Application of an autoregressive process to estimate genetic parameters and breeding values for daily milk yield in a tropical herd of lucerna cattle and in united states holstein herds
Autor: Carvalheira, J.G.V.
Asesor: Zapata Jaramillo, Carlos Mario (Thesis advisor)
Fecha: 1998
Programa: Bogotá - Medicina -Fisioterapia
Facultad: Facultad de Medicina

Resumen: The objectives of this study were to estimate from test day records the genetic and environmental (co)variance components, correlations, and breeding values to increase genetic gain in milk yield of Lucerna and US Holstein cattle. The effects of repeated observations (within cow) were explained by firstorder autoregressive processes within and across lactations using an animal model. Estimates of variance components and correlation coefficients between test days were obtained using derivative-free REML methodology. The autoregressive structure significantly reduced the model error component by disentangling the short-term environmental effects. The  additional information and the more heterogeneous environmental variances between lactations in the multiple-lactation test day model than in the first lactation model provided substantially larger estimates of additive genetic variance (0.62 kg2 for Lucerna; 14.73 kg2 for Holstein), heritability (0.13 for Lucerna; 0.42 for Holstein), and individual genetic merit. Rank correlations of breeding values from multiple lactations and from first lactations ranged from 0.18 to 0.37 for females and from 0.73 to 0.89 for males, respectively. Consequently, more selection errors  and less genetic gain would be expected from selection decisions based on an analysis of first lactation only, and  greater accuracy would be achieved from multiple lactations. Results indicated that substantial genetic gain was possible for milk yield in the Lucerna herd (34 kg/yr).  Estimates of genetic variance for Holsteins were larger than previously reported, which portends more rapid genetic progress in US herds also; under our assumptions, increases would be from 173 to 197 kg/yr

Application of an Autoregressive Process
to Estimate Genetic Parameters and Breeding
Values for Daily Milk Yield in a Tropical Herd
of Lucerna Cattle and in United States Holstein Herds
J.G.V. CARVALHEIRA,* R. W. BLAKE,* E. J. POLLAK,*
R. L. QUAAS,* and C. V. DURAN-CASTRO†
*Department of Animal Science,
Cornell University, Ithaca, 14853 NY
†Universidad Nacional de Colombia and
Hacienda Lucerna, Calle 34 Norte #9N-195,
Cali, Valle, Colombia
ABSTRACT (Key words: test day animal model, tropics, auto-
correlation, genetic evaluation)
The objectives of this study were to estimate from
test day records the genetic and environmental Abbreviation key: EPA = expected producing abil-
(co)variance components, correlations, and breeding ity, LTE = long-term environmental effect, ME =
values to increase genetic gain in milk yield of Lu- mature equivalent, STE = short-term environmental
cerna and US Holstein cattle. The effects of repeated effect, TD = test day.
observations (within cow) were explained by first-
order autoregressive processes within and across lac- INTRODUCTION
tations using an animal model. Estimates of variance
components and correlation coefficients between test Many cattle in the tropics come from a gene pool
days were obtained using derivative-free REML comprising multiple breeds for which the genetic ob-
methodology. The autoregressive structure signifi- jective capitalizes on breed differences in additive
cantly reduced the model error component by disen- merit for economically important traits. The forma-
tangling the short-term environmental effects. The tionofsyntheticorcompositebreedsforthesesettings
additional information and the more heterogeneous isattractiveasasimplealternativetocomplexstrate-
environmental variances between lactations in the gies of continuous crossbreeding. Studies of breeding
multiple-lactation test day model than in the first strategies in the tropics are scarce, especially for syn-
lactation model provided substantially larger esti- thetic breeds. Lucerna cattle, a synthetic dual-
mates of additive genetic variance (0.62 kg2 for Lu- purpose (milk and beef) Colombian breed that con-
cerna; 14.73 kg2 for Holstein), heritability (0.13 for tainsabout40%Holsteingenes(11), area product of
Lucerna; 0.42 for Holstein), and individual genetic this alternative strategy to align the genetic potential
merit.Rankcorrelations of breeding values from mul- for milk yield with the modest potentials for feed
tiple lactations and from first lactations ranged from nutrient supply, mainly from forages, in a tropical
0.18 to 0.37 for females and from 0.73 to 0.89 for environment.
males, respectively. Consequently, more selection er- More genetic information and more accurate esti-
rors and less genetic gain would be expected from matedbreedingvaluesmaybeachievablethroughthe
selection decisions based on an analysis of first lacta- analysis of test day (TD) records of milk yield in-
tion only, and greater accuracy would be achieved stead of cumulative lactation totals for genetic evalu-
from multiple lactations. Results indicated that sub- ation of potential parents. Improved information is
stantialgeneticgainwaspossibleformilkyieldinthe especially important in the tropics where data are
Lucerna herd (34 kg/yr). Estimates of genetic vari- scarce and costly, thus severely restricting selection
ance for Holsteins were larger than previously gains. Harville (14) suggested a first-order auto-
reported, which portends more rapid genetic progress regressive process to model the potentially variable
in US herds also; under our assumptions, increases permanent environmental effect across repeated lac-
would be from 173 to 197 kg/yr. tations of an individual cow. Kachman and Everett
(15) included an autocorrelation structure for residu-
als of the TD records in a lactation. Van Tassel et al.
(31) generated305-dcumulativetotalsfromadjusted
Received May 8, 1997.
Accepted May 28, 1998. TD milk yields using the hypothesis that TD records
1998 J Dairy Sci 81:2738–2751 2738AUTOREGRESSIVE TEST-DAY ANIMAL MODEL 2739
contain less residual variance and similar genetic TABLE1.Numberofrecordsandmeansfor305-dmatureequiva-
lent(ME) milkyield(kilograms)andwithin-herdstandarddevia-
variance compared with the totals. Wade and Quaas
tion (SD) class for nine selected Holstein herds.
(35) were the first to demonstrate the methodology
Year-season
for incorporating a first-order, autoregressive random
adjusted
effect for year-season into the mixed model equations means for
of a sire model. More milk records per cow ‡ 10 daily
Class1 Records ME yield
yields versus one cumulative total per lactation) are
(no.) X SD
expected to increase the number of unique contem-
Low 7266 9281 1508
porary groups of animal cohorts: the TD effect.
