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Prediction of Total Intake of Dry Matter and Net Energy in a Lactation
Prediction of Total Intake of Dry Matter and Net Energy in a Lactation T. L. MOORE and I. L. MAO Department of Animal SCience Michigan State University East Lansing 48824-1225 ABSTRACT
INTRODUCTION
Daily records on DM intake, net energy intake, and milk yield from 191 Holstein cows in six herds were used to study the differences in accuracy and precision among different methods of estimating total DM intake during a lactation. In using cumulative measures of intake from partial lactations to predict total intake, accuracy reached 85% at 100 d postpartum. Measurements of intake taken around midlactation gave better predictions of total intake than those taken during other periods of lactation. Methods were evaluated for estimating total feed intake during a lactation based on data collected intermittently and separated by either equal or unequal intervals throughout the lactation. The average percentage of bias across all sampling schemes was 6% or less of actual intake. Six of the seven sampling schemes using only 10 d of intake information throughout the lactation had correlations with actual intake of .97 or higher. For equally spaced methods, both accuracy and precision of estimation increased with increased frequency of sampling. For unequally spaced methods, accuracy increased with sampling frequency after 150 d in milk. Total milk production was used to predict feed intake during a lactation. Milk yield alone accounted for 37 and 33% of the variation of total intake using actual and estimated yields, respectively. (Key words: dry matter intake, estimation, lactation)
Data on feed consumption during a lactation provide essential information for research and management. In addition to nutrition research, these data can measure biological and economic parameters in dairy cattle, such as appetite and efficiency of milk production. In feeding trials, the quantity and quality of feed intake are measured daily by individual feeding, weighback, and chemical analysis through a lactation. However, this method is costly and unfeasible for large commercial farms. Savings in time and expense would be realized if accurate predictions of total intake during lactation could be made from only a few actual measurements of intake. Equations that have been developed to predict feed intake use variables such as BW, milk production, forage type, fiber content, age, parity, and season (4, 10, 11, 12). However, these equations predict intake for a single cow on a particular day. Very limited work has been done predicting feed intake for complete lactations. Gibson (7) examined the ability of measures of intake for partial lactation to predict feeding intake for the complete lactation and found that combinations of intake records separated by several weeks were more accurate than adjacent records from a single period. Griffin et aL (8) examined the part-whole relationships of feed intake during various portions of the lactation and found correlations of .71 to .86 when using feed intake records during 28-d periods in midlactation. Predicting total feed intake by measures only on sample days has not been previously studied, although lactation milk yield estimated by sample day yields has been studied by several workers (1, 2, 6). As early as 1942, Jensen et al. (9) described the positive relationship between feed intake and milk yield. Brown et al. (3) found, based on standardized partial regression coefficients, that milk yield was the most important variable in determining total intake of DM. This relationship agreed with work done by Dean et al.
Received August 9, 1989. Accepted November 27, 1989. 1990 J Dairy Sci 73:1255-1262
(5).
1255
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MOORE AND MAO
The objective was to examine the accuracy and precision of three approaches to estimate total DM intake during a lactation: 1) by data collected from various portions of the lactation; 2) by various sampling strategies, using both equally and unequally spaced sampling intervals; and 3) by actual and estimated lactation milk yields. MATERIALS AND METHODS
Data
Daily records of DM intake (DMI), estimated net energy intake (NEI), and milk production were collected from 405 Holstein cows of various parities from seven herds across the United States. Records on a total of 191 cows were used in this study. Records were discarded if lactation was shorter than 250 d or if data for DMI, NEI, or milk yield were missing for more than 2 consecutive d. Those records with 1 or 2 d missing were filled by linear interpolation. All daily records in a lactation started with the 12th d after calving. Total intake and milk yield were e<>mputed by summing respective daily records. Cows were fed a total mixed ration having different forage:concentrate ratios according to milk yield and days in lactation. Production was determined by a cow's milk yield during the period prior to 21 d postpartum in which all cows were fed similarly. All heifers were in one production group. The remaining production groups were defined as: high (greater than 35 kg/d), medium (28 to 34 kg/d), and low (23 to 28 kg/d). Forage:concentration ratios began at 50:50 for first lactation heifers and 60:40 for multiparous cows and gradually increased over lactation to 70:30 and 80:20 for heifers and cows, respectively. Diets were consistent across all herds, and all animals had access to feed for at least 12 hid. Prediction of Total Intake from Partial Lactation
Cumulative Records for Partial Lactations. Beginning on the 12th d postpartum, successive daily records were summed at 15-d increments throughout the lactation. Product-moment correlations of partial records with total intake were then computed. Records for Partial Lactations of Varying Lengths in Different Stages of Lactation. Intake Journal of Dairy Science Vol. 73.
No.5. 1990
measurements in intervals of fixed length during various stages of lactation were used to examine part-whole relationships. Six different fixed length intervals of 50, 80, 100, 125. 160, and 200 d were examined. Beginning on the 15th d postpartum, each of the fixed intervals covered the various stages of lactation by a 5-d increment. Within each fixed length interval at a certain stage of lactation, daily intakes were summed. To illustrate, using the 100-d interval length and beginning on d 15, the first partial record summed daily intake between d 15 and 115, the second between d 20 and 120, and continuing until the final partial record of the last 100 d of lactation. Productmoment correlations of partial lactation records with total intake were computed. Prediction of Total Intake by Sample Day Measures
Sample Day Measures from Equally Spaced Intervals. Six equally spaced sampling schemes were examined: one sample was taken every 3, 7, 14, 30, 60, or 90 d. Intake estimates from each sampling interval were obtained by linear interpolation between sample day intake records before summing the sample day records and the interpolated records. Each estimate was expressed as a deviation from actual intake. Mean difference from actual total intake, SD of differences, average percentage of error, and frequency of errors within ± 1, 3, 5, 10, and 15% of actual intake were computed for each sampling method. Sample Day Measures from Unequally Spaced Intervals. Seven unequally spaced sampling schemes, all based on 10 samples for a lactation, as in the equally spaced, 30-d method, were studied. The hypothesis was that peak period of intake should receive the heaviest emphasis in sampling to maximize the accuracy and precision of estimating the total intake. The period of peak intake was determined to be the IOO-d interval between d 50 and 150 postpartum based partially on the .89 part-whole correlation, which was highest among all lOO-d lengths at various stages of lactation. The other criterion used to determine peak period of intake was variation in average daily DMI, which ranged from 2.36 to 4.42 kg. The greatest variation in daily intake occurred between d 40 to 160 postpartum. To test the hypothesis, seven unequally spaced sampling schemes were con-
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ESTIMATION OF LACTATION FEED INTAKE
TABLE I. Sampling frequencies for equally and unequally spaced intervals during prepeak. peak. and postpeak intake periods in a lactation. Days in milk Sampling method Equally spaced intervals 3 d 7 d 14 d 30 d 60d 90d Unequally spaced intervals 8-1-l t 1-8-1 1-7-2 5-2-3 3-3-4 1-4-5 (30 d) 2-2-6 1-1-8
(Prepeak) 12-50 d
(Peak) 51-150 d
(Postpeak) 151-305 d
Total no. samples 2
12 6 3 I I I
32 14
56 24 12 5
100 44
8
1 8 7 2 3 4 2 I
1 1 5 3 1 2 I
7 4 2 1
2 2 1 1 2 3 4 5 6 8
22 10 5 4 10 10 10
10 10 10 10 10
lNwnber of samples taken for each intake period of lactation (Le.• prepeak. peak. and postpCak). 2Each sample was the measured amount of feed consumed for I d.
