Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

Inferência bayesiana na predição de valores genéticos do peso aos 365 dias de bovinos de corte

Data from purebred Simmental, Nellore and Canchim cattle breeds obtained from the respective Brazilian Associations of Breeders were used to estimate variance components and to predict genetic values for 365 days weight. The results obtained by Bayesian inference were compared to those from Restricted Maximum Likelihood (REML) and Best Linear Unbiased Prediction (BLUP), which are the most commonly used methods of estimation and prediction in animal breeding. The two methods presented similar point estimates but the study of the marginal posterior distributions in the Bayesian approach yields more detailed information about the parameters and other unknowns in the model.

Reinforcing and expanding the predictions of the disturbance vicariance hypothesis in Amazonian harlequin frogs: A molecular phylogenetic and climate envelope modelling approach

The disturbance vicariance hypothesis (DV) has been proposed to explain speciation in Amazonia, especially its edge regions, e. g. in eastern Guiana Shield harlequin frogs (Atelopus) which are suggested to have derived from a cool-adapted Andean ancestor. In concordance with DV predictions we studied that (i) these amphibians display a natural distribution gap in central Amazonia; (ii) east of this gap they constitute a monophyletic lineage which is nested within a pre-Andean/western clade; (iii) climate envelopes of Atelopus west and east of the distribution gap show some macroclimatic divergence due to a regional climate envelope shift; (iv) geographic distributions of climate envelopes of western and eastern Atelopus range into central Amazonia but with limited spatial overlap. We tested if presence and apparent absence data points of Atelopus were homogenously distributed with Ripley's K function. A molecular phylogeny (mitochondrial 16S rRNA gene) was reconstructed using Maximum Likelihood and Bayesian Inference to study if Guianan Atelopus constitute a clade nested within a larger genus phylogeny. We focused on climate envelope divergence and geographic distribution by computing climatic envelope models with MaxEnt based on macroscale bioclimatic parameters and testing them by using Schoener's index and modified Hellinger distance. We corroborated existing DV predictions and, for the first time, formulated new DV predictions aiming on species' climate envelope change. Our results suggest that cool-adapted Andean Atelopus ancestors had dispersed into the Amazon basin and further onto the eastern Guiana Shield where, under warm conditions, they were forced to change climate envelopes. © 2010 The Author(s).

Estudio de efectos ambientales y genéticos que influyen en la producción de leche y duración de lactación en bovinos de raza guzerat

Objective of present work was study a influence of environmental and genetic effects over characteristics of milk total production (PL) and lactation duration (DL), from 2572 lactations of 477 Guzerat cows, collected since 1957 to 2002, in Rio de Janeiro State. Environmental effects were analyzed by an statistical model that include male randomized effect, fixed effect of contemporary group, and the (co)variables age of cow (lineal and quadratic) and lactation duration. The contemporary group had significant effect just for PL. Bayesian inference was used to obtain estimatives of genetic parameters over an animal model, in which was included as fixed effect the contemporary group and the covariables age of cow (linear and quadratic). The estimates of heritability and repeatability were 0.36 and 0.75 for PL and 0.29 and 0.36 for DL, respectively. The estimated genetic correlation was 0.97. The heritability estimates for PL and DL were moderate, indicating that it is possible answer to the selection of the characteristics under study. The genetic correlation was high and indicates that selection for increase milk production will be accompanied with increase in lactation duration.

Genotype by environment interaction in different birth seasons for weight at 240, 365 and 450 days of age in Tabapuã cattle

The objective of this study was to evaluate the effect of genotype by environment interaction (GEI) on the weight of Tabapuã cattle at 240 (W240), 365 (W365) and 450 (W450) days of age. In total, 35,732 records of 8,458 Tabapuã animalswhich were born in the state of Bahia, Brazil, from 1975 to 2001, from 167 sires and 3,707 dams, were used. Two birth seasons were tested as for the environment effect: the dry (D) and rainy (R) ones. The covariance components were obtainedby a multiple-trait analysis using Bayesian inference, in which each trait was considered as being different in each season. Covariance components were estimated by software gibbs2f90. As for W240, the model was comprised of contemporary groups and cow age (in classes) as fixed effects; animal and maternal genetic additive, maternal permanent environmental and residual were considered as random effects. Concerning W365 and W450, the model included only the contemporary aged cow groups as fixed effects and the genetic additive and residual effects of the animal as the random ones. The GEI was assessed considering the genetic correlation, in which values below 0.80 indicated the presence of GEI. Regarding W365 and W450, the GEI was found in both seasons. As for post-weaning weight (W240), the effect of such interaction was not observed. ©2012 Sociedade Brasileira de Zootecnia.