Medium 9942 9768 1835
The use of TD models that accurately disentangle High 23,835 9461 2040
the covariance structure of environmental effects
1Threeherdsperstandarddeviation(SD) class:low=<1644kg
could increase the reliability of estimates of genetic
ofphenotypicSD,medium=1783to1898kgofphenotypicSD,and
prediction. Gain would also increase because of the high = >2022 kg of phenotypic SD.
reduction in the magnitude of residuals, thus increas-
ing theheritability of a single record or the mean of n
repeated records.
tion or Criollo breed, Harto´n del Valle. Red Milking
The primary objectives of this study were to com-
Shorthorn bulls were introduced in 1951 for beef and
pare the effectiveness of alternative (co)variance
other characteristics. The herd has been closed to
structures in TD models for partitioning random en-
outside breeding since 1958. Selection has been based
vironmental variation to estimate the components of
on milking performance(11). The resulting synthetic
genetic and environmental (co)variance and to in-
dual-purpose breed is now mostly reddish in coat
crease daily milk yield, especially for cattle in the
color; purportedly, about 40% of its genes come from
tropics. Secondary objectives were to estimate other
Holsteins, about 30% come from Milking Shorthorns,
parameters for daily milk yield, including contrasting
and about 30% come from Harto´n del Valle cattle
Holstein herd environments in the northeastern US.
(11). Artificial insemination using Lucerna semen
Steps included quantifying the biological responses in
was implemented in 1980, and sire selection was
different cattle systems, assessing the feasibility of
based primarily on the dams of sires pathway to
implementing the model and computational al-
increase milk yield. The Instituto Colombiano
gorithms in a multiple-herd scenario, and genetically
Agropecuario (Bogota´, Colombia) recognized Lucerna
evaluating Lucerna cows and sires and alternative
as a dual-purpose breed in 1983.
genetic improvement programs for this breed.
Data
MATERIALS AND METHODS
The first TD measurement of milk yield for Lu-
Tropical Climatology cerna cows was taken either on the 1st or the 15th d
and Lucerna Breed Formation of the month following calving and thereafter at
monthly intervals. Data consisted of 30,256 TD
Data were provided under a collaborative research records for the first three lactations of 1819 Lucerna
agreement by the Lucerna Cattle Breeders Associa- cows calving from 1985 to 1995. The final pedigree
tion (ASOLUCERNA) from the foundation herd, Ha- file consisted of 2538 animals, including these cows
cienda Lucerna (Bugalagrande, Valle del Cauca, and their ancestors.
Colombia). At an altitude of 960 m above sea level, Data from Holstein herds in the northeastern US
theannualmeantemperatureatHaciendaLucernais were from first, second, and third lactations of cows
about 24(cid:176) C, and mean temperature minima and max- calving from 1987 to 1995. Several studies (2, 9, 10,
ima range from 19 to 29(cid:176) C. The annual mean precipi- 19, 27, 29) showed that the genetic variance or
tation of about 1100 mm is distributed in two rainy heritability of milk yield in Holstein cows especially
seasons(April toMayandOctobertoDecember), and increasedwiththewithin-herdphenotypicvarianceof
relative humidity varies from 65 to 80%. mature equivalent (ME) yield in US and Latin
The Lucerna breed is the product of entrepreneur- American herd environments. Phenotypic means and
ship and a single-herd crossbreeding strategy fol- standard deviations for within-herd ME were ob-
lowed by inter se mating to form a new breed. Start- tained after adjustment for the effects of year and
ing in 1937, a crossbreeding program for milk was season of calving. Nine herds with similar mean
initiated with US Holstein bulls with a local founda- values for 305-d ME milk yields were chosen to
Journal of Dairy Science Vol. 81, No. 10, 19982740 CARVALHEIRA ET AL.
TABLE2.Numbersof testday(TD) records, fixedeffects,animals,andmeandailymilkyieldineight data files for first and multiple
lactations for the Lucerna and the Holstein breeds.
Holstein within-herd SD class1
Lucerna Low Medium High
Breed 12 1 + 2 + 33 1 1 + 2 + 3 1 1 + 2 + 3 1 1 + 2 + 3
Total TD records, no. 13,998 28,808 14,552 32,526 22,194 46,956 56,567 123,113
TD 120 129 208 217 300 301 282 283
Age, mo 8 10 8 15 9 15 9 15
DIM 33 99 97 291 99 295 99 297
Animals, no. 2326 2538 2748 3126 3753 4136 9958 10,935
Cows with records, no. 1584 1819 1845 2176 2569 2926 7213 8237
Mean TD records per cow, no. 9 16 8 15 9 16 8 15
Mean daily yield, kg 7.9 8.6 29.0 32.1 30.4 32.5 28.5 31.1
1Three herds per standard deviation (SD) class: low = <1644 kg of phenotypic SD for 305-d mature equivalent (ME) milk yield,
medium =1783 to 1898 kg of phenotypic SD for 305-d ME milk yield, and high =>2022 kg of phenotypic SD for 305-d ME milk yield.
2First lactations only.
3First, second, and third lactations.
represent three classes of phenotypic standard devia- TD Models
tion (three herds per class; Table 1). The final
A genetic TD model partitioning the random en-
pedigree files consisted of 3126, 4136, and 10,935
vironmental component into short-term environmen-
animals for the low, medium, and high classes of
tal (STE) effects (following a first-order autoregres-
phenotypic standard deviation.
sive process within cow and lactation), long-term
For all data, TD observations were deleted if a TD
environmental (LTE) effects (following a first-order
class contained <4observations or if DIM was >320d.
autoregressive process across lactations), and in-
Lactations were required to have at least 2 TD
dependent residuals was used to describe the data.
records per cow. Lactation records were deleted 1) if
Two animal models differing by the presence (full
initiated by abortion, 2) if missing either the date of
model) or absence (reduced model) of STE effects
birth or date of calving, 3) if first reported TD ex-
were applied to analyze TD observations in data for
ceeded75 DIM,4) if TD intervals were >75d, or 5) if
first lactation and multiple lactations. The full model
age at calving for Lucerna cows was not between 20
was as follows:
to45moforfirstparity(20 to36moforHolstein), 36
to60moforsecondparitytopermitasecondlactation
for the older primiparous cows (28 to 48 mo for y = HTD + age + DIM(H)
ijklmn i j k(l)
Holstein), and 55 to 90 mo for third parity (40 to 72 + a m + p m(l) + t n(ml) + e ijklmn
mo for Holstein). (The Lucerna management policy
wastocullcowsthatdidnotconceivewithin a year of
calving.) Other edits removed highly improbable lac- where
tation or TD yields.
y = amount of milk for an individual TD
The Lucerna cows were grouped in 10 classes by ijklmn
sample from the cow m,
ageatcalving:1classeachat£ 36mo,37 to38 mo,39
HTD = fixed effect due to cows tested in the
i
to 40 mo; 3 classes with 4-mo intervals from 41 to 52
same herd TD (HTD),
mo; 3 classes with 6-mo intervals from 53 to 70 mo; age = fixed effect of same age at calving,
j
and 1 class at ‡ 71 mo of age. Holstein cows were DIM(H) = fixed effect for contemporary cows
k(l)
placed into 15 classes by age at calving: 8 bimonthly testedinthesamelactationandDIM
classes from 20 to 36 mo, 6 classes with 4-mo inter- within herd (H),
vals from 37 to 60 mo, and cows at ‡ 61 mo of age. a m = random effect of animal,
p = random effect of LTE (only animals
Data from the Lucerna herd and from the Holstein m(l)
withrecordscontributetothiseffect)
standard deviation classes each provided 2 data
and assumed to follow a first-order
files—first lactations only and multiple lactations autoregressive process across lacta-
(first three lactations). These 8 data files are sum- tions,
marized in Table 2.
