Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Assessment of inbreeding depression in a Guzerat dairy herd: Effects of individual increase in inbreeding coefficients on production and reproduction

Influences of inbreeding on daily milk yield (DMY), age at first calving (AFC), and calving intervals (CI) were determined on a highly inbred zebu dairy subpopulation of the Guzerat breed. Variance components were estimated using animal models in single-trait analyses. Two approaches were employed to estimate inbreeding depression: using individual increase in inbreeding coefficients or using inbreeding coefficients as possible covariates included in the statistical models. The pedigree file included 9,915 animals, of which 9,055 were inbred, with an average inbreeding coefficient of 15.2%. The maximum inbreeding coefficient observed was 49.45%, and the average inbreeding for the females still in the herd during the analysis was 26.42%. Heritability estimates were 0.27 for DMY and 0.38 for AFC. The genetic variance ratio estimated with the random regression model for CI ranged around 0.10. Increased inbreeding caused poorer performance in DMY, AFC, and CI. However, some of the cows with the highest milk yield were among the highly inbred animals in this subpopulation. Individual increase in inbreeding used as a covariate in the statistical models accounted for inbreeding depression while avoiding overestimation that may result when fitting inbreeding coefficients.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Interethnic Differences in the Distribution of Matrix Metalloproteinases Genetic Polymorphisms Are Consistent with Interethnic Differences in Disease Prevalence

Interethnic differences exist in disease prevalence, especially with regard to cancer and cardiovascular diseases, which involve altered expression or activity of matrix metalloproteinases (MMPs). The hypothesis being tested in this study is that interethnic differences exist between blacks and whites with regard to the distribution of genetic variants of MMP polymorphisms and haplotypes. We examined the distribution of polymorphisms of MMP-2 and MMP-9 genes in 177 black and 140 white subjects. We studied the following polymorphisms: the C(-1306)T in the promoter of the MMP-2 gene, the C(-1562)T and a microsatellite -90(CA)(14-24) in the promoter, and the Q279R in exon 6 of the MMP-9 gene. We have also compared our results with those from Hapmap or Seattle SNPs Projects and estimated the haplotype frequency in these two ethnic groups. The ""C'' allele for the C(-1306)T polymorphism was more common in blacks (91.5%) than in whites (80.4%; p<0.0001). The ""T'' allele for the C(-1562)T polymorphism was more common in blacks (15.0%) than in whites (8.9%; p=0.0279), as well as the alleles with >21 repeats for the -90(CA)(14-24) were more common in blacks than in whites (61.9% in blacks and 49.3% in whites; p=0.0017). We found no interethnic differences for the Q279R polymorphism. Moreover, two haplotypes that combine ""detrimental'' alleles were found at higher frequencies in blacks than in whites (31% vs. 16.4%, respectively; p<0.05). The interethnic differences being reported here replicate those previously found with smaller number of subjects in the Hapmap or Seattle SNPs data and may help explain the higher prevalence of cancer and cardiovascular diseases in blacks compared with whites. Our findings suggest a proportional significance of these polymorphisms in each ethnic group.

