Mathematical methods in the breeding evaluation of small  horned ruminants

2019 ◽  
Vol 14 (3) ◽  
pp. 101-110
Author(s):  
K. A. Katkov ◽  
L. N. Skorykh ◽  
V. S. Pashtetsky ◽  
P. S. Ostapchuk ◽  
T. A. Kuevda
Keyword(s):  
Statistical Methods ◽  
Mixed Model ◽  
Statistical Tests ◽  
Live Weight ◽  
Breeding Value ◽  
System Of Equations ◽  
Data Set ◽  
Breeding Values ◽  
Genetic Groups ◽  
Biometric Model

Aim. Traditionally, prediction of breeding values of male small horned ruminants   (rams) by referring to levels of economically useful traits of their progeny is carried  out by methods of statistical analysis. However, at the same time, there is a forecasting method based on the use of a mixed biometric model. The solution of the system  of equations constituting a mixed biometric model is associated with certain difficulties caused by the peculiarity of the system matrix. It is proposed to use integrated  mathematical packages in the forecast, by which the system of equations can be  solved in several ways, followed by analysis of the results. The prediction of progeny  values is carried out by statistical methods using three statistical tests, as well as with  the use of a mixed biometric model. It is of interest to compare estimates obtained  by using statistical methods with estimates using a mixed biometric model. Material and Methods. The initial data set was the live weight of Qigai rams, the  progeny of a group of sixteen rams belonging to eight genetic groups.   Results. It was found that the forecast of breeding values of each animal using a  mixed biometric model substantially clarifies the rank of each animal in the group  being evaluated.   Conclusion. The refinement of the estimation of breeding value is related to the  effects of the genetic groups to which the animals belong in the mixed model, as well  as the degree of relationship between them. Also the mixed model also allows one to  isolate environmental effects from the overall assessment. Solving the system of  equations in several ways will improve the reliability of the forecast.

An application of Bayesian techniques to the genetic evaluation of growth traits in Eucalyptus globulus

1998 ◽  
Vol 28 (9) ◽  
pp. 1286-1294 ◽  
Author(s):  
F Soria ◽  
F Basurco ◽  
G Toval ◽  
L Silió ◽  
M C Rodriguez ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Eucalyptus Globulus ◽  
Maximum Likelihood Estimates ◽  
Breeding Value ◽  
Likelihood Method ◽  
Phenotypic Correlation ◽  
Data Set ◽  
Breeding Values ◽  
Bayesian Techniques ◽  
Self Pollination

A Bayesian procedure coupled with Gibbs sampling was implemented to obtain inferences about genetic parameters and breeding values for height and diameter of 7-year-old Eucalyptus globulus Labill. is described. The data set consisted of 21 708 trees from 260 open-pollinated families taken from 10 different Australian provenances, from one Spanish population, and from two clones. The trees are distributed over eight sites in the south of Spain, with 20 blocks per site. Data were corrected for heterogeneity of phenotypic variances between blocks. In the analysis, a self-pollination rate of 30% for the open-pollinated families is assumed in the relationship matrix. The posterior means (and standard deviations) of the heritabilities of height and diameter and the genetic and phenotypic correlation were 0.217 (0.014), 0.128 (0.084), 0.768 (0.028), and 0.799 (0.003). Results from the standard restricted maximum likelihood method were 0.173, 0.113, 0.759, and 0.798, respectively. Most of the discrepancy in heritability estimates from both methods can be attributed to the adjustement of residual maximum likelihood estimates to the assumed self-pollination rate, which ignores the presence of clones in the trial. The effect of the method of prediction of breeding values (best linear unbiased prediction or Bayesian techniques) on the genetic superiority of the selected trees was not important. Differences in breeding value among provenances and among families were evidenced for both traits.