structed such that one of the three periods of intake (i.e.. pre peak, peak, or postpeak) was sampled more frequently than the other two. Table I shows the sampling frequencies of the six equally spaced schemes and the seven unequally spaced schemes during the three stages of lactation. The unequally spaced schemes were arranged by increased sampling frequency during postpeak period. Estimates for unequally spaced methods also were obtained by linear interpolation between intake records for sample day, and expressed as a deviation from actual intake. Criteria used for comparing unequally spaced methods were the same as those for the equally spaced methods. The 30-d, equally spaced method was included in all comparisons between unequally spaced methods. Milk Yielcl as a Predictor of Total Intake
Simple Linear Regression Model.
where: Yi was the total intake during a lactation of cow i; bo was the common intercept; Xi was the lactation milk yield of cow i with b as the corresponding regression coefficient; and ei was the normally distributed random residual. The model was run with Xi being the actual lactation milk yield and was repeated with Xi being the estimated yield. Covariate Model. ygijkmn
Feed intake was predicted from actual and estimated total milk yields separately from either a simple regression model or from a covariate model. Actual milk yield was a simple sum of daily yield records, and estimated milk yield was obtained by linear interpolation using the same 30-d equally spaced method described for intake.
=
IJ. + Pg + Hi + Sj + Tk + bIXin + bz X2n + egijkrnn
Lm
+ where:
Ygijkrnn was the total intake during a lactation of cow n in production group m, treatment group k, season j, herd i, and parity g; Journal of Dairy Science Vol. 73.
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MOORE AND MAO
Il was the overall mean; P g was the fixed effect of parity g with g = I, 2, 3, 4~; Hi was the fixed effect of herd i with i = I, 2,... ,6; Sj was the fixed effect of calving season j with June through August as season 1, September through November as season 2, December through February as season 3, and March through Mayas season 4; Tk was the fixed effect of dietary treatment k with k = 1, 2, 3, 4;
Lm Xi n
X2n
egijkmn
was the first effect of production group with m = 1, 2, 3, 4; was a covariate of total milk production of cow n in the current lactation, with bi as the corresponding partial regression coefficient; was a covariate of length of current lactation ranging from 250 to 300 d of cow n with ~ as the corresponding partial regression coefficient; and was the nonnally distributed random residual.
The analysis according to this model was repeated, once with Xi n being the actual lactation milk yield and again with xl n being the estimated yield. RESULTS AND DISCUSSION
Results for NEI corresponded directly with results for OMI; therefore, only results pertaining to OMI are presented. Intake Curves
Total intake for a lactation averaged 5350 kg of OM. Figure I shows the daily averages and SO of OMI for all cows during lactation not adjusted for any factors. Both OMI and NEI curves were characterized by a rapid rise during the first 60 d after calving until peak intake was reached. Intake then begins to decline slowly and linearly for the remainder of lactation. Figure 2 shows the different levels and patterns of Journal of Dairy Science Vol. 73.
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AVERAGE OM] 191 LACTATIONS NGCMll
22
-....
20
IS 16
...
~
I.
12 10 0
50
100
150
200
.L-.
-250
300
DAYS IN LACTATION
Figure 1. Average (avg; e) and plus (*) and minus (+) 1 SD of OM intake (DMI) during a lactation.
intake among the four parity groups. Parity 1 resulted in the lowest intake and a sharp increase up until 50 d in milk. Parity 2 averaged slightly higher than parity 1, with a peak at 75 d but relatively little variation during a lactation. Parities 3 and 4 and greater averaged highest and followed similar patterns of intake, peaking at approximately 100 d in milk and with more variation than parities 1 or 2. Differences in intake among parities may be due to differences in BW caused by growth and production, but this factor was not considered in the study. Intake curves also were plotted according to treatment, herd, season, and production; however, no distinct differences among classes were observed. Prediction of Total Intake Measures from Partial lactations
Cwnulative Records for Partial Lactation. Table 2 shows correlations of cumulative subtotals of feed intake with 15-d increments beginning on the 12th d postpartum. As expected, the more cumulative records available, the greater the accuracy of prediction. However, at approximately 80 d of lactation, accuracy was increasing at a decreasing rate. Before midlactation at about 140 d, the correlation of cumulative intake with total feed intake was greater than .90. Partial Lactation Records of Varying Lengths During Different Stages of Lactation. Table 3 shows those partial lactation periods of intake that yielded the highest correlation with
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ESTIMATION OF LACTATION FEED INTAKE
AVERAGE OMI BY PARITY 24 IW eM! telll 23 22 21 20 19
18 17
115 1!5 14 13
12+--.-,,...----r---r---,.....----r-----,
o
!SO
100
1!SO
200
2!50
300
DAYS IN LtCTATIO'J
Figw-e 2. Average (avg) dry matter intake (DMl) during lactation for each of four lactation groups: parity 1 C-; n 55). parity 2 (+; n = 83). parity 3 (.; n = 31), parity 4 (CJ; n
=
= 22).
