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Department of Animal Sciences, University of Florida, Gainesville 32611
E-mail: devries{at}ufl.edu
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Key Words: economics • pregnancy • reproduction • abortion
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The value of a pregnancy for an individual cow can be defined as the difference in discounted future cash flows when she is pregnant compared with when she is not pregnant. The value of a new pregnancy has been reported to average approximately $200 (Eicker and Fetrow, 2003). In programmed AI breeding protocols, Stevenson (2001) estimated that the value of a new pregnancy was between $253 and $274, excluding the additional cost of the programmed AI breeding protocol compared with traditional breeding based on detected estrus. He showed that the value of pregnancy increased with lower estrus detection efficiency.
Per case, the cost of pregnancy loss (abortion) has been estimated at $640 (Thurmond and Picanso, 1990) and from $600 to $800 (Eicker and Fetrow, 2003). Pfeiffer et al. (1997) estimated the cost of an abortion caused by Neospora caninum infections at NZ$975 in New Zealand ($624). Peter (2000) documented a cost of $600 to $1,000 per midterm abortion. Weersink et al. (2002) estimated the cost of an abortion, including reproductive loss and reduced milk yield at CAN$1,476 in Canada ($1,286). Several of these estimates were intended as illustrations of special cases and were not herd or group averages. Furthermore, the methods used to obtain these values were not fully described or could be improved.
The hypothesis of this study was that the value of pregnancy varies greatly for individual cows, depending on the performance of the cow and that of the herd, the lactation number, the stage of lactation, the stage of gestation, prices, and breeding and replacement decisions. A systematic analysis of the value of pregnancy for individual cows may help dairy producers focus their resources on those nonpregnant cows that are economically the most important group to get pregnant. Furthermore, a systematic analysis should provide estimates of the cost of abortion for different groups of cows (e.g., by stage of gestation).
The objective of this study was to estimate the value of pregnancy for cows that differed in lactation number, stage of lactation, and milk yield. The effects of various replacement heifer costs, prices of milk, levels of herd performance (probability of pregnancy, probability of involuntary culling, 305-d milk yield, persistency of lactation), and breeding decisions (length of breeding period) were evaluated. Both the value of establishing a new pregnancy and the cost of pregnancy loss were studied.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Cows were categorized by a combination of milk yield (i, with i = 1 to 15, where i = 1 was the smallest milk yield and i = 15 was the largest milk yield), lactation number (k, with k = 1 to 12), month in lactation (mo, with mo = 1 to 24), and reproductive status (n, where n = 0 was a nonpregnant cow and n = 1 to 9 was the month of gestation for pregnant cows). Nonfeasible categories, for example where mo = 1 and n = 2, were excluded. Furthermore, CVi,k,mo,n,t was the discounted future cash flow given optimal breeding and replacement decisions for the individual cow and her future replacement in month t until the end of the planning horizon. It follows that the value of pregnancy during month n of gestation was calculated as VPi,k,mo,n,t = CVi,k,mo,n,t – CVi,k,mo,0,t. For example, VPi,k,mo,5,t was the value of the pregnancy at the start of the fifth month of gestation. The value of the pregnancy is equivalent to the cost of pregnancy loss if the cow should abort.
The value of pregnancy is equivalent to the difference in retention payoff (RPO) of 2 cows that are categorized similarly but that differ in that 1 cow is not pregnant (n = 0) and the other cow is pregnant (n 
1) and both RPO are greater than $0. The RPO is the discounted future cash flow from trying to keep the cow until the optimal time to cull her and her future replacement heifers (KEEPi,k,mo,n,t), minus the discounted future cash flow from immediately culling the cow and her future replacement heifers (CULLi,k,mo,n,t; van Arendonk, 1984). Thus, RPOi,k,mo,n,t = KEEPi,k,mo,n,t – CULLi,k,mo,n,t. Furthermore, CVi,k,mo,n,t = max(KEEPi,k,mo,n,t, CULLi,k,mo,n,t). If the RPO is greater than $0, then the optimal decision is to keep the cow at least 1 more month. If the RPO is less than $0, then the optimal decision is to immediately cull the cow, and usually immediately fill the slot with a replacement heifer. If both the nonpregnant and the pregnant cow have an RPO of less than $0, then the value of pregnancy equals $0 because the model assumes that the cull price is independent of pregnancy status and both cows would be replaced at the same time by identical replacement heifers. Thus, their discounted future cash flows are identical.