Repeatability and bias of estimated breeding values for dairy bulls and bull dams calculated from animal model evaluations

1993 ◽  
Vol 57 (2) ◽  
pp. 175-182 ◽  
Author(s):  
P. Uimari ◽  
E. A. Mäntysaari
Keyword(s):  
Animal Model ◽  
Dairy Cow ◽  
Relative Weight ◽  
Breeding Value ◽  
Potential Bias ◽  
Data Set ◽  
Breeding Values ◽  
Dairy Bulls ◽  
Estimated Breeding Values ◽  
Genetic Standard Deviation

AbstractAn animal model and an approximative method for calculating repeatabilities of estimated breeding values are used in Finnish dairy cow evaluation. Changes in estimated breeding values over time as daughters accumulate were studied. Special emphasis was given to the accuracy and potential bias in the pedigree indices of young sires. The data set used was the same as in the national evaluation and the traits investigated were protein yield and somatic cell count. The average repeatability in evaluation of bulls without daughters was 0·37. The empirical repeatability defined as a squared correlation between the pedigree index and the final sire proof was only 0·15. The reduction in the repeatability was attributed to the selection on pedigree index. The upward bias observed in pedigree indices was 5 kg (approx. 0·3 of genetic standard deviation). The bias was caused by the overestimation of bull dams' breeding value. Also the proofs of bull sires increased after the second crop of daughters. The correlation between the evaluations of the same sire calculated from two separate equal size daughter groups was 0·91 when the bull had 10 to 50 daughters and 0·87 with over 100 daughters. This illustrates how the relative weight of the pedigree decreases while more progeny information is accumulated in the evaluation.

scholarly journals Breeding value for type traits in beef cattle in theCzech Republic

2011 ◽  
Vol 50 (No. 9) ◽  
pp. 385-393 ◽  
Author(s):  
Z. Veselá ◽  
J. Přibyl ◽  
P. Šafus ◽  
L. Vostrý ◽  
K. Šeba ◽  
...  
Keyword(s):  
Fixed Effects ◽  
Genetic Correlations ◽  
Live Weight ◽  
Breeding Value ◽  
Body Measurements ◽  
Breeding Values ◽  
Production Type ◽  
Type Traits ◽  
Method Of Evaluation ◽  
Range Of Values

The type was evaluated in 5 424 young animals of twelve beef breeds. Ten type traits were evaluated: height at sacrum (HS), body length (BL), live weight (LW), front chest width (CW), chest depth (CD), pelvis (P), shoulder muscling (SM), back muscling (BM), rump muscling (RM) and production type (PT). The traits represent two groups: (1) traits scoring body measurements and body capacity (HS, BL, LW, CW, CD, P) and (2) traits scoring muscling (SM, BM, RM, PT). These fixed effects were included in the model: breed, sex, HYS, mother&rsquo;s age, linear regression on age at evaluation and average gain from birth to evaluation. Fixed effects in the model explained 40% to 60% of variability. The highest values of heritability coefficient were estimated for HS (h<sup>2</sup> = 0.51) and LW (h<sup>2</sup> = 0.50). BL had the lowest values of heritability coefficient (h<sup>2</sup> = 0.25). The values h<sup>2</sup> = 0.25&ndash;0.32 were calculated for the traits scoring body capacity (CW, CD, P). The range of values for muscling traits was h<sup>2</sup>&nbsp;= 0.26&ndash;0.35. The coefficient of heritability for PT was h<sup>2</sup> = 0.34. All traits scoring muscling and PT showed high genetic correlations (r<sub>g</sub> &gt; 0.95). The traits scoring body capacity (P, CW, CD) were highly genetically correlated with muscling r<sub>g</sub> &gt; 0.83. Breeding values were determined by a multi-trait animal model. Standard deviations of breeding values were higher in HS (s<sub>BV</sub> = 0.71) and LW (s<sub>BV</sub> = 0.84), which was connected with a different method of evaluation of these traits. They were in the range of 0.19 (BL) to 0.30 (RM) in the other traits. &nbsp;

scholarly journals Direct and Competition Additive Effects in Tree Breeding: Bayesian Estimation From an Individual Tree Mixed Model

2008 ◽  
Vol 57 (1-6) ◽  
pp. 45-56 ◽  
Author(s):  
E. P. Cappa ◽  
R. J. C. Cantet
Keyword(s):  
Environmental Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Phenotypic Variance ◽  
Tree Model ◽  
Data Set ◽  
Additive Variance ◽  
Individual Tree ◽  
Breeding Values ◽  
Competition Effects

