2 Maataloustieteellinen Aikakauskirja Vol. 59: 79—86, 1987 A simulation study for optimizing the use of dairy bulls in breeding programs J. JUGA, J. SYVÄJÄRVI, V. VILVA Dept, of Animal Breeding, Agricultural Research Centre SF-31600 Jokioinen, FINLAND Finnish Animal Breeding Association P.O. Box 40 SF-01301 Vantaa, FINLAND Dept, of Animat Breeding, The University of Helsinki SF-00710 Helsinki, FINLAND Abstract. Different breeding program alternatives in dairy cattle population were studied by simulation. Traits studied were milk production and a low heritability trait that is negatively correlated with milk production, e.g. fertility. The variable factors in the study were the num- ber of youngbulls to be tested, the number of daughters per bull in progeny testing, the num- ber of tested bulls to be used and the weights for selected traits in an overall index of the bull’s breeding value. The influence of variable factors on geneticresponse in milk production and fertility was studied by calculating the average of real genotypic values on both traits for all cows born in the same year and having a complete first lactation record. This was done for a 25 year period. The population structure used in simulation was like the Finnish milk recorded Ayrshire population in which there are ca. 250 000 cows. The genetic response in milk production was improved by increasing the selection intensity amongst bulls. The negative effect of selection for milk yield on fertility could be decreased by giving the fertility a larger indexed weight. If the milk production had a weight of 1 and genetic correlation between traits was —0.20 then increasing the weight of fertility from 0.1 to 0.3 did not affect significantly the response in milk production. Key words: Breeding program, Progeny testing Introduction From the genetic response in milk produc- tion reached in dairy cow population approxi- mately 70 —75 °7o is due to selection of Al-bulls. The transmittance of genetic superiority from bulls to cows is dependent on the use of tested and young bulls in the population. According to current breeding policy in Finland the best 30 % of cows are recommended to be insemi- 79 JOURNAL OF AGRICULTURAL SCIENCE IN FINLAND https://www.c-info.fi/en/info/?token=6PZXtLcyjSa4MRg8.h9IvEW4TU8beZ1mQRDc-vQ.RBKyG4MtA9HFM7UIH-WpyihU8Iczn3o2y74kjB_CkgET-yWxFZt8DDRiHjuO5UCS6gWLJN9A6d0agZRsUPwJfdRASIBbw4nWMc-X7OK1QZSpu0yM-gSEDLnkzrU2lqXBwJhjqb_yosjfA6SQMAYCAKB3Df5QmcRuroaJqPCHs-THyS7P18jBknGUTFe2mBlDVqo2RHVvOQ nated with a tested bull’s semen, 60 % of cows with a young bull’s semen and the poorest 10 % of cows with semen from beef bulls. The number of young bulls that can be tested depends on the testing capacity and on the efficiency of the use of testing capacity. The number of bulls to be tested is limited by the amount of semen available and the size of the testing station. In spite of these fixed fac- tors the breeding program can be improved by optimizing the selection intensity of tested bulls, the number of daughters in progeny test and the ratio of inseminations made with young and tested bulls. Several studies of the influence of various factors on the genetic response in milk yield have been made concurrently with AT. pro- grammes (e.g. Rendel and Robertson 1950, Robertson and Rendel 1950, Skjervold 1963, Skjervold and Langholz 1964 and Van Vleck 1964). Lindström (1969) has studied the predicted and realised genetic re- sponse in the Finnish dairy population. As a summary of the above mentioned studies he concluded that in large populations the genetic response depends rather more on the number of bulls to be tested than on the number of daughters per bull in progeny test, i.e. on the accuracy of the test. With an optimum use of AI, ideally an annual response of 2.0 —2.5 % could be reached in large populations (Van Vleck 1981), but in practise only 1.0 % or less has been achieved. Some of the main reasons for this reduction are