Acta argiculturae Slovenica, 98/2, 93–100, Ljubljana 2011

doi:10.2478/v10014-011-0025-5 COBISS:1.01Agriscategorycode:L01

ANALYSISOFLONGEVITYINSLOVENIANHOLSTEINCATTLE

KlemenPOTOČNIK1,VesnaGANTNER2,JurijKRSNIK1,MiranŠTEPEC1,BetkaLOGAR3,GregorGORJANC1

ReceivedAugust20,2011;acceptedSeptember22,2011.Delojeprispelo20.avgusta2011,sprejeto22.septembra2011.

1 Univ.ofLjubljana,BiotechnicalFac.Dept.ofAnimalScience,Groblje3,SI-1230Domžale,Slovenia2 J.J.StrossmayerUniv.inOsijek,Fac.ofAgriculture,TrgSvetogTrojstva3,31000Osijek,Croatia3 AgriculturalinstituteofSlovenia,Hacquetova17,SI-1000Ljubljana,Slovenia

Analysis of longevity in Slovenian holstein cattleThelongevityofSlovenianHolsteinpopulationwasana-

lysedusingsurvivalanalysiswithaWeibullproportionalhaz-ardmodel.DataspannedtheperiodbetweenJanuary1991andJanuary2010for116,200cowsfrom3,891herds.Longevitywasdescribedas the lengthofproductive life– fromfirstcalvingtillcullingorcensoring.Recordsabovethesixthlactationwerecensored to partially avoid preferential treatment. Statisticalmodelincludedtheeffectofageatfirstcalving,stageoflacta-tionwithinparity,yearlyherdsizedeviation,seasondefinedasyear,herd,andsire-maternalgrandsire(mgs).Someeffectshadtimevaryingcovariates,whichleadto1,839,307oronaverage16elementaryrecordspercow.Herdandsire-maternalgrand-sireeffectsweremodelledhierarchically.Pedigreeforsiresandmaternalgrandsiresincluded2,284entries.Estimatedvariancebetweenherdswas0.12,whilebetweensirevariancewas0.04.Heritabilitywasevaluatedat0.14.Genetictrendforsireswasunfavourable,butnotsignificant.Afurtherresearchisneededtodefinetherequirednumberofdaughterspersireandthedy-namicsofgeneticevaluationforsireswhosemajorityofdaugh-tersstillhavecensoredrecords.

Key words:cattle/breeds/SlovenianHolstein/longevity/Weibullproportionalhazardsmodel

Analiza dolgoživosti pri črno-beli pasmi goveda v SlovenijiZa analizo dolgoživosti smo pri slovenski črno-beli po-

pulaciji govedi uporabili metodologijo analize preživetja inWeibullov model sorazmernih ogroženosti. V analizo smovključilipodatke116.200kraviz3.891čredskoziobdobjeodjanuarja1991dojanuarja2010.Dolgoživostjebilapredstavlje-nakotdobaproduktivnegaživljenja,kijedefiniranakotšteviloodprvetelitvedoizločitvealidodatumazajemapodatkovzaživali,kisonatadatumbilešežive.Šestoinkasnejšelaktacijesmookrnilinakonecšeste laktacije,dasmoomililiprecenje-nostboljšihživali.Vstatističnimodelsmovključilivplivsta-rostiobprvitelitvi,stadijalaktacijeločenozavsakozaporednolaktacijo,spreminjanjevelikostičredemedleti,letotelitve,čre-do,očeta inmaterinegaočeta.Ravninekaterihvplivovsoča-sovnospremenljivi,karpovzroči,dasmovanaliziobravnavali1.839.307 zapisov ali povprečno 16 osnovnih zapisov na kra-vo.Čredainvplivočetazmaterinimočetomstabilavmodelvključenahierarhično.Rodovnikzaočeteinmaterineočetejeobsegal2.284zapisov.Ocenjenavariancazavplivčredejezna-šala0,12,medtemkojeocenavariancemedočetiznašala0,04.Dednostnideležjebilocenjenna0,14.Genetskitrendimane-gativnosmer,anistatističnoznačilen.Potrebnebodonadaljnjeraziskave,dabomodoločilizadostnoštevilohčerapobikuindinamiko obračunov plemenskih vrednosti za bike, ki imajovečinohčeraševfaziprireje.