Abstract An individual tree model with additive direct and competition effects is introduced to account for competitive effects in forest genetics evaluation. The mixed linear model includes fixed effects as well as direct and competition breeding values plus permanent environmental effects. Competition effects, either additive or environmental, are identified in the phenotype of a competitor tree by means of ‘intensity of competition’ elements (IC), which are non-zero elements of the incidence matrix of the additive competition effects. The ICs are inverse function of the distance and the number of competing individuals, either row-column wise or diagonally. The ICs allow standardization of the variance of competition effects in the phenotypic variance of any individual tree, so that the model accounts for unequal number of neighbors. Expressions are obtained for the bias in estimating additive variance using the covariance between half-sibs, when ignoring competition effects for row-plot designs and for single-tree plot designs. A data set of loblolly pines on growth at breast height is used to estimate the additive variances of direct and competition effects, the covariance between both effects, and the variance of permanent environmental effects using a Bayesian method via Gibbs sampling and Restricted Maximum Likelihood procedures (REML) via the Expectation- Maximization (EM) algorithm. No problem of convergence was detected with the model and ICs used when compared to what has been reported in the animal breeding literature for such models. Posterior means (standard error) of the estimated parameters were σ̂2Ad = 12.553 (1.447), σ̂2Ac = 1.259 (0.259), σ̂AdAc = -3.126 (0.492), σ̂2 p = 1.186 (0.289), and σ̂2e = 5.819 (1.07). Leaving permanent environmental competition effects out of the model may bias the predictions of direct breeding values. Results suggest that selection for increasing direct growth while keeping a low level of competition is feasible.

scholarly journals A Combined Analysis in Complementary Progeny Tests: Effects on breeding value accuracies

2016 ◽  
Vol 65 (1) ◽  
pp. 38-48 ◽  
Author(s):  
Eduardo P. Cappa ◽  
Michael U. Stoehr
Keyword(s):  
Mixed Model ◽  
Breeding Value ◽  
Forward Selection ◽  
Combined Analysis ◽  
Breeding Values ◽  
Mixed Model Approach ◽  
Additional Information ◽  
Genetic Entry ◽  
Sib Families ◽  
Progeny Tests

Abstract Complementary progeny tests allow for simultaneously ranking parents for their general combining ability (GCA) and within-family forward selection. To do this, progeny tests are established with different types of genetic entries (i.e., half-sib and full-sib seedlings, respectively), and different experimental designs. This study proposes a combined analysis of the GCA and full-sib (FS) tests using the mixed model approach to predict simultaneously the breeding values of grandparents, parents, full-sib families and offspring on the same scale. Moreover, a first order autoregressive spatial mixed model for the GCA tests was also implemented in the combined analysis. Our empirical study in coastal Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) shows that additional information provided from relatives and the overlap genetic entry among GCA and FS tests via the proposed combined analysis, improves the accuracies of breeding values compared to the non-combined analysis. The improvements in the accuracies of breeding values for backward and forward selections were generally modest. Spatial and combined analyses gave slightly better results than the non-spatial combined model.

Mixed model procedures for the Australian beef industry. 1. Multiple-trait model for estimation of breeding values for 200-day and final weights of cattle

1985 ◽  
Vol 36 (3) ◽  
pp. 527 ◽  
Author(s):  
H-U Graser ◽  
K Hammond
Keyword(s):  
Maternal Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Growth Traits ◽  
Breeding Value ◽  
Relationship Matrix ◽  
Beef Industry ◽  
Multiple Trait ◽  
Breeding Values ◽  
Numerator Relationship Matrix