simultaneous se- lection on several traits, low selection inten- sity among tested bulls and low accuracy in evaluating of bull dams (Van Vleck 1981). In addition to maximizing the genetic re- sponse of milk production Van Vleck (1964) and Lindhe (1968) considered also the net re- turns of AT. mating plans. According to Lindhe (1968) the programme that maximizes the genetic response is usually not best if the maximum net return is considered, but the maximum net return is usually reached before the maximum genetic response. The economical optimization of AT. breeding programs led into more sophisticated discounting procedures (McClintock & Cunningham 1974, and ITill 1974), in which the flow of selected genes is followed through different paths against time. The discounted return of an improvement that has been produced in breeding program, can be predicted by these methods. The method of McClintock and Cunningham (1974) has been used by Lindström and Vilva (1976) in optimizing the proportion of tested, young and beef bulls in the Finnish milk and meat breeding programme. In 1984 there were 642 000 dairy cows in Finland of which 307 920 were milk recorded. 247 587 of milk recorded cows were Ayrshire cows, 51460 were Friesian and 4640 were Finn cattle. Ca. 370 bulls can be tested annually in testing station out of 500 bull calfs born from bull dams. There has been a slight decrease in the number of bulls to be tested and an in- crease in the number of daughters per bull in progeny test, so that on average there have been 180 daughters per bull. To find out the optimum number of progeny tested bulls and young bulls for the breeding program with relatively constant resources, a simulationstudy was carried out. In a simula- tion study the annual genetic response can be presented as the real genetic mean of animals born in different years. The simulation meth- od is very flexible in studying the effects of different changes in the breeding programme. By using a simulation method the effect of random drift on genetic response can be esti- mated from the standard error of the mean over replicates. Simulation In the simulation study the population structure was designed to match with the Finn- ish milk recorded Ayrshire population. The fixed factors used in the study are given in Table 1. The factors varied in the study were the number of daughters per bull in progeny testing, i.e. the number of young bulls tested annually and the number of tested bulls to be used in the breeding program. The number of bull sires and the proportion of cows to be in- 80 Table I. The constants in the simulation study. population size 250,000 dairy cows replacement proportion 25 %or 63,000 Ist laet. /year proportions of bulls used for inseminations: 60 % with young bulls 34 % with tested bulls 6 % with beef bulls inseminations required: 1.7 inseminations/pregnancy young bulls; 10.7 inseminations/lactation record tested bulls: 3.6 inseminations/lactation record (37 % of Ist lactation records were made by daughters of young bulls 63 % of Ist lactation records were made by daughters of tested bulls) 6 bull sires/year tested bulls were used for 3 years generation interval in sire to son path was 8 years heritabilities: milk production 0.25 fertility 0.05 seminated with tested bull semen or with young bull semen were fixed (Table 1). The effect of these variable factors on the genetic response in milk production was studied by running different simulation alternatives with 20 replications of each. Animals were selected simultaneously on milk production and on a trait with a low heritability and with a negative genetic correlation (—0.20) with milk produc- tion, e.g. fertility. Although for the main ob- jective in selection, milk yield had a weight of 1 and fertility a weight of 0.1, some alternatives were run by giving more weight to fertility. The different alternatives studied are given in Table 2. Population means were presented for both