[Predicting the breeding value of bulls when selecting them according to the characteristics of their progenitors].
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Theoretical approaches to the estimation of shaping processes intensity in the early ontogenesis in poultry based on the parameters of growth intensity and uniformity have been considered. It is shown that the indices of growth uniformity defined during the 1st-3rd weeks of life have a significant correlation with the final live weight at the age of 7-8 weeks. This opens new prospects in prediction of the poultry flesh productivity.
An equivalent model for multibreed variance covariance estimation is presented. It considers the additive case including or not the segregation variances. The model is based on splitting the additive genetic values in several independent parts depending on their genetic origin. For each part, it expresses the covariance between relatives as a partial numerator relationship matrix times the corresponding variance component. Estimation of fixed effects, random effects or variance components provided by the model are as simple as any model including several random factors. We present a small example describing the mixed model equations for genetic evaluations and two simulated examples to illustrate the Bayesian variance component estimation.
Body measurements on Angus- (n = 374) and Polled Hereford-sired (n = 438) calves were used to quantify calf shape via multivariate factor analysis, and measurements on Polled Hereford-sired calves were further used to investigate relationships between calf shape and sire expected progeny differences (EPD) for birth weight and first-calf calving ease. Calf birth weight, head circumference, shoulder width, hip width, heart girth, cannon bone circumference and length, and body length were recorded at 24 h postpartum. Sire birth weight EPD was positively associated (P less than .05) with all calf measures but only with head and cannon circumference after adjustment for phenotypic birth weight and gestation length. Thus, at constant birth weight, calves from higher birth weight EPD bulls tended to have larger cannon and head circumferences. Calving ease EPD was negatively related (P less than .05) to all calf measures except shoulder width. After adjustment for birth weight, only cannon circumference was associated with calving ease EPD, and this effect was removed by additional adjustment for birth weight EPD. Thus, at constant birth weight, bulls with higher EPD for calving ease sired calves with smaller cannon circumference, but at constant birth weight EPD, body measures were not associated with calving ease EPD. Factor analysis defined underlying skeletal width and frame components of shape (independent of birth weight) for both sire breeds. Calf shape differed among sires and was in part explained by birth weight EPD. No additional variation in shape was explained by calving ease EPD. Calf shape seemed to add no information for prediction of dystocia to that provided by birth weight EPD.
Genetic trends for weaning weight were evaluated in 15 purebred herds in the United States participating in the Angus Herd Improvement. Records production testing program. Regression techniques were used for separate estimates of sire and dam contributions that were summed to estimate total herd trend. Sire contributions, calculated as the pooled within sire regression of weaning weight ratio on year of calf birth, ranged from .01 +/- .23 to 1.30 +/- .24 across the herds and average .51 ratio units/yr. Dam contributions, estimated as the pooled within dam regression of offspring weaning weight ratio, deviated from the contemporary paternal half-sib average ratio, on year of calf birth, ranged from .06 +/- .06 to .68 +/- .11 and averaged .34 ratio units/yr. A positive trend in direct effects was associated with a possible negative trend in maternal effects. The annual trend within herds ranged from .21 to 1.50 ratio units and averaged .85 units over all herds, representing 1.8 kg annual genetic gain in weaning weight.
Continuous genetic evaluation of dairy cattle with test-day models is desired in Finland. However, the computing time for the genetic evaluation is 4 d and exceeds the minimum of a weekend. Three parallel implementations of the preconditioned conjugate gradient iterative solver were programmed and compared to identify the best strategy for solving mixed model equations using parallel computing. The programs were used to solve two random regression test-day models with approximately 7.28 and 49.9 million unknowns. The latter model will be used in the Finnish dairy cattle evaluation. Computing times for the smaller model with the four processors available were 52, 32, and 27% of the single processor program when the complexity of the parallel program was increased. In practice, the best program required the most programming because the other parallel programs could not solve the larger model because of excess memory requirements. Parallel computing with four processors reduced the time to obtain solutions of Finnish dairy cattle evaluations to under 2 d. Benefit from parallel computing will be increased if amount of computing memory is increased.
An algorithm for estimating variance components (Method R) based on the linear regression coefficient (R) of recent (more accurate) on previous (less accurate) individual genetic predictions is presented. The previous prediction is obtained by analyzing a subsample of the whole data set. First raw moment of R equals 1 regardless of the distribution of observations and predictions. A condition such as the use of inappropriate variance components ratio (VC) can cause this regression to deviate from its expectation. If the computed R (Rc) is greater than 1, then VC ratio has been underestimated, and if Rc is less than 1, then VC ratio has been overestimated. Several iterations are performed, changing the VC ratio at each iteration, until Rc approximately equal to 1. When an Rc is obtained that is acceptably close to 1 (precision is reached), then the appropriate VC has been used. Method R does not require computation of the inverse of the coefficient matrix and has desirable properties of convergence, precision, and computing feasibility. Additional sampling variance in the estimate of VC is expected due to the requirement of taking a subsample of the entire data set to obtain the lower accuracy predictions. This sampling variance is shown to be small for simulated datasets of size n = 10,000 with no selection.