Journal of Dairy Science Vol. 81, No. 10, 1998AUTOREGRESSIVE TEST-DAY ANIMAL MODEL 2741
t n(ml) = random effect of STE nested within where A = numerator relationship matrix, s2 = the
cow and lactation and assumed to a
genetic variance component, J = LTE (co)variance
follow a first-order autoregressive
process, and matrix following a first-order autoregressive process
e ijklmn = random residual term. across the three lactations,s2 =LTE variance compo-
p
nent, r = LTE autocorrelation coefficient (for the
In matrix notation, the full model can be represented p
as single lactation analysis J reduces to Is2), S = STE
p
(co)variance matrix following a first-order auto-
y = Xb + Za + Mp + Qt + e, regressive process within lactations reflecting the as-
sumptionofindependenceofthiseffectbetweenlacta-
where y ~ N(Xb, V), b = unknown vector of fixed tions, F = autocorrelated block diagonal matrix cor-
effects, which, with known X, defines the mean;a, p, responding to the cow m with n TD samples in
and t = vectors representing the random effects of lactation 1, s2 = STE variance component 1, r =
t1 t1
animal,LTE,andSTEassociatedwithrecordsin y by
corresponding autocorrelation coefficient (for single
Z, M, and Q respectively; e = vector of residuals; and
lactation analysis, S reduces to diag{F} , R =
V = the (co)variance matrix. The expectations and ms2
t
(co)variances for this model are residual (co)variance matrix, s2 = residual variance
e
component, q = number of animals being evaluated,
ŒØ yœø (cid:230) ØŒ Xbøœ ØŒ V ZG MJ QS Røœ (cid:246) 1
(cid:231) (cid:247)
a 0 G 0 0 0 q 2 =number of animals having records,N = the total
p ~ N 0 ; J 0 0 numberofrecordsin theanalysis,I=identity matrix,
t 0 S 0 and ˜ = Kronecker tensor product.
º eß Ł º 0 ß º symm Rß ł The reduced model (ignoring the STE effect) had
the same assumptions as the full model, except that
and then (e.g., for l = 1, 2, 3 lactations) LTEisthe only random environmental effect measur-
ing potential correlations that were due to the cow
V = ZGZ¢ + MJM + (cid:229) 3 (Q S Q¢) + R, both within and between lactations.
l 1 l The parameters were estimated using derivative-
l=1
free REML (3, 28). Likelihood functions were max-
G = A s2,
q i a imized by the multivariate simplex (polytope) al-
Ø r2ø gorithm as described by Nelder and Mead(24). Con-
Œ 1 r œ
p p
J = s2 1 r ˜ Iq vergence was assumed when the variance of log-
p p 2 likelihoodfunctionsofthepolytopewas<10–8,andlog
º symm 1 ß
likelihoods after restarting did not differ (up to the
Ø Œ S 1 ø œ fourth decimal place). Models were compared by
S = S 2 , likelihood ratio tests (LRT, x2) with 2 df for the
º S 3ß analysis of first lactations and 6 df for the analysis of
multiple lactations (5).
S 1 = diag{F} m(l)s t2,
1
diag{F} = RESULTS AND DISCUSSION
m(l)
Œ œ
Ø ø
…
1 r t1 r t2 1 r tn 1–2 r tn 1–1 Full Model with STE Effect
r rn–2
1 t1 t1 Variance components and parameter estimates
. .
. . from analyses of first and multiple lactations for the
diag . . ,
Lucerna herd and for Holstein standard deviation
. . r t1 r t2 1 classes are in Tables 3 and 4. The log-likelihood
.
symm 1
r values, –2log(£), which maximized the likelihood
t1
functions for each model, are also given in the tables.
1
º ß Universally large differences between the–2log(£) of
m(l)
the full and reduced models clearly indicated that the
R = I Ns e2, fit to these data was best for the full model. Differ-
Journal of Dairy Science Vol. 81, No. 10, 19982742 CARVALHEIRA ET AL.
TABLE 3. Estimates of variance components(kilograms per day)2 for animal (sˆ2), long-term environment (sˆ2), short-term temporary
a p
environment (STE, sˆ2), residual (sˆ2), phenotype (sˆ2 ), heritabilities (hˆ2), and autocorrelations (rˆ) using test day animal models
t e PHENO
either including or ignoring a first-order autoregressive process for short-term environmental(STE) effects on daily milk yield in first
lactations from a herd of Lucerna cows and from each of the Holstein standard deviation (SD) classes.
Holstein within-herd SD class1
Lucerna Low Medium High
Parameter
estimate Include2 Ignore3 Include Ignore Include Ignore Include Ignore
sˆ a2 0.56 1.01 7.18 7.45 6.22 6.11 8.59 8.94
sˆ p2 <0.00 1.28 8.60 9.72 11.89 13.18 14.80 16.59
sˆ t2 3.24 . . . 8.96 . . . 10.14 . . . 10.49 . . .
rˆ t 0.83 . . . 0.57 . . . 0.61 . . . 0.58 . . .
sˆ e2 1.05 2.48 5.24 12.40 5.50 13.42 7.46 15.71
sˆ P2 HENO 4.84 4.77 29.98 29.56 33.74 32.71 41.34 41.24
hˆ2 0.11 0.21 0.24 0.25 0.18 0.19 0.21 0.22
–2log(£) 28,505.40 30,510.43 54,562.03 55,574.30 84,621.29 86,532.82 228,031.92 231,494.89
1ThreeherdsperSDclass:low=<1644kgofphenotypicSDfor305-dmatureequivalent(ME) milkyield,medium=1783to1898kgof
phenotypic SD for 305-d ME milk yield, and high =>2022 kg of phenotypic SD for 305-d ME milk yield.
2Model including the STE effect.
