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Analysis of longevity in Slovenian holstein cattle

Analysis of longevity in Slovenian holstein cattle doi:10.2478/v10014-011-0025-5 COBISS:1.01 Agriscategorycode:L01 KlemenPOTOCNIK1,VesnaGANTNER2,JurijKRSNIK1,MiranSTEPEC1,BetkaLOGAR3, GregorGORJANC1 ReceivedAugust20,2011;acceptedSeptember22,2011. Delojeprispelo20.avgusta2011,sprejeto22.septembra2011. Analysis of longevity in Slovenian holstein cattle ThelongevityofSlovenianHolsteinpopulationwasanalysedusingsurvivalanalysiswithaWeibullproportionalhazardmodel.DataspannedtheperiodbetweenJanuary1991and January2010for116,200cowsfrom3,891herds.Longevitywas described as the length of productive life ­ from first calving tillcullingorcensoring.Recordsabovethesixthlactationwere censored to partially avoid preferential treatment. Statistical modelincludedtheeffectofageatfirstcalving,stageoflactationwithinparity,yearlyherdsizedeviation,seasondefinedas year,herd,andsire-maternalgrandsire(mgs).Someeffectshad timevaryingcovariates,whichleadto1,839,307oronaverage 16elementaryrecordspercow.Herdandsire-maternalgrandsireeffectsweremodelledhierarchically.Pedigreeforsiresand maternalgrandsiresincluded2,284entries.Estimatedvariance betweenherdswas0.12,whilebetweensirevariancewas0.04. Heritabilitywasevaluatedat0.14.Genetictrendforsireswas unfavourable,butnotsignificant.Afurtherresearchisneeded todefinetherequirednumberofdaughterspersireandthedynamicsofgeneticevaluationforsireswhosemajorityofdaughtersstillhavecensoredrecords. Key words:cattle/breeds/SlovenianHolstein/longevity /Weibullproportionalhazardsmodel Analiza dolgozivosti pri crno-beli pasmi goveda v Sloveniji Za analizo dolgozivosti smo pri slovenski crno-beli populaciji govedi uporabili metodologijo analize prezivetja in Weibullov model sorazmernih ogrozenosti. V analizo smo vkljucilipodatke116.200kraviz3.891credskoziobdobjeod januarja1991dojanuarja2010.Dolgozivostjebilapredstavljenakotdobaproduktivnegazivljenja,kijedefiniranakotstevilo odprvetelitvedoizlocitvealidodatumazajemapodatkovza zivali,kisonatadatumbilesezive.Sestoinkasnejselaktacije smookrnilinakonecsestelaktacije,dasmoomililiprecenjenostboljsihzivali.Vstatisticnimodelsmovkljucilivplivstarostiobprvitelitvi,stadijalaktacijelocenozavsakozaporedno laktacijo,spreminjanjevelikosticredemedleti,letotelitve,credo,ocetainmaterinegaoceta.Ravninekaterihvplivovsocasovnospremenljivi,karpovzroci,dasmovanaliziobravnavali 1.839.307 zapisov ali povprecno 16 osnovnih zapisov na kravo.Credainvplivocetazmaterinimocetomstabilavmodel vkljucenahierarhicno.Rodovnikzaoceteinmaterineoceteje obsegal2.284zapisov.Ocenjenavariancazavplivcredejeznasala0,12,medtemkojeocenavariancemedocetiznasala0,04. Dednostnidelezjebilocenjenna0,14.Genetskitrendimanegativnosmer,anistatisticnoznacilen.Potrebnebodonadaljnje raziskave,dabomodolocilizadostnostevilohcerapobikuin dinamiko obracunov plemenskih vrednosti za bike, ki imajo vecinohcerasevfaziprireje. Kljucne besede:govedo/pasme/slovenskacrno-belapasma/dolgozivost/Weibullovmodelsorazmernihogrozenosti INTRODUCTION Longevityisatraitwithgreatimpactondairyproduction economy and is, therefore, of considerable importanceindairycattlebreedingprogrammes(Charffed- dineet al.,1996;StrandbergandSoelkner,1996).With theincreaseoflongevity,theproportionofmaturecows thatproducemoremilkincreases.Forexample,Strandberg(1996)estimatedthatanincreaseinlongevityfrom threetofourlactationsincreasesaveragemilkyieldper 1 Univ.ofLjubljana,BiotechnicalFac.Dept.ofAnimalScience,Groblje3,SI-1230Domzale,Slovenia 2 J.J.StrossmayerUniv.inOsijek,Fac.ofAgriculture,TrgSvetogTrojstva3,31000Osijek,Croatia 3 AgriculturalinstituteofSlovenia,Hacquetova17,SI-1000Ljubljana,Slovenia Acta argiculturae Slovenica, 98/2, 93­100, Ljubljana 2011 lactationandprofitperyearbetween11and13%.Inaddition,improvementinlongevitydecreasesreplacement costsandsomewhatincreasesselectionintensity. There are several ways to implement selection on longevityinthebreedinggoal,directlyorindirectly.Directlongevitycanberepresentedasthelengthof(productive)life(LPL)orstayability.IncattlebreedingLPL is usually defined as the elapsed time between the first calving and culling, while stayability is defined as a binarytraitthatmeasurescowsurvival(liveorculled)at acertainpointintime.TheuseofLPLispreferredsince stayability as a discrete trait provides less information. Unfortunately, LPL, as well as stayability, can be quantified only after the cows are culled, though both approachesprovidepartialinformationwhencowsurvives to the next "period" in life. Therefore, the information onthelongevityofdaughtersofasirebecomesavailable withtheincreasingageofasire.Thisinherentlyleadsto the prolonged generation interval. Low heritability for longevity(ShortandLawlor,1992;VollemaandGroen, 1996) induces unreliable estimation of breeding values (BV)basedonlyontheinformationofparentsorgrandparents. Due to long generation interval, breeding programmesalsoincludeindirectmeasuresoflongevityvia correlatedtraitssuchasfertility,health,andconformationtraits(Burnsideet