A few modifications were made to the optimization module described by De Vries (2004). First, the probability of abortion per month of gestation was included. If a cow aborted, it was assumed that she continued as an identical nonpregnant cow in the same lactation.
Furthermore, the probability of establishing a pregnancy per month was calculated as PR + (1 – PR) x PR x 9.4/21, where PR (pregnancy rate) was the probability of getting pregnant in a 21-d estrous cycle. The number of breedings per month for an eligible, nonpregnant cow was SR + (1 – PR) x SR x 9.4/21, where SR (service rate) was the probability of breeding in a 21-d estrous cycle. The SR equals the probability of estrus detection in a 21-d estrous cycle when breeding is based on detection of estrus alone. Therefore, PR = SR x probability of conception. These changes more accurately represent the probability of occurrence of breeding and pregnancy per month compared with the formulation in De Vries (2004). The consequences at realistic levels of PR and SR are minor.
Finally, a positive association was included between days not pregnant during a previous lactation and 305-d milk yield during the current lactation, using the multiplication factors from Funk et al. (1987). These factors ranged from 98% when the cow was 61 d not pregnant to 105% when the cow was 456 d not pregnant. The distribution of transition probabilities to the milk yields during the first month of the next lactation (van Arendonk, 1985), based on a 60% repeatability of the 305-d total milk yield (van Arendonk, 1986), was shifted slightly to obtain the adjusted 305-d total milk yields.
Breeding and replacement decisions in this study were optimal unless specified otherwise. The supply of replacement heifers was unlimited. The value of a new pregnancy was calculated for every nonpregnant cow that was eligible for breeding. Cows were eligible for breeding after 61 DIM until the end of the 15th month in lactation (d 456), unless the cow was culled earlier.
Results were calculated for herds in steady state, as determined by the herd performance module. Average results for subgroups of cows were obtained by weighing the probability that a cow was in a category in that subgroup multiplied by the value of pregnancy for that category (De Vries, 2004). For example, the herd average value of a new pregnancy was the weighted value of pregnancy of nonpregnant cows at various milk yields, lactations, and DIM.
Default Input Values
Input values for the bioeconomic module were chosen to represent a general Holstein dairy herd in the United States. Unless specified otherwise, input values were the same as in De Vries (2004).
Milk Yield.
Milk yield by month of lactation for non-pregnant cows per lactation was predicted by the diphasic logistic function, defined as
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where yDIM = milk yield at DIM and ai, bi, and ci are parameters for phase i; tanh is the hyperbolic tangent function; aibi is the peak yield for phase i; and ci is DIM at the peak yield for phase i (Grossman and Koops, 1988). This function was able to provide accurate estimates of milk yields for standard and extended lactations in other studies (Vargas et al., 2000). The 6 parameters of the diphasic logistic function were estimated from average peak yield, DIM at the peak yield, and 2X 305-d mature equivalent (ME) milk yields for the first, second, and third and greater lactations based on 2.2 million records completed in 2003. These averages were provided by the USDA Animal Improvement Programs Laboratory (AIPL) in Beltsville, Maryland. Actual 2X 305-d milk yields during the first and second lactations were assumed to be 83.3 and 90.9% of the ME yield (Norman et al., 1995). Because average peak yields and DIM at peak yield obtained from the AIPL were based on various milking frequencies but the 305-d ME yield was for 2X only, 305-d milk yields were estimated by adding 1,000 kg to the actual 2X 305-d milk yields, based on Erdman and Varner (1995). The Solver function in Microsoft Excel was used to minimize the difference between the actual and predicted 305-d milk yields given the following 4 constraints. Predicted DIM at the peak milk yield, predicted peak milk yield, and predicted 305-d milk yield were constrained to be within 20% of the actual averages obtained from the AIPL. In addition, the ratio of predicted daily yields at 280 and 60 DIM was constrained to be within 20% of 0.75, 0.59, and 0.57 for cows in their first, second, and third and greater lactations (Canadian Dairy Network, 2004), respectively. No feasible solutions could be found if the constraints were not satisfied. Meadows et al. (2005) used the same approach to estimate lactation curves for herds located in Ohio. Persistency of milk production in the current study was measured as the linear decline in predicted milk yield per day between DIM at peak milk yield and d 305. The results of fitting the diphasic logistic functions are shown in Table 1
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Pregnancy reduced milk production by 5, 10, and 15% in mo 5, 6, and 7 of gestation (De Vries, 2004). Cows were not lactating in mo 8 and 9 of gestation.