3Model ignoring the STE effect.
encesbetweenthelog-likelihoodvalueswereof multi- estimated genetic variance from the full model for
ple orders of magnitude (e.g., chi-squared critical daily milk yield in primiparous Lucerna cows was
valuesforP=0.0005with2and6df,respectively,are 45% smaller than the biased estimate from the
15.2 and 24.1; the smallest chi-squared value in this reduced model (Table 3), which could mean less
study is 1012). The full model was unequivocally genetic progress if the STE effect were ignored, espe-
superior for every analysis. Consequently, compari- cially in the dual-purpose Lucerna herd.
sons of results from the two models are primarily to Family ties in the Lucerna data were fewer than
emphasizetheopportunity losses in genetic gain from anticipated; 45% of records was from cows with
insufficiently disentangling the environmental effects
unknown sires. The resulting sparse relationship
from the genetic ones.
coefficient matrix probably constrained the estimated
heritability (hˆ2 = 0.11) because of partial confound-
Variance Components, Autocorrelations, ing of genotype and environment. More relationship
and Heritabilities of Daily Yield ties for all Holstein data files probably helped to
in First Lactation capture relatively more of the genetic variation and
gave heritability estimates from full and reduced
The TD records from Lucerna cows were highly
models that ranged from 0.18 to 0.25 (Table 3).
correlated (0.83), and most of the nongenetic vari-
Genetic relationships among the cattle being evalu-
ance caused by cow was explained by the STE effect.
ated are the only data permitting separation of the
Correlations between TD records in each of the three
geneticcomponentfromthenongeneticcomponentsin
Holstein classes for phenotypic standard deviation,
the cow effect. Meyer et al. (21) reported that the
although smaller than for the Lucerna classes, rang-
ingfrom0.51to0.61,weresimilar tothecoefficientof heritability ofmilk yield was underestimated for Aus-
0.58 used in the northeast TD evaluations (12). tralian Black and White cows from sire misidentifica-
The autocorrelation structure was clearly effective tion, which produced a less informative structure of
inremovingSTEinfluencesthat,if ignored,remained genetic covariance. Insufficiently dense relationship
partly confounded with the genetic component, espe- matrices may predispose smaller estimates of genetic
cially in Lucerna data. This confounding caused the variance (4).
genetic component of variance to be overestimated in Estimates of the phenotypic variance in the single
the reduced model in three of four data files. The lactation analysis were nearly the same from full and
Journal of Dairy Science Vol. 81, No. 10, 1998AUTOREGRESSIVE TEST-DAY ANIMAL MODEL 2743
reducedmodels(Table 3). Thisoutcomewasexpected Variance Components, Autocorrelations,
becausethemodelsdiffered only by an environmental and Heritabilities of Daily Yield
effect (STE) that, when ignored, would be contained in Multiple Lactations
in LTE and residual effects, if unconfounded with the
The competency of a statistical genetic model may
genetic component.
be measured by how effectively its effects explain the
Heritability estimates for first lactation milk yield
sources of variation contained in the data. The STE
from cows in the tropics vary by breed, location, and
componentwaseffectivein partitioning important en-
method of estimation, but tend to be smaller than in
vironmental effects in every data file, especially in
temperate regions. For example, Morales et al. (23)
multiple-lactation analyses. The magnitude of vari-
found heritability to be 0.12 for 305-d ME milk yield
ance component estimates for the STE effects(Table
for the Venezuelan Carora breed using REML with a
4) showedthatpracticallyall ofthenongenetic varia-
sire model. Stanton et al. (29) reported that esti- tion that was due to cow was accounted by this effect.
matesforsire(52%) andresidual(42%) variancesin The TD records were consistently highly correlated
Colombian Holstein herds were smaller than the esti- within lactations (‡ 0.72) in all data files.
mates from half-sisters of US Holstein sires in US Persistent environmental effects did not have
herds, but heritabilities were similar (0.29 vs. 0.24). major impact on the milking performance of Holstein
Mackinnon et al. (17) obtained a heritability esti- cows in this study. Therefore, the small residual LTE
mate of 0.09 for 305-d milk yield in a crossbred dairy contribution [and small correlation (£ 0.04) between
herd in Kenya (various percentages of Sahiwal, lactations] resulted from an STE effect already ac-
Brown Swiss, and Ayrshire genes). countingfornearlyalloftheenvironmentalvariation.
TABLE 4. Estimates of variance components(kilograms per day)2 for animal (sˆ2), long-term environment (sˆ2), short-term temporary
a p
environment(STE, sˆ2), residual(sˆ2), phenotype(sˆ2 ), heritabilities(hˆ2), andautocorrelations(rˆ andrˆ ) usingtestdayanimal
ti e PHENO p ti
modelseitherincludingorignoringafirst-orderautoregressiveprocessforshort-termenvironmental(STE) effectsondailymilkyieldin
multiple lactations (L) form a herd of Lucerna cows and from each of the Holstein standard deviation(SD) classes.
i
Holstein within-herd SD class1
Lucerna Low Medium High
Parameter
estimate Include2 Ignore3 Include Ignore Include Ignore Include Ignore
sˆ a2 0.62 0.68 11.37 6.51 12.33 6.00 14.73 8.61
sˆ p2 0.40 1.82 <0.00 16.40 <0.00 20.94 <0.00 20.72
rˆ p 1.00 0.33 0.01 0.36 0.02 0.40 0.04 0.47
sˆ t2 1 2.78 . . . 14.72 . . . 18.49 . . . 12.82 . . .
rˆ t1 0.80 . . . 0.78 . . . 0.80 . . . 0.82 . . .
sˆ t2 2 3.70 . . . 29.22 . . . 39.11 . . . 34.08 . . .
rˆ t2 0.77 . . . 0.79 . . . 0.81 . . . 0.77 . . .
sˆ t2 3 4.48 . . . 39.40 . . . 48.71 . . . 52.15 . . .
rˆ t3 0.74 . . . 0.78 . . . 0.80 . . . 0.72 . . .
sˆ e2 1.09 2.89 5.36 17.08 4.96 19.41 7.39 24.42
sˆ P2 HENO L 1 4.88 5.39 31.45 39.99 35.77 46.35 34.94 53.75
sˆ P2 HENO L 2 5.81 . . . 45.94 . . . 56.40 . . . 56.20 . . .
sˆ P2 HENO L 3 6.59 . . . 56.12 . . . 65.99 . . . 74.27 . . .
hˆ2 L 0.13 0.13 0.36 0.16 0.34 0.13 0.42 0.16
1
hˆ2 L 0.11 . . . 0.25 . . . 0.22 . . . 0.26 . . .
