Using Embryo Sexing Within Closed Mixed Multiple Ovulation and Embryo Transfer Schemes for Selection on Dairy Cattle J. J. COLLEAU Station de Gh6tique quantitative et appliqub lnstiM National de la Recherche Agronomique R8352 Jouy-enJosas Cedex, France ABSTRACT
Two types of multiple ovulation and embryo transfer schemes that included bull progeny testing were compared. In the juvenile schemes, embryos were collected at 16 to 18 mo of age without sexing, whereas, in the adult schemes, donors were chosen based on their first lactation record, and their embryos were systematically sexed. With the latter schemes, natural calves obtained at the first two calvings could compete with embryo transfer calves to be replacements. The optimal structure of this scheme was derived algebraically for the same number of transferred embryos as in the juvenile schemes. Predicted asymptotic annual genetic gains, after stabilization of genetic parameters taking into account the Bulmer effect, were found to be slightly in favor of the adult schemes for a given set of parameters (overall number of transferred embryos, number of embryos per collection, and embryo survival rate). In the adult schemes, the nucleus sizes were much larger than in the juvenile schemes, which allowed a higher selection differential on male paths, thus compensating for the longer generation interval. Asymptotic rate of genetic gain for Monte Carlo simulations were about 10 and 7% lower for juvenile and adult schemes, respectively, but still higher (20%) than the predicted value for the corresponding conventional scheme. Consequently, adult schemes with embryo sexing can be an efficient dter-
Received December 26, 1990. Accepted h4ay 30, 1991.
1991 J Dairy Sci 74:397>3984
native to juvenile schemes without embryo sexing. (Key words: genetic gain, biotechnology, multiple ovulation and embryo transfer, embryo transfer)
Abbreviation key: ET = embryo transfer, MOET = multiple ovulation and embryo transfer. INTRODUCTION
Since the pioneering work of Nicholas (10) and Nicholas and Smith (ll), increasing attention has been paid to nucleus breeding schemes using embryo transfer (ET) extensively, commonly referred to as multiple ovulation and embryo transfer (MOET) schemes. Some semiconservative adaptation of these proposals to retain progeny testing of d a q bulls in AI have been studied (2, 3, 4, 5). These "hybrid" or "mixed" MOET were shown to increase the rate of genetic gain substantially (20% or more) over that attainable in conventional selection schemes. As expected, rates of gain did not equal those in intensive true MOET, especially the juvenile ones. The objectives of this study were 1) to examine the impact that embryo sexing might have on rates of genetic gain in mixed MOET, 2) to compare deterministic and Monte Carlo simulation estimates of genetic gains under a Bulmer model, and 3) to examine optimal alternative breeding schemes. The evaluation procedure used here assumed an asymptotic linear rate of genetic gain. Strictly speaking, in the context of an assumed infinitesimal model, this implied that the sole correction to the usual overestimation according to Rendel and Robertson (12) would be accounting for the linkage disequilibrium induced by selection, i.e., the Bulmer effect (1). Indeed, accounting for losses of genetic variance through drift and inbreeding would not lead to an asymptotic linear rate of genetic gain (13, 14, 16, 17). 3973
3974
COLLEAU
TABLE 1. Input parameters used for predicting the efficiency of a conventional breedhg scheme. ~~
Variable
Value
Genetic parametas Heritability Repcatability Genetic correlation between lactations Population parameters J . tedfeanalcs Recorded AI bred females 5% Heifas sired by bulls on test Age at fmt calving Interval between calvings Number of AI to get a calf Overall c d m g rate up to 2 yr of age 96 Recorded cows from 1st to loth lactation Sire-son path Number of progeny-tested bull sires Usage period sirdaughter path Number of young bulls entering the AI center Number of young bulls actually progeny-tested Age when first proven Number of proven sires usage period Dam-son path Number of dams needed per young bull Minimum number of required lactations Damdaughter path % Culling on yield betweea lactation 1 and 2
MATERIALS AND METHODS
.25 SO 1
~ , O O 0 200,000
10% 2 F
IF 1.7
15% 26, 21, 17, 13. 9. 6. 4. 2. 1, 1 3 lyr 130 100 5.5 yr 13 lyr 6 3 33%