total intake over a lactation. None of the periods shown began earlier than 50 d postpartum, and all periods covered the peak period of intake, As expected, as interval lengthened, the correlation also increased. The correlation reached .89 when interval was 100 d between 50 and 150 d postpartum, which was defined as the peak period in this study. Intakes during shorter periods. measured during peak intake period, were as accurate as those during longer periods starting at the beginning of lactation for estimating total feed intake. For example, 70 to 120 d (50 d) and 12 to 102 d (100 d) postpartum had approximately
the same correlation (.85) with total intake. Given that feed intake declined only slightly after peak intake was reached (Figures 1 and 2), accuracy of predicting total feed intake would be expected to be maximized by using intake records taken during peak period and the period following peak intake. Griffin et al. (8) found similar results, with correlations of 28-d feed intake with lactation intake were larger during the 4th through 8th mo. Gibson (7) also pointed out that if only a few measurements could be taken. the best predictions of intake would be given by measurements taken at, or shortly after, midlactation. Prediction of Total Intake
by Semple Dey Measures
SampLe Day Measures from Equally Spaced Intervals. The average biases, their SD, and average percentage of bias were used to compare sampling methods (Table 4). All six methods with equally spaced sampling intervals underestimated total DMI during lactation. Average bias for DMI increased as sampling interval increased ranging from -1.07 kg in the 3-d method to -72.60 kg in the 90-d method. However, even under the 90-d interval, estimates deviated by approximately 73 kg, on average, or by 5.2% of actual intake. Therefore, under conditions in this feeding trial, the amount of accuracy that is lost due to a decrease in sampling frequency was small, even on a trimonthly (90-d) basis. Variation of the biases may provide a better indication of the predictive ability of each testing scheme than average error or bias. Error SD on methods with more frequent sampling were smaller, and, therefore, more precise. Standard deviations of biases for DMI ranged from 42.93
TABLE 2. Product-moment correlation between cumulative partial intake and total intake of DM in a lactation. Days in milk
Correlation
27
.458
42 57
.544 .659
72 87
.758 .814 .848 .874 .898
102 117 132 147 192
.915 .953
222
.969
282
.992
TABLE 3. Stage of lactation yielding highest correlation between partial DM intake in a fixed interval length and total DM intake in a lactation. Interval length
Period
(d)
(d in milk)
200 160 125 100
80--280 50--21D 55-180 50-150 70-150
80 50
60-110
Correlation .961 .928 .906
.891 .874
.847
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TABLE 4. Bias in estimation of laclalion total DM intake (DMJ) by various equally and unequally spaced sampling intervals. Sampling scheme Equally spaced intervals 3 d 7 d 14 d 30 d 60d 90d Unequally spaced intervals 8-1-1 1-8-1 1-7-2 5-2-3 3-3-4 1-4-5 (30 d) 2-2-6 1-1-8
Average bias
SE of Bias
Average % of bias
-1.07 -.35 -3.79 -41.14 -29.98 -72.60
42.93 84.65 117.20 193.23 281.16 339.88
.006 .013 .017 .028 .040 .052
.99 .99 98 .97 .93 .90
-75.15 -35.76 IU5 -10.10 -16.04 -41.16 7.56 -59.03
394.90 368,65 259.57 274.71 233.10 193.23 195.12 211.47
.059 .052 .037 .039 .033 .028 .028 .031
.87 .89 .94 .94 .95 .97 .97 .96
Correlation 1
lCorrelation between actual and estimated DM].
kg for the 3-d method up to 339.88 kg for the 9O-d method. Increases in sampling frequency for estimating lactation total intake gave higher correlations with actual lactation intake. Table 5 shows the percentage of the estimated lactation total intakes falling within limits (± I, 3, 5. 10, )5%) of the actual total intake. Frequency of large errors (5% or more) was higher in longer than in shorter test inter-
vals. As sampling frequency increased, the percentage of errors within ± 5% of actual intake increased almost 45% for both DMI and NEI but at a diminishing rate, suggesting there is an optimum number of samples to be taken after which additional samples result in increasingly smaller improvements in accuracy. Sample Day Measures from Unequally Spaced Intervals. Five of the seven unequally
TABLE 5. Proportion of estimated lactation total DM intakes by various sampling strategies within a given percentage of actual intake. Absolute percentage of error Sampling scheme Equally spaced intervals 3 d 7 d 14 d 30 d 60d 90d Unequally spaced intervals 8-1-1 1-8-1 1-7-2 5-2-3 3-3-4 1-4-5 (30 d) 2-2-6 1-1-8 Journal of Dairy Science Vol. 73.