2
hˆ2 L 0.09 . . . 0.20 . . . 0.19 . . . 0.20 . . .
3
–2log(£) 62,220.94 66,632.59 128,261.98 134,200.15 188,385.44 199,670.76 263,891.20 277,509.79
1ThreeherdsperSDclass:low=<1644kgofphenotypicSDfor305-dmatureequivalent(ME) milkyield,medium=1783to1898kgof
phenotypic SD for 305-d ME milk yield, and high =>2022 kg of phenotypic SD for 305-d ME milk yield.
2Model including the STE effect.
3Model ignoring the STE effect.
Journal of Dairy Science Vol. 81, No. 10, 19982744 CARVALHEIRA ET AL.
These STE effects occurred during the major (i.e., in heritability estimates agree with those reported in
lactating) portion of the productive lifetime of the other studies (1, 6, 11, 18, 27, 29). The full model
cow, which afforded relatively smaller impacts from gave the largest estimates of heritability in every
events during juvenile growth and dry periods. The Holstein data file.
estimates of the LTE autocorrelation coefficient for Estimates of genetic variance increased as the
the reduced model, which ignored STE effects, were within-herd phenotypic variance increased. This rela-
notonly substantially smaller(0.36 to 0.47) than the tionship was especially informative for the Holstein
estimates for within-lactation correlations in the standard deviation classes(with essentially the same
multiple-lactation analyses (0.72 to 0.82), but also genetic composition because of reliance on the same
were smaller than within-lactation correlations for a AIsirecompanies) incorroboratingresultsfromaTD
single lactation. In the reduced model correlations animal model: genetic variance especially increases
between TD records, the data within and between as phenotypic variation within herds increases and
lactations were consolidated in the LTE component; decreases as phenotypic variation decreases (8, 15,
the LTE autocorrelation coefficient was only moder- 19, 20, 27, 29, 33, 36). Therefore, evaluation methods
ately detectable. This pattern of correlations may be that account for this heterogeneity of variance (or
evidence that different factors influence TD variation interaction between genotype and environment) are
within (i.e, STE) and between (i.e., LTE) lactations, pertinent (8, 16, 20, 33). Furthermore, even if the
which implies the need to account separately for STE purported 40% proportion of Holstein genes in Lu-
and LTE. cernacattlewerethesameasthecontemporarygenes
Chronic environmental constraints may explain in these Holstein herds, a smaller genetic variation
the (auto)correlation between lactations of Lucerna for milk yield should be expected in the tropical en-
cows, which were uncorrelated in US cows(Table 4). vironment of the Lucerna cattle, which is more
A relatively greater contribution from LTE in the nutrient-limiting (25).
tropical setting was associated with near equal lacta-
tion curves for cows in all parities. These outcomes Predicting Future
may havearisenfrompersistently less environmental Daily Milk Yield
opportunity (e.g., low nutrient intake relative to lac-
Sometimeseconomicreasonsdictatethatcowswith
tation requirements) and the associated observation
high expected producing ability (EPA) remain in the
errors.
herd, regardless of genetic merit, because past lacta-
Estimates of genetic variance from multiple lacta-
tionyieldsarerepeatablein futureperformances.The
tions were about the same for Lucerna cattle and
EPA is the same as EBV except when genetic and
were larger for Holsteins relative to estimates from
environmental effects exist that are repeated from
the reduced model; this pattern differed from the
previous records.
analysis of first lactations only. This result was yet
The manner in which repeated environmental ef-
further evidence that the autoregressive(co)variance
fects are partitioned in our full model for multiple
structure for STE was highly effective in removing
lactations permits the prediction of TD yields within
otherwise confounded variation from the genetic com-
and between lactations. These EPA are linear combi-
ponent. In addition to larger genetic variances (Hol-
nations of the EBV of the cows and respective solu-
stein only), residual variances were reduced substan-
tions from the STE and LTE vectors.
tially when the STE effects were removed. Residual
The covariances for TD records for an individual
variances of the Lucerna and the low, medium, and
cow may be represented as
high standard deviation classes of Holsteins were 62,
69, 74, and 70% smaller, respectively, than the vari- cov(y , y ¢) = a sˆ2 + sˆ2 + r(l¢ –l) sˆ2
ances with the reduced model. mli mli mm a p tl tl
Estimates of the phenotypic variance for each lac-
within lactations (i¢ > i), and
tation were used to compute corresponding heritabili-
ties. Heritabilities decreased as parity increased be-
cause of larger environmental variances in later cov(y mli, y ml¢i) = a mmsˆ a2 + rˆ p(l¢–l)sˆ p2
lactations; these estimates ranged from 0.13 to 0.09
for Lucerna cattle and from 0.42 in first lactation of betweenlactations(l¢ >l), wherey =TDrecordiof
mli
the high within-herd standard deviation class to 0.19 cow m in lactation l.
in third lactation of the medium standard deviation Estimates of the long-term environmental variance
class for the Holstein herds. This pattern and range from multiple-lactation analyses for Holsteins were
Journal of Dairy Science Vol. 81, No. 10, 1998AUTOREGRESSIVE TEST-DAY ANIMAL MODEL 2745
TABLE5.Rankcorrelationsbetween genetic evaluations for daily predicting daily yields in current and future lacta-
milk yield from models either including or ignoring a first-order
tions.
autoregressiveprocessforshort-termenvironmental(STE) effects
in the first three lactations of Lucerna cows and Holstein cows in
each of three within-herd standard deviation (SD) classes. Rank Correlations
Rank correlation
Rank correlations between EBV from multiple-
Breed Males Females All lactation animal evaluations using either the full
Lucerna 0.98 0.98 0.98 model or the reduced model are in Table 5. Changes
Holstein1 in rank with correlations ranging from 0.91 to 0.99
Low 0.95 0.94 0.94 were small (29), as expected, because fixed effects
Medium 0.95 0.91 0.92 were identical. Consequently, rankings could only be
High 0.94 0.93 0.94
affectedbydifferentpartitioningoftheenvironmental
1Three herds per SD class: low =<1644 kg of phenotypic stan- variance components.
darddeviation(SD) for305-dmatureequivalent(ME) milkyield,
Especially relevant were correlations between
medium = 1783 to 1898 kg of phenotypic SD for 305-d ME milk
yield, and high = >2022 kg of phenotypic SD for 305-d ME milk evaluations using either single-trait (first lactations
yield. only) or multiple-trait (multiple lactations) analysis.
