A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

Genetic Variants in Matrix Metalloproteinase-9 Gene Modify Metalloproteinase-9 Levels in Black Subjects

Altered matrix metalloproteinases (MMPs) levels are involved in cardiovascular diseases and increased MMP-9 levels enhance the cardiovascular risk in apparently healthy subjects. We investigated the effects of MMP-9 gene polymorphisms and haplotypes on the circulating MMP-9 levels in healthy black subjects and the effects of an MMP-2 polymorphism on the plasma MMP-2 concentrations. We studied 190 healthy subjects, nonsmokers, self-reported as blacks (18-63 years). Genotypes for the MMP-2 C-1306T polymorphism and the MMP-9 C-1562T, 90(CA)(14-24) and Q279R polymorphisms (rs243865, rs3918242, rs2234681, and rs17576, respectively) were determined by TaqMan (R) Allele Discrimination assay and real-time polymerase chain reaction or restriction fragment length polymorphism. Alleles for the 90(CA)(14-24) polymorphism were grouped as low (L) when there were < 21 and high (H) when there were >= 21 CA repeats. The plasma levels of MMP-2 and MMP-9 were determined by gelatin zymography. The software PHASE 2.1 was used to estimate the haplotypes frequencies. Although we found no effects of the MMP-9 C-1562T or the Q279R polymorphisms on MMP-9 levels, higher MMP-9 levels were associated with the HH genotype for the -90(CA)(14-24) polymorphism compared with the HL or LL genotypes. Lower MMP-9 levels were found in carriers of the CRL haplotype (combining the C, R, and L alleles for the MMP-9 polymorphisms) compared with the CRH haplotype. Consistent with this finding, the CRL haplotype was more commonly found in subjects with low MMP-9 levels. The MMP-2 C-1306T polymorphism had no effects on the plasma MMP-2 levels. Our results show that MMP-9 genetic variations modify MMP-9 levels in black subjects and may offer biochemical evidence implicating MMP-9 in the pathogenesis of cardiovascular diseases in blacks.

Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

MODULARITY, NOISE, AND NATURAL SELECTION

Most biological systems are formed by component parts that are to some degree interrelated. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of modularity is that biological systems usually present an unequal distribution of the genetic variation among traits. Estimating the covariance matrix that describes these systems is a difficult problem due to a number of factors such as poor sample sizes and measurement errors. We show that this problem will be exacerbated whenever matrix inversion is required, as in directional selection reconstruction analysis. We explore the consequences of varying degrees of modularity and signal-to-noise ratio on selection reconstruction. We then present and test the efficiency of available methods for controlling noise in matrix estimates. In our simulations, controlling matrices for noise vastly improves the reconstruction of selection gradients. We also perform an analysis of selection gradients reconstruction over a New World Monkeys skull database to illustrate the impact of noise on such analyses. Noise-controlled estimates render far more plausible interpretations that are in full agreement with previous results.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

Longitudinal familial analysis of blood pressure involving parametric (co)variance functions

Abstract Background For analyzing longitudinal familial data we adopted a log-linear form to incorporate heterogeneity in genetic variance components over the time, and additionally a serial correlation term in the genetic effects at different levels of ages. Due to the availability of multiple measures on the same individual, we permitted environmental correlations that may change across time. Results Systolic blood pressure from family members from the first and second cohort was used in the current analysis. Measures of subjects receiving hypertension treatment were set as censored values and they were corrected. An initial check of the variance and covariance functions proposed for analyzing longitudinal familial data, using empirical semi-variogram plots, indicated that the observed trait dispersion pattern follows the assumptions adopted. Conclusion The corrections for censored phenotypes based on ordinary linear models may be an appropriate simple model to correct the data, ensuring that the original variability in the data was retained. In addition, empirical semi-variogram plots are useful for diagnosis of the (co)variance model adopted.

Female fertility in a Guzerat dairy subpopulation: Heterogeneity of variance components for calving intervals