± I
± 3
± 5
±10
± 15
.78 .48 .39 .20 .15 .12
.97 .92 .83 .64 .49 .34
1.00 .97 .95 .87 .70
1.00 1.00 .98 .96 .91 .87
1.00 1.00 1.00 .98 .96 .95
.08 .10 .12 .15 .17 .20 .21 .22
.30 .34 .49 .44 .57
.52 .58 .76 .65
.82 .89 .95 .87 .96 .96 .98 .95
.93 .97 .99 .92 .98 .98 .99 .97
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.54
.64
.77 .FJ7
.65 .58
.86 .78
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ESTIMATION OF LAcrATION FEED INTAKE
TABLE 6. Analysis of variance for predicting OMI by actual or estimaled milk yield. The F-values are shown and estimates of regression coefficienls are in parentheses. Simple regression model
Source of variation Intercept Parity Herd Season Treatmenl Production Milk yield Lactation length Residual SO R2 Correlation between actual and estimated OMI
Actual
Estimated
(5393)
(5721)
Covariate model Actual
1.75 8.63 a
1.13
(.423)"
(.403)"
1314.59 .36
1345.49 .33
.63
.57
spaced sampling schemes underestimated total intake (Table 4). Six of the seven schemes had correlations with total intake of .97 or greater. Average bias for OM) ranged from 7.56 kg for the samples taken: two prepeak, two peak, six postpeak intake period in a lactation (2-2-6) to -75.15 kg for the 8-1-1 sampling scheme. Accuracy and precision of estimation increased as sampling emphasis during postpeak period increased except for the extreme case of 1-1-8. Standard deviations of biases for OM) of 193.23 to 394.90 kg were observed for the 1-4-5 and 8-1-1 schemes, respectively. Results for the percentage of the estimates falling within given limits of the actual for the unequally spaced sampling intervals are in Table 5. The percentage of errors within ± 5% of actual increased over 35% as sampling increased during postpeak period. The highest occurrence of small errors was observed in the 1-4-5 and 2-2-6 methods. The 2-2-6 strategy proved to be the most accurate. However, the convenient 1-4-5 (30-d) method gave the highest precision from all sampling methods based on 10 samples in a lactation. Milk Yield as Predictor of Total Intake
3.03 b 4.02 a (.225)& (34.61)& 1020.20 .65 .81
Estimated
\.86 9.06 a .95 2.94 b 4.54" (.211)a (36.20)" 1023.56 .65 .81
small advantage in using actual over estimated yield to predict total intake. Regression coefficients for both actual and estimated yields were highly significant as shown in Table 6. As expected. actual yield gave only slightly higher precision according to residual SO than did estimated yield. Covariate Model. The covariate model used accounted for up to 65% of the variation in OMI during lactation when either actual or estimated yield was used. Partial regressions of intake on actual yield and on estimated yield both were highly significant, as were partial regressions of lactation length, for both OM! and NEI. These results also are shown in Table 6. Herd, production group, and treatment effects were significant when either actual or estimated yield was used. Therefore, application of the covariate model for the prediction of OM) requires knowledge of herd differences. Differences found in intakes between parities in Figure 2 were not significant in either case here after accounting for the other effects in the model. CONCLUSIONS
Simple Regression Model. Actual lactation milk yield alone accounted for 37%, and estimated yield accounted for 33% of the variation
Accuracy of predicting lactation total intake reached 85% at 100-<1 postpartum when using cumulative partial lactation measures of intake. Short-term measures of intake taken during
in total DMI. The difference of 4% indicates a
midlactation were as accurate as longer meaJournal of Dairy Science Vol. 73, No.5, 1990
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MOORE AND MAO
sures taken at the beginning of lactation for estimating total DMI during a lactation. When using sample day intake records at equal interval lengths during a lactation to estimate total intake, accuracy and precision increased as the sampling interval decreased. Sampling frequencies of 30 d or less predicted lactation feed intake better than partial records having 200 or less consecutive days of information. The 90-d method, with only 4 sample d in a lactation, had a correlation of .90 with actual intake equaling that of 100 d worth of information on consecutive days. For the seven unequally spaced sampling schemes based on only 10 d of sample intake records, six had correlations with total intake of .97 and higher. However, estimates of intake based on these 10 samples predicted intake better when sampling was heaviest after peak period intake in a lactation. In fact, from the estimate based on 10 sample d in a lactation, the 30-d method in most cases was better than the unequally spaced sampling schemes. Using milk yield as a predictor of lactation total intake did not prove to be as effective as the direct sampling of intake records; prediction accuracy was less than that obtained from 50 d of intake information. Factors not included in this study were the effect of BW and its predictive ability for total intake during lactation and the effect of date of first sample. Results from studies comparing sampling procedures for the estimation of lactation total milk yield have indicated the magnitude of the errors in the estimates may be dependent on the day of lactation on which the first sample was taken (2). Overall, however, the variation of daily intakes throughout a lactation was not large, and very few sample day records can produce accurate estimates of total intake during lactation. The feeding methods must be considered when these results are applied.
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ACKNOWLEDGMENT
The use of data and partial funding supplied by Eli Lilly Research Laboratory is gratefully acknowledged. REFERENCES I Anderson, S. M., I. L. Mao. and J. L. Gill. 1989. Effect of frequency and spacing of sampling on accuracy and precision of estimating total lactation milk yield and characteristics of the lactation curve. 1. Dairy Sci. 72: 2387. 2 Bayley. N. D., R. M. Liss, and J. E. Stallard. 1952. A comparison of bimonthly and quarterly testing with monthly testing for estimating dairy cattle production. J. Dairy Sci. 35:350. 3 Brown. C. A.. P. T. Chandler. and J. B. Holter. 1977. Development of predictive equations for milk yield and dry matter intake in lactating cows. J. Dairy Sci. 60: 1739. 4 Curran. M. K., R. H. Wimble. and W. Holmes. 1970. Prediction of the voluntary intake of food by dairy cows. \. Stall-fed cows in late pregnancy and early lactation. Anim. Prod. 12: 195. 5 Dean.G. W.,H. D. Carter, H. R. Wagstaff.S. O. Olayide. M. Ronning. and D. L. Bath. 1972. Production functions and linear programming models for dairy cattle feeding. Giannini Found. Monogr. No. 31, Dec. 1972. 6 Everett. R. W., B. T. McDaniel. and H. W. Carter. 1968. Accuracy of monthly. bimonthly, and trimonthly Dairy herd Improvement Association records. J. Dairy Sci. 51: 1051. 7 Gibson, J. P. 1987. Part-lactation predictors of complete lactation milk-energy yield, food intake, and food conversion efficiency. Livest. Prod. Sci. 17:323. 8 Griffm. C. D., D. O. Richardson, and J. Owen. 1971. Relationship of feed intake during various portions of the lactation to total intake. J. Dairy Sci. 54(Suppl. 1):451. (Abstr.) 9 Jensen, E., J. W. Klein. E. Rauchenstein, T. E. Woodward. and R. H. Smith. 1942. Input-output relationships in milk production. USDA Tech. Bull. 815. USDA, Washington, DC. 10 McCollough, M. E., 1973. Optimum feeding of dairy cows. Univ. of Georgia Press. Athens. II Rohweder. D. A.. N. Jorgensen, and R. F. Barnes. 1981. Proposed hay grading and standards based on laboratory analysis for evaluating quality. Page 534 in Proc. XlV In\. Grassl. Congr.• Westview Press. Boulder, CO. 12 Van Seest, P. J. 1%7. Symposium on factors influencing the voluntary intake of herbage by ruminants: voluntary intake in relation to chemical composition and digestibility. 1. Anim. Sci. 24:834.
