Genotype by environment interaction for production traits while accounting for heteroscedasticity.

Grazing (G) provides an alternative management system for dairy production. Heteroscedasticity (HV) of the data may bias estimates of genetic correlations of yield traits between environments, an indicator of genotype-by-environment interaction (GxE). The objective of this study was to investigate the effect of HV on estimates of heritabilities and genetic correlations for mature-equivalent milk, protein, and fat yield, and lactation-average somatic cell scores of daughters, and to determine if HV affects the ability of sire's predicted transmitting ability (PTA) to predict daughter production in G and confinement (C) herds. Data consisted of 72,489 records from 35,674 cows in 366 G herds from 11 states, and 117,629 records from 50,963 cows in 373 C herds from the same 11 states plus 1 geographically contiguous state. Herds were divided into variance quartiles (Q(V)1-Q(V)4) based on milk yield. A transformation was used to reduce HV by standardizing the within-herd standard deviation to the average across-herd standard deviation of a base year for each parity, and was similar to the method used in current USDA-DHIA genetic evaluations. Regression of daughter yield on sire PTA showed that PTA overestimated production of all traits in Q(V)1-Q(V)3 and of milk in Q(V)4 of G herds. For C herds, yields of milk in Q(V)1 and Q(V)2, and of protein and fat in Q(V)1 were overestimated, and protein was underestimated in Q(V)4. Reducing HV had little effect on G herds, but for C herds, regression did not differ from unity for milk and protein in Q(V)1 and Q(V)2. For milk, protein, and fat in G, heritabilities were approximately 0.17, 0.17, and 0.19, respectively. The heritabilities for milk, protein, and fat in C herds were approximately 0.16, 0.17, and 0.21, respectively. Genetic correlations between C and G did not suggest a GxE in 3 upper quartiles, but a possible GxE (correlation = 0.21, estimated standard error = 0.22) for the lowest quartile. Reducing HV did not affect estimates of heritabilities or genetic correlations. Results indicated that modest evidence for existence of GxE did not arise solely from HV.

Optimal contemporary group structure to maximize genetic progress through genetic evaluation of swine.

Accuracies of sire EPD were calculated for a typical growth trait and a typical maternal trait for alternative contemporary group structures. For a given family size (number of progeny tested for a sire in a contemporary group), accuracy increased as the number of sires increased and as the number of contemporary groups increased. An exponential equation was found to best predict accuracy from the number of sires and groups. Partial derivatives can be used to determine the optimal number of sires and groups for a given economic situation (fixed number of animals tested per group). It is recommended that progeny of at least two sires be represented in each contemporary group, but having more than five sires does not effectively increase accuracy further. Accuracy increases with a larger herd size, as more sires and more groups of pigs are tested. When the number of litters that can be tested is at its limit, accuracy is maximized with a small number of sires, and progeny divided among several contemporary groups. However, accuracy is only part of the herd's genetic improvement. Selection decisions must be made to avoid inbreeding, which can be a problem, particularly in small herds.

Efficacy of alternative multivariate best linear unbiased prediction models for genetic evaluation of swine.

A comparison of the accuracy of alternative BLUP evaluations of swine performance data is reported. A simulated data set of performance for days to market, backfat, number born alive, number weaned, and litter weight in six herds was used for the evaluation. The data structure was derived by using the performance records of six herds sampled from the American Yorkshire Club's STAGES (Swine Testing and Genetic Evaluation System) database. For growth traits, 10,360 pig records from 129 sires and 897 dams were recorded. For maternal traits, records on 2,598 litters of 1,209 sows from 147 sires and 585 dams were included. The actual observed performance of each record was removed and replaced with simulated performance. These simulated data were analyzed by within- and across-herd BLUP models using STAGES and Animal Model (AM) procedures. Results indicate that the alternative BLUP procedures produced similar estimates. Correlations between STAGES and AM EPD ranged from .84 to .95. Correlations between STAGES EPD and true genetic value (G) ranged from .41 to .74, and correlations between AM EPD and G ranged from .40 to .74. On average, AM EPD had a .04 larger correlation with G than did STAGES EPD, although the difference in the correlations was not significant (P greater than .05). Trends in EPD for sires, dams, and pigs or sows were the same. Likewise, standard errors of prediction for AM EPD averaged 4% smaller than those for STAGES EPD. Computationally, the AM procedures used 15 to 20 times as much processing time as did STAGES procedures.

Genetic improvement programs in livestock: swine testing and genetic evaluation system (stages).

Genetic evaluations for the U.S. swine industry are conducted by the eight purebred associations of the National Association of Swine Records. Within-herd evaluations of the growth traits (days to 105 kg [market] and backfat depth) were first reported in 1986. Analyses of the maternal traits (litter size at birth and weaning, and litter 21-d weight) were inaugurated in 1987. Expected progeny differences (EPD) are reported for all traits and for general, paternal, and maternal bioeconomic indexes. A sow productivity index combining only maternal traits is available. All records are adjusted according to National Swine Improvement Federation (NSIF) guidelines for effects such as number of pigs transferred at crossfostering and age at recorded observation prior to the BLUP evaluation. Within-herd analyses of individual contemporary groups are conducted immediately on receipt of performance records at each breed association office. All parents in the herd and the young pigs in the current group are evaluated. A report is returned to the breeder for use in herd selection and the EPD are placed in the pedigree file. The genetic base of each herd is defined as the first n tested pigs or litters, where n is the number of pigs registered annually within the herd. Change in mean EPD between groups is indicative of genetic trend. Periodic across-herd analyses are used to update interim within-herd analyses and a national sire summary is published.

Adapting best linear unbiased prediction (BLUP) for timely genetic evaluation: I. Progeny traits in a single contemporary group for each sex.

The first step of a procedure to partially circumvent the voluminous calculations with extremely large matrices for the usual algorithms for a BLUP (best linear unbiased prediction) approach is presented. This procedure, specific for a hierarchical portion of a model relevant to many animal breeding populations, is pertinent especially for polytocous species such as swine and poultry. For these, the occurrence of full-sib families makes the inclusion of dam effects in the model more necessary than in dairy or beef cattle models, where dam effects often are omitted. The formulas are derived for the hierarchical model for sires, dams within sires, individuals within full-sib family, and records within individuals, showing a relatively simple structure for such predictors. These formulas provide the basis for an alternative computing algorithm for obtaining evaluations having the statistical properties of best linear unbiased prediction. Formulas also are developed to approximate the prediction error variances for such models. Following this, the methodology for combining separate BLUP predictors, both error-independent and correlated, is developed.

Adapting best linear unbiased prediction (BLUP) for timely genetic evaluation: II. Progeny traits in multiple contemporary groups within a herd.

The second step of a procedure to partially circumvent the voluminous calculations for some BLUP (Best Linear Unbiased Prediction) computing algorithms for genetic evaluation is presented. In addition, the procedure allows timely evaluations of each contemporary group. This procedure is pertinent especially for polytocous species such as swine and poultry, for which the occurrence of full-sib families makes the inclusion of dam effects in the model necessary and tests are completed throughout the year. Formulas are developed for a model including sires, dams, individuals within full-sib families and records within individuals. This model has a fundamentally hierarchical structure but includes some cross-classification. The formulas for predictors combine information across contemporary groups within a herd and incorporate relationships between sires and(or) dams in that herd. Formulas to approximate prediction error variances also are developed.

Effects of culling on sire evaluations by mixed models.

The data consisted of the first two records for milk and fat yield of 677,800 daughters of 200 widely used Holstein sires. From these data, 10, 20, and 30% of second records were eliminated for least yield of milk in first lactation. Best Linear Unbiased Prediction evaluations of sires were obtained separately for both records and seconds only for culled and unculled groups and for all first records. Evaluations from second records were affected by culling with standard deviations for milk evaluations declining 58 kg as elimination of second records increased from 0 to 30%. Correlations between first and second milk evaluations declined from .84 to .70 as culling increased. Evaluations by both records showed little effect of culling with standard deviations declining only slightly with culling, and correlations among the evaluations close to unity. Adjustment of second evaluations for selection appeared to remove much effect of selection. Best Linear Unbiased Prediction evaluations and those based on the same daughters from Modified Contemporary Comparison procedures showed similar effects of culling and adjustment for culling and ranked bulls nearly identically.

Factors affecting stability of contemporary comparison evaluations of sires for milk yield.

Evaluations of sires for milk yield by contemporary comparison were used to determine factors associated with changes of evaluation over time. Changes in paired evaluations for 160 Holstein sires were final evaluations (Repeatability exceeding 90%) minus initial evaluations (Repeatability less than 70%). Multiple regression procedures were used to relate characteristics of initial sampling programs to changes in evaluations. Characteristics of initial evaluations associated with more stable evaluations included greater Repeatability for sires evaluated and for sires of contemporaries, higher producing, smaller sized herds with lower genetic merit of contemporaries, and less variation across herd-year-seasons in number of contemporary sires and producing ability of mates. Initial evaluations tending to increase over time were those from large herds of below average genetic merit (for contemporary sires) with greater than average variation in Repeatability of contemporary sires and less than average variance in number of contemporary sires and producing abilities of mates. Results suggested that most changes in evaluations of sires are from Mendelian sampling but that modest increases in stability of evaluations may be achieved through altered design of initial progeny testing programs.