Reproduction.
The probability of being inseminated during a 21-d estrous cycle (SR), and the probability of conception at 61 DIM were both set at 40% (Groenendaal et al., 2004). Thus, PR at 61 DIM was 16%. The probability of conception declined after 61 DIM by 2.6% per month, based on De Vries (2004).
The probability of abortion by month of gestation (n = 2 to 8) was set at 3.5, 2.5, 1.5, 0.5, 0.25, 0.1, and 0.1%, respectively (data adapted from Santos et al., 2004). Consequently, the total probability of abortion after the first month if the cow was not culled was 8.2%. The probability of fetal loss during the first month of pregnancy was set at 0% because the probability of conception was defined as the probability that the cow was pregnant 1 mo after breeding.
Involuntary Culling.
The probability of involuntary culling per month of lactation was set at 70% of the values reported in De Vries (2004) for the southeastern United States. This adjustment was made to obtain overall culling rates that were in better agreement with national averages reported for the dairy industry.
Prices.
Milk price was set at $0.31/kg. The replacement heifer cost was set at $1,600 per head and the calf price at $200. The replacement heifer cost was greater than the typical cost to raise a heifer and smaller than the typical cost to purchase a heifer in 2005 (Meadows et al., 2005).
Cull prices for voluntarily culled cows were set at $0.74/kg of BW (Meadows et al., 2005). Additional costs because of involuntary culling were set at $0. Instead, cull prices for involuntarily culled cows were set at 50% of the cull price of voluntarily culled cows. Feed cost per kilogram of DMI was set at $0.20 for lactating cows and $0.15 for dry cows (Groenendaal et al., 2004). Other variable costs were set at $1/cow per d. Future cash flows were discounted monthly at an 8% annual discount rate and were converted to their equivalent annual annuity values in the herd performance module (Keown et al., 2002).
Sensitivity Analyses
Sensitivity analyses were performed to evaluate the effects of changes in the input values on the value of pregnancy. Daily milk yield, milk price, replacement heifer cost, and probability of involuntary culling were multiplied by 1.2 or 0.8 to obtain 20% changes in these input values. The probability of conception at 61 DIM was set at 43.8 or 35.8% to obtain 20% changes in the probability of pregnancy (PR) if breeding was optimal. The last DIM when breeding was allowed was reduced to 365 d (12 mo) or 274 d (9 mo). Persistencies of lactation were increased or decreased by 0.025 kg/d. Decreased persistencies (steeper curves) were therefore – 0.061, – 0.110, and – 0.120 kg/d for first, second, and third and greater lactations; increased persistencies (flatter curves) were – 0.011, – 0.060, and – 0.070 kg/d, respectively. Parameters of the diphasic logistic function were reestimated with the following constraints. Total 305-d total milk yield and milk yield at 1 DIM were constrained to be the same as for the default inputs. Persistency was constrained to be exactly 0.025 kg/d smaller or greater than the default persistencies. Peak milk yield and DIM at peak milk yield were allowed to vary. Lactation curves for cows in their first and third and greater lactations having different persistencies are shown in Figure 1.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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. Milk sales were 91% of total sales. Feed costs were 45% of the total cost. Replacement costs (replacement heifer cost minus cow sales) were $474/cow per yr. Revenues minus feed costs were $5.40/d. Profit was $3.10 per 100 kg of milk. Breeding cost per pregnancy was $40. Average days to first service was 86 and average days to last breeding was 337. Five percent of breeding opportunities were delayed. The average value of a new pregnancy was $278. The average cost of a pregnancy loss was $555.
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. With conception at 61 DIM, the value of pregnancy increased from $81 during the first month of pregnancy to $841 during the last month of pregnancy. In this example, the value of pregnancy was equal to the difference between the RPO of the pregnant and nonpregnant cow, because both RPO were greater than $0 during the first 11 mo after calving. The RPO of the nonpregnant cow decreased from $993 in the first month after calving to less than $0 after 13 mo in milk, indicating that the cow should then be culled. The RPO of the pregnant cow varied from $1,015 for a new pregnancy to $956 in the last month of pregnancy. The reduction in RPO during midgestation was caused by the remaining risk of involuntary culling and abortion before the pregnancy was completed.