traits so that the improvement on milk production and the change in fertility could be followed. The expected genetic responses in milk pro- duction were calculated from (Rendel and Robertson 1950) _ AGsd + -^G I3S + AG|j|, Lss ■*" L S 1) + LqS L[)d where is the genetic change in different paths (designation: SS = for sire to son, SD = from sire to daughter, DS = from dam to son, and DD from dam to daughter) of gene trans- mission and Ljj is the generation interval in the respective path. The expected responses are given in Table 3. The correlated responses in SS and SD paths, in which selection was practised on milk and fertility, were calculated from (Falconer 1981) CAG, = * cov(a)n , where i is the selection intensity, ct, is the standard deviation of the index and cov(a)ll is the additive genetic covariance of milk pro- duction with the index. Model Only the information of males was stored for the future use in the simulation. The genotypic values for bull dams were generated and chosen so that the mean over four lacta- tions was above the selection criterion. Dams were randomly sampled because it was assumed that sires and dams are not related. The addi- tive genetic value of a young bull (j) for trait i (ay) was generated from his sire’s and dam’s additive genetic values (a Sj and aDi respective- ly) as a ij = o.s(aSi + aDj ) + mij, where is due to Mendelian sampling about the mean o.s(asi + aDj). 81 Table 2. The variable factors used in simulation alter- natives. number of number of number of young bulls daughters in tested bulls progeny test 1: 132 180 24 2: 132 180 12 3: 238 100 24 4: 238 100 12 5: 477 50 24 Weights that were used in overall selection index. The variable factors were the same as in alternative 1. milk production: fertility 6; 1 0.1 7; 1 0.2 8: 1 0.3 9: 1 1 where y,, is the mean of daughter group of bull j in trait i, a,, is the additive genetic value of bull j, Cy is the deviation of the daughter group mean from the bull’s additive genetic value. The model for two traits was ■y.n [a.n fx] fy = 0.5 + T + R y2j a2j z w , and VFe.n 3 a\\ aA | 2 1 o|i = +— =TT + RR’, e2j J 4n 1 aAI2 a\2 a|2 where The model for two traits was then a SI + aDIa o X 0.5 + L aS2 + aD2a2j y. where x and y are normally distributed ran- dom numbers ~N(0,1). aA\ °M2vK =LL’ , = 0.5 °AI2 aA2m2j where is the additive variance of trait i, aAij is the additive covariance between traits i and j. L is a lower triangular matrix from Cholesky decomposition of symmetric variance-covari- ance matrix V(mij). If r G = —0.20 then 0.707 0 L = —0.141 0.693 . To minimize computing time no individual daughters were generated, instead the mean of a daughter group for a bull as a deviation from the population mean. yij = 0.5aij + eij, T and R are lower triangular matrices defined as before, x,y,z,w are normally distributed random num- bers ~N(0,1), oli is the residual variance of trait i, nj is the number of daughters of bull j. The environmental correlation was assumed to be zero. If r 0 = —0.20 then 1 f 0.866 0 T = rij [—0.173 0.849 Bull’s predicted breeding values for both traits were evaluated from the formula (Ro- bertson and Rendel 1950) n.. 0.25 nj h? _o.sa|:= Yu,J 1+0.25(11—1)^ where ä|j is the predicted breeding value of bull j in trait i. hf is the heritability of trait i, Hj is the number of daughters of bull j. An overall index for bulls was calculated as the sum of these predicted breeding values by giving different weights for milk production and fertility at different alternatives (Table 2). 