Ključne besede:govedo/pasme/slovenskačrno-belapa-sma/dolgoživost/Weibullovmodelsorazmernihogroženosti

1 INTRODUCTION

Longevityisatraitwithgreatimpactondairypro-ductioneconomyand is, therefore,ofconsiderable im-portanceindairycattlebreedingprogrammes(Charffed-

dineet al.,1996;StrandbergandSoelkner,1996).Withtheincreaseoflongevity,theproportionofmaturecowsthatproducemoremilkincreases.Forexample,Strand-berg(1996)estimatedthatanincreaseinlongevityfromthreetofourlactationsincreasesaveragemilkyieldper

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lactationandprofitperyearbetween11and13%.Inad-dition,improvementinlongevitydecreasesreplacementcostsandsomewhatincreasesselectionintensity.

There are several ways to implement selection onlongevityinthebreedinggoal,directlyorindirectly.Di-rect longevitycanberepresentedasthe lengthof(pro-ductive) life(LPL)orstayability.IncattlebreedingLPLis usually defined as the elapsed time between the firstcalvingandculling,while stayability isdefinedasabi-narytrait thatmeasurescowsurvival(liveorculled)atacertainpointintime.TheuseofLPLispreferredsincestayability as a discrete trait provides less information.Unfortunately, LPL, as well as stayability, can be quan-tified only after the cows are culled, though both ap-proachesprovidepartialinformationwhencowsurvivesto the next “period” in life. Therefore, the informationonthelongevityofdaughtersofasirebecomesavailablewiththeincreasingageofasire.Thisinherentlyleadstothe prolonged generation interval. Low heritability forlongevity(ShortandLawlor,1992;VollemaandGroen,1996) induces unreliable estimation of breeding values(BV)basedonlyontheinformationofparentsorgrand-parents.

Due to long generation interval, breeding pro-grammesalsoincludeindirectmeasuresoflongevityviacorrelatedtraitssuchas fertility,health,andconforma-tiontraits(Burnsideet al.,1984).Additionalgainisdueto the fact that the data on these indirect traits can becollectedrelativelyearlyinthelifeofacow.Nonetheless,both representations of longevity (direct and indirect)haveameritinamodernbreedinggoal(Essl,1998).

Analysis of indirect representations of longevityis to a large extent done with a standard linear modelbased on the Gaussian (normal) distribution. SpecificapproachisneededforaproperanalysisoftheLPL,dueto the presence of live animals at the time of analysis(censored records) and changes in culling criteria overtheproductivelifeofcows(timevaryingcovariates)(e.g.Ducrocq et  al., 1988a). Exclusion of censored recordsfromtheanalysis,ortreatingthemasuncensoredleadstobiasedresults(Ducrocq,1994).Additionally,relation-shipbetweenlongevityanditseffectsisrathermultipli-cativethanadditive(e.g.Ducrocqet al.,1988a).Survivalanalysis can handle this kind of data. In the last yearsseveralcountriesintroduceddirectlongevityintherou-tine genetic evaluation of cattle and most of them usethe Weibull proportional hazard model (INTERBULL,2009),whichrepresentsaclassofmodelsinthefieldofsurvival analysis. Other statistical approaches (models)can also be used, but proportional hazard model havebetter properties (e.g. Caraviello et  al., 2004; Jamroziket al.,2008;Potočniket al.,2008).

Theaimof thisstudywas topresent theresultsof

genetic evaluation for the length of productive life inSlovenian Holstein population using a Weibull propor-tionalhazardmodel.