A multiple-trait mixed model is defined for regular use in the Australian beef industry for the estimation of breeding values for continuous traits of sires used non-randomly across a number of herds and/or years. Maternal grandsires, the numerator relationship matrix, appropriate fixed effects, and the capacity to partition direct and maternal effects are incorporated in this parent model. The model was fitted to the National Beef Recording Scheme's data bank for three growth traits of the Australian Simental breed, viz 200-, 365- and 550-day weights. Estimates are obtained for the effects of sex, dam age, grade of dam, age of calf and breed of base dam. The range in estimated breeding value is reported for each trait, with 200-day weight being partitioned into 'calves' and 'daughters' calves', for the Simmental sires commonly used in Australia. Estimates of the fixed effects were large, and dam age, grade of dam and breed of base dam had an important influence on growth to 365 days of age. The faster growth of higher percentage Simmental calves to 200 days continued to 550 days. Estimates of genetic variance for the traits were lower than reported for overseas populations of Simmental cattle, and the genetic covariance between direct and maternal effects for 200-day weight was slightly positive.

scholarly journals The relationship between genetic merit for yield and live weight, condition score, and energy balance of spring calving Holstein-Friesian dairy cows on grass based systems of milk production

2001 ◽  
Vol 26 (2) ◽  
pp. 297-303
Author(s):  
F. Buckley ◽  
P. Dillon ◽  
M. Rath ◽  
R.F. Veerkamp
Keyword(s):  
Energy Balance ◽  
Reproductive Performance ◽  
Live Weight ◽  
Breeding Value ◽  
Pedigree Information ◽  
Feeding System ◽  
Data Set ◽  
Genetic Merit ◽  
Weight Condition ◽  
Condition Score

AbstractThe objective of this study was to estimate the effects of genetic merit for milk yield on energy balance (EB), dry matter intake (DMI), and fertility for cows managed on three different grass based feeding systems, and to estimate possible interactions between genetic merit and feeding system. Individual animal intake estimates were obtained at pasture on 11 occasions across three grazing seasons. The data set contained 96 first lactation animals in 1995, 96 second lactation animals in 1996, and 72 third lactation animals in 1997. Half of these animals were of high (HG), and half of medium genetic merit (MG) for milk solids production. Genetic effects for the traits of interest were estimated as the contrast between the two genetic groups, and by the genetic regression of phenotypic performance on the estimated breeding value for fat and protein yield, based on pedigree information alone (PI). Significant effects of feeding system were observed on yields, DMI and EB, whereas there was no effect on live weight, condition score or reproductive performance. The interaction between genetic merit and feeding system was not significantly different from zero for any of the traits. Yields, grass DMI, and total DMI were all higher for HG than for MG, and also positively correlated (P<0.001) with PI. Furthermore, condition score, conception to first and second service, and pregnancy rate were significantly negatively correlated with PI. While at pasture, EB was positively (P<0.01) correlated with PI, although the contrast between HG and MG was not significantly different from zero. Condition score changes during very early lactation, demonstrated that HG had a more negative EB than MG. The results clearly illustrate the production potential of HG cows on grass based systems, however the reduced reproductive performance questions their suitability for seasonal calving systems.

Breeding Value Estimation for Pigs in Closed Nucleus Herds

1988 ◽  
Vol 1988 ◽  
pp. 12-12 ◽  
Author(s):  
Naomi R. Wray
Keyword(s):  
Fixed Effects ◽  
Mixed Model ◽  
Phenotypic Selection ◽  
Breeding Value ◽  
Simultaneous Estimation ◽  
Genetic Trend ◽  
Traditional Methods ◽  
Breeding Values ◽  
Value Estimation ◽  
The Uk

Best Linear Unbiased Prediction (BLUP) is now the method of choice for the estimation of breeding values in dairy and beef populations. The advantages of this mixed model methodology over traditional methods are well documented and include the simultaneous estimation of fixed effects and prediction of random effects and the utilization of records from all relatives to predict an individuals breeding value. In addition, account is taken of genetic trend and of reduction in genetic variance due to selection. In Canada, BLUP is now used for breeding value estimation of pigs but the structure of the Canadian pig industry is one of many herds practising selection with the herds linked by a widespread use of artificial insemination. The advantages of BLUP have not been investigated for the situation of the UK pig industry where most selection is performed within closed nucleus herds.The objectives of this study were to use computer simulation to determine rates of response, accuracy of prediction and accummulation of inbreeding for pigs in closed nucleus herds when selection decisions were based on estimated breeding values (EBVs) derived from BLUP compared to more traditional methods of phenotypic selection and index selection.