For models with only additive direct genetic effects, the rules of Westell combined with the Q-P transformation can be used to calculate the coefficients of mixed-model equations corresponding to the inverse elements of the numerator relationship matrix and group effects that are used to account for selection on ancestors that do not have records. Groups generally can be assigned on the basis of most recent ancestors without records. When maternal effects are in the model, most recent female ancestors without records contribute maternal effects to their progeny. If the vectors for additive direct and maternal effects do not include the same animals, numerator relationship matrices for direct and maternal effects and between direct and maternal effects are different. Even if they are the same, the Q-P transformation and Westell's rules do not lead to simplification for calculation of the coefficient matrix unless group assignment is the same for direct and maternal effects. This result can be achieved by including each female ancestor with offspring having records in both vectors and by assigning both of her parents to the same group she would have been assigned for a model including only direct effects. This strategy is equivalent to assigning group effects similarly for both direct and maternal effects and allows making use of the computational efficiency available from the Q-P transformation and Westell's rules, which are similar to Henderson's rules for calculating the inverse of the numerator relationship matrix.
Genotypes at a marker locus give information on transmission of genes from parents to offspring and that information can be used in predicting the individuals' additive genetic value at a linked quantitative trait locus (MQTL). In this paper a recursive method is presented to build the gametic relationship matrix for an autosomal MQTL which requires knowledge on recombination rate between the marker locus and the MQTL linked to it. A method is also presented to obtain the inverse of the gametic relationship matrix. This information can be used in a mixed linear model for simultaneous evaluation of fixed effects, gametic effects at the MQTL and additive genetic effects due to quantitative trait loci unlinked to the marker locus (polygenes). An equivalent model can be written at the animal level using the numerator relationship matrix for the MQTL and a method for obtaining the inverse of this matrix is presented. Information on several unlinked marker loci, each of them linked to a different locus affecting the trait of interest, can be used by including an effect for each MQTL. The number of equations per animal in this case is 2m + 1 where m is the number of MQTL. A method is presented to reduce the number of equations per animal to one by combining information on all MQTL and polygenes into one numerator relationship matrix. It is illustrated how the method can accommodate individuals with partial or no marker information. Numerical examples are given to illustrate the methods presented. Opportunities to use the presented model in constructing genetic maps are discussed.
The effects of inbreeding, heterosis, recombination loss, and percentage Holstein on the estimation of predicted transmitting abilities for fertility traits (calving interval, number of days from calving to first insemination, nonreturn rate, number of inseminations) and correlated traits (milk yield at test nearest d 110 and body condition score) were examined in a mixed population of Holstein and Friesian cattle. An unfavorable effect of percentage Holstein on calving interval was observed, resulting in a 12-d increase for pure Holsteins compared with pure Friesians. Insemination traits were less affected by percentage Holstein, with 3% more animals returning to first service within 56 d and 0.1 more inseminations required for Holstein animals. Heterosis and recombination loss affected some of the traits. Heterosis had a favorable effect on yield, with a 0.35-kg difference between a pure and cross-bred animal for test milk. There was a reduction of 1 d to first insemination between a pure and first-crossbred animal. Inbreeding had a significant and unfavorable effect on all traits. The difference between a noninbred animal and an animal with an inbreeding coefficient of 10% was a 2.8-d increase in calving interval, a 1.7-d increase in days to first insemination, a 1% increased probability to return to estrus at first service, 0.03 more inseminations, a 0.27-unit decrease in body condition, and a 0.54-kg decrease in milk on test nearest d 110. The effect of inbreeding depression was more pronounced at higher levels of inbreeding. The rank correlations between the predicted transmitting abilities for fertility and correlated traits, with and without the additional nonadditive effects in the model, were over 0.99. Steps should be taken to control the rise in inbreeding, or the effects on fertility and correlated traits such as milk production will begin to manifest themselves.
