FACTORS INFLUENCING BEST ANNUAL RACING TIME IN FINNISH HORSES 1 ABSTRACT

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1 FACTORS INFLUENCING BEST ANNUAL RACING TIME IN FINNISH HORSES 1 M. Ojala, L. D. Van Vleck 2 and R. L. Quaas 2 University f Helsinki Helsinki, Finland ABSTRACT The fixed effects f year f race, seasn f race, sex, methd f start, annual number f starts, length f race and racetrack were evaluated n best annual racing time in Finnish Hrses. Data included 1,378 recrds fr 554 hrses by 206 sires. Five mdels were assumed within the age grups frm 3 t 6 yr. The annual number f starts, methd f start and seasn f race effects were interrelated. An increase in number f starts was assciated with cnsiderable imprvement in a hrse's best annual racing time. Recrds shuld nt, hwever, be adjusted fr effect f annual number f starts because it wuld simultaneusly accunt fr part f genetic differences amng hrses. The largest estimates f heritability were btained fr best annual racing time when the mdel included the fixed year-seasn and sex effects. Crrespnding t this mdel, the estimate f repeatability fr best annual racing time ver the fur age grups was An example f best linear unbiased predictins f sires' breeding values based n prgeny recrds in ne r several ages is presented. (Key Wrds: Racehrses, Trtting, Racing Perfrmance, Envirnmental Factrs, Heritability, Repeatability.) Intrductin In mst cuntries racing assciatins rutinely summarie individual race recrds fr each hrse n an annual basis and n the basis f the whle racing career. If data cnsisting f race recrds are used t select individuals fr breeding purpses, recrds shuld be adjusted fr pertinent envirnmental effects. Data cnsisting f individual race recrds n trtters have been analyed by several authrs (Linner and Osterkrn, 1974; Katna and Osterkrn, 1977; Hint and Van Vleck, 1978; Katna, 1979; Ttley et al., 1983) t estimate effects influencing the recrds. The studies shw that numerus effects cntribute t the utcme f a race. It is nt bvius, hwever, fr which effects and hw these data shuld be adjusted when the bject is breeding evaluatin f trtters. When the data have been summaried 1 This study was financially supprted, in part, by the Finnish Trtting and Hrse Breed. Assc. 2Dept. f Anita. Sci., Crnelt Univ., Ithaca, NY Dept. f Anim. Breed. Received February 26, Accepted August 28, n an annual basis, the number and the interpretatin f the factrs influencing the best annual racing time bviusly differ frm thse influencing time recrds in individual races. The bjective f this study was t evaluate the effect f the year f race, seasn f race, sex, methd f start, annual number f starts, length f race and racetrack n best annual racing time in Finnish Hrses. Materials and Methds Data. The riginal set f data cnsisted f individual race recrds made by Finnish Hrses brn in 1967 r 1968 that tk part in trtting races at ages f 3 t 6 yr. The infrmatin in individual race recrds was summaried annually fr each hrse. A recrd used in this study was a. hrse's best annual racing time, expressed in secnds per kilmeter. There was a ttal f 1,378 recrds fr 554 hrses by 206 sires in the data. The numbers f hrses having a recrd at 3, 4, 5 r 6 yr f age were 216, 362, 373 and 427. In additin t a hrse's age, the fllwing infrmatin abut fixed factrs, which may influence a hrse's best annual racing time, was available: 1) year f race: 2 yr within each age grup ; 2) seasn f race: cded frm riginally 109 J. Anim. Sci :

