analysis of longevity in slovenian holstein cattle. acta agriculturae slovenica
DESCRIPTION
Potočnik, K., Gantner, V., Krsnik, J., Štepec, M., Logar, B., Gorjanc, G. 2011. Analysis of longevity in Slovenian Holstein cattle. Acta Agriculturae Slovenica, 98(2): 93-100.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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