The objective of this study was to determine the feasibility of genetic selection for health traits in dairy cattle using data recorded in on-farm herd management software programs. Data regarding displaced abomasum (DA), ketosis (KET), mastitis (MAST), lameness (LAME), cystic ovaries (CYST), and metritis (MET) were collected between January 1, 2001 and December 31, 2003 in herds using Dairy Comp 305, DHI-Plus, or PCDART herd management software programs. All herds in this study were either participants in the Alta Genetics (Watertown, WI) Advantage progeny testing program or customers of the Dairy Records Management Systems (Raleigh, NC) processing center. Minimum lactation incidence rates were applied to ensure adequate reporting of these disorders within individual herds. After editing, DA, KET, MAST, LAME, CYST, and MET data from 75,252 (313), 52,898 (250), 105,029 (429), 50,611 (212), 65,080 (340), and 97,318 (418) cows (herds) remained for analysis. Average lactation incidence rates were 0.03, 0.10, 0.20, 0.10, 0.08, and 0.21 for DA, KET, MAST, LAME, CYST, and MET (including retained placenta), respectively. Data for each disorder were analyzed separately using a threshold sire model that included a fixed parity effect and random sire and herd-year-season of calving effects; both first lactation and all lactation analyses were carried out. Heritability estimates from first lactation (all lactation) analyses were 0.18 (0.15) for DA, 0.11 (0.06) for KET, 0.10 (0.09) for MAST, 0.07 (0.06) for LAME, 0.08 (0.05) for CYST, and 0.08 (0.07) for MET. Corresponding heritability estimates for the pooled incidence rate of all diseases between calving and 50 d postpartum were 0.12 and 0.10 for the first and all lactation analyses, respectively. Mean differences in PTA for probability of disease between the 10 best and 10 worst sires were 0.034 for DA, 0.069 for KET, 0.130 for MAST, 0.054 for LAME, 0.039 for CYST, and 0.120 for MET. Based on the results of this study, it appears that genetic selection against common health disorders using data from on-farm recording systems is possible.
Individual observations are routinely used in livestock evaluations. In some cases, pooled data representing the joint but not individual performance of a group of animals may be available. For example, pooled feed intake may be measured on a pen of livestock. The usual mixed model approach to genetic evaluation can still be applied as an exact method in this setting, provided incidence and residual variance-covariance matrices are suitably modified to account for the pooling. Approximate evaluations may be achieved by treating average performance as if it pertained to each individual in the pool. Theoretical accuracies can be obtained as a function of elements of the inverse coefficient matrix. A 3-generation data set representing 1,000 animals with feed intake observations from 49 sires and 200 maternal grand sires was simulated with heritability of 0.34. Individual records were pooled to represent circumstances in which animals with records were collectively measured. Animals were allocated into pens at random, by sire, or by maternal grand sire. Simulation was replicated with unique fixed effects for each pen. Following evaluation from each method, the empirical accuracy or product-moment correlation between true (simulated) and estimated merit could be quantified. The analysis of individual observations resulted in empirical accuracy of 0.63 for animals on test and 0.77 for their sires. Pooling the observations in pens of 2, 4, or 12 animals reduced empirical accuracies for animals on test to 0.50, 0.41, and 0.21 when pooling was at random and 0.53, 0.47, and 0.34 when pooling was by sire. Simulating a fixed pen effect representing 10% phenotypic variation, but ignoring that effect in the evaluation minimally reduced empirical accuracies to 0.52, 0.46, and 0.33 when pooling by sire. Theoretical accuracies were in close agreement with empirical accuracies when the exact method was used. The approximate method that treated averages of pooled data as if they were individually observed overstated accuracy and should not be used. Selection on the basis of pooled observations can be almost as effective as using individual observations when pool sizes are small. The exact method to account for pooled data is no more complex than conventional procedures.
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Although cassava is a major food crop, its scientific breeding began only recently compared with other crops. Significant progress has been achieved, particularly in Asia where cassava is used mainly for industrial processes and no major biotic constraints affect its productivity. Cassava breeding faces several limitations that need to be addressed. The heterozygous nature of the crop and parental lines used to generate new segregating progenies makes it difficult to identify parents with good breeding values. Breeding so far has been mainly based on a mass phenotypic recurrent selection. There is very little knowledge on the inheritance of traits of agronomic relevance. Several approaches have been taken to overcome the constraints in the current methodologies for the genetic improvement of cassava. Evaluations at early stages of selection allow for estimates of general combining ability effect or breeding values of parental lines. Inbreeding by sequential self-pollination facilitates the identification of useful recessive traits, either already present in the Manihot gene pool or induced by mutagenesis.