females were superovulated as young heifers after matings to bull sires. Replacement females and young bulls for conventional Reference Conventlonal Scheme progeny testing are selected from natural and This scheme was the same as that of Col- ET-born calves when they are 6 to 8 mo of leau (3). This progeny testing scheme, samp- age, based on their dam’s performance in the ling 100 bulls& to select 13% as proven, with first 6 mo of first lactation. The time schedule 3 sires of bulls/yr in a 400,OOO breeding female and the population parameters involved are population, was used as a point of reference shown in Table 2. The full description is given for comparisons. Specific parameten are in by Colleau (3). Table 1 with greater detail presented by ColIn this kind of breeding scheme, selection leau (3). This scheme was predicted to gener- decisions on young females or males should be ate an annual genetic gain of .177 initial ge- made when they are 6 mo old because the first netic standard deviation, when accounting for lactation of their genetic dams starts several the Bulmer effect [instead of .226 according to months after their birth. In this situation, emRendel and Robertson’s formula (12)J.This bryo sexing would not add useful information because it could not be used to save resources: would correspond to about 90 kg of milk.. transferring a few male embryos would lead unavoidably to replacement male shortages or Juvenlle Nucleus Schemes to a substantial drop in the average breeding Without Embryo Sexing values of their dams. The same is also true for In these schemes, the selection paths in- female embryos. volving the males were identical to the sire-son The technical assumptions as to ET path in the conventional scheme. The nucleus parameters are the same as those of Colleau Journal of Dairy Science Vol. 74. No. 11, 1991
EMBRYO SEXING
3975
TABLE 2. Time schedule for nucleus females in the juvenile multiple ovulation and embvo transfer scheme. Period
Activity
(mo) 0-6
6 l&lS 29 35
Waiting for the yields results of dams (1Wmortality) Selection for mcleus replacement 2 embryo collections (30% nonresponse rate) F i t calving afler 2 AI (105%culling) Selection of dams of bulls and dams of cows
was set to 1000, 2000, or 4OOO as a constraint in addition to the natural constraint arising from the number of male calves needed for the regular progeny testing. For each sex, replacement could be obtained from three categories. Category 1 inAdult Nucleus Schemes cluded natural first calves born when the dam wlth Embryo Sexing is 2 yr old and chosen 1 yr later, based on the Mixed MOET adult schemes without em- dam’s first lactation performance. Category 2 bryo sexing were previously studied by Col- included natural second calves born when the leau (3). They were found to be clearly inferior dam is 3 yr old, based on the dam’s fist to juvenile schemes, even after optimization of lactation performance. Category 3 included nucleus size for a given overall number of calves born from sexed embryos when the embryos transferred. Under a deterministic mother is 4 yr old (on average, embryo collecBulmer model, the inferiority was about 15%. tion after 3 mo of lactation during the second For this reason, they were excluded from the lactation). If the genetic standard deviation is taken as present analysis. Embryo sexing might allow an exact fit of a unit, if dams are selected from their performthe resources (e.g., the number of recipient ance alone, and if Rendel and Robertson’s cows) according to the male and female needs formula (12) is used, the asymptotic annual gefor replacement. This could be done by screen- netic gain is AG = u/v with ing potential donors according to their first lactation results and collecting them during the middle of their second lactation (Table 3). Collecting selected donors during the middle of their first lactation would have probably generated better prospects with embryo sexing. Because the perspective adopted here is the same as that of Colleau (3), i.e., selection within dispersed nuclei when herds are not where specialized for breeding and are only enrolled in milk recording operations, the requirement K1 = twice the genetic selection differento delay inseminations on first lactation cows tial along the sire-son transmission until selection had been made was avoided. path (K1= 3.98 if no Bulmer effect Furthermore, the other alternative, to select on is assumed); very short lactations (2 mo), would have been K2 = twice the generation interval for the highly questioned by practitioners, at least for same path (13.5); lack of selection on persistency. h = square root of the heritability (h = .5 One of the most critical expense items in if no Bulmer effect is assumed); such a selection program is the overall number mi e: group size of category i of replaceof embryos transferred. Therefore, when o p ment males (& mi = M = constant timizing for annual genetic gain, this number = 130 throughout);
(3). Response rate to superovulation equals 70%. The number of collected embryos per flush and per treated cow equals 4 or 5. Survival rate of these embryos equals .4 or .6.
