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Effects of Clinical Ketosis on Test Day Milk Yields in Finnish Ayrshire Cattle
Effects of Clinical Ketosis on Test Day Milk Yields in Finnish Ayrshire Cattle J. C. DETILLEUX and Y. T. GR6HN Department of Clinical Sciences Section of Epidemiology College of Veterinary Medicine
R. L. QUAAS Department of Animal Science College of Agricultural and Life Sciences Cornell University Ithaca. NY 14853
ABSTRACT
INTRODUCTION
A linear model for repeated measurements was used to estimate the effects of clinical ketosis on 722,198 test day milk yields collected from September 1, 1985 to January 31, 1988 on 60,851 Finnish Ayrshire cows of parity <7. An index was created to differentiate among milk collected within 17 d following diagnosis of ketosis, milk collected before or >17 d after diagnosis, and milk collected on nonketotic cows. For each parity separately, the statistical model included fixed effects (ketosis, calving season, year and season of milk sampling, and stage of lactation) and random effects (herd and permanent and temporary environments) on test day milk yields. The pattern underlying correlations between temporary environmental effects was accommodated in the statistical model. Compared with those for nonketotic cows, lactation curves of cows with ketosis showed a depression in early lactation; estimated milk loss was 44.3 kg for 17 d after diagnosis. The 305-d milk yield of cows diagnosed with ketosis was estimated to be 141.1 kg higher than that of cows free of ketosis. Although milk losses occurred after ketosis, ketotic cows yielded more milk over the entire lactation than did nonketotic cows; and yields would have been even higher if cows had not had ketosis. (Key words: ketosis, test day milk, dairy cow)
Ketosis is primarily a disease of high yielding dairy cows (1) that occurs within a few weeks after calving (11). Clinical signs include lack of appetite, decreased milk yield, and loss of body condition (1, 12, 13). A widely accepted key factor in the etiology of ketosis is the inadequate supply of energy necessary for milk yield, which leads to negative energy balance, increased fat mobilization, and increased hepatic ketogenesis (2). The main objective of this study was to evaluate the effects of clinical ketosis on test day milk yields taken approximately every 30 DIM. Because the prevalence of ketosis is highest among high yielding cows, milk losses from ketosis cannot be estimated precisely from the traditional cumulative 305-d lactation yields. High yielding cows might lose milk during clinical ketosis and be misclassified as average yielding cows. Consequently, critical information is lost because the traditional estimation is not precise. Proper statistical modeling of test day milk yields should allow for effects that are specific to a cow on a particular test day and effects that are specific to a cow for her entire lactation.
Received March 14, 1994. Accepted June 10, 1994. 1994 J Dairy Sci 77:3316-3323
MATERIALS AND METHODS Data
Between September 1, 1985 and January 31, 1988, health records and monthly test day milk yields were recorded on 60,851 Finnish Ayrshire cows calving from September 1, 1985 to March 1, 1987. Individual cow records consisted of cow identification, herd, parity, date of calving, test day milk yield, and diagnosis of first occurrence of all diseases, as recorded 3316
3317
KETOSIS AND MILK LOSS
in the Finnish national disease recording system (11). Disease data included only cases treated by veterinarians during farm visits. No information was available on age at calving, number of days open, length of dry period, or pedigree. On average, 10 test day yields were collected per cow per lactation. Only data on the first 305 DIM and on cows of parity <7 were considered. To differentiate between cows with and without ketosis, a ketotic index was created for each test day milk yield collected. If a cow was free of ketosis during the entire lactation, all test day yields were included in the first category of the ketotic index. When a cow was diagnosed with ketosis during the lactation, each test day yield sampled before diagnosis or >17 d after the diagnosis of ketosis was included in category 2. Finally, test day yields collected on a cow with clinical ketosis within 17 d following the diagnosis were included in category 3. Each lactation was divided into 36 lactational stages. Milk records taken before d 100 were grouped by 5-d intervals, records from 101 to 230 DIM were grouped by 10-d intervals, and records from 231 to 305 DIM were grouped by 20-d intervals. Four seasons at calving and at milk sampling were defined as 3-mo intervals, starting in January. Milk samples recorded before December 31, 1986 were included in one test year category, and cows tested after January 1, 1987 constituted the other test year category. Statistical Analyses
To determine which autoregressive integrated moving average process adequately described the pattern underlying correlations between successive measurements, test day yields were analyzed with the following model, for each parity separately, and for each category of ki:
where y = vector of test day yields; y = fixed yector representing effects of calving season (4 categories), season within year of milk sampling (8 categories), and stage of lactation on test day yields (36 categories); I: = known incidence matrice relating y to y; and q = error
vector. During the study, some cows had milk yields measured in more than one lactation; although records for these cows were analyzed more than once, they appeared only once in each relevant parity. For cows treated or not treated for clinical ketosis during their lactations, autocorrelations (rk) and partial autocorrelations @k) between elements qt of q were computed up to lag k = 10 (16):
with t = 1,2,. . .n, and n = number of test day yields. Test day yields were then analyzed for each parity separately with the following model: y = X@ + Wh
+
Zp
+
e
PI
where y = vector of test day milk yields; /3 = vector of fixed effects affecting y; h = random vector representing herd effects on y; p = random vector representing permanent environmental effects on y; e = random vector representing temporary environmental effects on y; and X, W, and Z = known incidence matrices relating y to p, h, and p, respectively. Fixed effects @ included the ketotic index (3 categories), calving season (4 categories), season within year of milk sampling (8 categories), and stage of lactation (36 categories). All random vectors (h, p, and e) had null means and were uncorrelated. The term p accommodated for the variation in average test day milk yields among cows, and e accounted for the variation between repeated test day milk yields within cows (6). Also,