Phylogeography of Hypostomus strigaticeps (Siluriformes: Loricariidae) inferred by mitochondrial DNA reveals its distribution in the upper Paraná River basin

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Evaluation of mature cow weight: Genetic correlations with traits used in selection indices, correlated responses, and genetic trends in Nelore cattle

Genetic correlations of selection indices and the traits considered in these indices with mature weight (MW) of Nelore females and correlated responses were estimated to determine whether current selection practices will result in an undesired correlated response in MW. Genetic trends for weaning and yearling indices and MW were also estimated. Data from 612,244 Nelore animals born between 1984 and 2010, belonging to different beef cattle evaluation programs from Brazil and Paraguay, were used. The following traits were studied: weaning conformation (WC), weaning precocity (WP), weaning muscling (WM), yearling conformation (YC), yearling precocity (YP), yearling muscling (YM), weaning and yearling indices, BW gain from birth to weaning (BWG), postweaning BW gain (PWG), scrotal circumference (SC), and MW. The variance and covariance components were estimated by Bayesian inference in a multitrait analysis, including all traits in the same analysis, using a nonlinear (threshold) animal model for visual scores and a linear animal model for the other traits. The mean direct heritabilities were 0.21 ± 0.007 (WC), 0.22 ± 0.007 (WP), 0.20 ± 0.007 (WM), 0.43 ± 0.005 (YC), 0.40 ± 0.005 (YP), 0.40 ± 0.005 (YM), 0.17 ± 0.003 (BWG), 0.21 ± 0.004 (PWG), 0.32 ± 0.001 (SC), and 0.44 ± 0.018 (MW). The genetic correlations between MW and weaning and yearling indices were positive and of medium magnitude (0.30 ± 0.01 and 0.31 ± 0.01, respectively). The genetic changes in weaning index, yearling index, and MW, expressed as units of genetic SD per year, were 0.26, 0.27, and 0.01, respectively. The genetic trend for MW was nonsignificant, suggesting no negative correlated response. The selection practice based on the use of sires with high final index giving preference for those better ranked for yearling precocity and muscling than for conformation generates only a minimal correlated response in MW. © 2013 American Society of Animal Science. All rights reserved.

Analysis of genetic correlations of hip height with selection indices and mature weight in Nelore cattle

Body size is directly related to the productive and reproductive performance of beef cattle raised under free-range conditions. In an attempt to better plan selection criteria, avoiding extremes in body size, this study estimated the heritabilities and genetic correlations of yearling hip height (YH) and mature hip height (MH) with selection indices obtained at weaning (WI) and yearling (YI) and mature weight (MW). Data from 102,373 Nelore animals born between 1984 and 2010, which belong to 263 farms that participate in genetic evaluation programmes of beef cattle conducted in Brazil and Paraguay, were used. The (co)variance components and genetic parameters were estimated by Bayesian inference in multi-trait analysis using an animal model. The mean heritabilities for YH, MH and MW were 0. 56 ± 0. 06, 0. 47 ± 0. 02 and 0. 42 ± 0. 02, respectively. The genetic correlation of YH with WI (0. 13 ± 0. 01) and YI (0. 11 ± 0. 01) was practically zero, whereas a higher correlation was observed with MW (0. 22 ± 0. 03). Positive genetic correlations of medium magnitude were estimated between MH and WI and YI (0. 23 ± 0. 01 and 0. 43 ± 0. 02, respectively). On the other hand, a high genetic correlation (0. 68 ± 0. 03) was observed between the indicator traits of mature body size (MH and MW). Considering the top 20 % of sire (896 sires) in terms of breeding values for the yearling index, the rank sire correlations between breeding values for MH and MW was 0. 62. In general, the results indicate that selection based on WI and YI should not lead to important changes in YH. However, an undesired correlated response in mature cow height is expected, particularly when selection is performed using YI. Therefore, changes in the body structure of Nelore females can be obtained when MH and MW is used as a selection criterion for cows. © 2012 Institute of Plant Genetics, Polish Academy of Sciences, Poznan.