2 MATERIAL AND METHODS

2.1 DATA

Rawdatafor126,716SlovenianHolsteincowsbornfrom1982to2008wereprovidedbytheAgriculturalIn-stituteofSlovenia.Inordertouseolddatabuttoavoidmodelling thedataup to theyear1991, the truncationdatewassetatJanuary1st1991.Ontheotherside,thedateof last data collection was January 29th 2010. For cowsaliveatthattimelongevitywastreatedasrightcensored.Longevity was defined as the length of productive life(LPL)andwascalculatedasthenumberofdaysfromthefirstcalvingtoculling(uncensored/completerecords)orto themomentofdatacollection(incomplete/censoredrecords). The LPL of cows surviving beyond the sixthlactationwasalsocensored inorder toavoid theeffectofpreferentialtreatmentandtofocusonearlycullinginthelifeofacow.Cowswithmissingorinconsistentdatawithin the defined limits were removed (29,252 cows):culling before the date of truncation, calving date afterthedateofculling,noinformationfor600 daysaftercalv-ing,missingdataforthefirstthreelactations,daughtersofsireswithlessthan20daughters,andmissingcovariateorfactordata.

Thestructureofuseddataanddescriptivestatisticsare given in Table  1. Altogether LPL for 116,200 cowsfrom3891herdswereusedintheanalysis.Cowsintheanalysis were daughters of 707 sires, while the wholesire-maternalgrandsirepedigreeconsistedof2,284sires.Cowswereonaverageculledinthethirdlactation,which

Cows,no. 116,200Sires,no. 707Pedigree,no. 2,284Censoredrecords,% 41.0Numberoflactationsinlife

uncensoredrecords 3.0censoredrecords 3.0

Lengthofproductivelife,daysuncensoredrecords 1,095±660censoredrecords 1,129±754

Table 1: Structure of data and descriptive statistics (± standard deviation)Preglednica 1: Struktura podatkov in opisna statistika (± stan-dardni odklon)

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amountedto1,095 daysofproductivelife.Percentageofcensoredrecordswas41.0%.Censoredrecordshadaboutthesamemeans,butlargervariability.

2.2 SURVIVALANALYSIS

Weibull proportional hazards model was used fortheanalysisofLPL.ThismodelisbuiltupontheWeibulldistribution,whosedensity(1)andhazard(2)functionforthei-threcordtiare:

(ti|λ,ρ)=λρ(λti)ρ−1 exp(−(λti)

ρ), (1)

h(ti |λ,ρ)=λρ(λti)ρ, (2)

whereλ(scale)andρ(shape)arestrictlypositiveparam-eters. In proportional hazard model it is assumed thatthebaselinehazardfunctionchangesproportionallywithchangeincovariate(s)orfactorlevels.FortheanalysisofLPLthehazardfunctionwasmodelledas:

h(tijklmnop |λ,ρ,else)=h0(tijklmnop |λ,ρ)exp(ci+lj+yk+hl+dm+sn+1/2so), (3)

where:h(tijklmnop |λ,ρ,else)=hazardof cullingp-th cowgivenotherpa-

rameters,h0(tijklmnop |λ,ρ) =baselineWeibullhazardfunction(2),ci = i-th age at first calving: 0 (unknown) and

from19to50 months,lj = j-thlactationstage(1–60 days,61–150 days,

151–270 days,271-daystilldrying,anddryperiod)withinparity–altogether30levels;timevaryingfactor,

yk =k-th season defined as year (1990–2010);timevaryingfactor,

hl = l-thherd(3891levels);timevaryingfactor,dm =m-thherd sizedeviation incomparison to

previousyear(≤-70%,(-70%,-40%],(-40%,-10%], (-10%, 10%], (10%, 40%], (40%,70%],and>70%);timevaryingfactor,

sn+1/2so =n-th sire and the o-th maternal grandsire(onwardsbotheffectsaretermedsireeffect)ofthep-thcow.