2 110 OJALA ET AL. reprted mnth f race as winter (mnths 1 t 4), summer (6 t 9), fall and spring (10 t 12 and 5); 3) sex: stallin, mare and gelding; 4) methd f start: aut-start, which is a flying start behind a car, and vlt-start in which hrses are handicapped, based n ttal lifetime earnings r smetimes n best time in lifetime, by increments f 20 m behind the base distance; 5) annual number f starts: cded in six grups as 1, 2, 3 and 4; 5 t 9; 10 t 19; and ~20 starts; 6) length f race: cded as 2,000 m and 2,000 m; 7) racetrack: 11 individual tracks, and in additin 10 track grups frmed frm individual tracks n the basis f the lcatin in the cuntry. Sire and Residual Variance Cmpnents. The data set was edited s that each sire was required t have at least tw prgeny in an age grup. This resulted in a data set with 1,009 recrds. The numbers f hrses in the fur age grups were 151,259,278 and 321, respectively. There were, n average, five t six prgeny per sire within an age grup. These data were previusly analyed by Ojala and Van Vleck (1981) fr 24 traits under the assumptin f simple statistical mdels. T estimate sire and residual variances, the data were analyed using five different mdels. The linear mdel assumed within each age grup was in general frm: y=xb+zs+e, [1] where y is a N x 1 vectr f hrses' best annual racing times; X and Z are knwn incidence matrices with N rws and p and q clumns, respectively; b is a vectr f unknwn fixed effects f length p; s is a q 1 nn-bservable vectr f randm sire effects representing ne-half f sires' breeding values and e is a N 1 nn-bservable vectr f randm residual effects. It was assumed that the randm vectrs have null means and [:] ] 0 s 0 var = IO 2. The five mdels studied differed in the fixed part f equatin [1] as fllws: Mdel 1 (full mdel)-b cnsisted f yearseasn subclass, sex, methd f start-length f race subclass, annual number f starts and racetrack effects; Mdel 2-b cnsisted f year-seasn subclass, sex, methd f start and annual number f starts effects; Mdel 3-b cnsisted f year-seasn subclass, sex and methd f start effects; Mdel 4-b cnsisted f year-seasn subclass and sex effects; Mdel 5 (simple mdel)-b cnsisted f general mean nly. Cmpnents f variance were estimated using least-squares (LS) equatins in [2] based n equatin [1] : [x,x x, 1 ix,, L'y [2] In rder t perfrm calculatins, sire effects (s) were temprarily cnsidered fixed. This prcedure results in variance cmpnents that are estimates f Hendersn's methd 3 (Searle, 1971). Using estimates f sire and residual variances, heritabilities (h 2 ) f best annual racing time were estimated based n the intra-class crrelatin f paternal half-sibs. Apprximate standard errrs f heritabilities were calculated applying frmulas and in Falcner (1981). Estimatin Effects f Fixed Factrs. T estimate effects f fixed factrs and t btain crrectin factrs fr pre-adjusting the data, the LS equatins in [2] were mdified. A rati f estimated variances (2/as 2) was added t the diagnal elements f the Z~Z submatrix relating t the randm sire effect in the equatin [1]. This rati f variances can be accunted fr if an estimate f heritability fr the trait is knwn. Heritability f.25 fr best annual racing time was assumed. The mdified LS equatins, called the mixed mdel (MM) equatins accrding t Hendersn (1974), yield the same slutins as the generalied leastsquares (GLS) methd. Cnsequently, estimable functins f the fixed effects in the mdel are best linear unbiased estimates (BLUE). The estimable functin f interest in this study was a difference between the levels within a fixed factr, i.e., the effect f a level f a factr.

