analysis of longevity in slovenian holstein cattle
TRANSCRIPT
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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