4
where is the variance of herd effects, :o is the variance of permanent environmental effects, and is the error variance or variance of temporary environmental effects. The element rm of the matrix R is the autocorrelation
2
Journal of Dairy Science Vol. 77, No. 11, 1994
3318
DETILLEUX ET AL
coefficient between elements e, and e, of e at DIM m and n, respectively:
r,
RESULTS
Descriptive statistics on numbers of cows and milk yield in Table 1 and on ketosis Occurrence in Table 2 are given by parity for 60,851 Finnish Ayrshre cows. Of a total of 5975 herds, 5548 herds had on average 4.1 cows of parity 1. Six percent of all cows were treated for clinical ketosis. The percentage of cows with clinical ketosis increased with parity and reached a maximum in parity 4. The first diagnosis of clinical ketosis occurred within 8 wk after calving. For each parity, the percentage of cows with clinical ketosis was higher for cows yielding >6300 kg of 305-d milk. The percentage of treated cases of ketosis was lower in the spring and summer (April to September) than in other calving seasons. Recurrence of ketosis, measured as the percentage of cows with clinical ketosis in the preceding parity that were also treated for ketosis in the current parity, increased from 4.6% in parity 2 to 9.9% in parity 6. For cows treated or not treated for ketosis and for each parity separately, correlograms (plot of autocorrelation against lag) obtained from Model [ l ] showed a rapid exponential decay of autocorrelations with increasing lags (example in Figure 1). Partial autocorrelations showed a sharp decrease after lag 1 and were significant at lag 1 only. Autocorrelation at lag 1 was estimated at .7. Lactation curves were constructed by plotting estimated test day yields from Model [2] for cows treated or not treated for ketosis; solutions for stage of lactation and for the ketotic index were used to estimate test day
= P and a = It, - tnle
where t, tn = DIM at which test day milk yields Yn) were collected, r = autocorrelation coefficient estimated for k = 1 (Model [l]), and 8 2 0. For example, the case 0 = 1 yields the first-order autoregressive model, and the case 8 tending to yields the first-order moving average model (15). Because estimation of r in Model [ l ] assumed ordered and equally spaced time series (17), the term It, - t,l was used in Model [2] to account for unequal and nonconsecutive measurements (20). The computer algorithm for estimating 4 = and /3 was as follows: 00
[4, $, 41’
Start with initial estimates +(O). The algorithm was restarted with different priors. At step (p + l), compute the maximum likelihood estimate of @ as b@+’) = [X’V-1 XI- [x’V-1 y] using v = v(+@). Step (p + 1) of the algorithm yields the REML (16) estimate +@+I) using an expectation-maximization algorithm (5): B@) +@+I) = d@)(see Appendix). Iterate between steps 1 and 2. At step p, iterative improvement was measured as the ratio of s uared computable residuals [(= (d@)- B@) +L1y; (3)]. The values of the log-likelihood for y were computed at successive rounds of iteration to check iterative convergence at a global maximum.
TABLE 1. Descriptive statistics for test day samples, cows, and milk yields by parity in 60,851 Finnish Ayrshire cows. Paritv
Test day samples, no. Cows, no. Herds, no. Average herd size, no. of cows per herd Average test day yield, kg X SE Average milk yield in 305 DIM, kg X SE
1
2
216,116 22,816 5548 4.1
186,874 132,144 93,400 19,014 14,169 10,066 5286 4948 4384 3.6 2.9 2.3
Journal of Dairy Science Vol. 77, No. 11, 1994
17.14 .03 5075.9 10.8
3
18.71 .04 5707.3 13.0
4
20.45 .05 6076.1 14.8
5
6
57.763 6213 3499 1.8
36,101 3912 2626 1.5
20.86
20.73
.05
.06
6176.1 16.8
6187.5 19.6
20.51 .07 6144.9 24.0
3319
KETOSIS AND MILK LOSS TABLE 2. Lactational incidence risk (LIR)of clinical ketosis by parity in 60.851 Finnish Ayrshire cows. Parity 2
1
LIR,' W
3
4
5
6
4.8
5.1
7.1
7.7
7.1
6.1
33.4 25.4
33.6 28.7
30.0 22.3
29.1 20.2
29.6 22.9
33.2 26.6
4.0 4.6 5.0
3.7
5.2 7.2 9.3
6.5 8.1 8.9
5.0 6.7 9.5
4.0 6.1 7.6
13.4 6.1 4.2 9.2
15.2
18.8 10.2 4.5 13.6 6.2
20.4 10.6 4.6 13.3 6.0
17.8 9.7 3.6 13.5
14.6 7.5 4.6 12.3 9.9
D g of first diagnosis, DIM
X SE LlRl per 305-d milk yield, 96 4 1 0 0 kg 51004300 kg >6300 kg LIR' per calving season, % Jan-Mx Apr-Jun lul-Sep Oct-Dec Recurrence,* %
5.5
6.7
6.7 3.0 9.0 4.6
...
7.9
'Percentage of cows with clinical ketosis. *Percentage of cows with clinical ketosis in the preceding parity that were treated for ketosis during the current parity.
yields. In each parity, the lactation curves of cows with clinical ketosis showed a depression in early lactation and a shift upward before and
1.0
I
.9 .8 .7
*
.6
0'
I
f
.5
I
0 0
.4
I
.3 .2 .1
0 0
1
2
3
4
5 LAG
6
7
8
9
10
Figure 1. Autocorrelation p; correlation between yt and Yt-k) and partid autocorrelation (A;correlation be. .~ tween y! and Yt-k given yt-l, yt+ . .yt-(k-l)) between test day milk yields adjusted to the same stage of lactation and season, for third parity cows treated K A ) or not treated @,A) for ketosis. yt = Test days milk yield taken at time t, t = DIM (t = 1, 2,. . ,, lo), and k = lag (k = 0, 1,. . ., lo).
after the depression compared with the curves for nonketotic cows (example in Figure 2). Table 3 shows the differences in 305-d milk between nonketotic cows and cows with or without clinical ketosis within 17 d following the collection of milk. Those differences in 305-d milk were estimated using the solutions obtained in Model [2]. Cows with clinical ketosis yielded, on average, 141.1 kg more 305-d milk than nonketotic cows but yielded 44.3 kg less over 17 d following the diagnosis of ketosis (Table 3). The net 305-d milk gain for parity for ketotic cows over nonketotic cows was the least in parity 4 (86.7 kg; Table 3). Estimates for variance components are shown in Figure 3 for each parity separately. Herd variance increased from 3.9 kg2 in parity 1 to 6.8 kg2 in parities 24. Permanent environment variance reached a maximum, 6.4 kg2, in parities 22. Similar to the herd variance, temporary environmental variance increased from 5.1 kg2 in parity 1 to 9.3 kg2 in parities 24. DISCUSSION
Ketosis
losses associated Our data showed that with clinical ketosis did not overcome the adJournal of Dairy Science Vol. 77, No. 11. 1994
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DETILLEUX ET AL.