3 FACTORS INFLUENCING RACING TIME 111 These will be called differences later in this paper. The difference between tw levels f a fixed factr was tested fr statistical significance by the tw-tailed t-test (Snedecr and Cchran, 1967). Variances f differences were calculated as shwn by Searle (1971). Hrse and Residual Variance Cmpnents. The data set was edited s that each hrse was required t have at least tw recrds, i.e., a recrd in tw r mre f the fur age classes. The data set fr estimating hrse and residual variances and repeatability f best annual racing time included 1,244 recrds n 420 hrses. Cmpnents f variance were estimated fr bth pre-adjusted and unadjusted best annual racing times. Recrds were pre-adjusted fr all ther fixed effects in mdels 2 t 4, except fr year-seasn effects. Additive adjustment factrs were btained by reversing the sign f the differences in slutins. The equatin f the mdel was: y=xb+zh+e, [3] where y is a vectr f pre-adjusted best annual racing times n hrses aged 3 t 6 yr; X and Z are knwn incidence matrices; b is a vectr f fixed age-year-seasn subclass effects; h is a vectr f randm hrse effects representing the genetic effects and permanent envirnmental effects assciated with a hrse and e is a vectr f randm residual effects. It was assumed that the randm vectrs have null means and var [:l [i? 0 lci. In cmputing the cmpnents f variance, hrse effect was temprarily cnsidered fixed. The estimate f repeatability (r) fr best annual racing time was the estimated intraclass crrelatin. The apprximate standard errr f repeatability was calculated accrding t Falcner (1981). Sires' Breeding Values. Predictins f sires' breeding values within an age grup were btained jintly in the cntext f estimating differences between the levels f fixed factrs. As btained frm the MM equatins, predictins f ne-half f sires' breeding values are, accrding t Hendersn (1974), best linear unbiased predictins (BLUP). An verall predictin (acrss age grups) f a sire's breeding value may be btained using repeated recrds n prgeny. The mdel, based n Hendersn (1977), was: y=xb+zl s+z2 p+e, [4] where y is a vectr f pre-adjusted best annual racing times n sires' prgeny fr any f the ages f 3 t 6 yr; X, Z1 and Z2 are incidence matrices fr fixed effects, sires and prgeny, respectively; b is a vectr f fixed age-year-seasn effects, s is a randm vectr f ne half f sires' additive genetic values; p is a randm vectr representing the genetic effects nt accunted fr in s and permanent envirnmental effects assciated with the prgeny f sires and e is a randm vectr f residual effects. The randm vectrs, s, p and e, were assumed t have null means and variance-cvariance matrices Ias 2=I.25h 2 tl~,i 3 =I(r-.25h 2) a~ and I a~ = I (1 - r) ~, respectively. It was als assumed that cv (s, p') = cy (s, e') = cy (p, e') = O. Estimates f h 2 =.25 and r =.50 were assumed. Thus, the fllwing ratis f variances Oe/a s = 8 and Oe/a p were added in diagnal elements f sire x sire and prgeny prgeny submatrices n the left-hand side f the nrmal equatins as shwn by Hendersn (1977). Results and Discussin Estimates f Sire and Residual Variances. Mdel 1 represented the full mdel, including the fllwing fixed effects: year-seasn, sex, methd f start-length f race, number f starts and racetrack. Mdel 1 resulted in the smallest residual variance fr best annual racing time in each age grup (table 1). Omitting the racetrack and length f race effects frm mdel 1 increased the estimate f residual variance nly slightly (mdel 2). Sire variances were similar in