Journal of JXry Science Vol. 74, No. 11, 1991
3976
COLLEAU
TABLE 3. Time schedule for nucleus females in the adult multiple ovulation and embryo transfer scheme with embryo Sexing.
Activity
Period (mo)
Waiting for the yield results of dams, except for females born from adult ET1 (10% mortality) Selection for nucleus replacement First calving after 2 AI (10% culling) Selection of dams of bulls and dams of cows Second calving after 2 AI (10% cdmg); further selection of dams of bulls and dams of cows 1) for choosing natural second calves for replacement 2) for choosing the cows to be supaovulated Two embryo collections on the selected cows (30% nonresponse rate) Birth of adult ET M O I I ~ Y
0-9 9 24
33
36
38-40 48
'ET = Embryo transfer.
dam for category i of calves. For instance, if the proportion of heifers able to calve is .9, if intake into nucleus = an unknown the proportion of first lactation cows able to calve again is .9, and if the proportion of the variable); selection threshold for dams of cate- latter animals responding to superovulation is gory i of replacement males mea- .7, the values for y are y1 = .9, = .81, and y3 sured on a standard scale (mean = .57. Let us call ri the reproductive potential equal to 0, and variance equal to of the former three categories of dams expressed in terms of possible live calves of the 1); selection threshold for dams of cate- same sex per dam. If the survival rate of gory i of replacement females on natural calves is equal to .9, r1 = r;! = .45. If donors are flushed twice with five embryos per the same scale; corresponding probabilities that the collection and per treated cow, this means that standardized performance of any (2 x 5)/.7 = 14.3 embryos are obtained from possible candidate lies above the each responding donor. If the survival rate of thresholds; embryos is .6 and if the survival rate of ET standardized selection differentials calves is the same as for natural calves (.9), on the performances of the dams then r3 = .5 x 14.3 x .6 x .9 = 3.86. giving birth to the corresponding Under this set of parameters and setting no groups of each sex. Because nor- constraint on family contributions, we have mality is assumed, $ equals $yp' i
fi = group size of category i of replacement females (qfi = F = annual ti =
tr
=
* = pi*Pi I ,I, = ti ti
where $ is the ordinate of the
ti
standardized normal distribution at point ti. Correspondingly, I. = ti
and Li = age of dams (in years) for category i, regardless of the sex of calves. Longevity and reproduction parameters are needed for linking group sizes (mi, fi) to the corresponding selection thresholds (ti,$. Let US call yi the a priori probability that a young female of the nucleus will be a candidate as a Journal of Dairy Science Vol. 74, No. 11. 1991
where the numerator is the number of selected
dams, and the denominator is the number of potential dams.
