NON-GENETIC, ADDITIVE AND NON-ADDITIVE GENETIC EFFECTS FOR ANIMAL MODEL ANALYSES OF WEANING WEIGHTS IN A NELLORE

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1 NON-GENETIC, ADDITIVE AND NON-ADDITIVE GENETIC EFFECTS FOR ANIMAL MODEL ANALYSES OF WEANING WEIGHTS IN A NELLORE x HEREFORD MULTIBREED POPULATION IN BRAZIL A. de los Reyes 1, M. A. Elzo, L. A. Fries 3, V. M. Roso 3 nd R. Crvlheiro 3 1 Deprtent of Anil Production, School of Veterinry, Federl University of Goiás, Goiâni, GO, Brzil. 1 Postdoctorl reserch supported by CAPES, Brzil. Deprtent of Anil Sciences, University of Florid, Ginesville, Florid, USA 3 GenSys Consultores Associdos S/C Ltd., Porto Alegre, RS, Brzil SUMMARY Relible estites of genetic preters re essentil for plnning econoiclly vible ultibreed progrs. Additive direct (A D ) nd ternl (A M ), doinnce direct (H D ) nd ternl (H M ), nd episttic direct (E D ) nd ternl (E M ) genetic effects were estited for 05-dy wening weights using dt fro Brzilin Nellore x Hereford ultibreed popultion (4,8 clves, 60 sires, 31,381 ds). Estites fro the odel with the sllest stndrd errors were 4.30 ± 3.65 kg, ±.83 kg, ±.35 kg, 7.45 ±.44 kg, ±.35 kg, 7.45 ±.44 kg, ± 5.38 kg nd ±.57 kg for A D, A M, H D, H M, E D nd E M, respectively. Multicollinerity ffected estites. Results need to be revlidted with lrger nd ore blnced ultibreed dtset. INTRODUCTION Relible crossbreeding preter estites re required to design sound crossbreeding progr. Therefore, the choice of n pproprite genetic odel is iportnt for the nlysis of crossbred popultion (Kinghorn nd Vercoe, 1989). The ost coonly pplied odel in crossbreeding studies ws proposed by Dickerson (1969). Other uthors, such s Kinghorn (1980), Koch et l. (1985) nd Wolf et l. (1995) developed lterntive genetic odels tht llow seprte estition of heterosis (doinnce) nd episttic effects. Soe recent results hve confired the iportnce of episttic/recobintion effects for nlysis of crossbreeding beef cttle field dt (Fries et l., 000; Pientel et l., 004; Roso et l., 005). There is soe evidence tht non-dditive vrition due to Bos indicus x Bos turus intrlocus interctions y be coprble to dditive genetic vrition for vrious growth nd crcss trits in beef cttle (Elzo et l., 1998,b; Elzo et l., 001). The objectives of this study were to ssess direct nd ternl breed dditive, doinnce, nd episttic/recobintion fixed genetic effects nd to estite (co)vrince coponents for djusted wening weight t 05 dys of ge in Nellore x Hereford ultibreed popultion of beef cttle. MATERIAL AND METHODS

2 The dt were djusted wening weights (kg) t 05 dys of ge (W05) of nils fro Nellore x Hereford ultibreed beef cttle popultion enrolled by Conexão Delt G, obtined between 1974 nd 1999 fro 39 herds. The edited dtset consisted of 4,8 records, including both purebred nd crossbred clves of both sexes, produced b y AI. Only records with coplete infortion for clculting direct nd ternl doinnce nd episttic interction effects were kept. The genetic connectedness ong ultibreed conteporry groups (CG = herd-yer-seson-ngeent group-sex of clf) ws checked (CSET Progr; Elzo, 00). Only CG with t lest 10 records were retined. The finl dtset included 1,9 CG, 60 sires, nd 31,381 ds. The pedigree file coprised 71,8 nils. In ddition to CG, the cow ge t clving (CA) ws odeled s fourth order polynoil regression on CA cross breed groups of d (BGD). Preliinry nlyses showed tht CA x BGD interction effects were of little iportnce to odel fitting (less thn 0. % of R ). Coefficients for direct (A D ) nd ternl (A M ) breed dditive effects were defined s the proportion of Nellore breed in the breed coposition of the clf nd the d, respectively. Consequently, direct nd ternl dditive breed effects were estited s devitions fro Hereford. Coefficients for direct (H D ) nd ternl (H M ) doinnce effects were equl to expected direct nd ternl breed heterozygosities. For coprison purposes, coefficients for direct (E D ) nd ternl (E M ) episttic/recobintion loss effects were clculted in three fors, s proposed by Dickerson (1969), Kinghorn (1980) nd Fries et l. (000), respectively. The generl odel for W05, defined in trix nottion, ws s follows: y = Xb + Fv + Z + W + e, where, y = vector of observtions; b = vector of fixed prtil liner regressions on coefficients for direct nd ternl breed dditive, doinnce, nd episttic/recobintion loss genetic effects; v = vector of fixed non-genetic effects; = vector of rndo direct dditive genetic effects; = vector of rndo ternl dditive genetic effects; nd e = vector of rndo residul effects. Incidence trices X, F, Z nd W relte records to fixed genetic, fixed environentl, direct genetic nd ternl genetic effects, respectively. The vectors of rndo effects,, nd e were ssued to hve (co)vrince trices equl to A, A, nd I, respectively, where A is the dditive nuertor reltionship trix e ong nils nd I is n identity trix. All estites were obtined by the ASREML progr (Gilour et l., 000). Nine odels were tested (M 1 to M 7, nd M 71, M 7 ; Tble ). Model M 1 included non-genetic fixed nd rndo dditive direct nd ternl genetic effects. In odels M to M 7 the effects of inclusion of ech of the fixed genetic preter to be estited were tested. Models M 71 nd M 7 differed fro M 7 in the clcultion for of episttic/recobintion loss coefficients. Significnce of ech preter contribution between odels ws judged by Akike Infortion Criterion AIC =-logl + k (Akike, 1974) nd Byesin Infortion Criterion BIC= -logl + klog(n) (Schwrz, 1978), where k = nuber of independent estited preters, nd n = totl nuber of observtions. RESULTS AND DISCUSSION

3 The unblnced distribution of W05 records by breed-group-of sire x breed-group-of d clsses, nd soe BGS x BGD epty clsses re typicl of popultion produced by n incoplete ultibreed ting syste (Elzo nd Reyes, 004). The dtset coprised 16,690 (39%) crossbreed nils of 53 different genotypes. For ll odels (Tble ), the fourth order polynoil regression coefficients on cow ge t clving (CA) were very siilr in pttern nd vlues (± SE), suggesting independence fro other effects included. For exple, the estited vlues fro M 71 were 41.5 ±.60, -6.4 ± 0.58, 0.44 ± 0.05 nd ± 0.00 for β 1 to β 4, respectively. The contribution to odel fitting of ech individul liner regression on fixed genetic direct nd ternl dditive, doinnce nd episttic effects fro M 1 to M 7 ws significnt ccording to the AIC nd BIC vlues (Tble ), except for the coprison of M 7 nd M 6 for ternl episttic effects, where AIC vlues were equl, nd the BIC vlue for M 7 ws lrger thn for M 6, indicting lesser fit copred to M 6. Tble. Estites of dditive nd nondditive genetic effects, vrinces nd covrinces, nd genetic preters for wening weight (kg) djusted to 05 dys of ge in Brzilin Nellore x Hereford ultibreed popultion Model / Effects A M 1 M M 3 M 4 M 5 M 6 M 7 M 71 M 7 β 5 (A D ) β 6 (A M ) β 7 (H D ) β 8 (H M ) β 9 (E D ) B β 10 (E M ) B p h h r LogL Pr. C AIC C BIC C A M 1: y = µ + CG + Σ{β i (CA) i } ε; CG = Conteporry Group (Herd-Yer-Seson-Sex-Mngeent. group); β i (CA) i = Qurtic polynoil regression on cow clving ge (CA) in yers (CA = to 14), β i = β 1 to β 4 = prtil liner, qudrtic, cubic nd qurtic regression coefficient, respectively;,, = Rndo dditive direct nd ternl genetic, nd x effects, respectively; ε = Rndo residul effect; M = M 1 + β 5(A D); M 3 = M + β 6(A M); M 4 = M 3 + β 7(H D); M 5 = M 4 + β 8(H M); M 6 = M 5 + β 9(E D); M 7 = M 6 + β 10(E M); β 5 to β 10 = Prtil liner regression coefficients on direct (A D) nd ternl (A M) breed dditive, direct (H D) nd ternl (H M) heterosis, nd direct (E D) nd ternl (E M) episttic/recobintion loss fixed genetic effects, respectively.

4 , = Genetic dditive direct nd ternl effect vrinces, respectively; = Genetic dditive directternl covrince; = Phenotypic vrince; p h, h = Heritbilities of direct nd ternl effects, respectively; r = Genetic correltion between direct nd ternl effects; LogL = Log of likelihood function vlue of the odel. B M 7 -E D, E M estited ccording to epistzigosity concept of Fries et l. (000); M 71 -E D, E M estited s proposed by Dickerson (1969, 1973); M 7 -E D, E M estited ccording to Kinghorn (1980, 198). C Pr. -Nuber of independent estited preters; AIC -Akike Infortion Criterion; BIC -Byesin Infortion Criterion. Estites of episttic effects were negtive for E D nd positive for E M in M 7, M 71 nd M 7, but with lrge differences in gnitude. In M 7 estites were lrger for H D (38.0 kg) thn for H M (16.6 kg). Contrrily, higher estites of H D (15. to 16.7 kg) thn for H M (1.8 to 30.1 kg) were obtined in M 5, M 6, M 7, nd M 71, which vlues re in greeent with results fro Roso nd Fries (000). However, estites fro M 71 nd M 7 re in greeent with the interreltionship (H M71 = H M7 + ½ E M7 ) deonstrted by Wolf et l. (1995). Multicollinerity ong predictor vribles due to dt iblnce nd epty clsses, nd the sll proportion of crossbreed nils, out of purebred nd F 1, which should nifest episttic/recobintion effects, likely contributed to the poor fit of M 7 for E M nd soe instbility of estited preters. Spling correltions ong predictor vribles indicted dependencies between E D nd H M (0.9) nd E M nd H M (0.78) in M 7. Model M 7 showed strong ssocitions between E D nd H D (0.96) nd E M nd H M (0.95), nd, in contrst with M 7 nd M 71, lso high correltions between E D nd A D (0.66) nd A M (0.78). The sllest spling correltions were obtined in M 71. Consequently, estites of effects in M 71 hd the sllest stndrd errors. Bsed on these criteri, M 71 ws the ost dequte odel for this dtset, which is in greeent with Deeke et l. (003). The following estites (± SE) were obtined fro M 71 : ± 3.65 kg, ±.83 kg, ±.35 kg, 7.45 ±.44 kg, ± 5.38 kg nd ±.57 kg for A D, A M, H D, H M, E D nd E M, respectively. The H D nd H M estites represent direct heterosis of 10.3% nd ternl heterosis of 16.9 %, which re coprble to the results of Roso nd Fries (000). CONCLUSION A sttisticl odel with only breed dditive nd doinnce effects ws insufficient to ppropritely explin genetic nd environentl vribility in Nellore x Hereford ultibreed field dtset. Both heterosis nd epistsis were iportnt genetic effects tht needed to be ccounted for. Multicollinerity ppered to hve ffected the estition of genetic nd environentl effects. However, the lrge estites obtined for heterosis nd episttic effects would justify dditionl reserch work with lrger, nd perhps ore blnced dtsets to vlidte these results. REFERENCES Akike, H. (1974). IEEE Trnsctions on Autotic Control, 19: Deeke, S., Neser, F. W. nd Schoen, S. J. (003). J. Ani. Breed. Genet., 10:

5 Dickerson, G. E. (1969). Ani. Breed. Abst., 37: Fries, L. A. et l. (000). Asin-Aust. J. Ani. Sci., 13 (Suppl. B): 4. Elzo, M. A. (00). Progr CSET. ABMS, No. 54, University of Florid, Ginesville. p 11. Elzo, M. A., Mnrique, C., Oss, G. nd Acost, O. (1998). J. Ani. Sci., 76: Elzo, M. A., Mrtinez, G., Gonzlez, F. nd Huerts, H. (001). J. CORPOICA, 3(): Elzo, M. A. nd Reyes, A. (004). Ciênci Anil Brsileir, 5 (4): Elzo, M. A., West, R. L., Johnson, D. D. nd Wken, D. L. (1998b). J. Ani. Sci., 76: Gilour, A. R. et l. (000). ASREML Reference nul. NSW Agriculture, 800 Austrli. p 17. Kinghorn, B. P. (1980). J. Ani. Breed. Genet., 97: Kinghorn, B. P.; Vercoe, P. E. (1989). Ani. Prod., 49: Pientel, E. C. G. et l., (003). In.: Reunião Anul SBZ, 40. Snt Mri-RS, Brzil. CD-ROM. Roso, V.M., Schenkel, F.S., Miller, S.P. nd Wilton, J.W. (005). J. Ani. Sci., 83: Roso, V. M. nd Fries, L. A. (000). Rev. Brs. Zootec., 9 (3): Schwrz, G. (1978). Annls of Sttistics, 6: Wolf, J., Distl, O. et l. (1995). J. Ani. Breed. Genet., 11:

ECONOMETRIC THEORY. MODULE IV Lecture - 16 Predictions in Linear Regression Model

ECONOMETRIC THEORY. MODULE IV Lecture - 16 Predictions in Linear Regression Model ECONOMETRIC THEORY MODULE IV Lecture - 16 Predictions in Liner Regression Model Dr. Shlbh Deprtent of Mthetics nd Sttistics Indin Institute of Technology Knpur Prediction of vlues of study vrible An iportnt