When improvement is desired for several traits that may differ in variability, heritability, economic importance, and in the correlation among their phenotypes and genotypes, simultaneous multiple-trait index selection was more effective than independent culling levels or sequential selection. Such comparisons required definition of aggregate breeding value determined jointly by breeding values and economic importance of the component traits. The economic weight should approximate the partial regression of cost per unit of enterprise output value on breeding value for each trait. These can vary with production and marketing system, with performance of traits, and with breed role (i.e., paternal, maternal, or general) in crossbreeding systems. Genetic gains desired to maintain competitive ranking also may define the relative importance of traits. Because information available to estimate breeding values varies among the ages and categories of individuals under selection and because means are unknown, regressed (BLUP) predictions of trait breeding values are useful. They allow appropriate economic weights to be applied as the last step for predicting aggregate breeding values for individuals of different age classes, and they simplify choosing the proportions of selected breeders from each age class that maximize rate of change in aggregate breeding values. Inappropriate economic weights or errors in the parameters used to predict trait breeding values overestimate realized response in true aggregate breeding value.
1. We investigated the use of monthly production records for genetic evaluation of laying hens, derived from a test day model with random regression in dairy cattle and compared it with other models. 2. Records of 6450 hens, daughters of 180 sires and 1335 dams, were analysed using a model with restricted maximum likelihood (REML): traits considered were monthly and cumulative egg production. Five models were studied: (1) random regression with covariates derived from the regression of Ali and Schaeffer (Canadian Journal of Animal Science, 67: 637-644, 1987) (RRMAS), (2) random regression with covariates derived from quartic polynomial (RRMP4), (3) fixed regression with covariates derived from Ali and Schaeffer (FRM), (4) multiple trait (MTM) and (5) cumulative (CM). 3. The models were compared on the basis of Spearman rank correlations of individual breeding values and sire breeding values estimated from subsets of full-sib split data. The hens (about 10% per generation) which ranked highest on their estimated breeding values from different models were compared phenotypically with their full records. 4. The estimates of heritability resulting from RRMP4 were biased upward from the estimates obtained from MTM, so this model was discarded. The heritabilities for monthly productions from RRMAS and MTM showed a similar pattern. They were high for the 1st month of production, decreased to their lowest value at about month 5 of production and increased again to the end of lay. 5. Spearman rank correlations between animal breeding values estimated by monthly models (RRMAS, FRM and MTM) were high, between 0.91 and 0.98, whereas those between estimates of monthly models and CM were lower, from 0.85 to 0.87. The correlations estimated either from intermittent months of measurements (odd vs even months) or full records were generally high, from 0.93 to 0.99. Information from odd months of production could be sufficient for cost-efficient recording schemes. The RRMAS generally had the highest correlation of sire breeding values between subsets of full-sib records, followed by MTM, RM and CM. Monthly models selected hens with higher productivity than the cumulative model. 6. In conclusion, genetic evaluation based on monthly production may be better than using cumulative production and RRMAS appeared to be the best among the models tested here.
Many morphological and life-history traits show phenotypic plasticity that can be described by reaction norms, but few studies have attempted individual-level analyses of reaction norms in the wild. We analyzed variation in individual reaction norms between laying date and three climatic variables (local temperature, local rainfall, and North Atlantic Oscillation) of 1126 female collared flycatchers (Ficedula albicollis) with a restricted maximum likehood linear mixed model approach using random-effect best linear unbiased predictor estimates for the elevation (i.e., expected laying date in the average environment) and slope (i.e., adjustment in laying date as a function of environment) of females' reaction norms. Variation in laying date was best explained by local temperature, and individual females differed in both the elevation and the slope of their laying date-temperature reaction norms. As revealed by animal model analyses, there was weak evidence for additive genetic variance of elevation (h2 +/- SE = 0.09 +/- 0.09), whereas there was no evidence for heritability of slope (h2 +/- SE = 0.00 +/- 0.01). Selection analysis, using a female's lifetime production of fledglings or recruits as an estimate of her fitness, revealed significant selection for a lower phenotypic value and breeding value for elevation (i.e., earlier laying date at the average temperature). There was selection for steeper phenotypic values of slope (i.e., greater plasticity in the adjustment of laying date to temperature), but no significant selection on the breeding values of slope. Although these results suggest that phenotypic laying date is influenced by additive genetic factors, as well as by an interaction with the environment, selection on plasticity would not produce an evolutionary response.
Bovine lymphocyte antigens of class I were defined for 434 AI bulls of Norwegian Cattle, which is a dual purpose breed. The antigens w16, A2, and A8 occurred at highest frequencies. A gene substitution model was used to compare bovine lymphocyte antigens with total breeding value and breeding values for milk yield, milk fat percentage, milk protein percentage, and meat production. Several bovine lymphocyte antigens were significantly associated with the traits in question: low fat percentage was associated with A8, A10(w50), and A11; high milk protein percentage with A13; and low meat production with the rare antigen w1. Associations of the bovine lymphocyte antigens and milk yield were not significant.