Somatic cell score genetic parameter estimates of dairy cattle in Portugal using fractional polynomials 1

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1 Published December 4, 214 Somatic cell score geetic parameter estimates of dairy cattle i Portugal usig fractioal polyomials 1 A. M. Martis, 2 A. M. Silvestre, M. F. Petim-Batista, ad J. A. Colaço Departmet of Aimal Sciece Cetro de Ciêcia Aimal e Veteriária (CECAV), Uiversity of Trás-os-Motes ad Alto Douro, Vila Real, Portugal ABSTRACT: Milk somatic cell cout is a idicator trait for mastitis resistace. Geetic parameters for somatic cell score i the Portuguese Holstei-Friesia populatio were estimated by modelig the patter of geetic correlatio over the first 3 lactatios (days i milk) with a radom regressio model. Data records from the first 3 lactatios were from the atioal database of the Portuguese Holstei Associatio herds. Heritability estimates raged from.5 at the begiig of the lactatio for the 3 lactatios, to.7 at the ed of the lactatio period for the first ad third lactatios, to.9 for the secod lactatio. This icrease i the heritability values was due to a icrease i the geetic variace ad a decrease i the residual variaces. Geetic correlatios evaluated for mothly time poits were high (.65 to.99) for all 3 lactatios, whereas pheotypic correlatios were much less tha the geetic correlatios (.13 to.62). Key words: geetic parameter, Holstei cattle, somatic cell score 211 America Society of Aimal Sciece. All rights reserved. J. Aim. Sci : doi:1.2527/as INTRODUCTION 1 The authors thak the Associação Nacioal para o Melhorameto dos Bovios Leiteiros for providig all the ecessary iformatio. Thaks also are exteded to CECAV (Uiversity of Trás-os-Motes ad Alto Douro, Vila Real, Portugal) ad FCT (Fudação para a Ciêcia e a Tecologia, Lisboa, Portugal) for fiacial support. 2 Correspodig author: agela@utad.pt Received May 31, 21. Accepted Jauary 1, 211. Mastitis is the most frequet ad expesive disease i dairy cattle, but i may coutries, icludig Portugal, the occurrece of mastitis is ot routiely recorded. Give the ecoomic importace of mastitis, selectio for mastitis resistace should be cosidered i dairy breedig programs, but geetic evaluatio of cliical mastitis is particularly difficult because of its low heritability ad the categorical ature of the trait (Negussie et al., 28). Somatic cell cout (SCC) has bee cosidered the most suitable idicator trait for mastitis resistace i view of its medium to high geetic correlatio with mastitis ad its greater heritability tha mastitis (Mrode ad Swaso, 1996), as well as its ease of recordig. Geetic evaluatio of SCC is mostly based o somatic cell score (SCS), a logarithmic trasformatio of SCC to achieve ormality of distributio (Ali ad Shook, 198). The radom regressio models used i geetic evaluatio for SCS are advatageous because it is assumed that the shape of the lactatio curve is also iflueced by radom geetic ad permaet evirometal effects. I this way, the geetic ad permaet evirometal correlatios betwee SCS at differet days i milk (DIM) ca be less tha 1 (De Roos et al., 23). Furthermore, the model ca accommodate heterogeeous additive geetic ad permaet evirometal variaces durig the lactatio. The degree of heterogeeity may deped o the fuctios chose to model the traectory of lactatio. The mai obectives of this study were to estimate the (co)variace compoets ad geetic parameters of SCS i the first 3 parities of Portuguese Holstei-Friesia cows. MATERIALS AND METHODS Aimal Care ad Use Committee approval was ot obtaied for this study because data were obtaied from a existig database, the Bovifor (Campus Agrário de Vairão, Vila do Code, Porto, Portugal). Data Mothly test-day records of SCC for the first 3 lactatios i Portuguese Holstei-Friesia cows ad their geealogy were provided by the Associação Nacioal para o Melhorameto dos Bovios Leiteiros (Quita da Medela, Verdemilho, Aveiro, Portugal). From the origial data set, records with SCC of less tha 6, or greater tha 3,, cells/ml of milk were discarded. The aalysis was limited to the records of cows calvig i 27 ad 28 because of computatioal limitatios. 1281

2 1282 Martis et al. Records from cows with a ukow calvig date were ot icluded. Oly records from cows that had calved betwee 18 ad 4 mo, 28 ad 56 mo, ad 38 ad 72 mo i the first, secod, ad third parities, respectively, were used. At least 5 SCC records per lactatio were required. The test dates betwee 5 ad 35 DIM were used. Classes of herd test date (HTD) were created, ad HTD classes with 2 or more observatios were used. The fial edited data set icluded 251,578, 23,723, ad 143,294 records of SCC for 32,341, 26,198, ad 18,564 cows i their first, secod, ad third lactatio, respectively. The umbers of herds for lactatios 1 to 3 were 1,724, 1,717, ad 1,631, respectively, ad the umbers of HTD classes were 24,645, 24,214, ad 21,6, respectively. Te DIM classes were defied based o 3-d periods