al.,1984).Additionalgainisdue to the fact that the data on these indirect traits can be collectedrelativelyearlyinthelifeofacow.Nonetheless, both representations of longevity (direct and indirect) haveameritinamodernbreedinggoal(Essl,1998). Analysis of indirect representations of longevity is to a large extent done with a standard linear model based on the Gaussian (normal) distribution. Specific approachisneededforaproperanalysisoftheLPL,due to the presence of live animals at the time of analysis (censored records) and changes in culling criteria over theproductivelifeofcows(timevaryingcovariates)(e.g. Ducrocq et al., 1988a). Exclusion of censored records fromtheanalysis,ortreatingthemasuncensoredleads tobiasedresults(Ducrocq,1994).Additionally,relationshipbetweenlongevityanditseffectsisrathermultiplicativethanadditive(e.g.Ducrocqet al.,1988a).Survival analysis can handle this kind of data. In the last years severalcountriesintroduceddirectlongevityintheroutine genetic evaluation of cattle and most of them use the Weibull proportional hazard model (INTERBULL, 2009),whichrepresentsaclassofmodelsinthefieldof survival analysis. Other statistical approaches (models) can also be used, but proportional hazard model have better properties (e.g. Caraviello et al., 2004; Jamrozik et al.,2008;Potocniket al.,2008). Theaimofthisstudywastopresenttheresultsof 94 genetic evaluation for the length of productive life in Slovenian Holstein population using a Weibull proportionalhazardmodel. MATERIAL AND METHODS 2.1 DATA Rawdatafor126,716SlovenianHolsteincowsborn from1982to2008wereprovidedbytheAgriculturalInstituteofSlovenia.Inordertouseolddatabuttoavoid modelling the data up to the year 1991, the truncation datewassetatJanuary1st1991.Ontheotherside,thedate of last data collection was January 29th 2010. For cows aliveatthattimelongevitywastreatedasrightcensored. Longevity was defined as the length of productive life (LPL)andwascalculatedasthenumberofdaysfromthe firstcalvingtoculling(uncensored/completerecords)or tothemomentofdatacollection(incomplete/censored records). The LPL of cows surviving beyond the sixth lactation was also censored in order to avoid the effect ofpreferentialtreatmentandtofocusonearlycullingin thelifeofacow.Cowswithmissingorinconsistentdata within the defined limits were removed (29,252 cows): culling before the date of truncation, calving date after thedateofculling,noinformationfor600 daysaftercalving,missingdataforthefirstthreelactations,daughters ofsireswithlessthan20daughters,andmissingcovariate orfactordata. Thestructureofuseddataanddescriptivestatistics are given in Table 1. Altogether LPL for 116,200 cows from3891herdswereusedintheanalysis.Cowsinthe analysis were daughters of 707 sires, while the whole sire-maternalgrandsirepedigreeconsistedof2,284sires. Cowswereonaverageculledinthethirdlactation,which Table 1: Structure of data and descriptive statistics (± standard deviation) Preglednica 1: Struktura podatkov in opisna statistika (± standardni odklon) Cows,no. Sires,no. Pedigree,no. Censoredrecords,% Numberoflactationsinlife uncensoredrecords censoredrecords Lengthofproductivelife,days uncensoredrecords censoredrecords 1,095±660 1,129±754 3.0 3.0 116,200 707 2,284 41.0 amountedto1,095 daysofproductivelife.Percentageof censoredrecordswas41.0%.Censoredrecordshadabout thesamemeans,butlargervariability. 2.2 SURVIVALANALYSIS Weibull proportional hazards model was used for theanalysisofLPL.ThismodelisbuiltupontheWeibull distribution,whosedensity(1)andhazard(2)function forthei-threcordtiare: pedigree.TheusedWeibullproportionalhazardsmodel and the corresponding assumptions can be sketched in matrixformas: y|b,h,s, ~ Weibull (Xb+Zh+Ws, ), h| ~ Log - Gamma (,), s|G ~ Normal (0,G), where: b= avectorwithintercept ln())andparametersforthefollowing h= thevectorofparametersforherdeffect, s = thevectorofparametersforsireeffect, = Log-Gammadistributionparameter, G= additivegeneticcovariancematrixamongsires­aproductofnueffects: age at first calving, stage of lactation within parity, year, andthedeviationofherdsizefromyeartoyear, (4) (5) (6) (ti|,)=(ti)-1 exp(-(ti)), h(ti |,)=(ti), (1) (2) where(scale)and(shape)arestrictlypositiveparameters. In proportional hazard model it is assumed that thebaselinehazardfunctionchangesproportionallywith changeincovariate(s)orfactorlevels.Fortheanalysisof LPLthehazardfunctionwasmodelledas: h(tijklmnop |,,else)= h0(tijklmnop |,)exp(ci+lj+yk+hl+dm+sn+1/2so), (3) where: h(tijklmnop |,,else)=hazard of culling p-th cow given other pah0(tijklmnop |,) ci lj = baselineWeibullhazardfunction(2), = i-th age at first calving: 0 (unknown) and = j-thlactationstage(1­60 days,61­150 days, from19to50 months, 151­270 days,271-daystilldrying,anddry period)withinparity­altogether30levels; timevaryingfactor, timevaryingfactor, rameters, meratorrelationshipmatrixbetweensiresAsandadditivegenetic variancebetweensires(s2). Heritabilityaccordingtothemodel(3,4­6)wascalculatedfollowingMeszaroset al.