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Next, since there are four paths of selection for genetic improvement, such as sires to breed bulls (SB), sires to breed cows (SC), dams to breed bulls (DB), and dams to breed cows (DC) [4], we compared previously intended and actually practiced selection differentials for milk production and conformation traits for four paths of selection during the last two decades in Japan.
Linear regression analyses were performed on the selection differentials against the number of harvests to quantify increases in selection differential as a function of number of harvests.
Growth parameters [L.sub.[infinity]] and K jointly determine size-at-age, and it is on these parameters that we describe selection differentials. At the end of the simulation year, we computed a selection differential on each growth parameter as the percent difference between mean trait values ([L.sub.[infinity]] or K) of the unfished and fished parents.
There were some mitigating effects on the strength of selection by correlated characters as indicated by the slightly reduced selection differential, compared with the selection gradient.
Selection differentials in parents to be selected also increased, but could be realized in offspring after a period of time, which might be a source of the differences.
where [[??].sub.CS] is the estimate of the genetic gain with combined selection; C[??]v([CI.sub.ijk], [g.sub.ijk]) is the estimate of the additive genetic covariance between the scores of the combined selection index and the respective genetic values of the plants; [??] ([CI.sub.ijk]) is the variance of the selection index values; [SD.sub.CS] is the selection differential, obtained through the scores of the combined index.
Marker indices 7 and 8 included all markers that had a significant effect within a population, as determined by the individual marker tests, and had a selection differential with the proper sign as determined by Diaby and Casler (2005).
As noted, in the case of directional selection, the univariate coefficient, [Beta][prime], represents the regression slope of relative fitness on the standardized character as well as the selection differential, s[prime], which is the shift in the standardized population mean before and after selection.
This skewness will lead to a slight raising of the heritability estimate because, although both generation means and selection differentials suffer a decrease in their mean values, the latter are more affected by the skewed distribution, making the regression slope steeper.
Therefore, this estimate of broad-sense heritability overestimates the percentage of the selection differential that would be retained in a cycle of selection.

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