82 Table 3. Expected genetic response in milk production at different alternatives. L i r.A AG, DD 5.0 0.35 0.6 0.11 DS 6.52.39 0.670.80 SS (L =8.0) SD (L =7.5) a, cov(al,| i CAG, i CAG, 1: 0.497 0.250 2.06 1.04 1.46 0.73 2: 2.06 1.04 1.80 0.91» » » » » » » 3: 2,27 1.14 1.76 0.89 4: 2.27 1.14 2.06 1.04 5: 2.67 1.34 2.06 1.04» 6: 0.497 0.250 2.06 1.04 1.46 0.73 7: 0.494 0.246 1.03 0.72» » » » » » 8: 0.492 0.244 1.02 0.72 9: 0.510 0.230 0.93 0.66 Expected genetic response/year in s.d. units. (Phenotypic s.d. =800 kg). I 2 3 4 5 6 7 8 9 0.099 0.106 0.109 0.110 0.120 0.099 0.099 0.098 0.093 In the alternatives from 1 to 5 the weights of milk production and fertility were 1 and 0.1, respectively. Selection of tested bulls and bull sires was carried out on the basis of the overall index values. The program was run in two stages. A start- ing program, the same for all alternatives, with 20 replicates was first run to get the breeding program into a stable stage. Vari- ables in the starting program were the same as in the alternative 1 (Table 2). Thus all al- ternatives started from the same situation. A different number of young bulls was genera- ted annually in different alternatives (Table 2). Tested bulls were used over three years for producing replacement cows. The effect of different alternatives were followed for 25 years and 20 replicates were run of each al- ternative. Results and discussion All the possible alternatives could not be run because of the computing time required. Alternatives were selected as extreme examples to show the change in the response with dif- ferent breeding policies. The limiting factor is the number of tested bulls because we need a certain number of them to carry out all the inseminations in the population. The Figures 1 and 2 show that by decreas- ing the number of daughters per bull in pro- geny test or in other words, testing more bulls per year, the genetic response in milk produc- tion could be improved. The improvement was obvious when the number of daughters Fig. I. The genetic response in milk production with dif- ferent daughter group sizes in progeny test. The genetic s.d. is 400 kg. See table 2 for more ex- planation. 83 decreased from 180 to 100, but neligible when the number was further decreased from 100 to 50 (Fig. 1). The use of a smaller number of tested bulls in the program or the increase in the selection intensity among tested bulls lead to a higher genetic response in milk pro- duction (Fig. 2). Because of the large popula- tion size the standard error of the mean was very small, ca. 10kg, in all alternatives so that the estimates of the genetic response in milk yield can be considered as relatively accurate. The change in milk production after in- creasing the weight of fertility in overall selection index is presented in Fig. 3. When milk production had a weight of 1 and the genetic correlation between traits was —0.20, increasing the weight of fertility from 0.1 to 0.3 hardly decreased the genetic response of milk production. It had, however, a consid- erable effect on fertility (Fig. 4) so that the deterioration of fertility could be prohibited by putting more weight on it in the selection index. When both traits were given equal weight the fertility was even somewhat im- proved, but at the same time the response in milk yield clearly decreased (Figs. 3 and 4), even more than expected (Table 3). The results obtained from the simulation study were consistant with earlier studies and with the expected responses given in Table 3. The results indicate that the efficiency of the breeding program can be improved by more intensive selection of tested bulls and by testing more young bulls. By increasing the ef- ficiency of progeny testing scheme the re- sponse in milk production can be improved Fig. 2. The genetic response in milk production when the number of tested bulls selected per year and the number of daughters in progeny test varies. The genetic s.d. is400 kg. See Table 2 for more explanation. Fig. 3. The genetic response in milk production with dif- ferent weights used in overall index. The genetic s.d. is 400 kg. Fig. 4. The genetic change in fertility with different weights used in overall index. The genetic s.d. is 0.2 inseminations per pregnancy. 84 without any major changes in the testing capacity, in other words with small invest- ments. Also traits which have low heritabil- ity and which might be negatively correlated with milk production, such as fertility traits, some diseases etc., can be taken into account in breeding programs and some improvement can be expected by having appropriate weights References Falconer, D.S. 1981. Introduction to Quantitative Genetics. 2nd edn., Longman, London. Hill, W.G. 1974. Prediction and evaluation of response to selection with overlapping generations. Anim. Prod. 18; 117—139. Lindhe, B. 1976, Model simulation of A.1.-breeding within a dual-purpose breed of cattle. Acta Agr. Scand. 18: 33—41. Lindström, U.B. 1969. Genetic change in milk yield and fat percentage in artificially bred populations of Finn- ish dairy cattle. Acta Agr. Fenn. 114: 1—l2B. Lindström, U.B. and Vii va, V. 1976. Economic breeding for milk and beef in Finnish Ayrshire. Symp. on Ayr- shire Cattle Breeding, Finland, 20th—25th September, 1976. MtCuNTOCK, A.E. and Cunningham, E. P. 1974. Selec- tion in dual purpose cattle populations; Defining the breeding objective. Anim. Prod. 18: 237—247. Rendel, J.M. and Robertson, A. 1950. Estimation of genetic gain in milk yield by selection in a closed herd SELOSTUS in the selection index. If traits of low herita- bility are included, the number of daughters per bull in progeny testing has to be kept large enough for the accurate evaluation on such traits. Acknowledgements.The advice and comments of Dr. Asko Mäki-Tanila are greatly appreciated. of dairy cattle. J. Genetics 50: I—B. Robertson, A. and Rendel, J.M. 1950. The use of pro- geny testing with artificial insemination in dairy cattle. J. Genetics 50: 21—31. Skjervold, H. 1963. The optimum size of progeny groups and optimum use of young bulls in AI breeding. Acta Agr. Scand. 13: 131—140. Skjervold, H. and Langholz, H.J. 1964. Factors affect- ing the optimum structure of AI breeding in dairy cattle. Z. Tierz. Ziicht. biol. 80; 25—40. Van Vleck, L.D. 1964. Sampling the young sire in ar- tificial insemination. J. Dairy Sci. 47: 441—446. Van Vleck, L.D. 1981. Potential genetic impact of ar- tificial insemination, sex selection, embryo transfer, cloning, and selfing in dairy cattle. In Seidel, G.F. and Seidel, G.F. Jr. (eds.) New Technologies in Animal Breeding 1981. Academic Press, Inc., New York. pp. 221—242. Ms received March 23, 1987 Simulaatiot n Iki imis tarkoituksen- mukaisimmasta lypsykarjasonnien käytöstä jalostusohjelmissa J. Juga Kolieläinjaloslusosaslo Maatalouden tutkimuskeskus 31600 Jokioinen J. Syväjärvi Suomen Kotieläinjaloslusyhdislys PL 40 01301 Vantaa V. Viiva Kotieläimen jalosluslieleen laitos Helsingin yliopisto 00710 Helsinki Erilaisia lypsykarjan jalostusohjelmavaihtoehtoja tut- kittiin tietokonesimulaatiolla. Tarkastellut ominaisuudet olivat maitotuotos ja sen kanssa negatiivisesti korreloi- tuna! alhaisen periytyvyysasteen ominaisuus, esim. hedel- 85 mällisyys. Valinnan tehoon vaikuttavina tekijöinä tutkit- tiin jälkeläisarvosteltaviennuorsonnien lukumäärää, son- nikohtaista tytärmäärää, valiosonnien määrää ja sonnien kokonaisjalostusarvoon kuuluvien ominaisuuksien pai- notusta. Tekijöiden vaikutusta maitotuotoksessa ja hedelmäl- lisyydessä saavutettuunperinnölliseen edistymiseen ilmais- tiin laskemalla molemmille ominaisuuksille lehmien to- dellisten perinnöllisten arvojen vuosittaiset keskiarvot. Ja- lostusohjelmaa seurattiin 25 vuotta. Simulaatiossa käy- tetty populaatiorakenne pyrki jäljittelemään suomalais- ta ayrshirelehmien tarkkailupopulaaliota (noin 250 000 lehmää). Maitotuotoksen perinnöllinen edistyminen parani kun sonnien valintaintensiteettiä lisättiin. Maitotuotoksen va- linnasta johtunuttahedelmällisyyden huononemista voi- tiin hidastaa antamalla tälle ominaisuudelle suurempi pai- no kokonaisjalostusarvossa. Kun maitotuotoksella oli pai- no 1 ja ominaisuuksien välinen korrelaatio oli —0.20, he- delmällisyyden painonkohottaminen 0.1 :stä o.3:een ei vai- kuttanut merkittävästi maitotuotoksen jalostukselliseen paranemiseen. 86