4 112 OJALA ET AL. magnitude fr mdels 1 and 2. These tw statements apply fr all age grups except 3-yr-lds. Omissin f the number f starts effect frm mdel 2 resulted in a marked increase in bth sire and residual variances (mdel 3). This implies that the annual number f starts effect is assciated with bth additive genetic and envirnmental effects influencing a hrse's best annual racing time. Omitting the methd f start effect frm mdel 3 resulted in a slight increase in bth sire and residual variances (mdel 4). Residual variance fr best annual racing time was largest when the mdel included nly the fixed effect f the general mean (mdel 5). The statements regarding mdels 4 and 5 apply fr all age grups except 3-yr-lds. N general pattern culd be drawn abut sire and residual variances in the different age grups. This may be due t the limited number f recrds and partly t different samples f sires in the fur age grups. Estimates f heritability were largest when based n mdels 3 and 4. In ther wrds, the magnitude f heritabilities was the largest, abut.50 n average, when mdels included year-seasn and sex r these and methd f start as fixed effects (table 2). Estimates f heritability were assciated with large standard errrs (table 2). Cnsequently, the estimated heritabilities are f little value as estimates f parameter values. The merit f the estimated variance cmpnents and heritabilities in this study is that they give intimatins abut the nature f influences f the fixed factrs included in the different mdels. Effects f Fixed Factrs. Racetrack and length f race effects did nt accunt fr much f the variatin in best annual racing time (table 1). This is in accrd with the cncept that track effect des nt apply well t data cnsisting f hrses' best annual racing times. This is partly due t the specific feature attached t a hrse's best annual racing time: it is required that several f the favrably cntributing factrs ccur simultaneusly; timing f a hrse's peak perfrmance bviusly has a majr influence. Thus, in such data, the track effect mainly represents the quality f hrses t which races are being ffered n a particular track. Hrses' best annual racing times, expressed in secnds per kilmeter, imprved as the length f race increased. Only a cntrary result wuld have supprted adjusting fr this effect. The discrepancy is partly ex- TABLE 1. ESTIMATES OF SIRE AND RESIDUAL VARIANCES FOR BEST ANNUAL RACING TIME a Estimates f variance cmpnents Mdel b and surce by age f hrse f variance 3 yr 4 yr 5 yr 6 yr Mdel 1: (A, B, C, D, E) Sire Residual Mdel 2: (A, B, D, F) Sire Residual Mdel 3: (A, B, F) Sire Residual Mdel 4: (A, B) Sire Residual Mdel 5: (G) Sire Residual a Expressed m s/km. bfixed effects in the mdels are: year-seasn (A), sex (B), methd f start-length f race (C), number f starts (D), race track (E), methd f start (F), general mean (G).

5 FACTORS INFLUENCING RACING TIME 113 TABLE 2. ESTIMATES OF HERITABILITY (h 2 ) AND APPROXIMATE STANDARD ERRORS (SE) FOR BEST ANNUAL RACING TIME Age f hrse, yr Mdel a h 2 SE h 2 SE h 2 SE h 2 Avg f SE h ~ Mdel 1: (A, B, C, D, E) Mdel 2: (A, B, D, F) Mdel 3: (A, B, F) Mdel 4: (A, B) Mdel 5: (G) afixed effects in the mdels are: year-seasn (A), sex (B), methd f start-length f race (C), number f starts (D), race track (E), methd f start (F), general mean (G). plained by the fact that a large number f hrses had achieved their best annual racing time at a lng distance n vlt-start. Fr previus reasns, n adjustment fr racetrack and length f race culd be justified. The annual number f starts effect was ne f the majr factrs influencing a hrse's best annual racing time (table 3). An increase in the number f starts was assciated with a decrease, i.e., an imprvement, in a hrse's best annual racing time. This result is bvius because hrses with several starts had mre chances t express their ptential speed than hrses with a single r nly a few starts. The statement may als be interpreted t suggest that pr quality hrses acquire, in general, nly a few starts. Sme ther reasns cntributing t variatin in annual number f starts are differences in sundness amng hrses, and in expertise and enthusiasm amng wners and trainers f hrses. Thus, bth genetic and envirnmental effects bviusly cause the number f starts amng hrses t vary, as implied thrugh mdels 2 and 3 in tables 1 and 2. T avid remving additive genetic differences amng hrses, the number f starts effect was excluded frm mdel 3. Aut-start as a methd f start was superir t vlt-start (table 3). Althugh there is n dubt abut the general