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show the differences in total discounted future revenues and costs that determine the value of a new pregnancy for 12 cows categorized by lactation number, stage of lactation at conception, and relative milk yield. For example, a cow in her first lactation with 80% the milk yield of the average lactation curve that conceived at 61 DIM, and her replacement heifers, had $106 less in milk sales, $133 less in replacement costs, $31 less in feed costs, $27 less in breeding costs, and $1 less in other costs than an identical nonpregnant cow. Calf sales were $34 greater than for nonpregnant cows. Total revenues were reduced by $72 and total costs were reduced by $192. Therefore, the value of the new pregnancy was $120.
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Changes in the value of a new pregnancy by the stage of lactation and relative milk yield are shown in Figures 3 (first lactation) and 4 (second lactation). The value of a new pregnancy was observed to be smaller during early and late lactation. The value decreased more rapidly for cows in their second lactation. The value for high-producing cows peaked later in lactation.
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) was typically greater than the value of a new pregnancy (Table 3
), except in the rare case in which the pregnant cow should be culled. This was occasionally the case for low-producing older cows. The cost of pregnancy loss was then $0 because the cull price was assumed to be independent of pregnancy. The results in Table 4 show the cost of pregnancy loss at 1, 4, and 7 mo of gestation by relative milk yield, lactation number, and stage of lactation (61 or 243 DIM) at conception. Costs ranged from $0 to $1,373.
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Sensitivity Analyses
Realistic changes in the inputs could have significant effects on herd statistics, as shown in Table 5. As expected, increased daily milk yield, greater persistency, increased milk price, decreased replacement heifer cost, a greater probability of pregnancy, more opportunity to breed cows, and a decreased probability of involuntary culling were associated with increased profit per cow per year. Changes in the annual cull rate, the value of a new pregnancy, and the cost of pregnancy loss were not clearly associated with changes in profit per cow per year. A greater value of a new pregnancy was always associated with a greater cost of pregnancy loss. A greater value of pregnancy was associated with increased daily milk yield, reduced persistency of lactation, increased milk price, increased replacement heifer cost, decreased probability of pregnancy, less opportunity to breed cows, and decreased probability of involuntary culling. Major determinants of the value of pregnancy were persistency of lactation, replacement heifer cost, and probability of pregnancy. The value of pregnancy was smaller when cows were given more opportunity to become pregnant before culling, or when replacement costs were reduced.
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shows the value of a new pregnancy during first and second lactation by the stage of lactation, persistency of lactation, and probability of pregnancy. Persistency was greater (+0.025 kg/d) or smaller (– 0.025 kg/d) compared with the default situation, as in Table 5. The probability of pregnancy was set at 19.2 or 12.8%. In the first lactation, the value of a new pregnancy increased nearly linearly by days after calving to the last opportunity to get pregnant (end of mo 15 after calving), when both persistency and the probability of pregnancy were greater than in the default situation. Early in lactation, the value of pregnancy was negative or smaller than in all other situations. In all other situations, the value of pregnancy peaked between the fifth and eighth month after calving. The value of pregnancy decreased thereafter because cows were culled at greater milk yields. The value of pregnancy was $0 for second-lactation cows after 13 mo in milk because both the nonpregnant and the newly pregnant cow should be culled.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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No single complete description of a general herd is available in the literature. Therefore, default inputs in the model were necessarily based on various sources that may be different in location and time. Default inputs were chosen such that the resulting herd statistics (Table 2) were comparable with statistics published in several dairy farm financial surveys (Knoblauch et al., 2005; Moore Stephens Wurth Frazer and Torbet, 2005; Giesy et al., 2006). Although these surveys show regional differences, they also show large variations among dairy farms within regions.
The shape of the lactation curve was a major determinant of the value of pregnancy. Data describing recent lactation curve characteristics of large groups of cows (regions or nationally) were not found. Therefore, lactation curves used in this study were fitted on observed averages for peak yield, DIM at peak milk yield, and 2X 305-d ME yield obtained from the AIPL based on more than 2 million records from across the United States. A reasonably close fit was obtained (Table 1). The major difference was that predicted DIM at peak yield was earlier than actually reported but later than that used by others (Dekkers et al., 1998; Groenendaal et al., 2004; Meadows et al., 2005). Predicted persistencies of lactation in this study were between the persistencies used in those studies that varied widely.