TABLE 3. Estimated milk differences by parity for 305-d milk between cows treated or not treated for ketosis. Parity 1
2
3
33.9 169.9 136.0
44.3 172.1 127.8
47.1 200.1 153.0
4
S
6
52.6 139.3 86.7
36.4 221.3 184.9
51.8 209.9 158.1
0 Milk loss' Potential milk gain2 Net milk gain3
~~
~~
~~
~
~~
'For 17 d following diagnosis of ketosis. 2Potential milk gain for cows with clinical ketosis, Le., difference in 305-d milk between cows with clinical ketosis before or >I7 d following diagnosis and cows not mated for ketosis during the entire lactation. 3Net milk gain for cows with clinical ketosis. i.e.. difference in 305-d milk between cows treated or not treated for ketosis during the entire lactation
vantage of high milk yield in cows treated for clinical ketosis; nevertheless, if those highest yielding cows had not had ketosis, their yields would have been considerably greater. A positive association existed between percentage of clinical ketosis and 305-d milk yield (Table 2). Lactation curves of cows with clinical ketosis were depressed in early lactation (Figure 2); estimated milk loss was 44.3 kg for 17 d after diagnosis. Over all parities, solutions from Model [2] showed that cows with clinical ketosis during the lactation yielded, on average,
26
T
1
25 , 24
!
2 1
3
Journal of Dairy Science Vol. 77, No. 11, 1994
141.1 kg more milk over 305 d than did nonketotic cows (Table 3). Feeding practices, individual cow characteristics (age and genetic disposition), and general environmental factors (year, season, and housing system) are possible reasons for the positive association between occurrence of clinical ketosis and milk yield. Estimates of genetic correlations between 305-d milk and ketosis vary from 0 to .17 (10, 14) in Finnish Ayrshire cattle (IO) and are .65 in Norwegian heifers (18). Feeding practices that are insufficient to meet energy requirements for high milk yield may lead to negative energy balance, increased fat mobilization, and increased hepatic ketogenesis (2). Increased risk of ketosis during indoor feeding may be explained by inadequate nutrient intake (1 1) or decreased ability to utilize ketones in untrained muscle (22). Older high yielding cows may be unable to metabolize energy efficiently enough to support prioritized demands for high milk yield and, subsequently, may develop ketosis. In previous studies, clinical ketosis decreased cumulative milk yield by 66.0 kg (8.8%), 156.5 kg (12.7%), and 285.4 kg (8.2%) for DIM 1 to 21, 22 to 49, and 50 to 119, respectively (4). Increased milk ketone bodies were associated with a daily milk reduction of 1 to 1.4 kg (8) and a loss of 233.4 kg (8.5%) of FCM during the first 100 DIM (12). Those milk losses may be due to clinical ketosis, to diseases associated with ketosis, or both. Metabolic changes in early ketosis (hyperketonemia and hypoglycemia) may lead to loss of appetite that could explain the observed decline in milk yield (2). Clinical ketosis has also been as-
3321
KETOSIS AND MILK LOSS
sociated with metritis, paresis, abomasal disorder, mastitis, hypomagnesemia, and retained placenta (9), all of which can decrease milk yield. In this study, milk losses (2.6 kg/d) were probably underestimated because 1) cows may suffer milk loss immediately after the diagnosis of ketosis and then rapidly return to their previous yield before the next milk recording, 2) milk losses prior to the diagnosis of ketosis were not recorded, and 3) duration of clinical ketosis was limited to 17 d. In a previous study (4), cumulative milk yield for 21 d was 33 kg lower for cows treated for ketosis after the 21 DIM. In another study (13), cumulative milk yield was depressed by approximately 60 to 70 kg for at least 2 wk before the diagnosis of ketosis. Surprisingly, however, treatment was delayed until cows in that study (13) lost large amounts of milk.
10 9 8 Q 7 M 5 6
Mean incidence risk of treatment for clinical ketosis (6%), peak percentage of cows with clinical ketosis in parity 4, first occurrence of clinical ketosis within 8 wk after calving, and highest percentage of clinical ketosis during indoor feeding (October to March) (Table 2) are in accordance with previous studies of Finnish Ayrshire cattle (9, 10). The positive association between 305-d milk and Occurrence of ketosis may explain the increase in recurrence of ketosis (Table 2) across parities because low yielding cows are preferentially culled. Statistical Analyses
Because our statistical model should account for all known sources of variation on test day milk yields, Model [2] was more useful than Model [l]. However, estimation of all parameters directly from Model [2] necessi-
--
rl
--
Parity = 1
m
~-
\
Parity = 2
H
--
25
Parity = 3
2 5-4
rn
:-
Parity = 4
w Parity = 5
c,
!E
3-2 I -0
a
--
Parity = 6
--
Herd
Permanent
Temporary
Variance Components Figure 3. Estimated herd, permanent environmental, and temporary environmental variances in test day milk yields per parity. Journal of Dairy Science Vol. 77, No. 1 1 , 1994
3322
DETILLEUX ET AL.