for stage of lactatio groups, begiig at d 6 ad edig at d 35, with the purpose of reducig the total umber of combiatios ad hece the computatioal requiremets. It is well kow that SCC data are ot ormally distributed, ad other statistical aomalies were preset. Studies have idicated that the logarithmic trasformatio of SCC produces data with a more ormal distributio, icreased heritability, ad reduced heterogeeity of withi-herd ad withi-sire variaces (Shook, 26). Cosequetly, idividual SCC records for each mothly test day were trasformed to SCS (G. E. Shook, Uiversity of Wiscosi, Madiso, persoal commuicatio) as SCS = log 2 (SCC/1) + 4. Most authors use 3 istead of 4 as the costat i this formula because, i this way, the problem of egative values is overcome i the data. Model The uderlyig mea model for radom regressio aalysis of the SCS icludes terms to model the average tred of SCS durig the lactatio period ad selectio for other fixed effects to accout for evirometal factors ad possible iteractios amog them ad for the time tred. The time tred is modeled here via fractioal polyomials because of their simplicity, flexibility, ad parsimoy. Fractioal polyomials are a extesio of covetioal polyomials, but with real powers (Robert-Graié et al., 24). The fractioal polyomial of degree m (Robert-Graié et al., 22) is represeted as m m, ( t ξ, p )= ξ H (), t = where is the fractioal polyomial; m is the polyomial degree; =, 1,, m is a (m + 1) vector of ordered powers; t is a positive, real covariable; ξ = (ξ 1, ξ 2,, ξ m ) is the coefficiet vector; p = (p 1, p 2,... p m ) is the power vector; ad H t t p ()= ( ) if p p 1 ad H t H t t ()= 1 () l () if p = p 1. At the origi (for = ( ), H (t) = 1, ad p =. I this last formula, t p ) represets the Box-Tidwell trasformatio [i.e., ( p ) p t = t if p ( p ad t ) = l t if p = ]. For SCS, the geeral model used was Y = HTD + β AGE + β Z ikl i + α Z + km km km m= m= γ k Z m m= km km + ε ikl, where Y ikl is the lth SCS test-day record of cow k of the th age at calvig ad the ith herd test date; HTD i is the fixed effect of the ith HTD; β is the regressio coefficiet o the age of calvig (AGE) of cow k; β m represets the fixed regressio coefficiets, describig a DIM mea curve of the mth days i milk classes, α km ad γ km are the radom regressio coefficiets for the geetic ad permaet evirometal effects, respectively, of the mth days i milk classes of cow k; Z km is the m- powered variable i the polyomial evaluated as a fuctio of DIM of cow k; ad ε ikl is the radom residual effect, cosidered heterogeeous alog the lactatio. As recommeded by Robert-Graié et al. (24), the polyomial tested is a secod-order fractioal polyomial: ( t p)= + t + t ( t), 13 / 13 / 2, ξ, ξ ξ 1 ξ 2 l with p = (, 1/3, 1/3). Three rus of the previous model were performed for the first, secod, ad third parities. All calculatios were carried out usig the AS- Reml program (Gilmour et al., 22). RESULTS AND DISCUSSION Pheotypic Aalysis of SCC The basic statistics for SCC ad SCS are preseted i Table 1. The mea SCC icreased with lactatio umber. The maximum SCC value was 9,996, cells/ml i the third lactatio (Table 1). However, the umber of aimals with this SCC was small. The SCS meas were 3.54 ± 1.77, 4.7 ± 1.96, ad 4.45 ± 2.5 for the first, secod, ad third lactatios, respectively. These are greater values tha those obtaied i other studies, such as those by Reets et al. (1995), who reported 2.54 ± 1.56, 2.91 ± 1.71, ad 3.15 ± 1.79 for the first, secod, ad third lactatios, respectively, although we used 4, ot 3, as the offset. SCS by Stage of Lactatio Figure 1 shows the effect of DIM o SCS for the first 3 lactatios, which is iverted relative to the patter of the milk productio curve of each lactatio. The SCS

3 Somatic cell score geetic parameter estimates of Portuguese dairy cattle 1283 Figure 1. Tred of somatic cell scores (SCS) by days i milk (DIM) for the first, secod, ad third lactatios. was icreased i early lactatio. Thereafter, a sharp declie i SCS was observed. After 45 DIM, the SCS icreased steadily throughout the lactatio period. The variatio i SCS alog the lactatio period is i agreemet with those reported by Reets et al. (1995) ad Haile-Mariam et al. (21). Estimatio of Geetic Parameters for SCS For SCS, a large umber of heritability estimates ad variace compoets have bee reported i the literature (Mrode ad Swaso, 1996). Figure 2 ad Table 2 show SCS heritability estimates by DIM i the first 3 lactatios. The SCS mea heritability estimates were.6,.8, ad.6 for the first, secod, ad third lactatios, respectively, ad these results were similar to those obtaied by Haile-Mariam et al. (21) ad Mrode ad Swaso (23). The SCS heritability estimates icreased with stage of lactatio i the 3 lactatios ad were smaller for the first ad third lactatios (.5 to.7) compared with the secod lactatio (.5 to.9). This is i agreemet with patters of heritability for SCS reported by Petim-Batista et al. (22) ad