MACE For Conformation Traits

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1 MACE Fr Cnfrmatin raits L. Klei and. J. Lawlr Hlstein Assciatin USA, Inc., Brattlebr, Vermnt, USA Intrductin Multiple acrss cuntry evaluatins (MACE) fr prductin traits are nw rutinely cmputed and used in many cuntries. Hwever, fr cnfrmatin traits mst cuntries resrt t cnversin frmulas. Advantages assciated with MACE include: 1. Utilizatin f all infrmatin amng cuntries t generate internatinal breeding values. 2. Utilizatin f a bull's pedigree infrmatin as well as his wn infrmatin. 3. Re-ranking f bulls allwing fr pssible gentype by envirnment interactin and differences in trait definitin. 4. Simultaneus analysis f prfs frm multiple cuntries. his paper describes the implementatin f MACE fr cnfrmatin traits in the USA. Mdel he standard mdel (Schaeffer and Zhang, 1993) fr internatinal genetic evaluatins was used t analyze the data. his can be represented by: y = Cµ + ZQg + Zs+ e where: y : vectr f de-regressed prfs μ : vectr f cuntry effects g : vectr f genetic grup effects fr phantm parents s : vectr f randm sire effects e : vectr f residual effects fr de-regressed prfs C : incidence matrix assciating de-regressed prfs with cuntry effects Z : incidence matrix assciating de-regressed with sire prfs Q : incidence matrix assigning sires t phantm grups Distributins fr the randm variables are assumed t be: y s e where: Cµ + ZQg ZGZ + R GZ R ~ MVN 0, G 0 0 symm. R G : is the genetic (c)- matrix amng elements f s, G = G A where G is the genetic (c)- matrix amng the traits f interest and A is the numeratr relatinship matrix amng the unique animals represented in s R : is a diagnal matrix with diagnals equal t the rati f the residual in a cuntry divided by the number f daughters in that cuntry he mixed mdel equatins fr the equivalent mdel described by Quaas (1988) are (Sigurdssn and Bans, 1995): 15

2 1 1 C R C 0 C R Z Q A Q G Q A G symm. Z R Z + A G c C R g = 0 Qg + s Z R 1 1 y y Implementatin Official cnfrmatin data was btained frm Canada (CAN), France (FRA), Germany (DEU), Italy (IA), he Netherlands (NLD), and the United States (USA). raits cnsidered were the 12 standard and tw ptinal traits recmmended by the cmmittee n the wrld-wide harmnizatin f linear type classificatin (Cnssen et al., 1993), as well as fur additinal traits, Rear Legs Rear View, Feet and Leg Scre, Rear Udder Width, and Final Scre (Appendix 1). hese last fur traits are necessary t determine the USA type and prductin index (PI, Hlstein Assciatin USA, Inc. 1997). Selectin f trait cmbinatins fr each f the 18 USA traits was based n crrelatins f prfs fr bulls evaluated in bth cuntries. Fr each USA trait the freign trait shwing highest prf crrelatin was chsen. (Appendix 1). In additin t the direct cmputatin f the 18 traits, tw cmpsites, udder and feet & legs, were cmputed based n the MACE f the individual traits in the cmpsite (Hlstein Assciatin USA, Inc. 1997). Edits perfrmed n the data were similar t thse used fr the prductin traits by INERBULL. Hwever, recrds based n less than 10 daughters, recrds n bulls nt n an fficial AI testing scheme, r secnd cuntry prfs based n less than 75 daughters in less than 50 herds were all included as lng as the prf was reprted in the fficial type perfrmance file frm each cuntry. Recrds n bulls brn befre 1980 were eliminated t reduce time perid effects (Weigel, 1996). Phantm parent grups were assigned based n unknwn ancestr (sire, maternal grandsire, maternal granddam), year f birth, and cuntry f rigin. Birth years were divided int three year intervals. De-regressed prfs were cmputed using the deregressin prcedure described by Rzzi and Schaeffer (1996). Subsequently (c)- matrices G were estimated frm the de-regressed data using the EM-REML algrithm presented by Klei and Weigel (1998) using infrmatin n all bulls in all cuntries. MACE slutins were cmputed thrugh an LU decmpsitin (Glub and Van Lan, 1987) f the mixed mdel equatins using sparse matrix techniques (FSPAK, Perez-Encis et al., 1994). Reliabilities f the MACE prfs were btained by inverting the mixed mdel equatins using FSPAK t btain the apprpriate diagnal elements. Official reliabilities are based n the reliability fr PA. Results and Discussin Appendix I shws the prf crrelatins fr each f the 18 trait cmbinatins. Frm these tables it can be bserved that mst f the udder traits measured shw high crrelatins amng the cuntries reflecting great unifrmity in bserving these traits. Bdy traits, except Stature, shw high crrelatins amng sme f the cuntries while ther cuntries are mderate t lwly crrelatin. In this categry France has n trait that adequately crrelates with Dairy Frm (Angularity) and subsequently bulls with nly bservatins in France will have an evaluatin based n the US pedigree index fr this trait when reprted n the USA base. Fr feet and legs crrelatins are, again, high fr sme fr sme f the cuntries while lw amng thers. he nly exceptin amng these traits is Rear Leg Side View, ne f the standard traits. In this grup f traits n crrespnding traits culd be fund fr Rear Leg Rear View and Feet and Leg Scre in bth Germany and France resulting in pedigree indices fr bulls with nly bservatins in thse cuntries. In the USA, Final Scre is evaluated as a separate trait. be cnsistent with the natinal evaluatin it was decided that this shuld als be the case with Final Scre evaluated in MACE. Crrelatins fr USA Final Scre with the verall type traits in the ther cuntries were all higher then.75 and deemed adequate. In situatins where cuntries cmpute an verall type trait as a cmpsite f linear evaluatins this methd culd be applied. 16

