Quantifying shape of lactation curves, and benchmark curves for common dairy breeds and parities

Abstract

The MilkBot®(DairySight LLC,Argyle, NY; http://milkbot.com) lactation model provides a means of quantifying both shape and magnitude oflactation curves as a set of parameter values, each of which is associated with a single aspect of lactation curve shape. Lactation data may be fitted to the model to summarize a lactation as a set of parameter values which summarize the lactation as a whole. The scale parameter controls magnitude without changing the shape of the curve, the ramp parameter controls steepness of the post-parturient rise in milk production, the decay parameter controls the rate of late lactation decline, and the offset parameter defines a theoretical offset between the start of milk production and calving. The decay parameter is easily re-expressed mathematically as persistence to quantify the rate of decline in production after peak milk. Time and quantity of peak milk, or production for any day or period in the lactation may be calculated directly from parameter values.
 Aggregate normal lactation curves for mean and median milk production of Holstein, Jersey, Crossbred, Guernsey, Ayrshire, and Brown Swiss dairy cattle, stratified by parity, are calculated from a DHIA data set collected from 2005 through mid-2008 and covering over six million lactations and 51 million milk weights, mainly from farms in the eastern United States. These constitute benchmark curves that may be used as standards for normal milk production, or to quantify changes in normal productivity over time or with respect to other variables, or in econometric studies.

Investigating the effect of temporal, geographic, and management factors on US Holstein lactation curve parameters

“…As a result of the considerable effect of lactation group on parameters a and c, even lactation groups with comparable 305-d production levels exhibited substantial differences in the shape of the estimated lactation curves, particularly during the decay period of lactation. According to our findings and those of Ehrlich (2011), it is critical to distinguish the lactation curve parameters for the second lactation from those of later lactations. As illustrated in Figure 3, the milk yield of first-lactation cows after 200 DIM for 3×/d (and 222 DIM for 2×/d) would be greater than that of the second-lactation cows.…”

Herd level economic comparison between the shape of the lactation curve and 305 d milk production

“…In the current study, a (scale) was renamed magnitude of milk production (in kg/day) and b (ramp) was renamed time to peak yield (in days). d (decay) was transformed into a measure of persistency using the Equation ( 5 ):…”

“…In short, we used the cow test-day data to calculate HLCC. First, we fitted a lactation curve for each whole lactation with the MilkBot model using a proprietary maximum likelihood fitting algorithm of the DairySight fitting engine ( 5 ). The full MilkBot equation is shown as:…”

“…Additionally, lactation curve characteristics (LCC), describing the lactation curve in different ways, can also be used to evaluate the milk production performance of cows. LCCs are derived from a lactation curve model such as the classic Wood model ( 3 ), the Wilmink model ( 4 ) and the Milkbot model ( 5 ). The MilkBot model, for example, consists of the scale (representing the level of production), the ramp (representing the rising rate of milk production up to the peak level), the estimated time between the start of milk synthesis and calving (offset) and the rate of late lactation decline (decay).…”

“…The MilkBot model, for example, consists of the scale (representing the level of production), the ramp (representing the rising rate of milk production up to the peak level), the estimated time between the start of milk synthesis and calving (offset) and the rate of late lactation decline (decay). The latter can be easily transformed into a measure of persistency ( 5 ). Both M305 and LCC are commonly used to compare the milk production performance of cows ( 6 , 7 ) as well as economic performance ( 8 , 9 ).…”