validity f the result, it shuld be nted that nt all hrses had the pprtunity t race n bth methds f start. In additin, mre races are being ffered n vlt-start than n aut-start. This is als implied thrugh the relative number f hrses having achieved their best annual racing time n the tw methds f start. Althugh the influence f the methd f start effect was substantial n best annual racing time (table 3), its influence n the magnitude f sire and residual variances (table 1) and heritabilities (table 2) was negligible, as implied thrugh mdels 3 and 4. Anther, and perhaps a mre apprpriate, way t accunt fr the methd f start effect wuld have been t treat best annual racing time based n the tw methds f start as separate traits. Of year-seasn and sex effects, nly the seasn effect had a statistically significant influence n a hrse's best annual racing time (table 3). The purpse f having the seasn effect in the mdel was t accunt indirectly fr track cnditin. This effect wuld, hwever, apply better t a set f data cnsisting f individual race recrds. But when the data cmprise race recrds summaried annually fr hrses, inclusin f the seasn effect in the mdel may nt sufficiently serve its riginal purpse. This statement is partly based n the relatinship between the annual number f starts and seasn effects. It is unlikely, fr example, that hrses with several starts in a year achieve their best annual racing time during the early part f the year. Cnnectin between the tw fixed effects was als implied thrugh a marked increase in differences fr year-seasn effects in mdel 3 after excluding the number f starts effect frm mdel 2 (table 3). The methd f start effect is als partially cnnected t the number f starts and seasn effects fr the previus reasns. The results in the ther age grups were cnsistent with thse fr five-year-ld hrses in table 3. Estimates f Hrse and Residual Variances. The smallest estimate fr residual variance was

6 114 OJALA ET AL..~. r~ eq'~- 7 c Z eqem,~" ~xexl a,...1 > M V- e e~ Z I Z Z e~ M [... r-, 1,...4 g

7 FACTORS INFLUENCING RACING TIME 115 TABLE 4. ESTIMATES OF HORSE AND RESIDUAL VARIANCES, AND REPEATABILITIES (r) FOR BEST ANNUAL RACING TIME (BEST TIME) a Estimates f variance due t Trait and mdel b Hrse Residual r SE Best time pre-adjusted fr B, D and F Best time pre-adjusted fr B and F Best time pre-adjusted fr B Best time (nt pre-adjusted) , , , ,03 aexpressed in s/km. bmdel including the fixed age-year-seasn effect was fitted n recrds pre-adjusted within age grups fr the fixed sex (B), number f starts (D) and methd f start (F) effects frm mdel 2, fr B and F frm mdel 3 and fr B frm mdel 4, respectively. btained when hrses' best annual racing times were pre-adjusted fr sex, methd f start and number f starts effects (table 4-). Pre-adjusting best annual racing time fr these effects resulted als in the smallest estimate f hrse variance. Thus, the number f starts effect accunted fr bth genetic and envirnmental differences in hrses' best annual racing times. The mst favrable rati between these tw cmpnents f variance, as represented by the largest estimate f repeatability, was btained when the recrds had been pre-adjusted fr sex. In this case, the estimate f repeatability fr best annual racing time was Mdel f Cbice. Predictin f sires' breeding values requires the recrds n prgeny t be adjusted fr apprpriate fixed effects. Fr applicatins, the mdel shuld be as simple as pssible. In selectin f the mdel, the bias resulting frm deleting factrs frm the mdel, as well as the magnitude f the variances f the estimates, shuld als be cnsidered (Hcking, 1976). The data in this study were nt suitable fr btaining reliable estimates f genetic parameters, but may serve as a guide t achieve a better understanding f the nature f such data. The results were quite similar in the fur age grups studied. Chsing the apprpriate mdel frm the different alternatives was cmplicated by the fact that bth genetic and envirnmental effects were cnfunded with certain factrs. The effect f number f starts had a majr