Residual feed intake is defined as the difference between actual feed intake and that predicted on the basis of requirements for production and maintenance of body weight. Formulas were developed to obtain genetic parameters of residual feed intake from knowledge of the genetic and phenotypic parameters of the component traits. Genetic parameters of residual feed intake were determined for a range of heritabilities (h2 = .1, .3, or .5) for component traits of feed intake and production, and genetic (rg = .1, .5, or .9) and environmental (re = .1, .5, or .9) correlations between them. Resulting heritability of residual feed intake ranged from .03 to .84 and the genetic correlation between residual feed intake and production ranged from -.90 to .87. Heritability of residual feed intake depends considerably on the environmental correlation between feed intake and production. Residual feed intake based on phenotypic regression of feed intake on production usually contains a genetic component due to production. Residual feed intake based on genotypic regression of feed intake on production is genetically independent of production and its use is equivalent to use of a selection index restricted to hold production constant. Multiple-trait selection on residual feed intake, based on either phenotypic or genetic regressions, and production is equivalent to multiple-trait selection on feed intake and production. Residual energy intake in dairy cattle was examined as an example. Heritability of residual energy intake based on genotypic regression was close to zero and indicated that measurement of feed intake provides little additional genetic information over and above that provided by milk production and body weight. The principles outlined in this study have broader application than just to residual feed intake and apply to any trait that is defined as a linear function of other traits.

Studies involving the effects of single genes on quantitative traits may involve closed populations, selection may be practiced, and the quantitative trait of concern may also be influenced by background genes that are inherited in a polygenic manner. It is shown analytically that analysis of such data by ordinary least squares, the usual method of analysis, can lead to finding an excess of spurious significant effects of single genes, when no effect exists, for both randomly and directionally selected populations and can lead to bias in estimates of single-gene effects when selection has been practiced. The bias depends on heritability of the polygenic effects on the trait, selection intensity, mode of inheritance, magnitude of gene effect, gene frequency, and data structure. It is argued that when genotypes of individuals can be identified for all individuals with observations on the trait, use of mixed-model procedures under an animal model treating single-gene effects as fixed effects can provide unbiased estimates of single-gene effects and exact tests of associated hypotheses for pedigreed populations, even when selection is practiced. Results are illustrated through computer simulation.

Observations on 7416 Canadian Holstein cows were examined to estimate genetic parameters for the most common diseases of dairy cows. Mastitis, ovarian cyst, ketosis, milk fever, abomasal displacement, and culling that is due to reproductive failure or leg problems were analyzed as binomial traits, assuming an underlying threshold model that included fixed and random effects. Sire and residual components of variance were estimated by REML to provide heritability estimates from paternal half-sibs. A multiple-trait mixed model was also used to estimate genetic and environmental correlations between production and disease traits. Heritabilities of disease traits were relatively low and ranged from 0 to .15, except for displaced abomasum (h2 = .28). Evidence of genetic antagonism existed between incidence of mastitis and milk production. Incidence of milk fever was genetically associated with cows of lower genetic potential for production. Genetic associations between displaced abomasum and production traits were small, and estimates of genetic correlations between ovarian cyst and milk production were inconsistent across lactations. Ketosis was antagonistically associated genetically with production of milk and fat but was favorably associated with production of protein. The long-term cumulative effect of genetic selection against diseases might be useful to diminish their incidence.

Connectedness among management units (e.g., herds or regions) is of concern in genetic evaluation. When genetic evaluation is under an animal model, connections occur through A, the numerator relationship matrix. It is argued that the most appropriate measure of connectedness is the average prediction error variance (PEV) of differences in EBV between animals in different management units. It is shown that PEV of differences is influenced by average genetic relationship between and within management units, which in turn affects the variances of estimates of differences between management unit effects. When PEV of differences cannot be computed, use of one of three alternative measures is proposed; the gene-flow method that measures the exchange of genes between management units, measurement of genetic drift variance based on average relationships between and within management units, and measurement of the variance of estimated differences between management units effects. These were correlated with PEV of differences in a test simulation. The gene-flow method, which is simplest to compute, had the lowest correlation (.671). The drift variance and variance of management unit effects methods were highly correlated with PEV of differences (.924 and .995, respectively).

Genetic variances and covariances for the number of pigs born in total (NOBT), the number of pigs born alive (NOBA), and the number of weaned pigs (NOW) were estimated by REML under an animal model. Data on 30,357 and 42,041 litters born between 1977 and 1992 from Yorkshire and Landrace sows, respectively, were obtained from the Quebec Record of Performance sow productivity program. Data of the first four parities of litter size were used for four different analyses under an animal model: univariate analyses with direct genetic effects only, univariate analyses with maternal and direct genetic effects , seri0s of bivariate analyses with each parity treated as a different trait, and a series of bivariate analyses between NOBT, NOBA, and NOW within each parity. Heritabilities of different parities from univariate analyses under a direct genetic effects model ranged from .10 to .15, .09 to .14, and .06 to .08 for NOBT, NOBA, and NOW, respectively. Estimates of direct heritability from bivariate analyses between parties were consistent with estimates from univariate analyses in Landrace but not in Yorkshire. Genetic correlations between first and secondary parity in Yorkshire were .59, .49, and .17 for NOBT, NOBA, and NOW, and in Landrace were .90, .93, and .81, respectively. Influence of maternal effects on moderate correlations between first and secondary parity in Yorkshire was suggested. Genetic correlations averaged over all parities between NOBA and NOBT or NOW were .97 and .65 in Yorkshire and .97 and .82 in Landrace. A multiple-trait animal model with parities treated as different traits was recommended.