The accuracy of selection was theoretically evaluated when two records of different traits such as milk yield at different parities in dairy cattle were regarded as repeated records of a single trait because of their similar heritabilities and high genetic correlation. Initially, an equation for the accuracy of index selection for these two traits, r
IH, was decided. Then the accuracy of selection, r
ER, based on the total of the two records, was expressed as a function of repeatability and assumed heritability h
02 when two records of different traits were regarded as repeated records of a single trait. Furthermore, the accuracy of selection, r
RT, based on total records, was written using the true phenotypic and genetic parameters of the two traits. The ratios R
1 and R
2 were defined as r
ER/r
IH and r
RT/r
IH, respectively. In regard to the numerical evaluations of R
1 and R
2, the phenotypic, genetic and en- vironmental variances of traits 1 and 2 were assumed to be equal in Case I, Case II and Case III, respectively. Values between 0.1 and 0.5 were assigned to h
02. True heritability of the traits, h
12, h
22, changed under a practical restriction of h
12h
22 and h
12-h
02=h
02-h
22, i.e. h
02 is the mean of h
12 and h
22. The genetic and phenotypic correlations between them, rG, rp, were changed in realistic ranges. When the h
02 and h
12 were 0.1 and 0.11, respectively, the ratios RI took almost the same values in all three Cases and the ratios R
2 also showed nearly constant values in Cases I, II and III. However, when h
02 and h
22 were 0.1 and 0.15, respectively, R
1 in Case II was larger than the R
1s in Case I and Case III, and R
2 in Case II was smaller than the R
2s in Case I and Case III. When h
02 was 0.5, almost the same values for R
1 and R
2 were obtained in all three Cases. In Case II, R, increased with decreasing rG. When h
02 was 0.3 or 0.5, R
1 decreased only slightly with increasing h
12 and the effect of the change in rp on R
1 was small. However, when h
02 was 0.1, R
1 decreased with increasing h
12 and with increasing rp. R
2 decreased rapidly with increasing h
12 when h
02 was 0.1. The amount of decrease in R
2 with increasing h
12 was reduced as h
02 became higher, and when h
02 reached 0.5, R
2 hardly decreased. In most cases the changes in rG and rp did not largely affect R
2. The numerical evaluations suggested that the discrepancy between R
1 and R
2 was affected by the differences in heritability of the traits, and the levels of rG and rp between them when h
02 was low. These results futher suggested the need to evaluate the accuracy of selection based on different criteria when h
02 is low.
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