Genetic parameters for pre-weaning traits in Braunvieh cattle

The objective of this study was to estimate genetic parameters for pre-weaning traits of Braunvieh cattle raised under tropical conditions in Brazil. The weight and weight gain parameters were birth weight (BW, N = 9955), weight at 120 days of age (W120, N = 5901), weaning weight at 205 days (WW, N = 6970), weight gain from birth to 205 days (GAIN205, N = 6013), weight gain from birth to 120 days (GAIN120, N = 5135), and weight gain from 120 to 205 days (GAIN85, N = 4482). Variance components were estimated using the animal model with the MTDFREML software. The relationship matrix included 35,188 animals; phenotypic measures were available for 18,688. Direct and maternal heritability increased from birth to weaning, with estimates of 0.23 +/- 0.037, 0.25 +/- 0.050, 0.41 +/- 0.059 for direct heritability for BW, W120 and WW, respectively, 0.08 +/- 0.012, 0.15 +/- 0.032, 0.22 +/- 0.036 for maternal genetic effects, and 0.18, 0.14 and 0.16 for total heritability estimates. For pre-weaning gains, estimates of heritability were 0.36 +/- 0.059, 0.30 +/- 0.059, 0.12 +/- 0.035 for direct genetic effects of the traits GAIN205, GAIN120 and GAIN85, respectively, 0.23 +/- 0.038, 0.17 +/- 0.037, 0.03 +/- 0.029 for estimates of maternal heritability, and 0.12, 0.13, 0.16 for total heritability, respectively. Genetic correlations between weights were greater between measures taken at shorter intervals. This information can be used to optimize the design of programs for genetic improvement of Braunvieh cattle raised under tropical conditions.

Estimates of genetic trend for carcass traits in a commercial broiler line

Data from the slaughter of 24,001 chickens that were part of a selection program for the production of commercial broilers were used to estimate genetic trend for absolute carcass (CW), breast meat (BRW), and leg (LW) weights, and relative carcass (CY), breast meat (BRY), and leg (LY) weights. The components of (co) variance and breeding values of individuals were obtained by the restricted maximum likelihood method applied to animal models. The relationship matrix was composed of 132,442 birds. The models included as random effects, maternal additive genetic and permanent environmental for CW, BRW, LW, CY, and BRY, and only maternal permanent environmental for LY, besides the direct additive genetic and residual effects, and as fixed effects, hatch week, parents' mating group and sex. The estimates of genetic trend were obtained by average regression of breeding value on generation, and the average genetic trend was estimated by regression coefficients. The genetic trends for CW (+ 6.0336 g/generation), BRW (+ 3.6723 g/generation), LW (+ 1.5846 g/generation), CY (+ 0.1195%/generation), and BRY (+ 0.1388%/generation) were positive, and they were in accordance with the objectives of the selection program for these traits. The genetic trend for LY(-0.0019%/generation) was negative, possibly due to the strong emphasis on selection for BRY and the negative correlations between these two traits.

Genetic parameters for postweaning traits in Braunvieh cattle

Genetic parameters for traits related to postweaning growth in Braunvieh cattle, reared under tropical and sub-tropical conditions in Brazil, were studied. Weight traits were weight at 365 days of age (W365, N = 4055), at 450 days (W450, N = 3453), and at 550 days (W550, N = 1946), while weight gains were gain from weaning to 365 days of age (WGW365, N = 3060), from weaning to 450 days (WGW450, N = 2764), from weaning to 550 days (WGW550, N = 1531), from 365 to 550 days of age (WG365550, N = 1528), from 365 to 450 days (WG365450, N = 2401), and from 450 to 550 days (WG450550, N = 1563). A full animal model was used for estimating the variance components, using the MTDFREML software. The dataset contained 18,688 animals with phenotypic measures and 35,188 animals in the relationship matrix. Heritability estimates for postweaning weights decreased with age. For W365, W450 and W550, respectively, the direct heritability estimates were 0.29 +/- 0.061, 0.25 +/- 0.057, 0.16 +/- 0.060, maternal heritability was 0.20 +/- 0.035, 0.18 +/- 0.035, 0.13 +/- 0.052, and total heritability was 0.30, 0.35, 0.26. In this breed, maternal influence was found to be important up to 550 days of age. The greater genetic correlations between weights were observed for weights measured at shorter intervals. A large environmental effect was observed for weight gain between weaning and 550 days; this effect was greater for the gains between 365 and 550 days.