Correlations between these analyses disclosed major
changes in animal rank (Table 6) from considering
additional information on the same cows in an auto-
approximatelyzeroforeverystandarddeviationclass.
regressive process. The largest changes in rank were
This consistent result implies that subsequent TD
for Holstein females for which correlations across
yields within a lactation depend only on the genetic
standarddeviationgroupings within a herd were 0.18
and STE effects. Alternatively, TD yields in future
to 0.24. The rank correlation among Lucerna cows
lactations covary nearly entirely with the genetic
was 0.37, and only 3 Lucerna cows (each with 3
componentundertheassumptionthatSTEeffectsare
lactationrecords) werecommontolistings oftheelite
independent between lactations. Consequently,
10 females. A closer look at changes in rank between
repeatability—the proportion of phenotypic variance
analyses showed that 40% of the 100 Lucerna cows
that is due to genetic causes and to consistent obser-
with the highest EBV were primiparous cows. There-
vation errors from environmental effects across
fore, multiple-lactation analysis did not favor
lactations—was identical to the heritability of daily
pluriparouscowshavingmoreTDrecords.Changesin
milkyield.Therefore,forHolsteins,theEBVfromour
rank were principally from improved predictions from
TD animal model was the best predictor of daily milk
additional pedigree information from dams and sires.
yield in a subsequent lactation.
The same pattern occurred for Holstein groupings for
In contrast, estimates of the LTE variance compo-
which 33, 40, and 37% of primiparous cows were
nent from the multiple-lactation model were rela-
amongthetop100 cowsin thelow, medium,andhigh
tively important for the lower yielding herd of Lu-
classes of phenotypic standard deviation.
cerna cattle. Contributions from environmental
correlations between TD yields within and across lac-
tations are needed for the accurate prediction of EPA
of Lucerna cows.
TABLE6.Rankcorrelationsbetween genetic evaluations for daily
Methods of utilizing TD yields to compute
milkyieldusingananimalmodelwithafirst-orderautoregressive
305-d lactation records accumulate STE observation process for short-term environmental (STE) effects in multiple
errors and LTE observation errors in a completely lactations and first lactation analyses for Lucerna cows and Hol-
stein cows in each of three within-herd standard deviation (SD)
confounded manner; these errors can only be parti-
classes.
tioned from the genetic component in a large
between-lactation component. For production systems Rank correlation
with high yielding cattle that require intensive input Breed Males Females All
andthatofferproducerssubstantialcontroloverLTE,
Lucerna 0.73 0.37 0.38
it seems reasonable that most environmental in-
Holstein1
fluences causing correlations between TD records oc- Low 0.89 0.20 0.26
cur while cows are lactating (i.e., the STE effect). Medium 0.88 0.24 0.30
High 0.87 0.18 0.23
This scenario would leave little, if any, residual effect
for future lactations, especially in systems with high 1Three herds per SD class: low =<1644 kg of phenotypic stan-
yields. Consequently, a multiple-lactation TD model darddeviation(SD) for305-dmatureequivalent(ME) milkyield,
medium = 1783 to 1898 kg of phenotypic SD for 305-d ME milk
effectively provides greater heritability, greater
yield, and high = >2022 kg of phenotypic SD for 305-d ME milk
genetic gain in milk, and redefined repeatabilities for yield.
Journal of Dairy Science Vol. 81, No. 10, 19982746 CARVALHEIRA ET AL.
Sires also changed rank but less dramatically than
did females; correlations ranged from 0.73 in Lucerna
to 0.89 in Holstein cows (Table 6). Among the 10 top
sires from each analysis, 7 sires were in common for
Lucerna; and 8, 7, and 2 were in common for the low,
medium, and high Holstein classes of phenotypic
standard deviation, respectively.
The multiple-lactation TD animal model should be
effective for genetic evaluation of dairy production
systems in both tropical and temperate regions. The
addition of more TD records per cow, more daughters
per sire, and more pedigree information affects evalu-
ations because EBV is estimated by regressing the
adjusted phenotypic record toward the adjusted
phenotypic mean of zero (34). This regression coeffi-
cient varies with the heritability and repeatability of
daily milk yield and with the number of records tied
by genetic relationships. The multiple-lactation
analysis considered substantially more records from
cows with TD in more than one lactation, which
permitted adjustments for selection that precluded
some cows from having further lactations. Conse-
quently, the bias and sampling error of evaluations
were decreased, and concomitant increases occurred
in heritability and the accuracy of genetic evaluation.
Accuracy of Predicting
Breeding Values
Figure1.HistogramsoftheaccuraciesofEBVobtainedfromthe
The histograms in Figure 1 show the accuracies of
evaluations for multiple lactations (a) and first lactation (b)
EBV from evaluations of both multiple lactations and evaluationsforanimalsintheLucernaherdandinthelowpheno-
first lactation only for Lucerna and for Holsteins of typic standard deviation Holstein class.
low phenotypic standard deviation class. This pattern
also occurred in the other standard deviation classes.
A seemingly bimodal distribution appeared in every for the Lucerna herd (panel a) and for each of the
datafile(Figure 1). Data foranimals withthefewest three Holstein herds in the low phenotypic standard
observations and, therefore, lowest accuracies, deviation class (panel b). The mean annual genetic
clustered together around the lower mode. Data for trend for the Lucerna herd was nil, except for 1987 to
animals with highest accuracies, representing the 1989, when average genetic merit for daily milk yield
majority of animals in each data file, clustered increased by 0.7 kg. Our results indicate that the
around the higher mode. Also illustrated is the ex- opportunity for genetic progress in small populations
pected higher frequency of animals of both breeds in tropical environments—where nutrients are
with greater accuracies from the multiple-lactation limited and data are scarce, even for the above aver-
analysis. Accuracies were greater for Holsteins than age Lucerna situation—is either less available or un-
forLucernacattlebecausethegeneticrelationshipsof available unless environmental components can be
Holsteins had more ties. disentangled to obtain accurate EBV. This collabora-
tive project with ASOLUCERNA yielded the metho-
dologyandbaselinegeneticanalysestoenablegenetic
Genetic Trend
gains by finding more of the parents with highest
in Milk Yield
EBV.