tated maximization of the log-likelihood for the data in the two phases between which iteration continues until convergence is reached for all parameters (6, 15). This procedure was desirable but economically impossible because of limited time and computer funds, and, therefore, another method was chosen. First, r and 8 were estimated using Model [l], in which r was the autocorrelation between test day milk yields adjusted to the same seasons and stages of lactation, and 8 described the autoregressive integrated moving average process. Then the effects of clinical ketosis on test day milk yields (Model [2]) were estimated using the estimated r and e obtained in Model [l]. Although the residuals in Model [ l ] and Model [2] are different, autocorrelation was not expected to affect the estimates of the effects of clinical ketosis on test day milk yields because autocorrelation has little impact on actual point estimates (21). Correlograms and partial correlograms (Figure 1) obtained from Model [ I ] suggested that the error term in Model [l] may be adequately modeled with a first-order autoregressive model, that the autocorrelation between successive error terms is .7, and that the series of error terms is stationary (7). Therefore, the autocorrelation coefficient between error terms in Model [2] was taken as .7Q with a = Itm - tnl for DIM tm and tn (e = 1). Effects of herd on test day yields were treated as random because average herd sizes were very small (Table 1) (19). Under the assumptions of Model [2],estimates of repeatability (ratio of permanent environmental variance to total variance) decreased from .35 in parity 1 to .28 in parities 24. This decrease occurred because estimates of herd variance and temporary environmental variance reached a maximum in parity 24, but estimates of permanent environmental variance reached a maximum in parity 22 (Figure 3). For 305-d cumulative milk, the same permanent environmental effects (partly environmental and partly genetic in origin) might be used in analysis of test day milk yields for cows with parity >1. Therefore, test day milk in cows of parity 1 may be influenced by a trait that is genetically different from test day milk yield in cows of parity > I . J o m a l of Dairy Science Vol. 77, No. 11, 1994
CONCLUSIONS
An autoregressive model utilizing test day
milk yields during lactation provided precise estimates of milk losses and gains, which traditional models utilizing only 305-d milk yields are unable to do. Cows with clinical ketosis had a small decrease in milk yield during the ketotic episode compared with yield of nonketotic cows. Over the entire lactation, however, ketotic cows yielded significantly more milk than did nonketotic cows. Higher yielding cows tended to be at higher risk of ketosis, but, if they had not developed ketosis, their milk yield would have been even greater. Therefore, the best managers will ensure that high yielding cows are less susceptible to ketosis. ACKNOWLEDGMENTS
This work was partly supported by the USDA Animal Health and Disease Program. Computations supporting this research were performed at the Cornell National Supercomputer Facility, which is supported in part by the National Science Foundation, New York State, and the IBM Corporation. REFERENCES 1 Andersson, L., and U. Emanuelson. 1985. An epidemiological study of hyperketonemia in Swedish dairy cows: determinants and the relation to fertility. Prev. Vet. Med. 3:449. 2 Baird. G. D. 1982. Primary ketosis in the high producing dairy cow: clinical and subclinical disorders, treatment, prevention, and outlook. J. Dairy Sci. 65:l. 3Conte. S . D., and C. de Boor. 1972. Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill Book Co., New York. NY. 4Deluyker. H. A,, J. M. Gay, L. D. Weaver, and A . S. Azari. 1991. Change in milk yield with clinical diseases for a high producing dairy herd. J. Dairy Sci. 74: 436. 5 Dempster, A. P.. N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B 39:l. 6Diggle. P. J. 1988. An approach to the analysis of repeated measurements. Biometrics 44:959. 7 Diggle, P. J. 1990. Time Series: A Biostatistical Introduction. Oxford Univ. Press, New York, NY. 8 Dohoo, 1. R., and S . W. Martin. 1984. Subclinical ketosis: prevalence and associations with production and disease. Can. J. Comp. Med. 48:l. 9 Grijhn, Y. T., H. N. Erb, C. E. McCulloch, and H. S . Saloniemi 1989. Epidemiology of metabolic disorders in dairy cattle: association among host characteristics, disease, and production. J. Dairy Sci. 72:1876.
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KETOSIS AND MILK LOSS 10 Grohn. Y . T., and J. Syvaj%rvi. 1986. An epidemiological and genetic study on registered diseases in Finnish Ayrshire cattle. 111. Metabolic diseases. Acta Vet. Scand. 27:209. 11 Grohn. Y. T., J. R. Thompson, and M. L. Bruss. 1984. Epidemiology and genetic basis of ketosis in Finnish Ayrshire cattle. Prev. Vet. Med. 3:65. 12Gustafsson. K.. L. Andersson, and U. Emanuelson. 1993. Effect of hyperketonemia, feeding frequency and intake of concentrate and energy on milk yield in dairy cows. Anim. Prod. 5651. 13Lucey. S..G. J. Rowlands, and A. M. Russell. 1986. Short-term associations between disease and milk yield of h r y cows. J. Dairy Res. 53:7. 14Miintysaari. E. A., Y. T. Grohn, and R. L. Quaas. 1991. Clinical ketosis: phenotypic and genetic correlations between occurrences and with milk yield. J. Dairy Sci. 74:3985. 15 Munoz, A,. V. Carey, J. P. Schouten, M. Segal, and B. Rosner. 1992. A parametric family of correlation structures for the analysis of longitudinal data. Biometrics 48:733.
16Patterson. H. D., and R. Thompson. 1971. Recovery of inter-block information when block sizes are unequal. Biometrika 58545. 17 SAS" User's Guide: Statistics, Version 6 Edition. 1988. SAS Inst., Inc., Cary. NC. 18Simianer. H.. H. Solbu, and L. R. Schaeffer. 1991. Estimated genetic correlations between disease and yield traits in dairy cattle. J . Dairy Sci. 74:4358. 19Van Vleck, L. D. 1987. Contemporary groups for genetic evaluations. J. Dairy Sci. 70:2456. 20 Wade, K.M., and R. L. Quaas. 1993. Solutions to a system of equations involving a first-order autoregressive process. J. Dairy Sci. 76:3026. 21 Wade, K. M., R. L. Quaas, and L. D. Van Vleck. 1993. Estimation of the parameters involved in a firstorder autoregressive process for contemporary groups. J. Dairy Sci. 76:3033. 22 Winder, W. W., K.M. Baldwin, and J. 0. Holloszy. 1974. Exercise induced increase in the capacity of rat skeletal muscle to oxidize ketones. Can Physiol. Pharmacol. 53236.
APPENDIX
Expectation-Maxlmization Algorithm
The variance components in Model [ l ] were estimated using REML (16) with an expectationmaximization algorithm (5). Let the complete data e = y - XB, K'y = error contrasts of the incomplete data, +@I = estimates of variance components u i , 0: at round p, and 2 = BLUP(elK'y, +@?. For the E step, compute S@+I)= E [ee'lK'y, = 66' + var(6 - e ) (21). For
."p.
+@a
the M step, find +@+I) that maximizes Q = const
1 - -21 lnlvl - -tr[V-' 2
S@+')] with V = var(y).