Genetic parameters for milk yield, lactation length and calving intervals of murrah buffaloes from brazil

The major objective of this study was to estimate heritability and genetic correlations between milk yield (MY) and calving interval (CI) and lactation length (LL) in Murrah buffaloes using Bayesian inference. The database used belongs to the genetic improvement program of four buffalo herds from Brazil. To obtain the estimates of variance and covariance, bivariate analyses were performed with the Gibbs sampler, using the program MTGSAM. The heritability coefficient estimates were 0.28, 0.03 and 0.15 for MY, CI and LL, respectively. The genetic correlations between MY and LL was moderate (0.48). However, the genetic correlation between MY and CI showed large HPD regions (highest posterior density interval). Milk yield was the only trait with clear potential for genetic improvement by direct mass selection. The genetic correlation between MY and LL indicates that indirect selection using milk yield is a potentially beneficialstrategy.Theinterpretation of the estimated genetic correlation between MY and CI is difficult and could be spurious. ©2013 Sociedade Brasileira de Zootecnia.

Genetic variability for temperament indicators of Nellore cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multiple-trait random regression models for the estimation of genetic parameters for milk, fat, and protein yield in buffaloes

In this study, genetic parameters for test-day milk, fat, and protein yield were estimated for the first lactation. The data analyzed consisted of 1,433 first lactations of Murrah buffaloes, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, with calvings from 1985 to 2007. Ten-month classes of lactation days were considered for the test-day yields. The (co)variance components for the 3 traits were estimated using the regression analyses by Bayesian inference applying an animal model by Gibbs sampling. The contemporary groups were defined as herd-year-month of the test day. In the model, the random effects were additive genetic, permanent environment, and residual. The fixed effects were contemporary group and number of milkings (1 or 2), the linear and quadratic effects of the covariable age of the buffalo at calving, as well as the mean lactation curve of the population, which was modeled by orthogonal Legendre polynomials of fourth order. The random effects for the traits studied were modeled by Legendre polynomials of third and fourth order for additive genetic and permanent environment, respectively, the residual variances were modeled considering 4 residual classes. The heritability estimates for the traits were moderate (from 0.21-0.38), with higher estimates in the intermediate lactation phase. The genetic correlation estimates within and among the traits varied from 0.05 to 0.99. The results indicate that the selection for any trait test day will result in an indirect genetic gain for milk, fat, and protein yield in all periods of the lactation curve. The accuracy associated with estimated breeding values obtained using multi-trait random regression was slightly higher (around 8%) compared with single-trait random regression. This difference may be because to the greater amount of information available per animal. © 2013 American Dairy Science Association.

Genetic parameters for scrotal circumference, breeding soundness examination and sperm defects in young Nellore bulls

A total of 51,161 records of scrotal circumference measurements at 18 mo of age (SCI 8) and 17,648 records of sperm defects and breeding soundness of Nellore bulls (mean age of 22.5 mo), raised under extensive conditions, were analyzed to estimate coefficients of heritability and genetic correlations of morphological semen traits by Bayesian inference. The observed semen traits were classified as minor (MID). major (MAD), and total sperm defects (TD). The animals were classified according to breeding soundness as satisfactory and unsatisfactory potential breeders. The (co)variance components and breeding values were estimated by Gibbs sampling using the GIBBS2F90 program under an animal model that included contemporary group as fixed effect, age of animal as linear covariate, and direct additive genetic effects as random effects. Heritabilities of 0.40 ± 0.02, 0.16 ± 0.02, 0.04 ± 0.01, 0.15 ± 0.01, and 0.10 ± 0.01 were obtained for SCI8, MID, MAD, TD, and breeding soundness, respectively. The SC18 showed a positive and moderate correlation with breeding soundness (0.56 ± 0.04) and a negative and low correlation with MID (-0.23 ± 0.03), MAD (-0.16 ± 0.02), and TD (-0.24 ± 0.02). In conclusion, scrotal circumference showed the best response to selection among the traits studied and was favorably correlated with breeding soundness and sperm morphology in young Nellore bulls. © 2013 American Society of Animal Science. All rights reserved.

Filogeografia de Thoropa grupo miliaris (Anura: Cycloramphidae)

Pós-graduação em Biologia Animal - IBILCE

Evidências moleculares dos padrões evolutivos e filogeográficos de populações de Astyanax paranae (Pisces : Characidae) com base em caracteres do DNA mitocondrial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estimativa de componentes de (co)variância de características de crescimento na raça Brahman utilizando inferência bayesiana

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)