The above expressions show that only one parameter, Bi = yi$i, links mi to pi (and there-
EMBRYO SEXING
3977
generated by adding a random environmental effect (constant variance equal to 3) to a g e netic effect (initial genetic variance equal to l), which corresponds to the average parental breeding value plus a random within-family meiosis effect (constant variance equal to 3. This last assumption, not verified on real finite populations, was introduced for the sake of consistency when comparing results with Bulmer’s predictions. The selection pressures and p u p sizes used for these Monte Carlo simulations were those given by the optimization procedure under a deterministic Bulmer model for the same set of technical parameters. For the MOET with sexing, cohorts were annual, which generated overlapping generations as required. For the juvenile MOET, advantage was taken of the fact that the interval between generations along sire-son, sireDetermlnlstlc Evaluatlon of the Asyrnptotlc Rate daughter paths was almost exactly three times of Genetic Galn Under a Bulmer Model the corresponding value for the other paths. Male and female populations were consid- Therefore, the layout was the same as in the ered as infiite, and selection differentials were preceding scheme but with longer intervals computed accordingly. The only adjustments between cohorts (2.3 yr instead of 1). to Rendel and Robertson’s formda (12) inThe response to superovulation was simuvolved the genetic variances and, consequent- lated exactly as in the prediction, i.e., a probaly, the accuracies of selection indices. At the bility of nomesponse equal to .3 and, for equilibrium, genetic variances and accuracies responding cows, a constant number of transwere smaller than before selection. ferable embryos. The number of embryos used The calculations involved for the conven- for describing the situations corresponded to tional scheme and the nucleus breeding the average number of embryos for all cows, scheme without sexing are described in the as in the predictions. Appendix of Colleau (3). The extension to To ensure a good elimination of the erratic nucleus breeding schemes with sexing is (but systematic) variations occurring during straightforward (Appendix). However, because the establishment of a breeding program (7), the optimal values of the selection pressures pi the asymptotic rates of gain were evaluated and p: were the result of a calculation account- between cohorts 90 and 100 (starting from an ing for genetic variances and accuracies, the unselected population at cohort zero). Clearly, optimizing procedure should be performed stabilization of genetic parameters should have iteratively (“outer” iteration) across the been obtained. The regression coefficient of parameter space for variances (K1 and h may the average points on year was then measured. vary fmm one iteration to another). This even- Each average point represented the average of tually leads to a maximum genetic gaia under 200, 100 and 50 replicates for the schemes involving 1O00, 2000, and 4OOO embryos, restable population parameters. Typically, the number of inner iterations spectively. was 6, and the number of outer iterations was RESULTS 10; rules for convergence were relatively se vere (IAG,, - AG,ll
Two types of multiple ovulation and embryo transfer schemes that included bull progeny testing were compared. In the juvenile schemes, embryos were collected at 16 to 18 mo of age without sexing, whereas, in the adult schemes, donors were chosen based on their first lactation record, and their embryos were systematically sexed. With the latter schemes, natural calves obtained at the first two calvings could compete with embryo transfer calves to be replacements. The optimal structure of this scheme was derived algebraically for the same number of transferred embryos as in the juvenile schemes. Predicted asymptotic annual genetic gains, after stabilization of genetic parameters taking into account the Bulmer effect, were found to be slightly in favor of the adult schemes for a given set of parameters (overall number of transferred embryos, number of embryos per collection, and embryo survival rate). In the adult schemes, the nucleus sizes were much larger than in the juvenile schemes, which allowed a higher selection differential on male paths, thus compensating for the longer generation interval. Asymptotic rate of genetic gain for Monte Carlo simulations were about 10 and 7% lower for juvenile and adult schemes, respectively, but still higher (20%) than the predicted value for the corresponding conventional scheme. Consequently, adult schemes with embryo sexing can be an efficient dter-
Received December 26, 1990. Accepted h4ay 30, 1991.