(2010): , where: 2 log ( x) x 2 isatrigammafunctionusedtoevaluatethevarianceoflog-gammaprocess(5)givingbetweenherdvariance(h2),while thevalueof1istheunderlyingresidualvariance. (7) s2+¼s2isvarianceduetosireandmaternalgrandsireeffects(3), (1) ( x) = yk hl dm = k-th season defined as year (1990­2010); = l-thherd(3891levels);timevaryingfactor, = m-th herd size deviation in comparison to sn+1/2so = n-th sire and the o-th maternal grandsire previousyear(-70%,(-70%,-40%],(-40%, -10%], (-10%, 10%], (10%, 40%], (40%, 70%],and>70%);timevaryingfactor, (onwardsbotheffectsaretermedsireeffect) ofthep-thcow. Levelsoftimevaryingfactors(lactationstagewithin parity, year, herd, and herd size deviation) changed with cow "status" changes in time creating subsequent elementary records, while levels for others effects were constantoverwholelifetimeofacow.Altogether,there were1,839,307elementaryrecords.Herdandsireeffects were modelled hierarchically: log-gamma distribution for herd effect and multivariate normal for sire effect with additive genetic covariance matrix build from the DataprocessingwasdonewithSASsoftwarepackage(SASInstitute,2000),whileSurvivalKitversion3.10 (Ducrocq and Soelkner, 1998) was used for modelling andparameterestimation.Inthefirststepaseriesofloglikelihoodratiotestswereperformedforeffectsthatwere notmodelledhierarchically­theimportanceofeacheffectwastestedasacomparisonbetweenthefullmodel andthemodelwheretheeffectundertestingwasexcluded.Inthenextstepherdandsireeffectswereaddedto themodeltoobtainestimatesforallmodelparameters. Inresultsrelativeriskisequaltothevalueofsolutionsfor modelparametersonexponentialscale(3)proportional tosomespecifiedbaselinelevelthathasasolutionequal to1(e.g.26 monthsfortheageatfirstcalving).Eachplot of relative risks is also augmented with the number of censored and uncensored records per level of a factor. Inthecaseoftimevaryingfactorsonlythelastelementaryrecordofacowwasconsideredforcomputingthe numberofrecordsperlevelofafactor. Figure 1: Relative risk of culling and number of records by age at first calving Slika 1: Relativno tveganje za izlocitev in stevilo zapisov glede na starost ob prvi telitvi RESULTS AND DISCUSSION All effects included in the model were highly significant (P < 0.001), which is not surprising given the size of data set and the previous knowledge of effect importance for LPL. Distribution of age at first calving wasexpectedwiththemajorityofcowsintherangebetweentwoandthreeyearsofage(Figure 1).Relativerisk of culling increased almost linearly with the increasing age at first calving. Similar results were obtained also byVollemaandGroen(1998)andRogerset al.(1991), whileothersdidnotfoundsignificance(Ducrocqet al., 1988a;Ducrocq,1994)orconcludedthatthiseffectwas notimportant(Vukasinovicet al.,1997).Thiscanbeat leastpartiallyattributedtothefactthatourresultsdonot directly imply causal relationship between LPL and the Figure 2: Hazard of culling and number of records by stage of lactation within parity Slika 2: Ogrozenost za izlocitev in stevilo zapisov glede na stadij laktacije in zaporedno laktacijo Table 2: Estimates of model hyperparameters and derived quantities Preglednica 2: Ocene parametrov modela in izpeljanih kolicin Hyperparameter/Quantity Shape, Log-gammaparameter, Betweenherdvariance, = () 2 h (1) Estimate 2.00 8.50 0.12 0.04 0.16 0.14 Betweensirevariance,s2 Additivegeneticvariance,a2=4s2 Heritability, age at first calving. Results only imply that there is associationbetweenLPLandtheageatfirstcalvinginour population,whichindicatesthatcowsthathadlatefirst calvinghadalso someotherproblems(likelyrelatedto reproductivesuccess)thatincreasedriskofbeingculled early.Estimatesatthestartandtheendofconsideredage interval were very variable due to the smaller number ofrecords.Givenalmostlinearrelationship,variableresultsatmargins,andthatageistimeindependenteffect a possible approach would be to model this effect with linearregression.Regressionisnotappropriatefortime dependenteffectsduetotheexplosionofnumberofelementaryrecords. The stage of production has a significant effect on risk of a cow being culled due to biological (increased probability of mastitis at the start of lactation) or tech- nological factors (owners' decisions in the dry period). Since the stage of lactation within parity changes with increasingage(dependentvariable)werepresentedthis effectusingbaselinehazardfunction(3)multipliedwith thecorrespondingrelativeriskforeachstagewithinparity (Figure 2) for a fixed calving interval of 400 days. Numberofculledcowswashighestinthesecondparity anddroppedinlaterparities.Hazardincreasedovertime withconsiderablechangesattheendoflactation­that isintheperiodbetween271 daysafterlactationanddryoffandinthedryperiod.Virtuallythesameresultswere obtainedalsoinotherstudies(e.g.Ducrocq,1994;Vukasinovicet al.,1997;Potocniket al.,2010).Thefirstparity showeduniquepatternwithincreasedhazardinthefirst twoperiodsoflactation(1­60and61­150 days),which mightbeduetothehigherincidenceofhealthdisorders during early lactation. Similar estimates were obtained alsobyDucrocq(1994)andVukasinovicet al.