

Coordinated expression of embryo and endosperm tissues is required for proper seed development. The coordination among these two tissues is controlled by the interaction between multiple genes expressed in the embryo and endosperm genomes. In this article, we present a statistical model for testing whether quantitative trait loci (QTL) active in different genomes, diploid embryo and triploid endosperm, epistatically affect a trait expressed on the endosperm tissue. The maximum likelihood approach, implemented with the EM algorithm, was derived to provide the maximum likelihood estimates of the locations of embryo- and endosperm-specific QTL and their main effects and epistatic effects. This model was used in a real example for rice in which two QTL, one from the embryo genome and the other from the endosperm genome, exert a significant interaction effect on gel consistency on the endosperm. Our model has successfully detected Waxy, a candidate gene in the embryo genome known to regulate one of the major steps of amylose biosynthesis in the endosperm. This model will have great implications for agricultural and evolutionary genetic research.

Model for mapping imprinted quantitative trait loci in an inbred F2 design.

The role of imprinting in shaping development has been ubiquitously observed in plants, animals, and humans. However, a statistical method that can detect and estimate the effects of imprinted quantitative trait loci (iQTL) over the genome has not been extensively developed. In this article, we propose a maximum likelihood approach for testing and estimating the imprinted effects of iQTL that contribute to variation in a quantitative trait. This approach, implemented with the EM algorithm, allows for a genome-wide scan for the existence of iQTL. This approach was used to reanalyze published data in an F(2) family derived from the LG/S and SM/S mouse strains. Several iQTL that regulate the growth of body weight by expressing paternally inherited alleles were identified. Our approach provides a standard procedure for testing the statistical significance of iQTL involved in the genetic control of complex traits.

A framework to monitor environment-induced major genes for developmental trajectories: implication for a prenatal cocaine exposure study.

Whether there are specific genes involved in response to different environmental agents and how such genes regulate developmental trajectories during lifetime are of fundamental importance in health, clinical and pharmaceutical research. In this article, we present a novel statistical model for monitoring environment-induced genes of major effects on longitudinal outcomes of a trait. This model is derived within the maximum likelihood framework, incorporated by mathematical aspects of growth and developmental processes. A typical structural model is implemented to approximate time-dependent covariance matrices for the longitudinal trait. This model allows for a number of biologically meaningful hypothesis tests regarding the effects of major genes on overall growth trajectories or particular stages of development. It can be used to test whether and how major genetic effects are expressed differently under altered environmental agents. In a well-designed case-control study, our model has been employed to detect cocaine-dependent genes that affect growth trajectories for head circumference during childhood. The detected gene triggers significant effects on growth curves in both cocaine-exposed (case) and unexposed groups (control), but with different extents. Significant genotype-environment interactions due to this so-called environment-sensitive gene are promising for further studies toward its genomic mapping using polymorphic molecular markers.

A statistical model for the genetic origin of allometric scaling laws in biology.

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling (power-law) relationships between size and rate. Although such allometric relationships may be under genetic determination, their precise genetic mechanisms have not been clearly understood due to a lack of a statistical analytical method. In this paper, we present a basic statistical framework for mapping quantitative genes (or quantitative trait loci, QTL) responsible for universal quarter-power scaling laws of organic structure and function with the entire body size. Our model framework allows the testing of whether a single QTL affects the allometric relationship of two traits or whether more than one linked QTL is segregating. Like traditional multi-trait mapping, this new model can increase the power to detect the underlying QTL and the precision of its localization on the genome. Beyond the traditional method, this model is integrated with pervasive scaling laws to take advantage of the mechanistic relationships of biological structures and processes. Simulation studies indicate that the estimation precision of the QTL position and effect can be improved when the scaling relationship of the two traits is considered. The application of our model in a real example from forest trees leads to successful detection of a QTL governing the allometric relationship of third-year stem height with third-year stem biomass. The model proposed here has implications for genetic, evolutionary, biomedicinal and breeding research.

Exponential mapping of quantitative trait loci governing allometric relationships in organisms.

Allometric scaling relationships or quarter-power rules, as a universal biological law, can be viewed as having some genetic component, and the particular genes (or quantitative trait loci, QTL) underlying these allometric relationships can be mapped using molecular markers. We develop a mathematical and statistical model for mapping allometric QTL on the basis of nonlinear power functions using Taylor's approximation theory. Simulation studies indicate that the QTL position and effect can be estimated using our model, but the estimation precision can be improved from the higher- over lower-order approximation when the sample size used and gene effects are small. The application of our approach in a real example from forest trees leads to successful detection of a QTL governing the allometric relationship between 3rd-year stem height and 3rd-year stem biomass. It is expected that our model will have broad implications for genetic, evolutionary, biomedical and breeding research.

A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories.

The logistic or S-shaped curve of growth is one of the few universal laws in biology. It is certain that there exist specific genes affecting growth curves, but, due to a lack of statistical models, it is unclear how these genes cause phenotypic differentiation in growth and developmental trajectories. In this paper we present a statistical model for detecting major genes responsible for growth trajectories. This model is incorporated with pervasive logistic growth curves under the maximum likelihood framework and, thus, is expected to improve over previous models in both parameter estimation and inference. The power of this model is demonstrated by an example using forest tree data, in which evidence of major genes affecting stem growth processes is successfully detected. The implications for this model and its extensions are discussed.

Quantitative trait loci for growth trajectories in Populus.

Growth trajectories are a biological process important to plant and animal breeding, and to evolutionary genetic studies. In this article, we report the detection of quantitative trait loci (QTLs) responsible for growth trajectories in poplars that are used as a model system for the study of forest biology. These QTLs were localized on a genetic linkage map of polymorphic markers using a statistical mapping method incorporating growth-curve models. The effects of the QTLs on growth are described as a function of age, so that age-specific changes in QTL effects can be readily projected throughout the entire growth process. The QTLs identified display increased effects on growth when trees age, yet the timing of QTL activation is earlier for stem height than diameter, which is consistent with the ecological viewpoint of canopy competition. The implications of the results for breeding and silviculture are discussed.