1991 J Dairy Sci 74:397>3984
native to juvenile schemes without embryo sexing. (Key words: genetic gain, biotechnology, multiple ovulation and embryo transfer, embryo transfer)
Abbreviation key: ET = embryo transfer, MOET = multiple ovulation and embryo transfer. INTRODUCTION
Since the pioneering work of Nicholas (10) and Nicholas and Smith (ll), increasing attention has been paid to nucleus breeding schemes using embryo transfer (ET) extensively, commonly referred to as multiple ovulation and embryo transfer (MOET) schemes. Some semiconservative adaptation of these proposals to retain progeny testing of d a q bulls in AI have been studied (2, 3, 4, 5). These "hybrid" or "mixed" MOET were shown to increase the rate of genetic gain substantially (20% or more) over that attainable in conventional selection schemes. As expected, rates of gain did not equal those in intensive true MOET, especially the juvenile ones. The objectives of this study were 1) to examine the impact that embryo sexing might have on rates of genetic gain in mixed MOET, 2) to compare deterministic and Monte Carlo simulation estimates of genetic gains under a Bulmer model, and 3) to examine optimal alternative breeding schemes. The evaluation procedure used here assumed an asymptotic linear rate of genetic gain. Strictly speaking, in the context of an assumed infinitesimal model, this implied that the sole correction to the usual overestimation according to Rendel and Robertson (12) would be accounting for the linkage disequilibrium induced by selection, i.e., the Bulmer effect (1). Indeed, accounting for losses of genetic variance through drift and inbreeding would not lead to an asymptotic linear rate of genetic gain (13, 14, 16, 17). 3973
3974
COLLEAU
TABLE 1. Input parameters used for predicting the efficiency of a conventional breedhg scheme. ~~
Variable
Value
Genetic parametas Heritability Repcatability Genetic correlation between lactations Population parameters J . tedfeanalcs Recorded AI bred females 5% Heifas sired by bulls on test Age at fmt calving Interval between calvings Number of AI to get a calf Overall c d m g rate up to 2 yr of age 96 Recorded cows from 1st to loth lactation Sire-son path Number of progeny-tested bull sires Usage period sirdaughter path Number of young bulls entering the AI center Number of young bulls actually progeny-tested Age when first proven Number of proven sires usage period Dam-son path Number of dams needed per young bull Minimum number of required lactations Damdaughter path % Culling on yield betweea lactation 1 and 2
MATERIALS AND METHODS
.25 SO 1
~ , O O 0 200,000
10% 2 F
IF 1.7
15% 26, 21, 17, 13. 9. 6. 4. 2. 1, 1 3 lyr 130 100 5.5 yr 13 lyr 6 3 33%
females were superovulated as young heifers after matings to bull sires. Replacement females and young bulls for conventional Reference Conventlonal Scheme progeny testing are selected from natural and This scheme was the same as that of Col- ET-born calves when they are 6 to 8 mo of leau (3). This progeny testing scheme, samp- age, based on their dam’s performance in the ling 100 bulls& to select 13% as proven, with first 6 mo of first lactation. The time schedule 3 sires of bulls/yr in a 400,OOO breeding female and the population parameters involved are population, was used as a point of reference shown in Table 2. The full description is given for comparisons. Specific parameten are in by Colleau (3). Table 1 with greater detail presented by ColIn this kind of breeding scheme, selection leau (3). This scheme was predicted to gener- decisions on young females or males should be ate an annual genetic gain of .177 initial ge- made when they are 6 mo old because the first netic standard deviation, when accounting for lactation of their genetic dams starts several the Bulmer effect [instead of .226 according to months after their birth. In this situation, emRendel and Robertson’s formula (12)J.This bryo sexing would not add useful information because it could not be used to save resources: would correspond to about 90 kg of milk.. transferring a few male embryos would lead unavoidably to replacement male shortages or Juvenlle Nucleus Schemes to a substantial drop in the average breeding Without Embryo Sexing values of their dams. The same is also true for In these schemes, the selection paths in- female embryos. volving the males were identical to the sire-son The technical assumptions as to ET path in the conventional scheme. The nucleus parameters are the same as those of Colleau Journal of Dairy Science Vol. 74. No. 11, 1991