The goal for use of estimated lactation curves in the current study was to predict future milk yields in the remainder of the lactation for nonpregnant cows, whereas most published lactation curves are plots of average milk yield per DIM. Average milk yields observed in practice are affected by management, culling, and pregnancy, and are therefore biased predictors of future milk yields for cows earlier in lactation. Furthermore, predicted future milk yields during the remainder of the lactation should be updated as new information becomes available to make economically optimal breeding and replacement decisions later in lactation. This requires predictions of milk yields in lactations that will extend past the historical 305 DIM (Grossman and Koops, 2003).
The average value of a new pregnancy for the default inputs ($278) was similar to the value used by Stevenson (2001) and somewhat greater than the value reported by Eicker and Fetrow (2003). The default average cost of pregnancy loss ($555) was smaller than previously reported ($600 to $1,286). These differences were caused by differences in predicted cow performance, prices, and breeding and replacement decisions.
When the pregnancy was lost by abortion, the future performance of the cow in the current and (possibly) future lactations was assumed to be similar to that of the nonpregnant cow. The effect of abortion on future performance was not considered in this study, but affects future cash flow predictions. There is evidence, for example, that aborted cows are 5 times more likely to abort subsequently than are cows that never aborted (Peter, 2000). Abortion also has been associated with losses in milk yield (Pfeiffer et al., 1997; Weersink et al., 2002). A cow with compromised future performance as a result of abortion is more likely to be culled. The cost of pregnancy loss would be greater than reported in this study if these effects were included.
The value of a new pregnancy typically increased greatly when cows were given less time to get pregnant before they were culled or when replacement costs were greater. Consequently, cows with more persistent lactation curves had much smaller average values for new pregnancies. The importance of lactation persistency on economically optimal breeding and replacement decisions was previously documented (Dekkers et al., 1998; Vargas et al., 2000). The economic value of a new pregnancy was negative early in first lactation when these cows were more persistent, had a greater probability of pregnancy, and were relatively high producing. The negative value of a pregnancy implied that breeding should be delayed past the voluntary waiting period of 60 d used in this study. The finding that breeding should be delayed for such cows also has been reported by others (Dekkers et al., 1998; Rajala-Schultz et al., 2000).
Groenendaal et al. (2004) showed that the cost per extra nonpregnant day was smaller for relatively high-producing cows. Furthermore, costs per extra nonpregnant day were smaller and increased more slowly for first-lactation cows compared with older cows in that study. Those trends are similar to those for the value of pregnancy in the current study. Groenendaal et al. (2004) set the cost per nonpregnant day to $0 when it was optimal not to breed a relatively low-producing cow. In contrast, the optimal decision to delay breeding (and thus a negative cost per nonpregnant day) was sometimes associated with a positive value for pregnancy (not shown) in the current study. Delayed breeding increases the number of nonpregnant days by approximately 1 mo, whereas the average time to conceive after the start of the breeding period is typically longer. Therefore, the associated discounted future cash flows are different. The positive value of a new pregnancy therefore does not necessarily imply that a cow should be bred. Further investigation should clarify this relationship.
The variation in milk yield between cows within lactation was modeled as a percentage of the average lactation curve. Consequently, high-producing cows were slightly less persistent than the average-producing cow. In practice, persistencies of lactation also vary among cows of the same lactation that produce the same amount of milk in 305 d. Optimal breeding and replacement decisions, and consequently the value of pregnancy, depend on the prediction of the persistency of lactation for individual cows early in the lactation. Further investigation that includes prediction of individual lactation curves seems warranted.
Later in lactation, the average value of a new pregnancy typically was reduced because more newly pregnant cows were culled, especially those with relatively low milk yields, as well as identical nonpregnant cows. The difference in their future cash flow predictions was $0. Low-producing cows that would become pregnant in a later lactation were assumed to be milked for another 7 mo before dry off. The repeatability of 305-d total milk yields among lactations was 60% (van Arendonk, 1986). The optimization module therefore calculated that replacing these cows with average heifers would increase future cash flows. Early dry off for low-producing pregnant cows was not considered, but this might be economically advantageous. The value of pregnancy depended more on the relative milk yield of a cow compared with that of a replacement heifer than on the absolute milk yield.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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FOOTNOTES |
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Received for publication January 9, 2006. Accepted for publication May 11, 2006.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
) and a cow that became pregnant on d 61 after calving (
) by day after calving. Cows are in their first lactation with average lactation curves. Value of pregnancy is equal to the difference between the RPO of the pregnant and nonpregnant cow on the same days after calving because both RPO are greater than $0.
; 100%, •; 120%, 
) compared with an average lactation curve.
; Sg, 
; Ss, 
).