3 France nly supplied secnd cuntry prfs n USA bulls. his resulted in a limited number f ties with ther cuntries. Additinal data n secnd cuntry prfs frm France fr bulls frm these cuntries culd bst the prf crrelatins Figure 1 thrugh Figure 3 shw cnverted prfs and MACE prfs n ten bulls frm three f the cuntries fr Udder Cmpsite. One f the reasns t use a MACE mdel is that it is a refinement f the methd f using cnversin frmulas. his is well illustrated in Figure 1. Frm this figure it can be bserved that nne f these ten bulls change rank, hwever bulls C and D, which were equal under the cnversin methd, shw differences when using MACE t determine evaluatins n freign bulls. P r f A B C D E F G H I J Bull Cnverted Prf Mace Prf Figure 1. Cmparisn f cnverted and MACE prfs fr udder cmpsite fr 10 bulls frm cuntry I. Figure 2 shws that animals can re-re-rank when using MACE. If selectin fr udder cmpsite was based n a culling level f +1.00, cnverted prfs wuld have recmmended the use f bull A thrugh G. MACE, hwever, wuld have recmmended the use f A thrugh D, G and H. Even thugh individual differences fr these tw evaluatin methds are nt large, selectin decisins will be influenced. A similar situatin can be bserved fr cuntry III (Figure 3). Ranking f the tp five bulls based n cnverted prfs wuld be A, B, C, D, E while using cnversin methds, while the ranking when using MACE is B, A, D, C, E. P r f A B C D E F G H I J Bull Cnverted Prf Mace Prf Figure 2. Cmparisn f cnverted and MACE prfs fr udder cmpsite fr 10 bulls frm cuntry II. 17