The objectives of the present study were to determine if variance components of calving intervals varied with age at calving and if considering calving intervals as a longitudinal trait would be a useful approach for fertility analysis of Zebu dairy herds. With these purposes, calving records from females born from 1940 to 2006 in a Guzerat dairy subpopulation in Brazil were analyzed. The fixed effects of contemporary groups, formed by year and farm at birth or at calving, and the regressions of age at calving, equivalent inbreeding coefficient and day of the year on the studied traits were considered in the statistical models. In one approach, calving intervals (Cl) were analyzed as a single trait, by fitting a statistical model on which both animal and permanent environment effects were adjusted for the effect of age at calving by random regression. In a second approach, a four-trait analysis was conducted, including age at first calving (AFC) and three different female categories for the calving intervals: first calving females; young females (less than 80 months old, but not first calving); or mature females (80 months old or more). Finally, a two-trait analysis was performed, also including AFC and Cl, but calving intervals were regarded as a single trait in a repeatability model. Additionally, the ranking of sires was compared among approaches. Calving intervals decreased with age until females were about 80 months old, remaining nearly constant after that age. A quasi-linear increase of 11.5 days on the calving intervals was observed for each 10% increase in the female's equivalent inbreeding coefficient. The heritability of AFC was 0.37. For Cl. the genetic-phenotypic variance ratios ranged from 0.064 to 0.141, depending on the approach and on ages at calving. Differences among genetic variance components for calving intervals were observed along the animal's lifetime. Those differences confirmed the longitudinal aspect of that trait, indicating the importance of such consideration when accessing fertility of Zebu dairy females, especially in situations where the available information relies on their calving intervals. Spearman rank correlations among approaches ranged from 0.90 to 0.95, and changes observed in the ranking of sires suggested that the genetic progress of the population could be affected by the approach chosen for the analysis of calving intervals. (C) 2012 Elsevier ay. All rights reserved.

Genetic analysis of kernel oil content in tropical maize with design III and QTL mapping

Oil content and grain yield in maize are negatively correlated, and so far the development of high-oil high-yielding hybrids has not been accomplished. Then a fully understand of the inheritance of the kernel oil content is necessary to implement a breeding program to improve both traits simultaneously. Conventional and molecular marker analyses of the design III were carried out from a reference population developed from two tropical inbred lines divergent for kernel oil content. The results showed that additive variance was quite larger than the dominance variance, and the heritability coefficient was very high. Sixteen QTL were mapped, they were not evenly distributed along the chromosomes, and accounted for 30.91% of the genetic variance. The average level of dominance computed from both conventional and QTL analysis was partial dominance. The overall results indicated that the additive effects were more important than the dominance effects, the latter were not unidirectional and then heterosis could not be exploited in crosses. Most of the favorable alleles of the QTL were in the high-oil parental inbred, which could be transferred to other inbreds via marker-assisted backcross selection. Our results coupled with reported information indicated that the development of high-oil hybrids with acceptable yields could be accomplished by using marker-assisted selection involving oil content, grain yield and its components. Finally, to exploit the xenia effect to increase even more the oil content, these hybrids should be used in the Top Cross((TM)) procedure.

Genotype by environment interaction for birth and weaning weights of composite beef cattle in different regions of Brazil

The objectives of the present study were to characterize and define homogenous production environments of composite beef cattle in Brazil in terms of climatic and geographic variables using multivariate exploratory techniques and to use them to assess the presence of G x E for birth weight (BW) and weaning weight (WW). Data from animals born between 1995 and 2008 on 36 farms located in 27 municipalities of the Brazilian states were used. Fifteen years of climate observations (mean minimum and maximum annual temperature and mean annual rainfall) and geographic (latitude, longitude and altitude) data were obtained for each municipality where the farms were located for characterization of the production environments. Hierarchical and nonhierarchical cluster analysis was used to group farms located in regions with similar environmental variables into clusters. Six clusters of farms were formed. The effect of sire-cluster interaction was tested by single-trait analysis using deviance information criterion (DIC). Genetic parameters were estimated by multi-trait analysis considering the same trait to be different in each cluster. According to the values of DIC, the inclusion of sire-cluster effect did not improve the fit of the genetic evaluation model for BW and WW. Estimates of genetic correlations among clusters ranged from -0.02 to 0.92. The low genetic correlation among the most studied regions permits us to suggest that a separate genetic evaluation for some regions should be undertaken. (C) 2012 Elsevier B.V. All rights reserved.

The full Fisher matrix for galaxy surveys

Starting from the Fisher matrix for counts in cells, we derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key step is the classical approximation, which allows us to write the inverse of the covariance of the galaxy counts in terms of the naive matrix inverse of the covariance in a mixed position-space and Fourier-space basis. We then compute the Fisher matrix for the power spectrum in bins of the 3D wavenumber , the Fisher matrix for functions of position (or redshift z) such as the linear bias of the tracers and/or the growth function and the cross-terms of the Fisher matrix that expresses the correlations between estimations of the power spectrum and estimations of the bias. When the bias and growth function are fully specified, and the Fourier-space bins are large enough that the covariance between them can be neglected, the Fisher matrix for the power spectrum reduces to the widely used result that was first derived by Feldman, Kaiser & Peacock. Assuming isotropy, a fully analytical calculation of the Fisher matrix in the classical approximation can be performed in the case of a constant-density, volume-limited survey.