Mrode ad Swaso (23), despite our estimates beig less. The icrease i heritability with DIM was due to the icreasig tred i additive geetic variace ad the decrease i residual variace (Table 2). I Portugal, the daily SCS heritability estimates i the last atioal geetic evaluatio, obtaied by the autoregressive method (Associação Nacioal para o Melhorameto dos Bovios Leiteiros, 21), were.18, Figure 2. Traectory of estimated heritability for somatic cell score by days i milk (DIM) for the first, secod, ad third lactatios..17, ad.15 for the first, secod, ad third lactatios, respectively, which were greater tha ours. The results showed a decrease i heritability estimates at the ed of the lactatio for the 3 lactatios. Kostatiov et al. (29) reported aalogous results. Similar to heritabilities, estimates of geetic variace icreased with DIM (Figure 3) for the first lactatio. This tred i geetic variace is cosistet with the results of Haile-Mariam et al. (21). I the secod ad third lactatios, the geetic variace icreased with DIM util 45 DIM, decreased subsequetly util 165 DIM for the secod lactatio ad util 225 DIM for the third lactatio, ad icreased thereafter up to the ed of lactatio (Figure 3). Permaet evirometal variaces for SCS were greater tha the geetic variaces durig subsequet DIM (Table 2 ad Figure 4) for all 3 lactatios. The permaet evirometal variaces followed the same patter for the 3 lactatios, beig greater i the third lactatio. The tred i residual variaces (Table 2) was cosistet with those reported by Kostatiov et al. (29) for all 3 lactatios. The estimates had high startig values ad the decreased with DIM. This study ad the results of Haile-Mariam et al. (21) ad Mrode ad Swaso (23) showed greater residual variaces i early lactatio. Table 3 shows the geetic ad pheotypic correlatios for SCS alog DIM for the first 3 lactatios. The geetic correlatios raged from.67 to.99 for the Table 1. Basic statistics for somatic cell cout (SCC) ad somatic cell score (SCS) for the first, secod, ad third lactatios First Secod Third Item SCC, 1,/mL SCS SCC, 1,/mL SCS SCC, 1,/mL SCS Miimum Maximum 7, , , Mea SD

4 1284 Martis et al. Table 2. Estimates of variace compoets ad heritability (h 2 ) for somatic cell score by days i milk (DIM) classes for the first, secod, ad third lactatios 1 First lactatio Secod lactatio Third lactatio DIM G EP E h 2 G 1 EP E h 2 G 1 EP E h G = additive geetic variace; EP = permaet evirometal variace; E = residual variace. first lactatio, from.7 to.99 for the secod lactatio, ad from.66 to.99 for the third lactatio. I geeral, geetic correlatios declied with a icreasig iterval i DIM for all 3 lactatios. Correlatios betwee the closest (e.g., 16 ad 45 DIM) ad most distat DIM (e.g., 16 ad 285 DIM) were, respectively,.94 ad.67,.94 ad.7, ad.94 ad.66 for the first, secod, ad third lactatios. Negussie et al. (26) reported similar geetic correlatios for SCS alog DIM whe usig a radom regressio model with Legedre polyomials. Betwee distat DIM (28 ad 31 DIM), Mrode ad Swaso (23) showed correlatios ragig from.83 to.99,.5 to.98, ad.19 to.99 for the first, secod, ad third lactatios, respectively. Pösö ad Mätysaari (1996) ad Haile-Mariam et al. (21) reported a tred of daily geetic correlatios betwee SCS withi a lactatio for differet DIM that was similar to the fidigs of our study. The pheotypic correlatios were much less tha the correspodig geetic correlatios, but they followed a patter similar to the correspodig geetic correlatios for all 3 lactatios (Table 3). Negussie et al. (26) obtaied greater estimates of pheotypic correlatios for SCS throughout lactatios (.61 to.98 for the first lactatio ad.65 to.96 for later lactatios). I cotrast, Haile-Mariam et al. (21) ad Mrode ad Swaso (23) reported pheotypic correlatios similar to the fidigs of our study. The least pheotypic correlatios, of.13,.15, ad.17, were betwee 16 ad 285 DIM for the first, secod, ad third lactatios, respectively. I coclusio, the geetic parameters for SCS estimated i this study are i agreemet with the results from other studies. The heritability for SCS icreased with DIM, with a mea of.6 for the first ad third lactatios ad a mea of.8 for the secod lactatio. The geetic correlatios betwee SCS at differet DIM were high (.65) for all 3 lactatios, eve for the most distat DIM, ad the pheotypic correlatios were low (.13 to.58,.15 to.61, ad.17 to.62 for the first, secod, ad third lactatios, respectively), but with the same patter as for the geetic correlatios. The estimatio of those geetic parameters ad the types of effects ad model used will be the first step toward implemetig a geetic evaluatio for SCS i the Portuguese Holstei-Friesia populatio. Figure 3. Traectory of geetic variaces (G) for somatic cell score by days i milk (DIM) for the first, secod, ad third lactatios. Figure 4. Traectory of permaet evirometal variaces (EP) for somatic cell score by days i milk (DIM) for the first, secod, ad third lactatios.