The mean EBV by year of birth for the animals The genetic trends were heterogeneous among Hol-
that were evaluated represent trends in realized stein herds in the low standard deviation class
genetic progress for the period of this study (1984 to (Figure 2b). Two herds sustained gains throughout
1992). Figure2presentsacomparisonofthesetrends the period of the study; one herd hardly advanced
Journal of Dairy Science Vol. 81, No. 10, 1998AUTOREGRESSIVE TEST-DAY ANIMAL MODEL 2747
EBV except in 1 yr (herd 1). Trends in genetic merit
averaged nearly 1 kg in daily milk yield for this
8-yr period, which was also the outcome in the other
within-herd standard deviation classes. The cor-
responding average annual genetic progress in milk
yield was approximately 38 kg (1 kg/8 yr · 305 d in
lactation/yr), which was ~ 16% less than in the litera-
ture (12, 32) for the northeastern US Holstein popu-
lation. Van Tassel and Van Vleck (32) reported a
potentialannualgeneticgain of96 kgforHolsteinsin
the northeastern US. When their equations were up-
dated with genetic variance estimates from the
present study, the theoretical annual genetic gain for
milk yield nearly doubled to 173, 180, and 197 kg/yr
for the low, medium, and high standard deviation
groups, respectively, which suggests advantages from
also using a multiple-lactation TD model in US
genetic evaluations.
Figure3.ManagementtrendsbytestdatefromJanuary1985to
November1995intheLucernaherd(a) andfromJanuary1987to
November1995foreachHolsteinherdinthelowphenotypicstan-
dard deviation class (b).
Cow Age and Herd
Management Effects
The TD models also help to quantify herd manage-
ment effects and individual cow productivity. The
effectsofage andlactation curvewereestimatedfrom
the data from individual farms. Interactions between
Holstein herd and age of cow at calving were not
detected (P > 0.4). Consequently, a common age at
calving effect was fitted.
Figure 3a shows the management trend in the
Lucerna herd from 1985 to 1995 and in each Holstein
herd in the low phenotypic standard deviation class
from1987 to1995(Figure 3b). Within-year variation
in average daily milk for Lucerna cows represents
changes in production caused by seasonal differences
and management, probably reflecting quality, availa-
bility and costs of feeds, and other economic factors.
There was a long-term decline of ~ 2 kg in average
daily milk yield from 1986 to 1994, followed by a
quick recovery in the last year of this study. Overall,
Figure 2. Genetic trends for the period 1984 to 1992 in the
there was no net change in the average daily milk
Lucerna herd (a) and for each Holstein herd (b) in the low
phenotypic standard deviation class. yield of Lucerna cows during this 10-yr period. This
Journal of Dairy Science Vol. 81, No. 10, 19982748 CARVALHEIRA ET AL.
lack of net gain from management illustrates the ment (12), which may help to evaluate promising
severity of constraints affecting the dual-purpose interventions and to identify bottlenecks in produc-
production systems in the tropics. To increase the tivity.
milkyieldpercowisamajorchallengewithoutaccess
to economical resources to increase dietary energy Lactation Curves
density (26), which typically leads managers to seek
Theability topredictfutureTDrecords depends on
profit margins by controlling input costs (25).
the accuracy of the modeled lactation curves [e.g., I.
Conversely, the US Holstein herds had much
A. Papjcsik and B. Bodero, 1988, unpublished data;
greater fluctuations in daily milk yield across years,
(7, 13, 30)]. Methods to estimate the parameters of
perhaps from dietary changes and seasonal variation.
the lactation curve have included functional forms
Herd differences were large (Figure 3b). The consis-
such as density functions (e.g., Wood’s equation),
tent rise in average daily milk yield in the winter
multiphasic logistic functions, and fourth- or fifth-
months may have reflected a seasonal calving policy
order polynomial regressions. Lactation curves also
to take advantage of higher milk prices during this
can be estimated by obtaining the least squares solu-
season. Overall, these herds showed a positive
tions for TD milk yield on the fixed effect of DIM,
management trend of about 8 kg during the 8 yr which was the method used in this study.
studied. Comparison of lactation curves is another tool for
The effects of TD were adjusted to a common age identifying limitations in nutrition and management
and stage of lactation so that fluctuations in adjusted programs. Figure 4 shows the lactation curves for
TD milk yield are likely to be caused by feeding and each of the three parities for the Lucerna herd
other management effects. The management trend in (Figure 4a), for primiparous Holstein cows in the
daily milk yield monitorstheefficacyofherd manage- herds constituting the low standard deviation class
Figure4.Lactationcurvesshowingmilkyieldontestdays(TD) foreachofthethreeparitiesintheLucernaherd(a), forprimiparous
Holsteincowsintheherdsconstitutingthelowstandarddeviationclass(b), foreachofthethreeparitiesinoneHolsteinherdfromthe
low standard deviation class (c), and for each of three parities in one Holstein herd from the high standard deviation class (d).
Journal of Dairy Science Vol. 81, No. 10, 1998AUTOREGRESSIVE TEST-DAY ANIMAL MODEL 2749
(Figure 4b), for each of the three parities in one limitations on available information for this study
Holstein herd from the low standard deviation class and the emphasis on milk yield for Lucerna cattle.
(Figure 4c), and for each of the three parities in one The herd composition (animals available for the
Holstein herd from the high standard deviation class selection process) assumed for this study was based
(Figure 4d). on actual numbers of cattle that are kept on the two
For Lucerna cows, the nearly identical lactation ASOLUCERNA farms recording data. Because AI is
curves for different parities and a barely discernible available, male pathways were unrestricted. For fe-
early peak (between 30 and 40 d) probably signified males, a 30% rate of annual substitution (cullings)
a limited nutrientsupport of milk yield. Coupled with was assumed for an annual calving rate of 80%(50%
observations that Lucerna cows are chronically thin, female births) and a 90% survival rate from birth to
these results suggest not only a severe constraint first calving. Consequently, the Lucerna population
phenotypically (Figure 4a), which may have fostered was assumed to comprise 50 males and 700 females.
the autocorrelation between lactations, but also a To maintain the male population, 97 cows are
compression of genetic variance (Table 4). needed for the dam of sires pathway (97 · 0.5 · 0.8 ·
The lower milk yield of primiparous Holstein cows 0.9), whichcorrespondsto~ 14%ofthefemalepopula-
in herd 1 (Figure 4b) may have reflected less atten- tion. With a substitution rate of 30%, then 210 fe-
tion to heifer management, which seemed associated males need to be born per year; this number already
with the subsequent large differential for milk yields accounts for rates of calving and survival and implies
between second and third lactations in this herd the need for 583 cows (or ~ 83% of the female popula-
(Figure 4c). Lactation curves in one herd from the tion) for the dam of dams path. The selected fraction
high phenotypic standard deviation class(Figure 4d) ofmaleseitherforthesireofsirespath(~ 10%) orthe
aretypicalexceptforthegreateryieldofsecondlacta- sire of dams path (~ 70%), followed the typical recom-
tion cows than for older cows. Reasons for these mendation of 1 bull per 20 cows to make available a
anomalies may be due to differences in the manage- larger pool of sires to restrict inbreeding. Although
mentpracticesofeachfarm.Thisby-productofanaly- current inbreeding is unknown, in closed populations
sis of TD (i.e., lactation curves adjusted for STE such as Lucerna cattle, care must be taken to avoid
effects) may be especially useful for managing lacta- detrimental effects from inbreeding, especially in fit-
tion in dual-purpose cattle systems in the tropics. ness traits.