Matrix Metalloproteinase (MMP)-2 Genetic Variants Modify the Circulating MMP-2 Levels in End-Stage Kidney Disease

Background: Matrix metalloproteinases (MMPs) play important roles in the pathophysiology of renal diseases, and imbalanced MMP-2 and its endogenous inhibitor (the tissue inhibitor of metalloproteinases-2; TIMP-2) are implicated in the vascular alterations of end-stage kidney disease (ESKD) patients. We have examined whether MMP-2 gene polymorphisms and haplotypes modify MMP-2 and TIMP-2 levels in ESKD patients as well as the effects of hemodialysis on the concentrations of these biomarkers. Methods: We determined MMP-2 and TIMP-2 plasma levels by gelatin zymography and ELISA, respectively, in 98 ESKD patients and in 38 healthy controls. Genotypes for two relevant MMP-2 polymorphisms (C-T-1306 and C-T-735 in the promoter region) were determined by TaqMan (R) allele discrimination assay and real-time polymerase chain reaction. The software program PHASE 2.1 was used to estimate the haplotype frequencies. Results: We found increased plasma MMP-2 and TIMP-2 levels in ESKD patients compared to controls (p<0.05), and hemodialysis decreased MMP-2 (but not TIMP-2) levels (p<0.05). The T allele for the C-T-735 polymorphism and the C-T haplotype were associated with higher MMP-2 (but not TIMP-2) levels (p<0.05), whereas the C-T-1306 had no effects. Hemodialysis decreased MMP-2 (but not TIMP-2) levels independently of MMP-2 genotypes or haplotypes (p<0.05). Conclusions: MMP-2 genotypes or haplotypes modify MMP-2 levels in ESKD patients, and may help to identify patients with increased MMP-2 activity in plasma. Hemodialysis reduces MMP-2 levels independently of MMP-2 genetic variants. Copyright (C) 2012 S. Karger AG, Basel

Functional matrix metalloproteinase (MMP)-9 genetic variants modify the effects of hemodialysis on circulating MMP-9 levels

Background: Altered levels of matrix metalloproteinases (MMPs) and their inhibitors, the tissue inhibitors of metalloproteinases (TIMPs), are involved in cardiovascular alterations associated with end stage kidney disease (ESKD). Genetic polymorphisms in MMP-9 gene affect MMP-9 levels. We examined how MMP-9 polymorphisms and haplotypes affect the changes in plasma MMP-9 and TIMP-1 levels found in patients with ESKD undergoing hemodialysis. Methods: We studied 94 ESKD patients undergoing hemodialysis for at least 3 months. MMP-9 and TIMP-1 were measured by ELISA in plasma from blood samples collected before and after a session of hemodialysis. Genotypes for three MMP-9 polymorphisms (C-1562T, rs3918242; -90 (CA)(14-24), rs2234681; and Q279R, rs17576) were determined by Taqman (R) Allele Discrimination Assay and real-time polymerase chain reaction. Haplotype frequencies were determined with the software program PHASE 2.1. Results: Hemodialysis increased MMP-9 and TIMP-1 levels (P<0.05). Genotypes had no effects on baseline MMP-9 and TIMP-1 levels (P>0.05). Hemodialysis increased MMP-9 and TIMP-1 levels in subjects with the CC (but not CT or TT) genotype for the C-1562T polymorphism (P<0.05), and increased MMP-9 levels in subjects with the QQ (but not QR or RR) genotype for the Q279R polymorphism (P<0.05), whereas the CA(n)(14-24) polymorphism had no major effects. While MMP-9 haplotypes had no effects on baseline MMP-9 levels (P>0.05), hemodialysis increased MMP-9 levels and MMP-9/TIMP-1 ratios in subjects carrying the CLQ haplotype (P = 0.0012 and P = 0.0045, respectively). Conclusion: ESKD patients with the QQ genotype for the Q279R polymorphism or with the CLQ haplotype are exposed to more severe increases in MMP-9 levels after hemodialysis. Such patients may benefit from the use of MMP inhibitors. (C) 2012 Elsevier B.V. All rights reserved.

