Quantifying inter-group variability in lactation curve shape and magnitude with the MilkBot^®lactation model

Abstract

Genetic selection programs have driven development of most lactation models, to estimate the magnitude of animals’ productive capacity from sampled milk production data. There has been less attention to management and research applications, where it may also be important to quantify the shape of lactation curves, and predict future daily milk production for incomplete lactations since residuals between predicted and actual daily production can be used to quantify the response to an intervention. A model may decrease the confounding effects of lactation stage, parity, breed, and possibly other factors depending on how the model is constructed and used, thus increasing the power of statistical analyses. Models with a mechanistic derivation may allow direct inference about biology from fitted production data. The MilkBot® lactation model is derived from abstract suppositions about growth of udder capacity. This permits inference about shape of the lactation curve directly from parameter values, but not direct conclusions about physiology. Individual parameters relate to the overall scale of the lactation, the ramp, or rate of growth around parturition, decay describing the senescence of productive capacity (inversely related to persistence), and the relatively insignificant time offset between calving and the physiological start of milk secretion. A proprietary algorithm was used to fit monthly test data from two parity groups in 21 randomly selected herds, and results displayed in box-and-whisker charts and Z-test tables. Fitted curves are constrained by the MilkBot® equation to a single peak that blends into an exponential decline in late lactation. This is seen as an abstraction of productive capacity, with actual daily production higher or lower due to random error plus short-term environmental effects. The four MilkBot® parameters, and metrics calculated directly from them including fitting error, peak milk and cumulative production, can be used to describe and compare individual lactations or groups of lactations. There is considerable intra-herd and inter-herd variability in scale, ramp, decay, RMSE, peak milk, and cumulative production, suggesting that management and environment have significant influence on both shape and magnitude of normal lactation curves.

Effect of Calf Gender on Milk Yield and Fatty Acid Content in Holstein Dairy Cows

“…[34] Daily milk component values were estimated by linear interpolation between test points. Lactation 305-day totals were then calculated by symbolic integration of the Milkbot® equation to give 305-day Milk Yield (M305) and by summation of daily predicted milk yield times component concentration to give fat yield (F305), protein yield (P305), saturated fatty acids (SFA305), monounsaturated fatty acids (MONO305) and polyunsaturated fatty acids (POLY305).…”

Using Geometric Morphometrics to Quantify Variation of Shape and Magnitude of the Pattern of Milk Production of Dairy Cattle

“…They have been also used to investigate other aspects of the cow's lactation including evaluating its variation by the influence of factors and variables related to management, environment, and physiology [5]- [11]; detecting different shapes of lactation curves [12] [13]; modeling extended lactations [14]- [17]; and quantifying the shape variability of lactation models [18] [19]. Milk yield (or magnitude) and the shape (or pattern), which are determined by the physiological process of the cow's mammary gland, are intrinsic features of any lactation curve.…”

“…The appropriate analysis of shapes in this field has been hindered by difficulty and lack of a standard method [19]. However, the geometric morphometric (GM) methods, which provide analyses for quantifying, testing, and visualizing shape variation and its covariation with biotic and abiotic variables [21]- [23], has already proved to contribute to increase the scientific rigor in the description of shape on Biology, Medicine, and Engineering [24] [25].…”

Invited review: Helping dairy farmers to improve economic performance utilizing data-driving decision support tools

“…The tool fits observed data to pre-defined lactation curves functions of either MilkBot (Ehrlich, 2011; four parameters) or Wood's model (Wood, 1967; three parameters) according to farm observed data by fitting parameters using least squares optimization when comparing observed v. predicted data. The results of fitting are the coefficient values of the selected function in mathematical terms.…”