INTRODUCTION
Daily records on DM intake, net energy intake, and milk yield from 191 Holstein cows in six herds were used to study the differences in accuracy and precision among different methods of estimating total DM intake during a lactation. In using cumulative measures of intake from partial lactations to predict total intake, accuracy reached 85% at 100 d postpartum. Measurements of intake taken around midlactation gave better predictions of total intake than those taken during other periods of lactation. Methods were evaluated for estimating total feed intake during a lactation based on data collected intermittently and separated by either equal or unequal intervals throughout the lactation. The average percentage of bias across all sampling schemes was 6% or less of actual intake. Six of the seven sampling schemes using only 10 d of intake information throughout the lactation had correlations with actual intake of .97 or higher. For equally spaced methods, both accuracy and precision of estimation increased with increased frequency of sampling. For unequally spaced methods, accuracy increased with sampling frequency after 150 d in milk. Total milk production was used to predict feed intake during a lactation. Milk yield alone accounted for 37 and 33% of the variation of total intake using actual and estimated yields, respectively. (Key words: dry matter intake, estimation, lactation)
Data on feed consumption during a lactation provide essential information for research and management. In addition to nutrition research, these data can measure biological and economic parameters in dairy cattle, such as appetite and efficiency of milk production. In feeding trials, the quantity and quality of feed intake are measured daily by individual feeding, weighback, and chemical analysis through a lactation. However, this method is costly and unfeasible for large commercial farms. Savings in time and expense would be realized if accurate predictions of total intake during lactation could be made from only a few actual measurements of intake. Equations that have been developed to predict feed intake use variables such as BW, milk production, forage type, fiber content, age, parity, and season (4, 10, 11, 12). However, these equations predict intake for a single cow on a particular day. Very limited work has been done predicting feed intake for complete lactations. Gibson (7) examined the ability of measures of intake for partial lactation to predict feeding intake for the complete lactation and found that combinations of intake records separated by several weeks were more accurate than adjacent records from a single period. Griffin et aL (8) examined the part-whole relationships of feed intake during various portions of the lactation and found correlations of .71 to .86 when using feed intake records during 28-d periods in midlactation. Predicting total feed intake by measures only on sample days has not been previously studied, although lactation milk yield estimated by sample day yields has been studied by several workers (1, 2, 6). As early as 1942, Jensen et al. (9) described the positive relationship between feed intake and milk yield. Brown et al. (3) found, based on standardized partial regression coefficients, that milk yield was the most important variable in determining total intake of DM. This relationship agreed with work done by Dean et al.
Received August 9, 1989. Accepted November 27, 1989. 1990 J Dairy Sci 73:1255-1262
(5).
1255
1256
MOORE AND MAO
The objective was to examine the accuracy and precision of three approaches to estimate total DM intake during a lactation: 1) by data collected from various portions of the lactation; 2) by various sampling strategies, using both equally and unequally spaced sampling intervals; and 3) by actual and estimated lactation milk yields. MATERIALS AND METHODS
Data
Daily records of DM intake (DMI), estimated net energy intake (NEI), and milk production were collected from 405 Holstein cows of various parities from seven herds across the United States. Records on a total of 191 cows were used in this study. Records were discarded if lactation was shorter than 250 d or if data for DMI, NEI, or milk yield were missing for more than 2 consecutive d. Those records with 1 or 2 d missing were filled by linear interpolation. All daily records in a lactation started with the 12th d after calving. Total intake and milk yield were e<>mputed by summing respective daily records. Cows were fed a total mixed ration having different forage:concentrate ratios according to milk yield and days in lactation. Production was determined by a cow's milk yield during the period prior to 21 d postpartum in which all cows were fed similarly. All heifers were in one production group. The remaining production groups were defined as: high (greater than 35 kg/d), medium (28 to 34 kg/d), and low (23 to 28 kg/d). Forage:concentration ratios began at 50:50 for first lactation heifers and 60:40 for multiparous cows and gradually increased over lactation to 70:30 and 80:20 for heifers and cows, respectively. Diets were consistent across all herds, and all animals had access to feed for at least 12 hid. Prediction of Total Intake from Partial Lactation
Cumulative Records for Partial Lactations. Beginning on the 12th d postpartum, successive daily records were summed at 15-d increments throughout the lactation. Product-moment correlations of partial records with total intake were then computed. Records for Partial Lactations of Varying Lengths in Different Stages of Lactation. Intake Journal of Dairy Science Vol. 73.
No.5. 1990
measurements in intervals of fixed length during various stages of lactation were used to examine part-whole relationships. Six different fixed length intervals of 50, 80, 100, 125. 160, and 200 d were examined. Beginning on the 15th d postpartum, each of the fixed intervals covered the various stages of lactation by a 5-d increment. Within each fixed length interval at a certain stage of lactation, daily intakes were summed. To illustrate, using the 100-d interval length and beginning on d 15, the first partial record summed daily intake between d 15 and 115, the second between d 20 and 120, and continuing until the final partial record of the last 100 d of lactation. Productmoment correlations of partial lactation records with total intake were computed. Prediction of Total Intake by Sample Day Measures
Sample Day Measures from Equally Spaced Intervals. Six equally spaced sampling schemes were examined: one sample was taken every 3, 7, 14, 30, 60, or 90 d. Intake estimates from each sampling interval were obtained by linear interpolation between sample day intake records before summing the sample day records and the interpolated records. Each estimate was expressed as a deviation from actual intake. Mean difference from actual total intake, SD of differences, average percentage of error, and frequency of errors within ± 1, 3, 5, 10, and 15% of actual intake were computed for each sampling method. Sample Day Measures from Unequally Spaced Intervals. Seven unequally spaced sampling schemes, all based on 10 samples for a lactation, as in the equally spaced, 30-d method, were studied. The hypothesis was that peak period of intake should receive the heaviest emphasis in sampling to maximize the accuracy and precision of estimating the total intake. The period of peak intake was determined to be the IOO-d interval between d 50 and 150 postpartum based partially on the .89 part-whole correlation, which was highest among all lOO-d lengths at various stages of lactation. The other criterion used to determine peak period of intake was variation in average daily DMI, which ranged from 2.36 to 4.42 kg. The greatest variation in daily intake occurred between d 40 to 160 postpartum. To test the hypothesis, seven unequally spaced sampling schemes were con-
1257
ESTIMATION OF LACTATION FEED INTAKE
TABLE I. Sampling frequencies for equally and unequally spaced intervals during prepeak. peak. and postpeak intake periods in a lactation. Days in milk Sampling method Equally spaced intervals 3 d 7 d 14 d 30 d 60d 90d Unequally spaced intervals 8-1-l t 1-8-1 1-7-2 5-2-3 3-3-4 1-4-5 (30 d) 2-2-6 1-1-8
(Prepeak) 12-50 d
(Peak) 51-150 d
(Postpeak) 151-305 d
Total no. samples 2
12 6 3 I I I
32 14
56 24 12 5
100 44
8
1 8 7 2 3 4 2 I
1 1 5 3 1 2 I
7 4 2 1
2 2 1 1 2 3 4 5 6 8
22 10 5 4 10 10 10
10 10 10 10 10
lNwnber of samples taken for each intake period of lactation (Le.• prepeak. peak. and postpCak). 2Each sample was the measured amount of feed consumed for I d.