Matrix metalloproteinase-9 genetic variations affect MMP-9 levels in obese children

Objective: Matrix metalloproteinase-9 (MMP-9) is involved in the atherosclerotic process and functional polymorphisms in the MMP-9 gene affect MMP-9 expression/activity, and are associated with cardiovascular diseases. However, no study has tested the hypothesis that functional MMP-9 polymorphisms could affect MMP-9 levels in obese children. We investigated whether three MMP-9 gene polymorphisms (C-1562T (rs3918242), 90(CA)((14-24)) (rs2234681) and Q279R (rs17576)), or haplotypes, affect MMP-9 levels in obese children. Methods: We studied 175 healthy control children and 127 obese children. Plasma MMP-9, tissue inhibitor of MMPs (TIMP)-1 and adiponectin concentrations were measured using enzyme-linked immunosorbent assay. Results: We found similar MMP-9 genotypes, allelic and haplotypes distributions in the two study groups (P > 0.05). However, we found lower plasma MMP-9 concentrations in obese subjects carrying the CC or the QQ genotypes for the C-1562T and the Q279R polymorphisms, respectively, in obese children compared with children with the other genotypes, or with non-obese children with the same genotypes (all P < 0.05). Moreover, we found lower MMP-9 levels and lower MMP-9/TIMP-1 ratios (which reflect net MMP-9 activity) in obese children carrying the H2 haplotype (which combines the C, H and Q alleles for the three polymorphisms, respectively) when compared with obese children carrying the other haplotypes, or with non-obese children carrying the same haplotype (P < 0.05). Conclusions: Our findings show that MMP-9 genotypes and haplotypes affect MMP-9 levels in obese children and adolescents, and suggest that genetic factors may modify relevant pathogenetic mechanisms involved in the development of cardiovascular complications associated with obesity in childhood. International Journal of Obesity (2012) 36, 69-75; doi:10.1038/ijo.2011.169; published online 16 August 2011

Genetic relationship between growth and reproductive traits in Nellore cattle

The objective of this study was to evaluate the genetic relationship between postweaning weight gain (PWG), heifer pregnancy (HP), scrotal circumference (SC) at 18 months of age, stayability at 6 years of age (STAY) and finishing visual score at 18 months of age (PREC), and to determine the potential of these traits as selection criteria for the genetic improvement of growth and reproduction in Nellore cattle. The HP was defined as the observation that a heifer conceived and remained pregnant, which was assessed by rectal palpation at 60 days. The STAY was defined as whether or not a cow calved every year up to the age of 6 years, given that she was provided the opportunity to breed. The Bayesian linear-threshold analysis via the Gibbs sampler was used to estimate the variance and covariance components applying a multitrait model. Posterior mean estimates of direct heritability were 0.15 +/- 0.00, 0.42 +/- 0.02, 0.49 +/- 0.01, 0.11 +/- 0.01 and 0.19 +/- 0.00 for PWG, HP, SC, STAY and PREC, respectively. The genetic correlations between traits ranged from 0.17 to 0.62. The traits studied generally have potential for use as selection criteria in genetic breeding programs. The genetic correlations between all traits show that selection for one of these traits does not imply the loss of the others.

Effects of Matrix Metalloproteinase (MMP)-2 Polymorphisms on Responsiveness to Antihypertensive Therapy of Women with Hypertensive Disorders of Pregnancy

Imbalanced matrix metalloproteinase (MMP) expression, including MMP-2, has been demonstrated in pre-eclampsia. However, little is known about the effect of polymorphisms in MMP-2 gene on hypertensive disorders of pregnancy. We examined whether two functional MMP-2 polymorphisms (g.-1306C>T and g.-735C>T) are associated with pre-eclampsia and/or gestational hypertension and whether these polymorphisms affect therapeutic responses in women with these conditions. We studied 216 healthy pregnant women (HP), 185 patients with gestational hypertension (GH) and 216 patients with pre-eclampsia (PE). They were stratified as responsive or non-responsive to antihypertensive therapy according to clinical and laboratorial parameters of therapeutic responsiveness. Genomic DNA was extracted from whole blood and genotypes for g-1306C>T and g.-735C>T polymorphisms were determined by real-time PCR using Taqman allele discrimination assays. Haplotype frequencies were inferred using the PHASE 2.1 program. The distributions of MMP-2 genotypes and haplotypes were similar in HP, GH and PE patients (p > 0.05). In addition, we found no significant differences in MMP-2 genotype or haplotype frequencies when GH or PE patients were classified as responsive or non-responsive to antihypertensive therapy (p > 0.05). Our results suggest that MMP-2 polymorphisms do not affect the susceptibility to hypertensive disorders of pregnancy. In parallel, MMP-2 polymorphisms apparently do not affect the responsiveness to antihypertensive therapy of women with these hypertensive disorders of pregnancy.