(1997). Herd size dynamics has also influence on culling criteria. In general herd expansion lowers risk, while riskishigherinshrinkingherds.HerdsinSloveniaare ingeneralsmall,sothereissubstantialvariabilityinherd sizechangesfromyeartoyear.Majorityofrecords(censoredornot)wereintherangeof-40to40%ofherdsize change.Relativeriskforcullingwasratherconstantfor herdsizechangelevelsabove-40%,whileitincreasedfor thetwolevelsbellowthisthresholdasexpected­cows from herds with decreasing size have larger probability ofbeingculled.Weigelet al.(2003)calculatedtherelative culling risk of high producing (top 20%) and low Figure 3: Relative risk of culling and number of records by levels of variation in herd size between years Slika 3: Relativno tveganje za izlocitev in stevilo zapisov glede na letno spremembo velikosti crede producing (bottom 20%) cows relative to average cows inthesameherdwithregardtoherdsizechanges.They determinedthat,beforeherdexpansion,lowproducing cowswere4.2timesmorelikelytobeculledthanaverage cows,whilehighproducingcowswereonly0.5timesas likelytobeculledasaveragecows.Afterherdexpansion, therelativeriskforlowproducingcowsdroppedto2.6 timesthatofaveragecows,andtheriskforhighproducing cows increased slightly to 0.7 times that of average cows,whichclearlyshowstheeffectofherdexpansionon thereducedriskofculling. Cullingcriteriaalsochangewithtime.Possiblereasonsarediseaseoutbreakinpopulation,changeofprices, milkquota,etc.Inordertocapturesuchvariationsweincludedinthemodeleffecttoseasondefinedasyear.Our dataspannedperiodbetween1991and2010(Figure 4). Relativeriskofcullingwasverylowinthefirstyearsdue tolackofrecordsinthatperiod,butreachedoveralllevel aftertheyear1995.Afterthisyearweobserveoverallincreaseinrelativeriskofcullingoveryears.Asharpdecreaseinriskwasestimatedfortheyear2002,whichcan beattributedtofarmers'decisiontokeepmoreanimals onfarminordertogethighermilkquotaandsubsidies per farm with the forthcoming new quota and subsidy systeminSloveniaatthatperiod.Riskwaslogicallyvery lowinthelastyear(2010)duetothelargenumberoflive (censored)animalsintheanalysis. Based on the used statistical model, between sire variancewasestimatedto0.04,whilebetweenherdvariancewasestimatedto0.12(Table 2).Thesevaluesareon exponential scale of the Weibull model (3) and do not have meaningful units related to the analysed variable (LPL).EstimatedheritabilityusingtheapproachofMeszaroset al.(2010)was0.14,whichissimilartothevaluesreportedinAustria(0.18)andGermany(0.16)and relatively high comparing with other countries that are membersofINTERBULL(INTERBULL,2009). Breeding values for LPL were presented on scale with mean 100 and standard deviation 12 with favourable values (longer LPL) above 100. Genetic trend by yearofbirthforsiresintheperiod1984­2005showsthat there was no selection on longevity (Figure 5). Overall trend was negative (-0.12 ± 0.14), but not significant (p=0.385).Differencesbetweenyearswereminimalexcept for the last four years. This could be attributed to thesmallernumberofevaluatedsiresandtothefactthat thesesireshavealotofdaughterswithcensoredrecords. Theaccuracyofgeneticevaluationhighlydepends ontheratioofcensoredanduncensoredrecords.Asthe proportionofcensoredrecordsdecreases,theevaluation accuracyincreases.Also,itisnecessarytohavesufficient numberofdaughterspersire.Vukasinovicet al.(1997) stated that more than 30 to 40% of censored records would lead to inaccurate results. Same authors stated thatsmallnumberofdaughterspersirewithoutanyor only few uncensored records biases sires ranking. Egger-Danner et al. (1993) performed retrospective study wheretheycomparedtherankingofsiresfromafulldata filewithoutcensoredrecordsandfromatruncateddata with a different proportion of censored records. They observedthatrankcorrelationsbetweenbreedingvalues droppedastheproportionofcensoringincreased.Fur- Figure 4: Relative risk of culling and number of records by year Slika 4: Relativno tveganje za izlocitev in stevilo zapisov glede na leto Figure 5: Genetic trend for the length of productive life in Slovenian Holstein sires Slika 5: Genetski trend za dolgozivost pri plemenjakih slovenske crno-bele pasme therresearchisneededinourpopulationtodetermine theimpactofcensoredrecordsontheaccuracyofgenetic evaluationaswellastodeterminehowmanydaughters persireareneeded. CONCLUSION Survival analysis methodology was applied for the geneticevaluationoflongevity(definedasthelengthof productive life) in Slovenian Holstein cattle. Statistical modelincludedtheeffectofageatfirstcalving,lactation stagewithinparity,yearlyherdsizedeviation,year,herd, and additive genetic effect as captured by sire and maternalgrandsireeffects.Parameterestimatesweresimilar tostudiesinothercountries.Genetictrendwasslightly negative (unfavourable), yet not significant. Relatively high differences between average breeding values were observedinlastyears.Asaccuracyofgeneticevaluation highly depends on the number of daughters per evaluated sire and on the ratio of censored and uncensored recordsfurtherinvestigationsareneeded. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Agriculturae Slovenica de Gruyter