Random regression models to estimate test-day milk yield genetic parameters Holstein cows in Southeastern Brazil

A total of 152,145 weekly test-day milk yield records from 7317 first lactations of Holstein cows distributed in 93 herds in southeastern Brazil were analyzed. Test-day milk yields were classified into 44 weekly classes of DIM. The contemporary groups were defined as herd-year-week of test-day. The model included direct additive genetic, permanent environmental and residual effects as random and fixed effects of contemporary group and age of cow at calving as covariable, linear and quadratic effects. Mean trends were modeled by a cubic regression on orthogonal polynomials of DIM. Additive genetic and permanent environmental random effects were estimated by random regression on orthogonal Legendre polynomials. Residual variances were modeled using third to seventh-order variance functions or a step function with 1, 6,13,17 and 44 variance classes. Results from Akaike`s and Schwarz`s Bayesian information criterion suggested that a model considering a 7th-order Legendre polynomial for additive effect, a 12th-order polynomial for permanent environment effect and a step function with 6 classes for residual variances, fitted best. However, a parsimonious model, with a 6th-order Legendre polynomial for additive effects and a 7th-order polynomial for permanent environmental effects, yielded very similar genetic parameter estimates. (C) 2008 Elsevier B.V. All rights reserved.

Covariance functions for body weight from birth to maturity in Nellore cows

The objective of this study was to estimate (co)variance functions using random regression models on Legendre polynomials for the analysis of repeated measures of BW from birth to adult age. A total of 82,064 records from 8,145 females were analyzed. Different models were compared. The models included additive direct and maternal effects, and animal and maternal permanent environmental effects as random terms. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of animal age (cubic regression) were considered as random co-variables. Eight models with polynomials of third to sixth order were used to describe additive direct and maternal effects, and animal and maternal permanent environmental effects. Residual effects were modeled using 1 (i.e., assuming homogeneity of variances across all ages) or 5 age classes. The model with 5 classes was the best to describe the trajectory of residuals along the growth curve. The model including fourth- and sixth-order polynomials for additive direct and animal permanent environmental effects, respectively, and third-order polynomials for maternal genetic and maternal permanent environmental effects were the best. Estimates of (co) variance obtained with the multi-trait and random regression models were similar. Direct heritability estimates obtained with the random regression models followed a trend similar to that obtained with the multi-trait model. The largest estimates of maternal heritability were those of BW taken close to 240 d of age. In general, estimates of correlation between BW from birth to 8 yr of age decreased with increasing distance between ages.

Parâmetros genéticos para idade ao primeiro parto estimados por diferentes modelos para rebanhos da raça Nelore

Com objetivo de estimar parâmetros genéticos e estudar a utilização de diferentes efeitos em avaliações genéticas para idade ao primeiro parto (IPP) por diferentes modelos, foram utilizados registros de IPP de animais da raça Nelore, nascidos entre os anos de 1990 e 2005. Foram considerados os seguintes modelos (M): M1, incluindo o efeito fixo de GC1 (constituído pelos animais nascidos na mesma fazenda e ano), além da covariável, peso aos 365 dias de idade (efeito linear e quadrático), totalizando 24.263 registros de IPP; M2, considerando os efeitos fixos de GC1, ano e estação de parição, totalizando 59.792 registros de IPP e M3, incluindo os efeitos fixos de GC2 (agrupando os animais nascidos na mesma fazenda, ano e que conceberam no mesmo manejo reprodutivo), ano e estação de parição, totalizando 59.792 registros de IPP. As estimativas dos componentes de variância e herdabilidade e os valores genéticos (VG) foram obtidos pelo método da máxima verossimilhança restrita, com a inclusão da matriz de parentesco disponível. As diferenças esperadas na progênie (DEPs) foram obtidas dividindo os VG por dois. Após a obtenção desses resultados, foram realizadas correlações entre os VG e o ranqueamento das DEPs dos reprodutores para IPP, utilizando-se o procedimento PROC CORR (SAS, 2003). Ao se considerar o ano e a estação de parto nos modelos de análise (M2 e M3), esses produziram um maior R², indicando que tais modelos conseguiram explicar, em maior grau, as diferenças existentes entre os animais para IPP. As herdabilidades estimadas foram de baixa magnitude (0,14 e 0,15). As correlações entre os VG obtidas por diferentes modelos foram 0,73 (M1 x M2); 0,91 (M2 x M3) e 0,66 (M1 x M3).

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Genetic diversity of turmeric germplasm (Curcuma longa; Zingiberaceae) identified by microsatellite markers

Turmeric (Curcuma longa) is a triploid, vegetatively propagated crop introduced early during the colonization of Brazil. Turmeric rhizomes are ground into a powder used as a natural dye in the food industry, although recent research suggests a greater potential for the development of drugs and cosmetics. In Brazil, little is known about the genetic variability available for crop improvement. We examined the genetic diversity among turmeric accessions from a Brazilian germplasm collection comprising 39 accessions collected from the States of Goias, Mato Grosso do Sul, Minas Gerais, Sao Paulo, and Para. For comparison, 18 additional genotypes were analyzed, including samples from India and Puerto Rico. Total DNA was extracted from lyophilized leaf tissue and genetic analysis was performed using 17 microsatellite markers (single-sequence repeats). Shannon-Weiner indexes ranged from 0.017 (Minas Gerais) to 0.316 (Sao Paulo). Analyses of molecular variance (AMOVA) demonstrated major differences between countries (63.4%) and that most of the genetic diversity in Brazil is found within states (75.3%). Genotypes from Sao Paulo State were the most divergent and potentially useful for crop improvement. Structure analysis indicated two main groups of accessions. These results can help target future collecting efforts for introduction of new materials needed to develop more productive and better adapted cultivars.

Genetic trend estimates of meat quality traits in a male broiler line

The present research was conducted to estimate the genetic trends for meat quality traits in a male broiler line. The traits analyzed were initial pH, pH at 6 h after slaughter, final pH, initial range of falling pH, final range of falling pH, lightness, redness, yellowness, weep loss, drip loss, shrink loss, and shear force. The number of observations varied between 618 and 2125 for each trait. Genetic values were obtained by restricted maximum likelihood, and the numerator relationship matrix had 107,154 animals. The genetic trends were estimated by regression of the broiler average genetic values with respect to unit of time (generations), and the average genetic trend was estimated by regression coefficients. Generally, for the traits analyzed, small genetic trends were obtained, except for drip loss and shear force, which were higher. The small magnitude of the trends found could be a consequence of the absence of selection for meat quality traits in the line analyzed. The estimates of genetic trends obtained were an indication of an improvement in the meat quality traits in the line analyzed, except for drip loss.

Genetic parameters for productive life traits and reproductive efficiency traits at 6 years in Nellore cattle

The objective of the present study was to estimate (co)variance components for length of productive life (LPL) and some alternative reproductive traits of 6-year-old Nellore cattle. The data set contained 57,410 records for age at first calving from Nellore females and was edited to remove animal records with uncertain paternity and cows with just one piece of calving information. Only animals with age at first calving ranging from 23 to 48 months and calving intervals between 11 and 24 months were kept for analysis. LPL and life production ( LP) were used to describe productive life. LPL was defined as the number of months a cow was kept in the herd until she was 6 years old, given that she was alive at first calving and LP was defined as total number of calves in that time. Four traits were used to describe reproductive traits: two breeding efficiencies on original scale were estimated using Wilcox and Tomar functions (BEW and BET, respectively), and two breeding efficiencies transformed (ASBEW and ASBET, respectively), using the function [arcsine (square root (BEi/100))]. Estimates of heritability for measures of LPL and LP were low and ranged from 0.04 to 0.05. Estimates of heritability for breeding efficiencies on original and transformed scales oscillated from 0.18 to 0.32. Estimates of genetic correlations ranged from -0.57 to 0.79 for LPL and other traits and from 0.28 to 0.63 for LP and other traits.