4 P r f A B C D E F G H I J Bull Cnverted Prf Mace Prf Figure 3. Cmparisn f cnverted and MACE prfs fr udder cmpsite fr 10 bulls frm cuntry III. Cnclusins MACE can be used t cmpute evaluatins fr cnfrmatin traits. MACE prvides a refinement in determining genetic ptential f freign bulls thrugh a refinement f the statistical mdel used t describe the data. As ppsed t cnversin methds, MACE allws fr the re-ranking f bulls resulting in a mdificatin f selectin decisins bth when using independent culling levels and when usage f sires is dependent n the prf f the bull. Acknwledgments his research was made pssible with financial assistance f the Natinal Assciatin f Animal Breeders. Literature cited Cnssen, D.L., de Graaf, F.M., Diers, H., Hewitt, D.W. & Hdgins, D.L Eurpean and wrld-wide harmnizatin f linear type classificatin. Definitin f traits and estimatin f breeding values. Prc. f the pen sessin f the INERBULL annual meeting. Aug Aarhus, Denmark. Glub, G.H. & Van Lan, C.F Matrix Cmputatins. 5 th Printing. he Jhns Hpkins University Press. Baltimre. Maryland. Hlstein Assciatin USA, Inc Sire Summaries. August Brattlebr, Vermnt. Klei, L. & Weigel, K A methd t estimate crrelatins amng traits in different cuntries using data n all bulls. Paper presented at the INERBULL pen meeting. Jan Rtura, New Zealand. Perez-Encis, M., Misztal, I. & Elz, M. A FSPAK: An interface fr public dmain sparse matrix rutines. In Prc. 5 th. Wrld Cngress n Genetics Applied t Livestck Prductin. Vl. 22:87. Quaas, R.L Additive genetic mdel with grups and relatinships. J. Dairy Sci. 71, Rzzi, P. & Schaeffer, L.R New deregressin prcedure used n type traits. Paper presented at INERBULL wrkshp. Nv Verden, Germany. Schaeffer, L.R. & Zhang, W Multi-traits, acrss cuntry evaluatin f dairy sires. Prc. f the pen sessin f the INERBULL annual meeting. Aug Aarhus, Denmark. Sigurdssn, A. & Bans, G Estimatin f genetic crrelatins between cuntries. Prc. f the pen sessin f the INERBULL annual meeting. Sept Prague, Czech Republic. Weigel, K.A Effect f time perid f data used in internatinal dairy sire evaluatins. Paper presented at INERBULL wrkshp. Nv Verden, Germany. 18

5 Appendix I MACE Crrelatins Fr Cnfrmatin raits August 1997 Heritabilities n diagnal Stature USA Stature CAN Stature NLD Stature DEU Stature IA Sacrum Height FRA Strength USA Chest Width CAN Chest Width NLD Chest Width DEU Strength IA Chest Width FRA Bdy Depth USA Capacity CAN Bdy Depth NLD Bdy Depth DEU Bdy Depth IA Chest Width FRA Dairy Frm USA Dairy Character CAN ype Milk NLD Angularity DEU Angularity IA FRA Missing values indicate that n crrespnding trait culd be determined. Rump Angle USA Pin Setting CAN Rump Angle NLD Rump Angle DEU Rump Angle IA Rump Angle FRA Rump Width USA Pin Width CAN Rump Width NLD Rump Width DEU hurl Width IA Hip Width FRA

6 MACE Crrelatins Fr Cnfrmatin raits Cntinued Rear Leg Side View USA Rear Leg Set CAN Rear Leg Set NLD Rear Leg Set DEU Legs Side IA Rear Leg Set FRA Rear Leg Rear View USA Ft Angle CAN Feet and Legs NLD DEU Ft Angle IA FRA Missing values indicate that n crrespnding trait culd be determined. Ft Angle USA Ft Angle CAN Claw Diagnal NLD Ft Angle DEU Ft Angle IA Heel Depth FRA Feet and Leg Scre USA Ft Angle CAN Feet and Legs NLD DEU Ft Angle IA FRA Missing values indicate that n crrespnding trait culd be determined. Fre Udder USA Fre Attachment CAN Fre Udder NLD Fre Udder DEU Fre Attachment IA Udder Depth FRA Rear Udder Height USA Rear Attachment CAN Rear Udder Height NLD Rear Udder Height DEU Rear Udder Height IA Rear Udder Height FRA

7 MACE Crrelatins Fr Cnfrmatin raits Cntinued Rear Udder Width USA Rear Attachment CAN Rear Udder Height NLD Rear Udder Height DEU Rear Udder Width IA Rear Udder Height FRA Udder Cleft USA Median Suspensry CAN Udder Cleft NLD Central Ligament DEU Ligament IA Udder Cleft FRA Udder Depth USA Udder Depth CAN Udder Depth NLD Udder Depth DEU Udder Depth IA Udder Depth FRA Frnt eat Placement USA Fre eat Placement CAN eat Placement NLD eat Placement DEU eats Psitin IA eat Placement Frnt FRA eat Length USA Fre eat Length CAN eat Length NLD eat Length DEU eats Length IA eat Length FRA PA USA Cnfrmatin CAN Final Scre NLD Bdy ype DEU Final Scre IA ype Cmpsite FRA

A Matrix Representation of Panel Data

A Matrix Representation of Panel Data web Extensin 6 Appendix 6.A A Matrix Representatin f Panel Data Panel data mdels cme in tw brad varieties, distinct intercept DGPs and errr cmpnent DGPs. his appendix presents matrix algebra representatins