Analysis of longevity in Slovenian holstein cattle

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doi:10.2478/v10014-011-0025-5 COBISS:1.01 Agriscategorycode:L01 KlemenPOTOCNIK1,VesnaGANTNER2,JurijKRSNIK1,MiranSTEPEC1,BetkaLOGAR3, GregorGORJANC1 ReceivedAugust20,2011;acceptedSeptember22,2011. Delojeprispelo20.avgusta2011,sprejeto22.septembra2011. Analysis of longevity in Slovenian holstein cattle ThelongevityofSlovenianHolsteinpopulationwasanalysedusingsurvivalanalysiswithaWeibullproportionalhazardmodel.DataspannedtheperiodbetweenJanuary1991and January2010for116,200cowsfrom3,891herds.Longevitywas described as the length of productive life ­ from first calving tillcullingorcensoring.Recordsabovethesixthlactationwere censored to partially avoid preferential treatment. Statistical modelincludedtheeffectofageatfirstcalving,stageoflactationwithinparity,yearlyherdsizedeviation,seasondefinedas year,herd,andsire-maternalgrandsire(mgs).Someeffectshad timevaryingcovariates,whichleadto1,839,307oronaverage 16elementaryrecordspercow.Herdandsire-maternalgrandsireeffectsweremodelledhierarchically.Pedigreeforsiresand maternalgrandsiresincluded2,284entries.Estimatedvariance betweenherdswas0.12,whilebetweensirevariancewas0.04. Heritabilitywasevaluatedat0.14.Genetictrendforsireswas unfavourable,butnotsignificant.Afurtherresearchisneeded todefinetherequirednumberofdaughterspersireandthedynamicsofgeneticevaluationforsireswhosemajorityofdaughtersstillhavecensoredrecords. Key words:cattle/breeds/SlovenianHolstein/longevity /Weibullproportionalhazardsmodel Analiza dolgozivosti pri crno-beli pasmi goveda v Sloveniji Za analizo dolgozivosti smo pri slovenski crno-beli populaciji govedi uporabili metodologijo analize prezivetja in Weibullov model sorazmernih ogrozenosti. V analizo smo vkljucilipodatke116.200kraviz3.891credskoziobdobjeod januarja1991dojanuarja2010.Dolgozivostjebilapredstavljenakotdobaproduktivnegazivljenja,kijedefiniranakotstevilo odprvetelitvedoizlocitvealidodatumazajemapodatkovza zivali,kisonatadatumbilesezive.Sestoinkasnejselaktacije smookrnilinakonecsestelaktacije,dasmoomililiprecenjenostboljsihzivali.Vstatisticnimodelsmovkljucilivplivstarostiobprvitelitvi,stadijalaktacijelocenozavsakozaporedno laktacijo,spreminjanjevelikosticredemedleti,letotelitve,credo,ocetainmaterinegaoceta.Ravninekaterihvplivovsocasovnospremenljivi,karpovzroci,dasmovanaliziobravnavali 1.839.307 zapisov ali povprecno 16 osnovnih zapisov na kravo.Credainvplivocetazmaterinimocetomstabilavmodel vkljucenahierarhicno.Rodovnikzaoceteinmaterineoceteje obsegal2.284zapisov.Ocenjenavariancazavplivcredejeznasala0,12,medtemkojeocenavariancemedocetiznasala0,04. Dednostnidelezjebilocenjenna0,14.Genetskitrendimanegativnosmer,anistatisticnoznacilen.Potrebnebodonadaljnje raziskave,dabomodolocilizadostnostevilohcerapobikuin dinamiko obracunov plemenskih vrednosti za bike, ki imajo vecinohcerasevfaziprireje. Kljucne besede:govedo/pasme/slovenskacrno-belapasma/dolgozivost/Weibullovmodelsorazmernihogrozenosti INTRODUCTION Longevityisatraitwithgreatimpactondairyproduction economy and is, therefore, of considerable importanceindairycattlebreedingprogrammes(Charffed- dineet al.,1996;StrandbergandSoelkner,1996).With theincreaseoflongevity,theproportionofmaturecows thatproducemoremilkincreases.Forexample,Strandberg(1996)estimatedthatanincreaseinlongevityfrom threetofourlactationsincreasesaveragemilkyieldper 1 Univ.ofLjubljana,BiotechnicalFac.Dept.ofAnimalScience,Groblje3,SI-1230Domzale,Slovenia 2 J.J.StrossmayerUniv.inOsijek,Fac.ofAgriculture,TrgSvetogTrojstva3,31000Osijek,Croatia 3 AgriculturalinstituteofSlovenia,Hacquetova17,SI-1000Ljubljana,Slovenia Acta argiculturae Slovenica, 98/2, 93­100, Ljubljana 2011 lactationandprofitperyearbetween11and13%.Inaddition,improvementinlongevitydecreasesreplacement costsandsomewhatincreasesselectionintensity. There are several ways to implement selection on longevityinthebreedinggoal,directlyorindirectly.Directlongevitycanberepresentedasthelengthof(productive)life(LPL)orstayability.IncattlebreedingLPL is usually defined as the elapsed time between the first calving and culling, while stayability is defined as a binarytraitthatmeasurescowsurvival(liveorculled)at acertainpointintime.TheuseofLPLispreferredsince stayability as a discrete trait provides less information. Unfortunately, LPL, as well as stayability, can be quantified only after the cows are culled, though both approachesprovidepartialinformationwhencowsurvives to the next "period" in life. Therefore, the information onthelongevityofdaughtersofasirebecomesavailable withtheincreasingageofasire.Thisinherentlyleadsto the prolonged generation interval. Low heritability for longevity(ShortandLawlor,1992;VollemaandGroen, 1996) induces unreliable estimation of breeding values (BV)basedonlyontheinformationofparentsorgrandparents. Due to long generation interval, breeding programmesalsoincludeindirectmeasuresoflongevityvia correlatedtraitssuchasfertility,health,andconformationtraits(Burnsideet al.,1984).Additionalgainisdue