Levelsoftimevaryingfactors(lactationstagewith-in parity, year, herd, and herd size deviation) changedwith cow “status” changes in time creating subsequentelementary records, while levels for others effects wereconstantoverwholelifetimeofacow.Altogether,therewere1,839,307elementaryrecords.Herdandsireeffectswere modelled hierarchically: log-gamma distributionfor herd effect and multivariate normal for sire effectwith additive genetic covariance matrix build from the

pedigree.TheusedWeibullproportionalhazardsmodeland thecorrespondingassumptionscanbe sketched inmatrixformas:

y|b,h,s,ρ ~ Weibull (Xb+Zh+Ws, ρ), (4)

h|γ ~ Log − Gamma (γ,γ), (5)

s|G ~ Normal (0,G), (6)

where:

b=avectorwithinterceptρ ln(γ))andparametersforthefollowingeffects: ageatfirst calving, stageof lactationwithinparity, year,andthedeviationofherdsizefromyeartoyear,

h= thevectorofparametersforherdeffect,s = thevectorofparametersforsireeffect,γ=Log-Gammadistributionparameter,G=additivegeneticcovariancematrixamongsires–aproductofnu-

meratorrelationshipmatrixbetweensiresAsandadditivegeneticvariancebetweensires(σs

2).

Heritabilityaccordingtothemodel(3,4–6)wascal-culatedfollowingMeszaroset al.(2010):

, (7)

where:

σs2+¼σs

2 isvarianceduetosireandmaternalgrandsireeffects(3),

)(log)( 2

2)1( x

xx Γ

∂∂

=ψisatrigammafunctionusedtoevaluatethevari-

anceoflog-gammaprocess(5)givingbetweenherdvariance(σh2),while

thevalueof1istheunderlyingresidualvariance.

DataprocessingwasdonewithSASsoftwarepack-age(SASInstitute,2000),whileSurvivalKitversion3.10(Ducrocq and Soelkner, 1998) was used for modellingandparameterestimation.Inthefirststepaseriesoflog-likelihoodratiotestswereperformedforeffectsthatwerenotmodelledhierarchically–theimportanceofeachef-fectwastestedasacomparisonbetweenthefullmodelandthemodelwheretheeffectundertestingwasexclud-ed.Inthenextstepherdandsireeffectswereaddedtothemodeltoobtainestimatesforallmodelparameters.Inresultsrelativeriskisequaltothevalueofsolutionsformodelparametersonexponentialscale(3)proportionaltosomespecifiedbaselinelevelthathasasolutionequalto1(e.g.26 monthsfortheageatfirstcalving).Eachplotof relative risks is also augmented with the number ofcensored and uncensored records per level of a factor.Inthecaseoftimevaryingfactorsonlythelastelemen-taryrecordofacowwasconsideredforcomputingthenumberofrecordsperlevelofafactor.

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3 RESULTS AND DISCUSSION

All effects included in the model were highly sig-nificant (P  <  0.001), which is not surprising given thesize of data set and the previous knowledge of effectimportance forLPL.Distributionofageatfirst calvingwasexpectedwiththemajorityofcowsintherangebe-tweentwoandthreeyearsofage(Figure 1).Relativerisk

of culling increasedalmost linearlywith the increasingage at first calving. Similar results were obtained alsobyVollemaandGroen(1998)andRogerset al. (1991),whileothersdidnotfoundsignificance(Ducrocqet al.,1988a;Ducrocq,1994)orconcludedthatthiseffectwasnotimportant(Vukasinovicet al.,1997).Thiscanbeatleastpartiallyattributedtothefactthatourresultsdonotdirectly implycausal relationshipbetweenLPLand the

Figure 1: Relative risk of culling and number of records by age at first calvingSlika 1: Relativno tveganje za izločitev in število zapisov glede na starost ob prvi telitvi