Comparison of rolling front and discrete generation breeding strategies for trees

1998 ◽  
Vol 28 (7) ◽  
pp. 987-993 ◽  
Author(s):  
Nuno MG Borralho ◽  
Gregory W Dutkowski
Keyword(s):  
Stochastic Simulation ◽  
Mixed Model ◽  
Accurate Prediction ◽  
Breeding Value ◽  
Breeding Strategies ◽  
Breeding Values ◽  
Generation Interval ◽  
Value Estimation ◽  
Discrete Generation

Discrete generation and rolling front breeding strategies are compared in terms of gain and inbreeding over a period of 40 years using stochastic simulation. In the rolling front strategy, crosses are made between the best available trees in each year, and new progeny trials are established using the crosses done in the previous year, rather than waiting for all crosses in that generation to be completed. For a given amount of resources, the rolling front strategy resulted in 25-35% greater gains per year, mainly due to a shorter generation interval. Inbreeding was also higher in the rolling front, although gains per unit of inbreeding were consistently greater than with the discrete generation strategy. Despite the smaller size of trials and greater imbalance between trials in rolling front, the results suggest that breeding value estimation using mixed-model BLUP is robust enough to ensure accurate prediction of breeding values and maintain the advantage of the rolling front strategy.

Endogenous pulsing and stimulated release of growth hormone in dairy calves of high and low genetic merit

1993 ◽  
Vol 56 (1) ◽  
pp. 1-8 ◽  
Author(s):  
J. A. Woolliams ◽  
K. D. Angus ◽  
S. B. Wilson
Keyword(s):  
Growth Hormone ◽  
Jugular Vein ◽  
Live Weight ◽  
Dairy Calves ◽  
Regression Coefficients ◽  
Breeding Value ◽  
Genetic Groups ◽  
The Difference ◽  
Maintenance Requirements ◽  
Time Of Administration

AbstractFifty-five calves aged 105 days of age, of both sexes, belonging to two genetic groups (H, high or L, low) differing in their predicted breeding value (PBV) by 78 kg for fat plus protein yield, were individually penned for 3 weeks with the final 2 weeks on a diet designed to provide energy close to their maintenance requirements. The calves were then cannulated in the jugular vein and blood was sampled every 15 min for 25 h. Following this a growth hormone releasing factor (GRF) preparation was administered on up to four occasions, being one of (per kg live weight) either 0·2 or 0·4 μg GRF (treatments SGRF or DGRF respectively) or 0·2 μg thyrotropin releasing hormone (TRH). On each occasion blood samples were taken at −15, 4, 8,12,16, 20 and 45 min relative to the time of administration and up to four further occasions, one prior to and three within 32 min of administration. Samples were assayed for growth hormone (GH).GH concentration of troughs prior to an episode of GH release was 1·19-fold greater in H compared with L calves with concentrations decreasing to 0·9 of their previous values each h. Trough and peak concentrations had repeatabilities of 0·21 and 0·26 respectively (both P < 0·05). There was no association between PBV and either peak concentrations, number of pulses (4·84 per 25 h) or mean GH concentration (13·3 μg/l).GH released was only 1·11-fold greater after DGRF than SGRF. The difference in the regression coefficients for PBV between SGRF and DGRF was small, as it was for the difference between coefficients for the two sexes. The pooled coefficient was 0·00342 loge units per kg (s.e. 0·00157; P< 0·05) indicating a 1·31-fold greater response in H than in L calves. The correlation between responses to SGRF and DGRF was 0·482 and the repeatability of SGRF was 0·338; a pooled repeatability was estimated as 0·362(P < 0·01). The regression of GH release on PBV for TRH was 0·00345 (s.e. 0·00330). For all secretagogues, response depended on prior concentrations.It was concluded that GH release following GRF administration was positively related to PBV in dairy calves and response was moderately repeatable; furthermore, although aspects of endogenous secretion may be related to PBV they suffer from measurement difficulties.

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