to the fact that the data on these indirect traits can be collectedrelativelyearlyinthelifeofacow.Nonetheless, both representations of longevity (direct and indirect) haveameritinamodernbreedinggoal(Essl,1998). Analysis of indirect representations of longevity is to a large extent done with a standard linear model based on the Gaussian (normal) distribution. Specific approachisneededforaproperanalysisoftheLPL,due to the presence of live animals at the time of analysis (censored records) and changes in culling criteria over theproductivelifeofcows(timevaryingcovariates)(e.g. Ducrocq et al., 1988a). Exclusion of censored records fromtheanalysis,ortreatingthemasuncensoredleads tobiasedresults(Ducrocq,1994).Additionally,relationshipbetweenlongevityanditseffectsisrathermultiplicativethanadditive(e.g.Ducrocqet al.,1988a).Survival analysis can handle this kind of data. In the last years severalcountriesintroduceddirectlongevityintheroutine genetic evaluation of cattle and most of them use the Weibull proportional hazard model (INTERBULL, 2009),whichrepresentsaclassofmodelsinthefieldof survival analysis. Other statistical approaches (models) can also be used, but proportional hazard model have better properties (e.g. Caraviello et al., 2004; Jamrozik et al.,2008;Potocniket al.,2008). Theaimofthisstudywastopresenttheresultsof 94 genetic evaluation for the length of productive life in Slovenian Holstein population using a Weibull proportionalhazardmodel. MATERIAL AND METHODS 2.1 DATA Rawdatafor126,716SlovenianHolsteincowsborn from1982to2008wereprovidedbytheAgriculturalInstituteofSlovenia.Inordertouseolddatabuttoavoid modelling the data up to the year 1991, the truncation datewassetatJanuary1st1991.Ontheotherside,thedate of last data collection was January 29th 2010. For cows aliveatthattimelongevitywastreatedasrightcensored. Longevity was defined as the length of productive life (LPL)andwascalculatedasthenumberofdaysfromthe firstcalvingtoculling(uncensored/completerecords)or tothemomentofdatacollection(incomplete/censored records). The LPL of cows surviving beyond the sixth lactation was also censored in order to avoid the effect ofpreferentialtreatmentandtofocusonearlycullingin thelifeofacow.Cowswithmissingorinconsistentdata within the defined limits were removed (29,252 cows): culling before the date of truncation, calving date after thedateofculling,noinformationfor600 daysaftercalving,missingdataforthefirstthreelactations,daughters ofsireswithlessthan20daughters,andmissingcovariate orfactordata. Thestructureofuseddataanddescriptivestatistics are given in Table 1. Altogether LPL for 116,200 cows from3891herdswereusedintheanalysis.Cowsinthe analysis were daughters of 707 sires, while the whole sire-maternalgrandsirepedigreeconsistedof2,284sires. Cowswereonaverageculledinthethirdlactation,which Table 1: Structure of data and descriptive statistics (± standard deviation) Preglednica 1: Struktura podatkov in opisna statistika (± standardni odklon) Cows,no. Sires,no. Pedigree,no. Censoredrecords,% Numberoflactationsinlife uncensoredrecords censoredrecords Lengthofproductivelife,days uncensoredrecords censoredrecords 1,095±660 1,129±754 3.0 3.0 116,200 707 2,284 41.0 amountedto1,095 daysofproductivelife.Percentageof censoredrecordswas41.0%.Censoredrecordshadabout thesamemeans,butlargervariability. 2.2 SURVIVALANALYSIS Weibull proportional hazards model was used for theanalysisofLPL.ThismodelisbuiltupontheWeibull distribution,whosedensity(1)andhazard(2)function forthei-threcordtiare: pedigree.TheusedWeibullproportionalhazardsmodel and the corresponding assumptions can be sketched in matrixformas: y|b,h,s, ~ Weibull (Xb+Zh+Ws, ), h| ~ Log - Gamma (,), s|G ~ Normal (0,G), where: b= avectorwithintercept ln())andparametersforthefollowing h= thevectorofparametersforherdeffect, s = thevectorofparametersforsireeffect, = Log-Gammadistributionparameter, G= additivegeneticcovariancematrixamongsires­aproductofnueffects: age at first calving, stage of lactation within parity, year, andthedeviationofherdsizefromyeartoyear, (4) (5) (6) (ti|,)=(ti)-1 exp(-(ti)), h(ti |,)=(ti), (1) (2) where(scale)and(shape)arestrictlypositiveparameters. In proportional hazard model it is assumed that thebaselinehazardfunctionchangesproportionallywith changeincovariate(s)orfactorlevels.Fortheanalysisof LPLthehazardfunctionwasmodelledas: h(tijklmnop |,,else)= h0(tijklmnop |,)exp(ci+lj+yk+hl+dm+sn+1/2so), (3) where: h(tijklmnop |,,else)=hazard of culling p-th cow given other pah0(tijklmnop |,) ci lj = baselineWeibullhazardfunction(2), = i-th age at first calving: 0 (unknown) and = j-thlactationstage(1­60 days,61­150 days, from19to50 months, 151­270 days,271-daystilldrying,anddry period)withinparity­altogether30levels; timevaryingfactor, timevaryingfactor, rameters, meratorrelationshipmatrixbetweensiresAsandadditivegenetic variancebetweensires(s2). Heritabilityaccordingtothemodel(3,4­6)wascalculatedfollowingMeszaroset al.