EMBRYO SEXING
3975
TABLE 2. Time schedule for nucleus females in the juvenile multiple ovulation and embvo transfer scheme. Period
Activity
(mo) 0-6
6 l&lS 29 35
Waiting for the yields results of dams (1Wmortality) Selection for mcleus replacement 2 embryo collections (30% nonresponse rate) F i t calving afler 2 AI (105%culling) Selection of dams of bulls and dams of cows
was set to 1000, 2000, or 4OOO as a constraint in addition to the natural constraint arising from the number of male calves needed for the regular progeny testing. For each sex, replacement could be obtained from three categories. Category 1 inAdult Nucleus Schemes cluded natural first calves born when the dam wlth Embryo Sexing is 2 yr old and chosen 1 yr later, based on the Mixed MOET adult schemes without em- dam’s first lactation performance. Category 2 bryo sexing were previously studied by Col- included natural second calves born when the leau (3). They were found to be clearly inferior dam is 3 yr old, based on the dam’s fist to juvenile schemes, even after optimization of lactation performance. Category 3 included nucleus size for a given overall number of calves born from sexed embryos when the embryos transferred. Under a deterministic mother is 4 yr old (on average, embryo collecBulmer model, the inferiority was about 15%. tion after 3 mo of lactation during the second For this reason, they were excluded from the lactation). If the genetic standard deviation is taken as present analysis. Embryo sexing might allow an exact fit of a unit, if dams are selected from their performthe resources (e.g., the number of recipient ance alone, and if Rendel and Robertson’s cows) according to the male and female needs formula (12) is used, the asymptotic annual gefor replacement. This could be done by screen- netic gain is AG = u/v with ing potential donors according to their first lactation results and collecting them during the middle of their second lactation (Table 3). Collecting selected donors during the middle of their first lactation would have probably generated better prospects with embryo sexing. Because the perspective adopted here is the same as that of Colleau (3), i.e., selection within dispersed nuclei when herds are not where specialized for breeding and are only enrolled in milk recording operations, the requirement K1 = twice the genetic selection differento delay inseminations on first lactation cows tial along the sire-son transmission until selection had been made was avoided. path (K1= 3.98 if no Bulmer effect Furthermore, the other alternative, to select on is assumed); very short lactations (2 mo), would have been K2 = twice the generation interval for the highly questioned by practitioners, at least for same path (13.5); lack of selection on persistency. h = square root of the heritability (h = .5 One of the most critical expense items in if no Bulmer effect is assumed); such a selection program is the overall number mi e: group size of category i of replaceof embryos transferred. Therefore, when o p ment males (& mi = M = constant timizing for annual genetic gain, this number = 130 throughout);
(3). Response rate to superovulation equals 70%. The number of collected embryos per flush and per treated cow equals 4 or 5. Survival rate of these embryos equals .4 or .6.
Journal of JXry Science Vol. 74, No. 11, 1991
3976
COLLEAU
TABLE 3. Time schedule for nucleus females in the adult multiple ovulation and embryo transfer scheme with embryo Sexing.
Activity
Period (mo)
Waiting for the yield results of dams, except for females born from adult ET1 (10% mortality) Selection for nucleus replacement First calving after 2 AI (10% culling) Selection of dams of bulls and dams of cows Second calving after 2 AI (10% cdmg); further selection of dams of bulls and dams of cows 1) for choosing natural second calves for replacement 2) for choosing the cows to be supaovulated Two embryo collections on the selected cows (30% nonresponse rate) Birth of adult ET M O I I ~ Y
0-9 9 24
33
36
38-40 48
'ET = Embryo transfer.