structed such that one of the three periods of intake (i.e.. pre peak, peak, or postpeak) was sampled more frequently than the other two. Table I shows the sampling frequencies of the six equally spaced schemes and the seven unequally spaced schemes during the three stages of lactation. The unequally spaced schemes were arranged by increased sampling frequency during postpeak period. Estimates for unequally spaced methods also were obtained by linear interpolation between intake records for sample day, and expressed as a deviation from actual intake. Criteria used for comparing unequally spaced methods were the same as those for the equally spaced methods. The 30-d, equally spaced method was included in all comparisons between unequally spaced methods. Milk Yielcl as a Predictor of Total Intake
Simple Linear Regression Model.
where: Yi was the total intake during a lactation of cow i; bo was the common intercept; Xi was the lactation milk yield of cow i with b as the corresponding regression coefficient; and ei was the normally distributed random residual. The model was run with Xi being the actual lactation milk yield and was repeated with Xi being the estimated yield. Covariate Model. ygijkmn
Feed intake was predicted from actual and estimated total milk yields separately from either a simple regression model or from a covariate model. Actual milk yield was a simple sum of daily yield records, and estimated milk yield was obtained by linear interpolation using the same 30-d equally spaced method described for intake.
=
IJ. + Pg + Hi + Sj + Tk + bIXin + bz X2n + egijkrnn
Lm
+ where:
Ygijkrnn was the total intake during a lactation of cow n in production group m, treatment group k, season j, herd i, and parity g; Journal of Dairy Science Vol. 73.
:"lo. 5. 1990
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MOORE AND MAO
Il was the overall mean; P g was the fixed effect of parity g with g = I, 2, 3, 4~; Hi was the fixed effect of herd i with i = I, 2,... ,6; Sj was the fixed effect of calving season j with June through August as season 1, September through November as season 2, December through February as season 3, and March through Mayas season 4; Tk was the fixed effect of dietary treatment k with k = 1, 2, 3, 4;
Lm Xi n
X2n
egijkmn
was the first effect of production group with m = 1, 2, 3, 4; was a covariate of total milk production of cow n in the current lactation, with bi as the corresponding partial regression coefficient; was a covariate of length of current lactation ranging from 250 to 300 d of cow n with ~ as the corresponding partial regression coefficient; and was the nonnally distributed random residual.
The analysis according to this model was repeated, once with Xi n being the actual lactation milk yield and again with xl n being the estimated yield. RESULTS AND DISCUSSION
Results for NEI corresponded directly with results for OMI; therefore, only results pertaining to OMI are presented. Intake Curves
Total intake for a lactation averaged 5350 kg of OM. Figure I shows the daily averages and SO of OMI for all cows during lactation not adjusted for any factors. Both OMI and NEI curves were characterized by a rapid rise during the first 60 d after calving until peak intake was reached. Intake then begins to decline slowly and linearly for the remainder of lactation. Figure 2 shows the different levels and patterns of Journal of Dairy Science Vol. 73.
No.5, 1990
AVERAGE OM] 191 LACTATIONS NGCMll
22
-....
20
IS 16
...
~
I.
12 10 0
50
100
150
200
.L-.
-250
300
DAYS IN LACTATION
Figure 1. Average (avg; e) and plus (*) and minus (+) 1 SD of OM intake (DMI) during a lactation.
intake among the four parity groups. Parity 1 resulted in the lowest intake and a sharp increase up until 50 d in milk. Parity 2 averaged slightly higher than parity 1, with a peak at 75 d but relatively little variation during a lactation. Parities 3 and 4 and greater averaged highest and followed similar patterns of intake, peaking at approximately 100 d in milk and with more variation than parities 1 or 2. Differences in intake among parities may be due to differences in BW caused by growth and production, but this factor was not considered in the study. Intake curves also were plotted according to treatment, herd, season, and production; however, no distinct differences among classes were observed. Prediction of Total Intake Measures from Partial lactations
Cwnulative Records for Partial Lactation. Table 2 shows correlations of cumulative subtotals of feed intake with 15-d increments beginning on the 12th d postpartum. As expected, the more cumulative records available, the greater the accuracy of prediction. However, at approximately 80 d of lactation, accuracy was increasing at a decreasing rate. Before midlactation at about 140 d, the correlation of cumulative intake with total feed intake was greater than .90. Partial Lactation Records of Varying Lengths During Different Stages of Lactation. Table 3 shows those partial lactation periods of intake that yielded the highest correlation with
1259
ESTIMATION OF LACTATION FEED INTAKE
AVERAGE OMI BY PARITY 24 IW eM! telll 23 22 21 20 19
18 17
115 1!5 14 13
12+--.-,,...----r---r---,.....----r-----,
o
!SO
100
1!SO
200
2!50
300
DAYS IN LtCTATIO'J
Figw-e 2. Average (avg) dry matter intake (DMl) during lactation for each of four lactation groups: parity 1 C-; n 55). parity 2 (+; n = 83). parity 3 (.; n = 31), parity 4 (CJ; n
=
= 22).