(2010): , where: 2 log ( x) x 2 isatrigammafunctionusedtoevaluatethevarianceoflog-gammaprocess(5)givingbetweenherdvariance(h2),while thevalueof1istheunderlyingresidualvariance. (7) s2+¼s2isvarianceduetosireandmaternalgrandsireeffects(3), (1) ( x) = yk hl dm = k-th season defined as year (1990­2010); = l-thherd(3891levels);timevaryingfactor, = m-th herd size deviation in comparison to sn+1/2so = n-th sire and the o-th maternal grandsire previousyear(-70%,(-70%,-40%],(-40%, -10%], (-10%, 10%], (10%, 40%], (40%, 70%],and>70%);timevaryingfactor, (onwardsbotheffectsaretermedsireeffect) ofthep-thcow. Levelsoftimevaryingfactors(lactationstagewithin parity, year, herd, and herd size deviation) changed with cow "status" changes in time creating subsequent elementary records, while levels for others effects were constantoverwholelifetimeofacow.Altogether,there were1,839,307elementaryrecords.Herdandsireeffects were modelled hierarchically: log-gamma distribution for herd effect and multivariate normal for sire effect with additive genetic covariance matrix build from the DataprocessingwasdonewithSASsoftwarepackage(SASInstitute,2000),whileSurvivalKitversion3.10 (Ducrocq and Soelkner, 1998) was used for modelling andparameterestimation.Inthefirststepaseriesofloglikelihoodratiotestswereperformedforeffectsthatwere notmodelledhierarchically­theimportanceofeacheffectwastestedasacomparisonbetweenthefullmodel andthemodelwheretheeffectundertestingwasexcluded.Inthenextstepherdandsireeffectswereaddedto themodeltoobtainestimatesforallmodelparameters. Inresultsrelativeriskisequaltothevalueofsolutionsfor modelparametersonexponentialscale(3)proportional tosomespecifiedbaselinelevelthathasasolutionequal to1(e.g.26 monthsfortheageatfirstcalving).Eachplot of relative risks is also augmented with the number of censored and uncensored records per level of a factor. Inthecaseoftimevaryingfactorsonlythelastelementaryrecordofacowwasconsideredforcomputingthe numberofrecordsperlevelofafactor. Figure 1: Relative risk of culling and number of records by age at first calving Slika 1: Relativno tveganje za izlocitev in stevilo zapisov glede na starost ob prvi telitvi RESULTS AND DISCUSSION All effects included in the model were highly significant (P < 0.001), which is not surprising given the size of data set and the previous knowledge of effect importance for LPL. Distribution of age at first calving wasexpectedwiththemajorityofcowsintherangebetweentwoandthreeyearsofage(Figure 1).Relativerisk of culling increased almost linearly with the increasing age at first calving. Similar results were obtained also byVollemaandGroen(1998)andRogerset al.(1991), whileothersdidnotfoundsignificance(Ducrocqet al., 1988a;Ducrocq,1994)orconcludedthatthiseffectwas notimportant(Vukasinovicet al.,1997).Thiscanbeat leastpartiallyattributedtothefactthatourresultsdonot directly imply causal relationship between LPL and the Figure 2: Hazard of culling and number of records by stage of lactation within parity Slika 2: Ogrozenost za izlocitev in stevilo zapisov glede na stadij laktacije in zaporedno laktacijo Table 2: Estimates of model hyperparameters and derived quantities Preglednica 2: Ocene parametrov modela in izpeljanih kolicin Hyperparameter/Quantity Shape, Log-gammaparameter, Betweenherdvariance, = () 2 h (1) Estimate 2.00 8.50 0.12 0.04 0.16 0.14 Betweensirevariance,s2 Additivegeneticvariance,a2=4s2 Heritability, age at first calving. Results only imply that there is associationbetweenLPLandtheageatfirstcalvinginour population,whichindicatesthatcowsthathadlatefirst calvinghadalso someotherproblems(likelyrelatedto reproductivesuccess)thatincreasedriskofbeingculled early.Estimatesatthestartandtheendofconsideredage interval were very variable due to the smaller number ofrecords.Givenalmostlinearrelationship,variableresultsatmargins,andthatageistimeindependenteffect a possible approach would be to model this effect with linearregression.Regressionisnotappropriatefortime dependenteffectsduetotheexplosionofnumberofelementaryrecords. The stage of production has a significant effect on risk of a cow being culled due to biological (increased probability of mastitis at the start of lactation) or tech- nological factors (owners' decisions in the dry period). Since the stage of lactation within parity changes with increasingage(dependentvariable)werepresentedthis effectusingbaselinehazardfunction(3)multipliedwith thecorrespondingrelativeriskforeachstagewithinparity (Figure 2) for a fixed calving interval of 400 days. Numberofculledcowswashighestinthesecondparity anddroppedinlaterparities.Hazardincreasedovertime withconsiderablechangesattheendoflactation­that isintheperiodbetween271 daysafterlactationanddryoffandinthedryperiod.Virtuallythesameresultswere obtainedalsoinotherstudies(e.g.Ducrocq,1994;Vukasinovicet al.,1997;Potocniket al.,2010).Thefirstparity showeduniquepatternwithincreasedhazardinthefirst twoperiodsoflactation(1­60and61­150 days),which mightbeduetothehigherincidenceofhealthdisorders during early lactation. Similar estimates were obtained alsobyDucrocq(1994)andVukasinovicet al.