dam for category i of calves. For instance, if the proportion of heifers able to calve is .9, if intake into nucleus = an unknown the proportion of first lactation cows able to calve again is .9, and if the proportion of the variable); selection threshold for dams of cate- latter animals responding to superovulation is gory i of replacement males mea- .7, the values for y are y1 = .9, = .81, and y3 sured on a standard scale (mean = .57. Let us call ri the reproductive potential equal to 0, and variance equal to of the former three categories of dams expressed in terms of possible live calves of the 1); selection threshold for dams of cate- same sex per dam. If the survival rate of gory i of replacement females on natural calves is equal to .9, r1 = r;! = .45. If donors are flushed twice with five embryos per the same scale; corresponding probabilities that the collection and per treated cow, this means that standardized performance of any (2 x 5)/.7 = 14.3 embryos are obtained from possible candidate lies above the each responding donor. If the survival rate of thresholds; embryos is .6 and if the survival rate of ET standardized selection differentials calves is the same as for natural calves (.9), on the performances of the dams then r3 = .5 x 14.3 x .6 x .9 = 3.86. giving birth to the corresponding Under this set of parameters and setting no groups of each sex. Because nor- constraint on family contributions, we have mality is assumed, $ equals $yp' i
fi = group size of category i of replacement females (qfi = F = annual ti =
tr
=
* = pi*Pi I ,I, = ti ti
where $ is the ordinate of the
ti
standardized normal distribution at point ti. Correspondingly, I. = ti
and Li = age of dams (in years) for category i, regardless of the sex of calves. Longevity and reproduction parameters are needed for linking group sizes (mi, fi) to the corresponding selection thresholds (ti,$. Let US call yi the a priori probability that a young female of the nucleus will be a candidate as a Journal of Dairy Science Vol. 74, No. 11. 1991
where the numerator is the number of selected
dams, and the denominator is the number of potential dams.
The above expressions show that only one parameter, Bi = yi$i, links mi to pi (and there-
EMBRYO SEXING
3977
generated by adding a random environmental effect (constant variance equal to 3) to a g e netic effect (initial genetic variance equal to l), which corresponds to the average parental breeding value plus a random within-family meiosis effect (constant variance equal to 3. This last assumption, not verified on real finite populations, was introduced for the sake of consistency when comparing results with Bulmer’s predictions. The selection pressures and p u p sizes used for these Monte Carlo simulations were those given by the optimization procedure under a deterministic Bulmer model for the same set of technical parameters. For the MOET with sexing, cohorts were annual, which generated overlapping generations as required. For the juvenile MOET, advantage was taken of the fact that the interval between generations along sire-son, sireDetermlnlstlc Evaluatlon of the Asyrnptotlc Rate daughter paths was almost exactly three times of Genetic Galn Under a Bulmer Model the corresponding value for the other paths. Male and female populations were consid- Therefore, the layout was the same as in the ered as infiite, and selection differentials were preceding scheme but with longer intervals computed accordingly. The only adjustments between cohorts (2.3 yr instead of 1). to Rendel and Robertson’s formda (12) inThe response to superovulation was simuvolved the genetic variances and, consequent- lated exactly as in the prediction, i.e., a probaly, the accuracies of selection indices. At the bility of nomesponse equal to .3 and, for equilibrium, genetic variances and accuracies responding cows, a constant number of transwere smaller than before selection. ferable embryos. The number of embryos used The calculations involved for the conven- for describing the situations corresponded to tional scheme and the nucleus breeding the average number of embryos for all cows, scheme without sexing are described in the as in the predictions. Appendix of Colleau (3). The extension to To ensure a good elimination of the erratic nucleus breeding schemes with sexing is (but systematic) variations occurring during straightforward (Appendix). However, because the establishment of a breeding program (7), the optimal values of the selection pressures pi the asymptotic rates of gain were evaluated and p: were the result of a calculation account- between cohorts 90 and 100 (starting from an ing for genetic variances and accuracies, the unselected population at cohort zero). Clearly, optimizing procedure should be performed stabilization of genetic parameters should have iteratively (“outer” iteration) across the been obtained. The regression coefficient of parameter space for variances (K1 and h may the average points on year was then measured. vary fmm one iteration to another). This even- Each average point represented the average of tually leads to a maximum genetic gaia under 200, 100 and 50 replicates for the schemes involving 1O00, 2000, and 4OOO embryos, restable population parameters. Typically, the number of inner iterations spectively. was 6, and the number of outer iterations was RESULTS 10; rules for convergence were relatively se vere (IAG,, - AG,ll