total intake over a lactation. None of the periods shown began earlier than 50 d postpartum, and all periods covered the peak period of intake, As expected, as interval lengthened, the correlation also increased. The correlation reached .89 when interval was 100 d between 50 and 150 d postpartum, which was defined as the peak period in this study. Intakes during shorter periods. measured during peak intake period, were as accurate as those during longer periods starting at the beginning of lactation for estimating total feed intake. For example, 70 to 120 d (50 d) and 12 to 102 d (100 d) postpartum had approximately
the same correlation (.85) with total intake. Given that feed intake declined only slightly after peak intake was reached (Figures 1 and 2), accuracy of predicting total feed intake would be expected to be maximized by using intake records taken during peak period and the period following peak intake. Griffin et al. (8) found similar results, with correlations of 28-d feed intake with lactation intake were larger during the 4th through 8th mo. Gibson (7) also pointed out that if only a few measurements could be taken. the best predictions of intake would be given by measurements taken at, or shortly after, midlactation. Prediction of Total Intake
by Semple Dey Measures
SampLe Day Measures from Equally Spaced Intervals. The average biases, their SD, and average percentage of bias were used to compare sampling methods (Table 4). All six methods with equally spaced sampling intervals underestimated total DMI during lactation. Average bias for DMI increased as sampling interval increased ranging from -1.07 kg in the 3-d method to -72.60 kg in the 90-d method. However, even under the 90-d interval, estimates deviated by approximately 73 kg, on average, or by 5.2% of actual intake. Therefore, under conditions in this feeding trial, the amount of accuracy that is lost due to a decrease in sampling frequency was small, even on a trimonthly (90-d) basis. Variation of the biases may provide a better indication of the predictive ability of each testing scheme than average error or bias. Error SD on methods with more frequent sampling were smaller, and, therefore, more precise. Standard deviations of biases for DMI ranged from 42.93
TABLE 2. Product-moment correlation between cumulative partial intake and total intake of DM in a lactation. Days in milk
Correlation
27
.458
42 57
.544 .659
72 87
.758 .814 .848 .874 .898
102 117 132 147 192
.915 .953
222
.969
282
.992
TABLE 3. Stage of lactation yielding highest correlation between partial DM intake in a fixed interval length and total DM intake in a lactation. Interval length
Period
(d)
(d in milk)
200 160 125 100
80--280 50--21D 55-180 50-150 70-150
80 50
60-110
Correlation .961 .928 .906
.891 .874
.847
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No.5. 1990
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MOORE AND MAO
TABLE 4. Bias in estimation of laclalion total DM intake (DMJ) by various equally and unequally spaced sampling intervals. Sampling scheme Equally spaced intervals 3 d 7 d 14 d 30 d 60d 90d Unequally spaced intervals 8-1-1 1-8-1 1-7-2 5-2-3 3-3-4 1-4-5 (30 d) 2-2-6 1-1-8
Average bias
SE of Bias
Average % of bias
-1.07 -.35 -3.79 -41.14 -29.98 -72.60
42.93 84.65 117.20 193.23 281.16 339.88
.006 .013 .017 .028 .040 .052
.99 .99 98 .97 .93 .90
-75.15 -35.76 IU5 -10.10 -16.04 -41.16 7.56 -59.03
394.90 368,65 259.57 274.71 233.10 193.23 195.12 211.47
.059 .052 .037 .039 .033 .028 .028 .031
.87 .89 .94 .94 .95 .97 .97 .96
Correlation 1
lCorrelation between actual and estimated DM].
kg for the 3-d method up to 339.88 kg for the 9O-d method. Increases in sampling frequency for estimating lactation total intake gave higher correlations with actual lactation intake. Table 5 shows the percentage of the estimated lactation total intakes falling within limits (± I, 3, 5. 10, )5%) of the actual total intake. Frequency of large errors (5% or more) was higher in longer than in shorter test inter-
vals. As sampling frequency increased, the percentage of errors within ± 5% of actual intake increased almost 45% for both DMI and NEI but at a diminishing rate, suggesting there is an optimum number of samples to be taken after which additional samples result in increasingly smaller improvements in accuracy. Sample Day Measures from Unequally Spaced Intervals. Five of the seven unequally
TABLE 5. Proportion of estimated lactation total DM intakes by various sampling strategies within a given percentage of actual intake. Absolute percentage of error Sampling scheme Equally spaced intervals 3 d 7 d 14 d 30 d 60d 90d Unequally spaced intervals 8-1-1 1-8-1 1-7-2 5-2-3 3-3-4 1-4-5 (30 d) 2-2-6 1-1-8 Journal of Dairy Science Vol. 73.