Table 7 shows the input values corresponding to
the genetic gain equations for two, three, and four
Optimizing Genetic Progress
paths of selection. The assumed generation intervals
in the Lucerna Herd
were based on previous reports(32, 34); an arbitrary
The effectiveness of a breeding program is meas- inflation was 10% to account partially for later matu-
ured by genetic achievement in the target population rity in tropical cattle that were reared on less
(22), which requires reliable records for genetic anal- nutrient-dense diets compared with maturity of cattle
ysis. The TD records for Lucerna cattle provide the in temperate environments. The mean age at first
prerequisite conditions for an effective breeding pro- calving was 38 mo for Lucerna cows and 28 mo for
gram. Nevertheless, results from this investigation Holsteins. The genetic gain for each selection alterna-
revealed the need for a proper analytical model to tive and corresponding theoretical maxima for ex-
avoid confounding important environmental effects pected annual gains also are in Table 7. As expected,
with the genetic component, especially in production annual gain is greater when all genetic pathways are
settings that restrict genetic expression. For the Lu- utilized. A genetic gain in milk of 34 kg/yr is poten-
cerna herd, a multiple-lactation TD animal model tially achievable for Lucerna, which is only 11% less
should be used that considers all TD records, includ- than that obtained by the US Holstein herds in this
ing partial lactation records of cows that were sold or study.
culled, to generate the most accurate EBV. The usual approach to maximizing genetic gain is
An appropriate selection goal for dual-purpose cat- to calculate the expected genetic gain for different
tle might be to maximize net economic returns from combinations of records and fractions of animals
increased average daily milk yield per generation selected, which influence each other and the genera-
without simultaneously decreasing the beef output tion interval, and then choosing the combination
per cow on a lifetime basis. However, the selection yielding greatest genetic gain (34). More paths of
alternatives we considered are only for potential selection, however, imply greater expense (economi-
genetic gains in average daily milk yield because of cally and organizationally) in executing a breeding
Journal of Dairy Science Vol. 81, No. 10, 19982750 CARVALHEIRA ET AL.
TABLE7.Populationfractionsforselectedanimals,selectionintensities,averagepredictionaccuracies
for the estimated breeding values, generation intervals, genetic standard deviation (sˆ ), genetic
a
superiorityduetotheselectedpath(D) andcomparativedailyand yearly genetic gain in milk (Dg)
obtained by exploiting two, three, or four paths of selection for the Lucerna population.
Two paths Three paths Four paths
DS DD SD DS DD SS SD DS DD
Fraction selected 0.14 0.83 0.70 0.14 0.83 0.10 0.70 0.14 0.83
Selection intensity 1.51 0.30 0.80 1.51 0.30 1.92 0.80 1.51 0.30
Accuracy of prediction 0.69 0.65 0.72 0.69 0.65 0.76 0.72 0.69 0.65
Generation interval, yr 6.00 7.50 5.00 6.00 7.50 5.00 5.00 6.00 7.50
sˆ a, kg 0.79 0.79 0.79 0.79 0.79 0.79 0.79 0.79 0.79
D, kg/d 0.83 0.16 0.45 0.83 0.16 1.15 0.45 0.83 0.16
Dg, kg/d 0.073 0.078 0.110
Dg, kg/yr 22 24 34
program. The optimal genetic program for the Lu- resources. Validation of the model would require
cerna breed (two, three, or four paths of selection), either an analysis of data subsets in different time
therefore, is the one that maximizes net economic frames or, preferably, a comparison of genetic predic-
returns to the cost of implementing breedings and tions of sires with independent samples of daughters
storing and analyzing data in a timely manner to and herds.
inform those persons making selection decisions. The present study showed that substantial genetic
Differences in genetic gain from ignoring certain progress in milk yield is indeed achievable in small
pathways permit the computation of the correspond- populations that are managed in environments with
ing opportunity losses in genetic gain. limited resources (e.g., the nucleus population of two
Lucerna herds that we considered) using an animal
model that autoregressively accounts for STE and
CONCLUSIONS
LTE effects. Unbiased estimates and, therefore,
The TD animal models offer the opportunity to genetic gain for dual-purpose cattle systems in tropi-
improvethegeneticevaluationofdairycattleintropi- calsettingswithfewdataislikelytobesmall(or nil)
cal and temperate production situations. An obvious unless TD yields are adjusted for the autoregressive
advantage is the large increase in information from STE structure influencing daily milk production.
more records and the ability to account for temporal Autoregressive structures also may be valuable in
effects of herd management, which reduces residual analyzing other time-dependent livestock traits (e.g.,
variance components, thus increasing estimated growth, measures associated with disease, and para-
heritability and the accuracy of predicting EBV. site resistance), which may merit further investiga-
tion.
The first-order autoregressive structure for
residual effects of TD records within a lactation
greatly reduced the model error component by better ACKNOWLEDGMENTS
disentangling the random STE effects. The multiple-
We especially thank the Dura´n-Castro and Molina-
lactation TD model resulted in the largest estimates
Dura´n families, the principal constituents of the Lu-
ofgeneticvarianceandheritability andgave themost
cerna Cattle Breeders Association, ASOLUCERNA,
accurate estimates of individual genetic merit for
for providing the data for this study. This work con-
daily milk yield by admitting more information and
tributes to the S284 Regional Project, Genetic En-
heterogeneous environmental variances between lac-
hancement of Health and Survival for Dairy Cattle.
tations. These findings were confirmed by biological
The study was partially supported by the Cornell
evidence in a wide range of herd environments for Theory Center (Ithaca, NY), which receives major
whichthefullmodelwassuperiortootherapproaches fundingfromtheNationalScienceFoundation(NSF)
relying on a LTE effect but ignoring STE effects. (Arlington, VA), New York State, and from the Ad-
Although these properties of the multiple-lactation vanced Research Projects Agency(ARPA) (Washing-
TD animal model enhance the value of information ton, DC), the National Institutes of Health (NIH)
from any data base, they are especially important for (Bethesda, MD), the IBM Corporation (Armonk,
limited-size data files from production systems in the NY), and other members of the Cornell Theory
tropics that are constrained in environment and Center Corporate Research Institute.
Journal of Dairy Science Vol. 81, No. 10, 1998AUTOREGRESSIVE TEST-DAY ANIMAL MODEL 2751
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