Because all herds are independent, V is a block diagonal matrix V = diag[Vh] for h = 1,2,. . .H and Vh = Jh a 2h + D h + F h Ue2 where H = number of herds, Jh = nh X nh matrix Of IS, n h = number of test day yields per herd, D h = diag[Ji] = nh x nh block diagonal matrix with J i on the diagonal, Jj = n, x n, matrix of Is, n, = number of test day yields per cow, and F h = diag[Ri] with Ri = n, x nc autocorrelation matrix. Then, the step p of the expectation-maximization algorithm yields B@) +@+l) = p@) where
."p
B = and
Journal of Dairy Science Vol. 77, No. 11, 1994
R. L. QUAAS Department of Animal Science College of Agricultural and Life Sciences Cornell University Ithaca. NY 14853
ABSTRACT
INTRODUCTION
A linear model for repeated measurements was used to estimate the effects of clinical ketosis on 722,198 test day milk yields collected from September 1, 1985 to January 31, 1988 on 60,851 Finnish Ayrshire cows of parity <7. An index was created to differentiate among milk collected within 17 d following diagnosis of ketosis, milk collected before or >17 d after diagnosis, and milk collected on nonketotic cows. For each parity separately, the statistical model included fixed effects (ketosis, calving season, year and season of milk sampling, and stage of lactation) and random effects (herd and permanent and temporary environments) on test day milk yields. The pattern underlying correlations between temporary environmental effects was accommodated in the statistical model. Compared with those for nonketotic cows, lactation curves of cows with ketosis showed a depression in early lactation; estimated milk loss was 44.3 kg for 17 d after diagnosis. The 305-d milk yield of cows diagnosed with ketosis was estimated to be 141.1 kg higher than that of cows free of ketosis. Although milk losses occurred after ketosis, ketotic cows yielded more milk over the entire lactation than did nonketotic cows; and yields would have been even higher if cows had not had ketosis. (Key words: ketosis, test day milk, dairy cow)
Ketosis is primarily a disease of high yielding dairy cows (1) that occurs within a few weeks after calving (11). Clinical signs include lack of appetite, decreased milk yield, and loss of body condition (1, 12, 13). A widely accepted key factor in the etiology of ketosis is the inadequate supply of energy necessary for milk yield, which leads to negative energy balance, increased fat mobilization, and increased hepatic ketogenesis (2). The main objective of this study was to evaluate the effects of clinical ketosis on test day milk yields taken approximately every 30 DIM. Because the prevalence of ketosis is highest among high yielding cows, milk losses from ketosis cannot be estimated precisely from the traditional cumulative 305-d lactation yields. High yielding cows might lose milk during clinical ketosis and be misclassified as average yielding cows. Consequently, critical information is lost because the traditional estimation is not precise. Proper statistical modeling of test day milk yields should allow for effects that are specific to a cow on a particular test day and effects that are specific to a cow for her entire lactation.
Received March 14, 1994. Accepted June 10, 1994. 1994 J Dairy Sci 77:3316-3323
MATERIALS AND METHODS Data
Between September 1, 1985 and January 31, 1988, health records and monthly test day milk yields were recorded on 60,851 Finnish Ayrshire cows calving from September 1, 1985 to March 1, 1987. Individual cow records consisted of cow identification, herd, parity, date of calving, test day milk yield, and diagnosis of first occurrence of all diseases, as recorded 3316
3317
KETOSIS AND MILK LOSS
in the Finnish national disease recording system (11). Disease data included only cases treated by veterinarians during farm visits. No information was available on age at calving, number of days open, length of dry period, or pedigree. On average, 10 test day yields were collected per cow per lactation. Only data on the first 305 DIM and on cows of parity <7 were considered. To differentiate between cows with and without ketosis, a ketotic index was created for each test day milk yield collected. If a cow was free of ketosis during the entire lactation, all test day yields were included in the first category of the ketotic index. When a cow was diagnosed with ketosis during the lactation, each test day yield sampled before diagnosis or >17 d after the diagnosis of ketosis was included in category 2. Finally, test day yields collected on a cow with clinical ketosis within 17 d following the diagnosis were included in category 3. Each lactation was divided into 36 lactational stages. Milk records taken before d 100 were grouped by 5-d intervals, records from 101 to 230 DIM were grouped by 10-d intervals, and records from 231 to 305 DIM were grouped by 20-d intervals. Four seasons at calving and at milk sampling were defined as 3-mo intervals, starting in January. Milk samples recorded before December 31, 1986 were included in one test year category, and cows tested after January 1, 1987 constituted the other test year category. Statistical Analyses
To determine which autoregressive integrated moving average process adequately described the pattern underlying correlations between successive measurements, test day yields were analyzed with the following model, for each parity separately, and for each category of ki:
where y = vector of test day yields; y = fixed yector representing effects of calving season (4 categories), season within year of milk sampling (8 categories), and stage of lactation on test day yields (36 categories); I: = known incidence matrice relating y to y; and q = error
vector. During the study, some cows had milk yields measured in more than one lactation; although records for these cows were analyzed more than once, they appeared only once in each relevant parity. For cows treated or not treated for clinical ketosis during their lactations, autocorrelations (rk) and partial autocorrelations @k) between elements qt of q were computed up to lag k = 10 (16):
with t = 1,2,. . .n, and n = number of test day yields. Test day yields were then analyzed for each parity separately with the following model: y = X@ + Wh
+
Zp
+
e
PI
where y = vector of test day milk yields; /3 = vector of fixed effects affecting y; h = random vector representing herd effects on y; p = random vector representing permanent environmental effects on y; e = random vector representing temporary environmental effects on y; and X, W, and Z = known incidence matrices relating y to p, h, and p, respectively. Fixed effects @ included the ketotic index (3 categories), calving season (4 categories), season within year of milk sampling (8 categories), and stage of lactation (36 categories). All random vectors (h, p, and e) had null means and were uncorrelated. The term p accommodated for the variation in average test day milk yields among cows, and e accounted for the variation between repeated test day milk yields within cows (6). Also,