5 Somatic cell score geetic parameter estimates of Portuguese dairy cattle Table 3. Estimates of geetic (below diagoal) ad pheotypic (above diagoal) correlatios betwee somatic cell score o selected days i milk (DIM) i the first, secod, ad third lactatios 1285 Lactatio ad DIM DIM First Secod Third LITERATURE CITED Ali, A. K. A., ad G. E. Shook A optimum trasformatio for somatic cell cocetratio i milk. J. Dairy Sci. 63: Associação Nacioal para o Melhorameto dos Bovios Leiteiros (ANABLE). 21. Avaliação Geética Nacioal Touros da Raça Holstei Frísia Março 21. ANABLE, Aveiro, Portugal. De Roos, A. P. W., A. G. F. Harbers, ad G. de Jog. 23. Geetic parameters of test-day somatic cell score estimated with a radom regressio model. Iterbull Bull. 31. It. Bull Eval. Serv., Uppsala, Swede. Gilmour, A. R., B. J. Gogel, B. R. Cullis, S. J. Welham, ad R. Thompso. 22. ASReml User Guide Release 1.. VSN It., Hemel Hempstead, UK. Haile-Mariam, M., M. E. Goddard, ad P. J. Bowma. 21. Estimates of geetic parameters for daily somatic cell cout of Australia dairy cattle. J. Dairy Sci. 84: Kostatiov, K. V., K. T. Beard, M. E. Goddard, ad J. H. J. va der Werf. 29. Geetic evaluatio of Australia dairy cattle for somatic cell scores usig multi-trait radom regressio testday model. J. Aim. Breed. Geet. 126: Mrode, R. A., ad G. J. T. Swaso Geetic ad statistical properties of somatic cell cout ad its suitability as a idirect meas of reducig the icidece of mastitis i dairy cattle. Aim. Breed. Abstr. 64: Mrode, R. A., ad G. J. T. Swaso. 23. Estimatio of geetic parameters for somatic cell cout i the first three lactatios usig radom regressio. Livest. Prod. Sci. 79: Negussie, E., M. Koivula, E. A. Mätysaari, ad M. Lidauer. 26. Geetic evaluatio of somatic cell score i dairy cattle cosiderig first ad later lactatios as two differet but correlated traits. J. Aim. Breed. Geet. 123: Negussie, E., I. Stradé, ad E. A. Mätysaari. 28. Geetic associatio of cliical mastitis with test-day somatic cell score ad milk yield durig first lactatio of Fiish Ayrshire cows. J. Dairy Sci. 91: Petim-Batista, F., J. L. Foulley, C. Robert-Graié, A. Silvestre, ad J. Colaço. 22. SCS aalysis i Portuguese dairy cows usig radom coefficiet models. I Proc. 7th World Cogr. Geet. Appl. Livest. Prod., Motpellier, Frace. Commu. No Pösö, J., ad A. Mätysaari Relatioships betwee cliical mastitis, somatic cell score, ad productio for the first three lactatios of Fiish Ayrshire. J. Dairy Sci. 79: Reets, R., J. Jamrozik, L. R. Schaeffer, ad J. C. M. Dekkers Estimatio of geetic parameters for test day records of somatic cell score. J. Dairy Sci. 78: Robert-Graié, C., J.-L. Foulley, E. Maza, ad R. Rupp. 24. Statistical aalysis of somatic cell scores via mixed model methodology for logitudial data. Aim. Res. 53: Robert-Graié, C., E. Maza, R. Rupp, ad J. L. Foulley. 22. Use of fractioal polyomial for modelig somatic cell scores i dairy cattle. I Proc. 7th World Cogr. Geet. Appl. Livest. Prod., Motpellier, Frace. Commu. No Shook, G. E. 26. Maor advaces i determiig appropriate selectio goals. J. Dairy Sci. 89: