### INTRODUCTION

### MATERIALS AND METHODS

*p*

*).*

_{SD}*n*refers to the number of daughters per young bull,

*P*is the test capacity for the progeny testing program, t is the rate of cow population registered for milk recording in Iran and

*rr*

*and*

_{sd}*rr*

*are replacement rates in SD pathway and in cows, respectively. The numeric values of these parameters for the typical situation in Iran are summarized in Table 1. The value of*

_{f}*d*

*and*

_{sex}*In*

*, and consequently the*

_{sex}*p*

*, was calculated depending on the applied strategy as follows:*

_{SD}*d*= number of vials of sperm accessible from a proven bull per year;

*FH*= the rate of heifers in the population;

*Inc*= average number of service per conception in cows;

*CPRates2*= cumulative pregnancy rate up to the second service in strategy S2;

*CPRates*= cumulative pregnancy rate in the first service in strategy S1;

*Inh*= number of services per conception in heifers after insemination with conventional semen;

*Inhsex*= number of services per conception in heifers after insemination with sex sorted semen. The cumulative pregnancy rate was calculated according to formulas in Joezy-Shekalgorabi and Shadparvar [21].

*d*) by 3.5 was that we assumed that for supplying a vial of sex sorted semen, about 3.5 vials of conventional semen was necessary (De Jarnette, personal communication).

*CRstoc*) varied from 50% to 90%. The conception rate of sex sorted semen was therefore obtained by multiplying the conventional semen conception rate and

*CRstoc*. Also, in all scenarios, conception rate of conventional and sexed semen was assumed constant over consequent services. The

*p*

*was estimated for the 3 strategies and for different values of conception rates. The results were compared to a control strategy (CC strategy), where no sex sorted semen was applied for heifers.*

_{SD}*p*

*given the input parameters (i.e.*

_{SD}*CRconh*and

*CRstoc*), we also tried to find the optimum equation that fit equitably to the trend line obtained in various strategies.

### RESULTS AND DISCUSSION

*p*

*in sexed semen based strategies are illustrated via 3D plots and counter plots in Figures 1 to 3. The value of the*

_{SD}*p*

*in all scenarios of the CS strategy was greater than that of the S2 and S1 strategies. The range of variation in*

_{SD}*p*

*was about 21.84% to 30.9%, 21.02% to 22.43%, and 19.1% to 20.72% for strategies CS, S2 and S1, respectively. The value of*

_{SD}*dsex*was constant when continuously utilizing of sex sorted semen. The values of

*Insex*decreased when

*CRstoc*and

*CRconh*were increased. Due to the direct relation of between selection proportion and

*Insex*, the trend of changes in

*p*

*was similar to the trend for the number of services per conception. In the S2 strategy, the increase in conception rate of sexed versus conventional semen led to an initial increase followed by a subsequent decrease in the*

_{SD}*p*

*(Figure 2) while in the S1 strategy, the increase in*

_{SD}*CRstoc*led to an increase in the selection proportion. Different (direct and reverse) relations of

*Insex*and

*dsex*with

*p*

*was the reason for different trend lines of S2 and S1 strategies, compared with CS strategy.*

_{SD}*p*

*considering all effective parameters (*

_{SD}*i.e.*conception rate of conventional semen in heifers, the rate of conception rate of sexed vs conventional semen) are presented in Table 2. All the strategies were equitably fitted to a second order paraboloid equation (adjusted

*R*

^{2}was greater than 90%) which indicates the possibility of predicting

*p*

*with a reasonable accuracy. The predicted trend line equations for the S2 and S1 strategies were more similar to each other, compared to the predicted trend line equation for the CS strategy.*

_{SD}