influence n bth genetic, including the additive genetic, and envirnmental variatin. If selectin is fr imprving a hrse's capacity fr speed as characteried by best annual racing time, hrses with an increasing number f starts in a year wuld be favred. This is fully in accrd with a prper selectin gal in breeding trtters. Year and sex effects did nt exert a significant influence n best annual racing time in this study. These effects shuld, hwever, be included in the mdel if evaluatin f sires' breeding values is within an age grup. The methd f start effect shuld als be prperly accunted fr. This cnclusin agrees with results fr mdels used by ROnningen (1975) and Langlis (1984) in analying similar data. Sires' Breeding Values. Predictins f sires' breeding values within each age grup were btained simultaneusly with the estimatin f effects f fixed factrs fr mdels 2 t 4. Ranking f sires based n BLUP fr ne-half f sires' breeding values was quite cnsistent within an age grup fr the three mdels. Slight differences ccurred between ranking f sires within the fur age grups fr mdel 4 (table 5). Sire evaluatin, which was based n a cmbinatin f recrds at all ages, was parallel t thse based n recrds f 5- and 6-yr-ld prgeny. Bth within-age-grup and verall evaluatins f sires are bviusly useful fr hrsemen. This is supprted by bservatins n a recent sire evaluatin in which substantial differences ccurred between the within-age-grup evaluatins fr sme sires (Ojala, 1985). Additive relatinships amng the male ancestrs f the prgeny will be implemented, as shwn by Hendersn (1975), in the sire evaluatin prcedure. This wuld increase the accuracy f evaluatins fr sires having small prgeny grups. The bias due t selectin f

8 116 OJALA ET AL. e~ U ~:e~.~ I I I 9 9 mates fr the sires evaluated wuld als be reduced by including the maternal grandsire effect in a mdel. In additin, sire evaluatins shuld als include ther measures f racing perfrmance, as traits based n earnings and placings, t supplement the best annual racing time. F- L~ ~e r,-.1 > N m M N u4,..1 m O, m 0J Zc~ rn U O. ~ m O. e ~ N ~ d ~ I I I 7~,,~ e. ca I~.~ Literature Cited Falcner, D. S Intrductin t Quantitative Genetics (2nd Ed.). Lngman Inc., New Yrk. Hendersn, C. R General flexibility f linear mdel techniques fr sire evaluatin. J. Dairy Sci. 57:963. Hendersn, C. R Inverse f a matrix f relatinships due t sires and maternal grandsires. J. Dairy Sci. 58:1917. Hendersn, C. R Predictin f future recrds. In: E. Pllak, O. Kempthrne and T. B. Bailey, Jr. (Ed.) Prc. Int. Cnf. Quantitative Genet. pp Iwa State Univ. Press, Ames. Hint, R. L. and L. D. Van Vleck Factrs influencing racing perfrmance f the Standardbred pacer. J. Anim: Sci. 46:60. Hcking, R. R The analysis and selectin f variables in linear regressin. Bimetrics 32:1. Katna, ~ Envirnmental factrs influencing the racing perfrmance f the German trtter. Paper, 30th Annu. Meet. Eur. Assc. Anita. Prd. Katna, /J. and K. Osterkrn Genetischstatistische Auswertung des Leistungsmerkmals Renneit in der deutschen Traberppuladnen. Ziichtungskunde 49:185. Langlis, B Heritability and genetic crrelatins fr best racing times and earnings in 2-6 year ld French Trtters (in French with English summary). Paper, 35th Annu. Meet. Eur. Assc. Anita. Prd. Linner, M.Th. and K. Osterkrn Z~ichterische Auswertung der Rennleistung yn Traberpferden der Jahrggnge 1963 und 1964 in der BRD. ZUchtungskunde 46:168. Ojala, M Sire index fr trtters (in Finnish). Hevsurheilu 61: N. 34. Ojala, M. J. and L. D. Van Vleck Measures f racetrack perfrmance with regard t breeding evaluatin f trtters. J. Anita. Sci. 53:611. RiSnningen, K Genetic and envirnmental factrs fr traits in the Nrth-Swedish trtter. Z. Tier. Ziichtungsbil. 92:164. Searle, S. R Linear Mdels. Jhn Wiley and Sns, Inc., New Yrk. Snedecr, G. W. and W. G. Cchran Statistical Methds (6th Ed.). Iwa State Cllege Press, Ames. Tlley, E. A., D. R. Ntter and T. J. Marlwe Heritability and repeatability f speed fr 2- and 3-year-ld Standardbred racehrses. J. Anita. Sci. 56:1294. ~_~.~ -~ ~