Figure 2: Hazard of culling and number of records by stage of lactation within paritySlika 2: Ogroženost za izločitev in število zapisov glede na stadij laktacije in zaporedno laktacijo

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age at first calving. Results only imply that there is as-sociationbetweenLPLandtheageatfirstcalvinginourpopulation,whichindicatesthatcowsthathadlatefirstcalvinghadalsosomeotherproblems(likelyrelated toreproductivesuccess)thatincreasedriskofbeingculledearly.Estimatesatthestartandtheendofconsideredageinterval were very variable due to the smaller numberofrecords.Givenalmostlinearrelationship,variablere-sultsatmargins,andthatageistimeindependenteffectapossibleapproachwouldbe tomodel thiseffectwithlinearregression.Regressionisnotappropriatefortimedependenteffectsduetotheexplosionofnumberofel-ementaryrecords.

Thestageofproductionhasa significanteffectonrisk of a cow being culled due to biological (increasedprobabilityofmastitisat thestartof lactation)or tech-

nological factors (owners’decisions in thedryperiod).Since the stage of lactation within parity changes withincreasingage(dependentvariable)werepresentedthiseffectusingbaselinehazardfunction(3)multipliedwiththecorrespondingrelativeriskforeachstagewithinpar-ity (Figure  2) for a fixed calving interval of 400  days.Numberofculledcowswashighestinthesecondparityanddroppedinlaterparities.Hazardincreasedovertimewithconsiderablechangesattheendoflactation–thatisintheperiodbetween271 daysafterlactationanddry-offandinthedryperiod.Virtuallythesameresultswereobtainedalsoinotherstudies(e.g.Ducrocq,1994;Vuka-sinovicet al.,1997;Potočniket al.,2010).Thefirstparityshoweduniquepatternwithincreasedhazardinthefirsttwoperiodsoflactation(1–60and61–150 days),whichmightbeduetothehigherincidenceofhealthdisordersduring early lactation. Similar estimates were obtainedalsobyDucrocq(1994)andVukasinovicet al.(1997).

Herd size dynamics has also influence on cullingcriteria. In general herd expansion lowers risk, whilerisk ishigher inshrinkingherds.Herds inSloveniaareingeneralsmall,sothereissubstantialvariabilityinherdsizechangesfromyeartoyear.Majorityofrecords(cen-soredornot)wereintherangeof−40to40%ofherdsizechange.Relativeriskforcullingwasratherconstantforherdsizechangelevelsabove−40%,whileitincreasedforthetwolevelsbellowthisthresholdasexpected–cowsfromherdswithdecreasingsizehave largerprobabilityofbeingculled.Weigelet al.(2003)calculatedtherela-tive culling risk of high producing (top 20%) and low

Hyperparameter/Quantity EstimateShape,ρ 2.00Log-gammaparameter,γ 8.50Betweenherdvariance,σh

2=ψ(1)(γ) 0.12Betweensirevariance,σs

2 0.04Additivegeneticvariance,σa

2=4σs2 0.16

Heritability, 0.14

Table 2: Estimates of model hyperparameters and derived quantitiesPreglednica 2: Ocene parametrov modela in izpeljanih količin

Figure 3: Relative risk of culling and number of records by levels of variation in herd size between yearsSlika 3: Relativno tveganje za izločitev in število zapisov glede na letno spremembo velikosti črede

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producing (bottom 20%) cows relative to average cowsinthesameherdwithregardtoherdsizechanges.Theydeterminedthat,beforeherdexpansion, lowproducingcowswere4.2timesmorelikelytobeculledthanaveragecows,whilehighproducingcowswereonly0.5timesaslikelytobeculledasaveragecows.Afterherdexpansion,therelativeriskforlowproducingcowsdroppedto2.6timesthatofaveragecows,andtheriskforhighproduc-ing cows increased slightly to 0.7 times that of averagecows,whichclearlyshowstheeffectofherdexpansiononthereducedriskofculling.

