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In statistical modelling, the effects of singlenucleotide polymorphisms (SNPs) are often regarded as time-independent. However, for traits recorded repeatedly, it is very interesting to investigate the behaviour of gene effects over time. In the analysis, simulated data from the 13th QTL-MAS Workshop (Wageningen, The Netherlands, April 2009) was used and the major goal was the modelling of genetic effects as time-dependent. For this purpose, a mixed model which describes each effect using the thirdorder Legendre orthogonal polynomials, in order to account for the correlation between consecutive measurements, is fitted. In this model, SNPs are modelled as fixed, while the environment is modelled as random effects. The maximum likelihood estimates of model parameters are obtained by the expectation–maximisation (EM) algorithm and the significance of the additive SNP effects is based on the likelihood ratio test, with p-values corrected for multiple testing. For each significant SNP, the percentage of the total variance contributed by this SNP is calculated. Moreover, by using a model which simultaneously incorporates effects of all of the SNPs, the prediction of future yields is conducted. As a result, 179 from the total of 453 SNPs covering 16 out of 18 true quantitative trait loci (QTL) were selected. The correlation between predicted and true breeding values was 0.73 for the data set with all SNPs and 0.84 for the data set with selected SNPs. In conclusion, we showed that a longitudinal approach allows for estimating changes of the variance contributed by each SNP over time and demonstrated that, for prediction, the pre-selection of SNPs plays an important role.
Daughter yield deviations (DYDs) of bulls and yield deviations (YDs) of cows, besides estimated breeding values (EBVs), are standard measures of animals’ genetic merits in routine genetic evaluations worldwide. In this contribution, we first point out differences and similarities between DYDs and EBVs calculated for milk, fat and protein yields. While the latter measure represents the additive polygenic value of an animal, the former consists of both the additive polygenic and residual components. Then, a summary of DYDs and YDs calculated for the Polish population of dairy cattle is presented. The estimated correlations between DYDs and EBVs are generally high, but vary considerably depending on the minimum number of daughters used for calculation of DYDs and on the accuracy of calculated DYDs. Using DYDs estimated for each production year for 16 452 bulls, we demonstrate how to use DYDs for the validation of genetic trend estimated in the model used for genetic evaluation. Based on genotypic data of 252 bulls, we show that DYDs can be used for the estimation of candidate gene effects. For each of the yield traits, the within-bull genetic trend was relatively high, ranging between 1.39% of genetic standard deviation per production year for milk and 7.67% of genetic standard deviation per production year for fat, both in the 2nd lactation. Out of 8 polymorphisms tested, 5 showed a significant correlation with DYD, with the highest effect attributed to the polymorphism within the leptin receptor gene, whose additive effect was estimated as 247.33 kg of milk at 2nd parity.
Our study aims at statistical modelling of changes in the level of air pollution in the area of Szczawno Zdrój in Poland throughout the period of 1989-2003, which was marked by a decrease in coal production as well as by rapid increases in traffic intensity. Sulphur dioxide and the nitrogen dioxide were chosen as pollution indicators. Changes of the averaged concentrations across years are modelled by 5 regression models: linear, logarithmic, 2nd degree polynomial, 3rd degree polynomial and 4th degree polynomial. Changes in average yearly concentrations of pollutants during the 1980s and 1990s indicate considerable improvement of air quality regarding sulphur dioxide and nitrogen dioxide contents. A noticeable tendency toward a decrease in air pollution results from limiting of sulphur dioxide emission sources, which translates into liquidation of especially burdensome industrial plants, installation of devices for sulphur removal from fumes, and substantial reduction of air pollution coming from the Czech Republic and Germany.
In the future an approach incorporating cows’ measured phenotypes and marker genotypes of cows and bulls within a single model can be applied. The most important advantage of such a model is the simultaneous use of pedigree and marker-based genomic relationship data. Such a solution allows the use of both genotyped and non-genotyped animals in the prediction procedure. This pilot study is aimed towards implementation of a one-step approach in a random regression test day model context for the Polish Holstein Friesian population, considering various ways of adjusting the relationship matrix. Data consisted of 890 animals (10 genotyped bulls, 100 cows with phenotypic data and 780 ancestors without genotypes or phenotypes). Random regression test day models with a polygenic effect on milk yield modeled by second order Legendre polynomials for the estimation of variance-covariance parameters and were used for prediction of genomically enhanced breeding values (GEBV). In this model, a matrix combining pedigree and marker-based information was used instead of a traditional numerator relationship matrix. In this matrix the proportions of information coming from pedigree and markers were defined by weighting parameters w and 1-w for pedigree and marker-based information matrices, respectively. Various weights of the two sources of information were considered. The accuracy of GEBV both for genotyped bulls and for cows with phenotypes was highest for weighting parameter w=0 and lowest for w=l. Incorporating genomic information into a conventional genetic evaluation improves reliabilities of breeding value prediction, however, pedigree information is important to maintain the stability of evaluation for non-genotyped animals. Implementation of the single-step approach in a random regression test day model framework is very attractive for genomic prediction in dairy cattle, since it allows to incorporate genomic information directly into a conventional genetic evaluation. However, for accurate predictions it is essential to achieve the right balance between the numerator relationship and markers-based relationship information.