4
where is the variance of herd effects, :o is the variance of permanent environmental effects, and is the error variance or variance of temporary environmental effects. The element rm of the matrix R is the autocorrelation
2
Journal of Dairy Science Vol. 77, No. 11, 1994
3318
DETILLEUX ET AL
coefficient between elements e, and e, of e at DIM m and n, respectively:
r,
RESULTS
Descriptive statistics on numbers of cows and milk yield in Table 1 and on ketosis Occurrence in Table 2 are given by parity for 60,851 Finnish Ayrshre cows. Of a total of 5975 herds, 5548 herds had on average 4.1 cows of parity 1. Six percent of all cows were treated for clinical ketosis. The percentage of cows with clinical ketosis increased with parity and reached a maximum in parity 4. The first diagnosis of clinical ketosis occurred within 8 wk after calving. For each parity, the percentage of cows with clinical ketosis was higher for cows yielding >6300 kg of 305-d milk. The percentage of treated cases of ketosis was lower in the spring and summer (April to September) than in other calving seasons. Recurrence of ketosis, measured as the percentage of cows with clinical ketosis in the preceding parity that were also treated for ketosis in the current parity, increased from 4.6% in parity 2 to 9.9% in parity 6. For cows treated or not treated for ketosis and for each parity separately, correlograms (plot of autocorrelation against lag) obtained from Model [ l ] showed a rapid exponential decay of autocorrelations with increasing lags (example in Figure 1). Partial autocorrelations showed a sharp decrease after lag 1 and were significant at lag 1 only. Autocorrelation at lag 1 was estimated at .7. Lactation curves were constructed by plotting estimated test day yields from Model [2] for cows treated or not treated for ketosis; solutions for stage of lactation and for the ketotic index were used to estimate test day
= P and a = It, - tnle
where t, tn = DIM at which test day milk yields Yn) were collected, r = autocorrelation coefficient estimated for k = 1 (Model [l]), and 8 2 0. For example, the case 0 = 1 yields the first-order autoregressive model, and the case 8 tending to yields the first-order moving average model (15). Because estimation of r in Model [ l ] assumed ordered and equally spaced time series (17), the term It, - t,l was used in Model [2] to account for unequal and nonconsecutive measurements (20). The computer algorithm for estimating 4 = and /3 was as follows: 00
[4, $, 41’
Start with initial estimates +(O). The algorithm was restarted with different priors. At step (p + l), compute the maximum likelihood estimate of @ as b@+’) = [X’V-1 XI- [x’V-1 y] using v = v(+@). Step (p + 1) of the algorithm yields the REML (16) estimate +@+I) using an expectation-maximization algorithm (5): B@) +@+I) = d@)(see Appendix). Iterate between steps 1 and 2. At step p, iterative improvement was measured as the ratio of s uared computable residuals [(= (d@)- B@) +L1y; (3)]. The values of the log-likelihood for y were computed at successive rounds of iteration to check iterative convergence at a global maximum.
TABLE 1. Descriptive statistics for test day samples, cows, and milk yields by parity in 60,851 Finnish Ayrshire cows. Paritv
Test day samples, no. Cows, no. Herds, no. Average herd size, no. of cows per herd Average test day yield, kg X SE Average milk yield in 305 DIM, kg X SE
1
2
216,116 22,816 5548 4.1
186,874 132,144 93,400 19,014 14,169 10,066 5286 4948 4384 3.6 2.9 2.3
Journal of Dairy Science Vol. 77, No. 11, 1994
17.14 .03 5075.9 10.8
3
18.71 .04 5707.3 13.0
4
20.45 .05 6076.1 14.8
5
6
57.763 6213 3499 1.8
36,101 3912 2626 1.5
20.86
20.73
.05
.06
6176.1 16.8
6187.5 19.6
20.51 .07 6144.9 24.0
3319
KETOSIS AND MILK LOSS TABLE 2. Lactational incidence risk (LIR)of clinical ketosis by parity in 60.851 Finnish Ayrshire cows. Parity 2
1
LIR,' W
3
4
5
6
4.8
5.1
7.1
7.7
7.1
6.1
33.4 25.4
33.6 28.7
30.0 22.3
29.1 20.2
29.6 22.9
33.2 26.6
4.0 4.6 5.0
3.7
5.2 7.2 9.3
6.5 8.1 8.9
5.0 6.7 9.5
4.0 6.1 7.6
13.4 6.1 4.2 9.2
15.2
18.8 10.2 4.5 13.6 6.2
20.4 10.6 4.6 13.3 6.0
17.8 9.7 3.6 13.5
14.6 7.5 4.6 12.3 9.9
D g of first diagnosis, DIM
X SE LlRl per 305-d milk yield, 96 4 1 0 0 kg 51004300 kg >6300 kg LIR' per calving season, % Jan-Mx Apr-Jun lul-Sep Oct-Dec Recurrence,* %
5.5
6.7
6.7 3.0 9.0 4.6
...
7.9
'Percentage of cows with clinical ketosis. *Percentage of cows with clinical ketosis in the preceding parity that were treated for ketosis during the current parity.
yields. In each parity, the lactation curves of cows with clinical ketosis showed a depression in early lactation and a shift upward before and
1.0
I
.9 .8 .7
*
.6
0'
I
f
.5
I
0 0
.4
I
.3 .2 .1
0 0
1
2
3
4
5 LAG
6
7
8
9
10
Figure 1. Autocorrelation p; correlation between yt and Yt-k) and partid autocorrelation (A;correlation be. .~ tween y! and Yt-k given yt-l, yt+ . .yt-(k-l)) between test day milk yields adjusted to the same stage of lactation and season, for third parity cows treated K A ) or not treated @,A) for ketosis. yt = Test days milk yield taken at time t, t = DIM (t = 1, 2,. . ,, lo), and k = lag (k = 0, 1,. . ., lo).
after the depression compared with the curves for nonketotic cows (example in Figure 2). Table 3 shows the differences in 305-d milk between nonketotic cows and cows with or without clinical ketosis within 17 d following the collection of milk. Those differences in 305-d milk were estimated using the solutions obtained in Model [2]. Cows with clinical ketosis yielded, on average, 141.1 kg more 305-d milk than nonketotic cows but yielded 44.3 kg less over 17 d following the diagnosis of ketosis (Table 3). The net 305-d milk gain for parity for ketotic cows over nonketotic cows was the least in parity 4 (86.7 kg; Table 3). Estimates for variance components are shown in Figure 3 for each parity separately. Herd variance increased from 3.9 kg2 in parity 1 to 6.8 kg2 in parities 24. Permanent environment variance reached a maximum, 6.4 kg2, in parities 22. Similar to the herd variance, temporary environmental variance increased from 5.1 kg2 in parity 1 to 9.3 kg2 in parities 24. DISCUSSION
Ketosis
losses associated Our data showed that with clinical ketosis did not overcome the adJournal of Dairy Science Vol. 77, No. 11. 1994
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DETILLEUX ET AL.