(1997). Herd size dynamics has also influence on culling criteria. In general herd expansion lowers risk, while riskishigherinshrinkingherds.HerdsinSloveniaare ingeneralsmall,sothereissubstantialvariabilityinherd sizechangesfromyeartoyear.Majorityofrecords(censoredornot)wereintherangeof-40to40%ofherdsize change.Relativeriskforcullingwasratherconstantfor herdsizechangelevelsabove-40%,whileitincreasedfor thetwolevelsbellowthisthresholdasexpected­cows from herds with decreasing size have larger probability ofbeingculled.Weigelet al.(2003)calculatedtherelative culling risk of high producing (top 20%) and low Figure 3: Relative risk of culling and number of records by levels of variation in herd size between years Slika 3: Relativno tveganje za izlocitev in stevilo zapisov glede na letno spremembo velikosti crede producing (bottom 20%) cows relative to average cows inthesameherdwithregardtoherdsizechanges.They determinedthat,beforeherdexpansion,lowproducing cowswere4.2timesmorelikelytobeculledthanaverage cows,whilehighproducingcowswereonly0.5timesas likelytobeculledasaveragecows.Afterherdexpansion, therelativeriskforlowproducingcowsdroppedto2.6 timesthatofaveragecows,andtheriskforhighproducing cows increased slightly to 0.7 times that of average cows,whichclearlyshowstheeffectofherdexpansionon thereducedriskofculling. Cullingcriteriaalsochangewithtime.Possiblereasonsarediseaseoutbreakinpopulation,changeofprices, milkquota,etc.Inordertocapturesuchvariationsweincludedinthemodeleffecttoseasondefinedasyear.Our dataspannedperiodbetween1991and2010(Figure 4). Relativeriskofcullingwasverylowinthefirstyearsdue tolackofrecordsinthatperiod,butreachedoveralllevel aftertheyear1995.Afterthisyearweobserveoverallincreaseinrelativeriskofcullingoveryears.Asharpdecreaseinriskwasestimatedfortheyear2002,whichcan beattributedtofarmers'decisiontokeepmoreanimals onfarminordertogethighermilkquotaandsubsidies per farm with the forthcoming new quota and subsidy systeminSloveniaatthatperiod.Riskwaslogicallyvery lowinthelastyear(2010)duetothelargenumberoflive (censored)animalsintheanalysis. Based on the used statistical model, between sire variancewasestimatedto0.04,whilebetweenherdvariancewasestimatedto0.12(Table 2).Thesevaluesareon exponential scale of the Weibull model (3) and do not have meaningful units related to the analysed variable (LPL).EstimatedheritabilityusingtheapproachofMeszaroset al.(2010)was0.14,whichissimilartothevaluesreportedinAustria(0.18)andGermany(0.16)and relatively high comparing with other countries that are membersofINTERBULL(INTERBULL,2009). Breeding values for LPL were presented on scale with mean 100 and standard deviation 12 with favourable values (longer LPL) above 100. Genetic trend by yearofbirthforsiresintheperiod1984­2005showsthat there was no selection on longevity (Figure 5). Overall trend was negative (-0.12 ± 0.14), but not significant (p=0.385).Differencesbetweenyearswereminimalexcept for the last four years. This could be attributed to thesmallernumberofevaluatedsiresandtothefactthat thesesireshavealotofdaughterswithcensoredrecords. Theaccuracyofgeneticevaluationhighlydepends ontheratioofcensoredanduncensoredrecords.Asthe proportionofcensoredrecordsdecreases,theevaluation accuracyincreases.Also,itisnecessarytohavesufficient numberofdaughterspersire.Vukasinovicet al.(1997) stated that more than 30 to 40% of censored records would lead to inaccurate results. Same authors stated thatsmallnumberofdaughterspersirewithoutanyor only few uncensored records biases sires ranking. Egger-Danner et al. (1993) performed retrospective study wheretheycomparedtherankingofsiresfromafulldata filewithoutcensoredrecordsandfromatruncateddata with a different proportion of censored records. They observedthatrankcorrelationsbetweenbreedingvalues droppedastheproportionofcensoringincreased.Fur- Figure 4: Relative risk of culling and number of records by year Slika 4: Relativno tveganje za izlocitev in stevilo zapisov glede na leto Figure 5: Genetic trend for the length of productive life in Slovenian Holstein sires Slika 5: Genetski trend za dolgozivost pri plemenjakih slovenske crno-bele pasme therresearchisneededinourpopulationtodetermine theimpactofcensoredrecordsontheaccuracyofgenetic evaluationaswellastodeterminehowmanydaughters persireareneeded. CONCLUSION Survival analysis methodology was applied for the geneticevaluationoflongevity(definedasthelengthof productive life) in Slovenian Holstein cattle. Statistical modelincludedtheeffectofageatfirstcalving,lactation stagewithinparity,yearlyherdsizedeviation,year,herd, and additive genetic effect as captured by sire and maternalgrandsireeffects.Parameterestimatesweresimilar tostudiesinothercountries.Genetictrendwasslightly negative (unfavourable), yet not significant. Relatively high differences between average breeding values were observedinlastyears.Asaccuracyofgeneticevaluation highly depends on the number of daughters per evaluated sire and on the ratio of censored and uncensored recordsfurtherinvestigationsareneeded.

Journal

Acta Agriculturae Slovenicade Gruyter

Published: Dec 1, 2011

References