In statistical models, a quantitative trait locus (QTL) effect has been incorporated either as a fixed or as a random term, but, up to now, it has been mainly considered as a time-independent variable. However, for traits recorded repeatedly, it is very interesting to investigate the variation of QTL over time. The major goal of this study was to estimate the position and effect of QTL for milk, fat, protein yields and for somatic cell score based on test day records, while testing whether the effects are constant or variable throughout lactation. The analysed data consisted of 23 paternal half-sib families (716 daughters of 23 sires) of Chinese Holstein-Friesian cattle genotyped at 14 microsatellites located in the area of the casein loci on BTA6. A sequence of three models was used: (i) a lactation model, (ii) a random regression model with a QTL constant in time and (iii) a random regression model with a QTL variable in time. The results showed that, for each production trait, at least one significant QTL exists. For milk and protein yields, the QTL effect was variable in time, while for fat yield, each of the three models resulted in a significant QTL effect. When a QTL is incorporated into a model as a constant over time, its effect is averaged over lactation stages and may, thereby, be difficult or even impossible to be detected. Our results showed that, in such a situation, only a longitudinal model is able to identify loci significantly influencing trait variation.
A total of 306 boars (108 Large White and 198 Landrace) were genotyped for 52 candidate SNPs to determine which of the polymorphisms influence growth rate, meat content and selection index. The effects of SNPs were estimated by a mixed linear model including a random additive polygenic animal effect, fixed effects of SNPs including additive, and pairwise additive-by-additive epistases, year*season of birth, breed and RYR1 genotype. In order to estimate all possible pairwise SNP combinations without overparameterising the model a stochastic approach was adopted. A total of 1 350 replications of the model were generated, each containing five randomly selected SNPs. The final estimates of the fixed effects of the model equaled an average out of the replications. The hypothesis of a nonzero effect of SNP was tested by the Wald test. Among 4 257 estimates calculated, many significant (P<0.01), but mostly minor effects (below 1 phenotypic standard deviation) were recorded. The selected SNPs will be further investigated to determine which may be used in MAS.
The aim of the study was to fit the genomic evaluation model to Polish Holstein-Friesian dairy cattle. A training data set for the estimation of additive effects of single nucleotide polymorphisms (SNPs) consisted of 1227 Polish Holstein-Friesian bulls. Genotypes were obtained by the use of Illumina BovineSNP50 Genotyping BeadChip. Altogether 29 traits were considered: milk-, fat- and protein- yields, somatic cell score, four female fertility traits, and 21 traits describing conformation. The prediction of direct genomic values was based on a mixed model containing deregressed national proofs as a dependent variable and random SNP effects as independent variables. The correlations between direct genomic values and conventional estimated breeding values estimated for the whole data set were overall very high and varied between 0.98 for production traits and 0.78 for non return rates for cows. For the validation data set of 232 bulls the corresponding correlations were 0.38 for milk-, 0.37 for protein-, and 0.32 for fat yields, while the correlations between genomic enhanced breeding values and conventional estimated breeding values for the four traits were: 0.43, 0.44, 0.31, and 0.35. This model was able to pass the interbull validation criteria for genomic selection, which indicates that it is realistic to implement genomic selection in Polish Holstein-Friesian cattle.
The transmission-disequilibrium test (TDT) is a model-free method to detect linkage between a marker and a trait locus. Originally developed to map disease genes in human genetics, this statistic has been recently extended to deal with quantitative characters. The emphasis of current research is on investigating statistical properties of the test applied to data from livestock populations. For various constellations of sample parameters, it is shown via simulation that the empirically derived null hypothesis distribution of TDT remains in good agreement with its asymptotic distribution while its power is satisfactory only for very close linkage. TDT is then applied to a real data set from milk production data of a dairy cattle population.
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