TABLE 3. Estimated milk differences by parity for 305-d milk between cows treated or not treated for ketosis. Parity 1
2
3
33.9 169.9 136.0
44.3 172.1 127.8
47.1 200.1 153.0
4
S
6
52.6 139.3 86.7
36.4 221.3 184.9
51.8 209.9 158.1
0 Milk loss' Potential milk gain2 Net milk gain3
~~
~~
~~
~
~~
'For 17 d following diagnosis of ketosis. 2Potential milk gain for cows with clinical ketosis, Le., difference in 305-d milk between cows with clinical ketosis before or >I7 d following diagnosis and cows not mated for ketosis during the entire lactation. 3Net milk gain for cows with clinical ketosis. i.e.. difference in 305-d milk between cows treated or not treated for ketosis during the entire lactation
vantage of high milk yield in cows treated for clinical ketosis; nevertheless, if those highest yielding cows had not had ketosis, their yields would have been considerably greater. A positive association existed between percentage of clinical ketosis and 305-d milk yield (Table 2). Lactation curves of cows with clinical ketosis were depressed in early lactation (Figure 2); estimated milk loss was 44.3 kg for 17 d after diagnosis. Over all parities, solutions from Model [2] showed that cows with clinical ketosis during the lactation yielded, on average,
26
T
1
25 , 24
!
2 1
3
Journal of Dairy Science Vol. 77, No. 11, 1994
141.1 kg more milk over 305 d than did nonketotic cows (Table 3). Feeding practices, individual cow characteristics (age and genetic disposition), and general environmental factors (year, season, and housing system) are possible reasons for the positive association between occurrence of clinical ketosis and milk yield. Estimates of genetic correlations between 305-d milk and ketosis vary from 0 to .17 (10, 14) in Finnish Ayrshire cattle (IO) and are .65 in Norwegian heifers (18). Feeding practices that are insufficient to meet energy requirements for high milk yield may lead to negative energy balance, increased fat mobilization, and increased hepatic ketogenesis (2). Increased risk of ketosis during indoor feeding may be explained by inadequate nutrient intake (1 1) or decreased ability to utilize ketones in untrained muscle (22). Older high yielding cows may be unable to metabolize energy efficiently enough to support prioritized demands for high milk yield and, subsequently, may develop ketosis. In previous studies, clinical ketosis decreased cumulative milk yield by 66.0 kg (8.8%), 156.5 kg (12.7%), and 285.4 kg (8.2%) for DIM 1 to 21, 22 to 49, and 50 to 119, respectively (4). Increased milk ketone bodies were associated with a daily milk reduction of 1 to 1.4 kg (8) and a loss of 233.4 kg (8.5%) of FCM during the first 100 DIM (12). Those milk losses may be due to clinical ketosis, to diseases associated with ketosis, or both. Metabolic changes in early ketosis (hyperketonemia and hypoglycemia) may lead to loss of appetite that could explain the observed decline in milk yield (2). Clinical ketosis has also been as-
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KETOSIS AND MILK LOSS
sociated with metritis, paresis, abomasal disorder, mastitis, hypomagnesemia, and retained placenta (9), all of which can decrease milk yield. In this study, milk losses (2.6 kg/d) were probably underestimated because 1) cows may suffer milk loss immediately after the diagnosis of ketosis and then rapidly return to their previous yield before the next milk recording, 2) milk losses prior to the diagnosis of ketosis were not recorded, and 3) duration of clinical ketosis was limited to 17 d. In a previous study (4), cumulative milk yield for 21 d was 33 kg lower for cows treated for ketosis after the 21 DIM. In another study (13), cumulative milk yield was depressed by approximately 60 to 70 kg for at least 2 wk before the diagnosis of ketosis. Surprisingly, however, treatment was delayed until cows in that study (13) lost large amounts of milk.
10 9 8 Q 7 M 5 6
Mean incidence risk of treatment for clinical ketosis (6%), peak percentage of cows with clinical ketosis in parity 4, first occurrence of clinical ketosis within 8 wk after calving, and highest percentage of clinical ketosis during indoor feeding (October to March) (Table 2) are in accordance with previous studies of Finnish Ayrshire cattle (9, 10). The positive association between 305-d milk and Occurrence of ketosis may explain the increase in recurrence of ketosis (Table 2) across parities because low yielding cows are preferentially culled. Statistical Analyses
Because our statistical model should account for all known sources of variation on test day milk yields, Model [2] was more useful than Model [l]. However, estimation of all parameters directly from Model [2] necessi-
--
rl
--
Parity = 1
m
~-
\
Parity = 2
H
--
25
Parity = 3
2 5-4
rn
:-
Parity = 4
w Parity = 5
c,
!E
3-2 I -0
a
--
Parity = 6
--
Herd
Permanent
Temporary
Variance Components Figure 3. Estimated herd, permanent environmental, and temporary environmental variances in test day milk yields per parity. Journal of Dairy Science Vol. 77, No. 1 1 , 1994
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DETILLEUX ET AL.
