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).

Direct (D) and maternal (M) parameters for birth weight (BW), preweaning gain (WG) and calving ease (CE) were estimated for Angus (AN), Hereford (HE), Charolais (CH), Simmental (SM) and Shorthorn (SS). Data for the study were collected by Agriculture Canada from 1973 to 1983 for use in the National Sire Monitoring Program. Variances were estimated for each breed by a modified Method IV applied to a sire-maternal grandsire model with herd-year-seasons and age of dam × sex of calf as fixed effects. Genetic correlations (D/M) between D and M effects for WG in AN, HE, SS, CH and SM were −0.54, −0.42, −0.14, −0.26 and −0.45, respectively. Corresponding estimates of direct heritability for WG were 0.39, 0.30, 0.39, 0.27 and 0.43 and of maternal heritability 0.21, 0.27, 0.26, 0.16 and 0.20. Estimates for BW were similar to those for WG. Estimates of the D/M correlation for CE were −0.43, −0.15, −0.32, −0.74 and −0.27, of the direct heritability 0.28, 0.17, 0.19, 0.33 and 0.21, and of the maternal heritability 0.22, 0.13, 0.19, 0.23 and 0.27 for AN, HE, SS, CH and SM, respectively. Genetic trend and the introduction of new genetic lines are expected to have influenced parameter estimates. Due to negative D/M correlation estimates and moderate maternal heritabilities, selection for both the D and M components of maternal traits is advised. Key words: Variance, direct, maternal, heritability, genetic correlation, beef cattle