± I
± 3
± 5
±10
± 15
.78 .48 .39 .20 .15 .12
.97 .92 .83 .64 .49 .34
1.00 .97 .95 .87 .70
1.00 1.00 .98 .96 .91 .87
1.00 1.00 1.00 .98 .96 .95
.08 .10 .12 .15 .17 .20 .21 .22
.30 .34 .49 .44 .57
.52 .58 .76 .65
.82 .89 .95 .87 .96 .96 .98 .95
.93 .97 .99 .92 .98 .98 .99 .97
No.5. 1990
.54
.64
.77 .FJ7
.65 .58
.86 .78
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ESTIMATION OF LAcrATION FEED INTAKE
TABLE 6. Analysis of variance for predicting OMI by actual or estimaled milk yield. The F-values are shown and estimates of regression coefficienls are in parentheses. Simple regression model
Source of variation Intercept Parity Herd Season Treatmenl Production Milk yield Lactation length Residual SO R2 Correlation between actual and estimated OMI
Actual
Estimated
(5393)
(5721)
Covariate model Actual
1.75 8.63 a
1.13
(.423)"
(.403)"
1314.59 .36
1345.49 .33
.63
.57
spaced sampling schemes underestimated total intake (Table 4). Six of the seven schemes had correlations with total intake of .97 or greater. Average bias for OM) ranged from 7.56 kg for the samples taken: two prepeak, two peak, six postpeak intake period in a lactation (2-2-6) to -75.15 kg for the 8-1-1 sampling scheme. Accuracy and precision of estimation increased as sampling emphasis during postpeak period increased except for the extreme case of 1-1-8. Standard deviations of biases for OM) of 193.23 to 394.90 kg were observed for the 1-4-5 and 8-1-1 schemes, respectively. Results for the percentage of the estimates falling within given limits of the actual for the unequally spaced sampling intervals are in Table 5. The percentage of errors within ± 5% of actual increased over 35% as sampling increased during postpeak period. The highest occurrence of small errors was observed in the 1-4-5 and 2-2-6 methods. The 2-2-6 strategy proved to be the most accurate. However, the convenient 1-4-5 (30-d) method gave the highest precision from all sampling methods based on 10 samples in a lactation. Milk Yield as Predictor of Total Intake
3.03 b 4.02 a (.225)& (34.61)& 1020.20 .65 .81
Estimated
\.86 9.06 a .95 2.94 b 4.54" (.211)a (36.20)" 1023.56 .65 .81
small advantage in using actual over estimated yield to predict total intake. Regression coefficients for both actual and estimated yields were highly significant as shown in Table 6. As expected. actual yield gave only slightly higher precision according to residual SO than did estimated yield. Covariate Model. The covariate model used accounted for up to 65% of the variation in OMI during lactation when either actual or estimated yield was used. Partial regressions of intake on actual yield and on estimated yield both were highly significant, as were partial regressions of lactation length, for both OM! and NEI. These results also are shown in Table 6. Herd, production group, and treatment effects were significant when either actual or estimated yield was used. Therefore, application of the covariate model for the prediction of OM) requires knowledge of herd differences. Differences found in intakes between parities in Figure 2 were not significant in either case here after accounting for the other effects in the model. CONCLUSIONS
Simple Regression Model. Actual lactation milk yield alone accounted for 37%, and estimated yield accounted for 33% of the variation
Accuracy of predicting lactation total intake reached 85% at 100-<1 postpartum when using cumulative partial lactation measures of intake. Short-term measures of intake taken during
in total DMI. The difference of 4% indicates a
midlactation were as accurate as longer meaJournal of Dairy Science Vol. 73, No.5, 1990
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MOORE AND MAO
sures taken at the beginning of lactation for estimating total DMI during a lactation. When using sample day intake records at equal interval lengths during a lactation to estimate total intake, accuracy and precision increased as the sampling interval decreased. Sampling frequencies of 30 d or less predicted lactation feed intake better than partial records having 200 or less consecutive days of information. The 90-d method, with only 4 sample d in a lactation, had a correlation of .90 with actual intake equaling that of 100 d worth of information on consecutive days. For the seven unequally spaced sampling schemes based on only 10 d of sample intake records, six had correlations with total intake of .97 and higher. However, estimates of intake based on these 10 samples predicted intake better when sampling was heaviest after peak period intake in a lactation. In fact, from the estimate based on 10 sample d in a lactation, the 30-d method in most cases was better than the unequally spaced sampling schemes. Using milk yield as a predictor of lactation total intake did not prove to be as effective as the direct sampling of intake records; prediction accuracy was less than that obtained from 50 d of intake information. Factors not included in this study were the effect of BW and its predictive ability for total intake during lactation and the effect of date of first sample. Results from studies comparing sampling procedures for the estimation of lactation total milk yield have indicated the magnitude of the errors in the estimates may be dependent on the day of lactation on which the first sample was taken (2). Overall, however, the variation of daily intakes throughout a lactation was not large, and very few sample day records can produce accurate estimates of total intake during lactation. The feeding methods must be considered when these results are applied.
Journal of Dairy Science Vol. 73,
No.5, 1990
ACKNOWLEDGMENT
The use of data and partial funding supplied by Eli Lilly Research Laboratory is gratefully acknowledged. REFERENCES I Anderson, S. M., I. L. Mao. and J. L. Gill. 1989. Effect of frequency and spacing of sampling on accuracy and precision of estimating total lactation milk yield and characteristics of the lactation curve. 1. Dairy Sci. 72: 2387. 2 Bayley. N. D., R. M. Liss, and J. E. Stallard. 1952. A comparison of bimonthly and quarterly testing with monthly testing for estimating dairy cattle production. J. Dairy Sci. 35:350. 3 Brown. C. A.. P. T. Chandler. and J. B. Holter. 1977. Development of predictive equations for milk yield and dry matter intake in lactating cows. J. Dairy Sci. 60: 1739. 4 Curran. M. K., R. H. Wimble. and W. Holmes. 1970. Prediction of the voluntary intake of food by dairy cows. \. Stall-fed cows in late pregnancy and early lactation. Anim. Prod. 12: 195. 5 Dean.G. W.,H. D. Carter, H. R. Wagstaff.S. O. Olayide. M. Ronning. and D. L. Bath. 1972. Production functions and linear programming models for dairy cattle feeding. Giannini Found. Monogr. No. 31, Dec. 1972. 6 Everett. R. W., B. T. McDaniel. and H. W. Carter. 1968. Accuracy of monthly. bimonthly, and trimonthly Dairy herd Improvement Association records. J. Dairy Sci. 51: 1051. 7 Gibson, J. P. 1987. Part-lactation predictors of complete lactation milk-energy yield, food intake, and food conversion efficiency. Livest. Prod. Sci. 17:323. 8 Griffm. C. D., D. O. Richardson, and J. Owen. 1971. Relationship of feed intake during various portions of the lactation to total intake. J. Dairy Sci. 54(Suppl. 1):451. (Abstr.) 9 Jensen, E., J. W. Klein. E. Rauchenstein, T. E. Woodward. and R. H. Smith. 1942. Input-output relationships in milk production. USDA Tech. Bull. 815. USDA, Washington, DC. 10 McCollough, M. E., 1973. Optimum feeding of dairy cows. Univ. of Georgia Press. Athens. II Rohweder. D. A.. N. Jorgensen, and R. F. Barnes. 1981. Proposed hay grading and standards based on laboratory analysis for evaluating quality. Page 534 in Proc. XlV In\. Grassl. Congr.• Westview Press. Boulder, CO. 12 Van Seest, P. J. 1%7. Symposium on factors influencing the voluntary intake of herbage by ruminants: voluntary intake in relation to chemical composition and digestibility. 1. Anim. Sci. 24:834.