tated maximization of the log-likelihood for the data in the two phases between which iteration continues until convergence is reached for all parameters (6, 15). This procedure was desirable but economically impossible because of limited time and computer funds, and, therefore, another method was chosen. First, r and 8 were estimated using Model [l], in which r was the autocorrelation between test day milk yields adjusted to the same seasons and stages of lactation, and 8 described the autoregressive integrated moving average process. Then the effects of clinical ketosis on test day milk yields (Model [2]) were estimated using the estimated r and e obtained in Model [l]. Although the residuals in Model [ l ] and Model [2] are different, autocorrelation was not expected to affect the estimates of the effects of clinical ketosis on test day milk yields because autocorrelation has little impact on actual point estimates (21). Correlograms and partial correlograms (Figure 1) obtained from Model [ I ] suggested that the error term in Model [l] may be adequately modeled with a first-order autoregressive model, that the autocorrelation between successive error terms is .7, and that the series of error terms is stationary (7). Therefore, the autocorrelation coefficient between error terms in Model [2] was taken as .7Q with a = Itm - tnl for DIM tm and tn (e = 1). Effects of herd on test day yields were treated as random because average herd sizes were very small (Table 1) (19). Under the assumptions of Model [2],estimates of repeatability (ratio of permanent environmental variance to total variance) decreased from .35 in parity 1 to .28 in parities 24. This decrease occurred because estimates of herd variance and temporary environmental variance reached a maximum in parity 24, but estimates of permanent environmental variance reached a maximum in parity 22 (Figure 3). For 305-d cumulative milk, the same permanent environmental effects (partly environmental and partly genetic in origin) might be used in analysis of test day milk yields for cows with parity >1. Therefore, test day milk in cows of parity 1 may be influenced by a trait that is genetically different from test day milk yield in cows of parity > I . J o m a l of Dairy Science Vol. 77, No. 11, 1994
CONCLUSIONS
An autoregressive model utilizing test day
milk yields during lactation provided precise estimates of milk losses and gains, which traditional models utilizing only 305-d milk yields are unable to do. Cows with clinical ketosis had a small decrease in milk yield during the ketotic episode compared with yield of nonketotic cows. Over the entire lactation, however, ketotic cows yielded significantly more milk than did nonketotic cows. Higher yielding cows tended to be at higher risk of ketosis, but, if they had not developed ketosis, their milk yield would have been even greater. Therefore, the best managers will ensure that high yielding cows are less susceptible to ketosis. ACKNOWLEDGMENTS
This work was partly supported by the USDA Animal Health and Disease Program. Computations supporting this research were performed at the Cornell National Supercomputer Facility, which is supported in part by the National Science Foundation, New York State, and the IBM Corporation. REFERENCES 1 Andersson, L., and U. Emanuelson. 1985. An epidemiological study of hyperketonemia in Swedish dairy cows: determinants and the relation to fertility. Prev. Vet. Med. 3:449. 2 Baird. G. D. 1982. Primary ketosis in the high producing dairy cow: clinical and subclinical disorders, treatment, prevention, and outlook. J. Dairy Sci. 65:l. 3Conte. S . D., and C. de Boor. 1972. Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill Book Co., New York. NY. 4Deluyker. H. A,, J. M. Gay, L. D. Weaver, and A . S. Azari. 1991. Change in milk yield with clinical diseases for a high producing dairy herd. J. Dairy Sci. 74: 436. 5 Dempster, A. P.. N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B 39:l. 6Diggle. P. J. 1988. An approach to the analysis of repeated measurements. Biometrics 44:959. 7 Diggle, P. J. 1990. Time Series: A Biostatistical Introduction. Oxford Univ. Press, New York, NY. 8 Dohoo, 1. R., and S . W. Martin. 1984. Subclinical ketosis: prevalence and associations with production and disease. Can. J. Comp. Med. 48:l. 9 Grijhn, Y. T., H. N. Erb, C. E. McCulloch, and H. S . Saloniemi 1989. Epidemiology of metabolic disorders in dairy cattle: association among host characteristics, disease, and production. J. Dairy Sci. 72:1876.
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KETOSIS AND MILK LOSS 10 Grohn. Y . T., and J. Syvaj%rvi. 1986. An epidemiological and genetic study on registered diseases in Finnish Ayrshire cattle. 111. Metabolic diseases. Acta Vet. Scand. 27:209. 11 Grohn. Y. T., J. R. Thompson, and M. L. Bruss. 1984. Epidemiology and genetic basis of ketosis in Finnish Ayrshire cattle. Prev. Vet. Med. 3:65. 12Gustafsson. K.. L. Andersson, and U. Emanuelson. 1993. Effect of hyperketonemia, feeding frequency and intake of concentrate and energy on milk yield in dairy cows. Anim. Prod. 5651. 13Lucey. S..G. J. Rowlands, and A. M. Russell. 1986. Short-term associations between disease and milk yield of h r y cows. J. Dairy Res. 53:7. 14Miintysaari. E. A., Y. T. Grohn, and R. L. Quaas. 1991. Clinical ketosis: phenotypic and genetic correlations between occurrences and with milk yield. J. Dairy Sci. 74:3985. 15 Munoz, A,. V. Carey, J. P. Schouten, M. Segal, and B. Rosner. 1992. A parametric family of correlation structures for the analysis of longitudinal data. Biometrics 48:733.
16Patterson. H. D., and R. Thompson. 1971. Recovery of inter-block information when block sizes are unequal. Biometrika 58545. 17 SAS" User's Guide: Statistics, Version 6 Edition. 1988. SAS Inst., Inc., Cary. NC. 18Simianer. H.. H. Solbu, and L. R. Schaeffer. 1991. Estimated genetic correlations between disease and yield traits in dairy cattle. J . Dairy Sci. 74:4358. 19Van Vleck, L. D. 1987. Contemporary groups for genetic evaluations. J. Dairy Sci. 70:2456. 20 Wade, K.M., and R. L. Quaas. 1993. Solutions to a system of equations involving a first-order autoregressive process. J. Dairy Sci. 76:3026. 21 Wade, K. M., R. L. Quaas, and L. D. Van Vleck. 1993. Estimation of the parameters involved in a firstorder autoregressive process for contemporary groups. J. Dairy Sci. 76:3033. 22 Winder, W. W., K.M. Baldwin, and J. 0. Holloszy. 1974. Exercise induced increase in the capacity of rat skeletal muscle to oxidize ketones. Can Physiol. Pharmacol. 53236.
APPENDIX
Expectation-Maxlmization Algorithm
The variance components in Model [ l ] were estimated using REML (16) with an expectationmaximization algorithm (5). Let the complete data e = y - XB, K'y = error contrasts of the incomplete data, +@I = estimates of variance components u i , 0: at round p, and 2 = BLUP(elK'y, +@?. For the E step, compute S@+I)= E [ee'lK'y, = 66' + var(6 - e ) (21). For
."p.
+@a
the M step, find +@+I) that maximizes Q = const
1 - -21 lnlvl - -tr[V-' 2
S@+')] with V = var(y).
Because all herds are independent, V is a block diagonal matrix V = diag[Vh] for h = 1,2,. . .H and Vh = Jh a 2h + D h + F h Ue2 where H = number of herds, Jh = nh X nh matrix Of IS, n h = number of test day yields per herd, D h = diag[Ji] = nh x nh block diagonal matrix with J i on the diagonal, Jj = n, x n, matrix of Is, n, = number of test day yields per cow, and F h = diag[Ri] with Ri = n, x nc autocorrelation matrix. Then, the step p of the expectation-maximization algorithm yields B@) +@+l) = p@) where
."p
B = and
Journal of Dairy Science Vol. 77, No. 11, 1994