Cullingcriteriaalsochangewithtime.Possiblerea-sonsarediseaseoutbreakinpopulation,changeofprices,milkquota,etc.Inordertocapturesuchvariationswein-cludedinthemodeleffecttoseasondefinedasyear.Ourdataspannedperiodbetween1991and2010(Figure 4).Relativeriskofcullingwasverylowinthefirstyearsduetolackofrecordsinthatperiod,butreachedoveralllevelaftertheyear1995.Afterthisyearweobserveoverallin-creaseinrelativeriskofcullingoveryears.Asharpde-creaseinriskwasestimatedfortheyear2002,whichcanbeattributedtofarmers’decisiontokeepmoreanimalsonfarminordertogethighermilkquotaandsubsidiesper farm with the forthcoming new quota and subsidysysteminSloveniaatthatperiod.Riskwaslogicallyverylowinthelastyear(2010)duetothelargenumberoflive(censored)animalsintheanalysis.

Based on the used statistical model, between sirevariancewasestimatedto0.04,whilebetweenherdvari-ancewasestimatedto0.12(Table 2).Thesevaluesareonexponential scale of the Weibull model (3) and do not

have meaningful units related to the analysed variable(LPL).EstimatedheritabilityusingtheapproachofMes-zaroset al.(2010)was0.14,whichissimilartotheval-uesreportedinAustria(0.18)andGermany(0.16)andrelativelyhighcomparingwithothercountries thataremembersofINTERBULL(INTERBULL,2009).

Breeding values for LPL were presented on scalewithmean100and standarddeviation12with favour-able values (longer LPL) above 100. Genetic trend byyearofbirthforsiresintheperiod1984–2005showsthatthere was no selection on longevity (Figure  5). Overalltrend was negative (−0.12 ± 0.14), but not significant(p=0.385).Differencesbetweenyearswereminimalex-cept for the last four years. This could be attributed tothesmallernumberofevaluatedsiresandtothefactthatthesesireshavealotofdaughterswithcensoredrecords.

Theaccuracyofgeneticevaluationhighlydependsontheratioofcensoredanduncensoredrecords.Astheproportionofcensoredrecordsdecreases,theevaluationaccuracyincreases.Also,itisnecessarytohavesufficientnumberofdaughterspersire.Vukasinovicet al.(1997)stated that more than 30 to 40% of censored recordswould lead to inaccurate results. Same authors statedthatsmallnumberofdaughterspersirewithoutanyoronly few uncensored records biases sires ranking. Egg-er-Danner et  al. (1993) performed retrospective studywheretheycomparedtherankingofsiresfromafulldatafilewithoutcensoredrecordsandfromatruncateddatawith a different proportion of censored records. Theyobservedthatrankcorrelationsbetweenbreedingvaluesdroppedastheproportionofcensoringincreased.Fur-

Figure 4: Relative risk of culling and number of records by yearSlika 4: Relativno tveganje za izločitev in število zapisov glede na leto

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therresearchisneededinourpopulationtodeterminetheimpactofcensoredrecordsontheaccuracyofgeneticevaluationaswellastodeterminehowmanydaughterspersireareneeded.

4 CONCLUSION

Survivalanalysismethodologywasapplied for thegeneticevaluationoflongevity(definedasthelengthofproductive life) in Slovenian Holstein cattle. Statisticalmodelincludedtheeffectofageatfirstcalving,lactationstagewithinparity,yearlyherdsizedeviation,year,herd,andadditivegenetic effect as capturedby sire andma-ternalgrandsireeffects.Parameterestimatesweresimilartostudiesinothercountries.Genetictrendwasslightlynegative (unfavourable), yet not significant. Relativelyhigh differences between average breeding values wereobservedinlastyears.Asaccuracyofgeneticevaluationhighlydependson thenumberofdaughtersperevalu-ated sire and on the ratio of censored and uncensoredrecordsfurtherinvestigationsareneeded.

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