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.

The effects of metabolic diseases (MD) occurring during the transition period on milk production of dairy cows have been evaluated in many different ways, often with conflicting conclusions. The present study used a fitted lactation model to analyze specific aspects of lactation curve shape and magnitude in cows that avoided culling or death in the first 120 d in milk (DIM). Production and health records of 1,946 lactations in a 1-yr follow-up study design were collected from a transition management facility in Germany to evaluate both short- and long-term effects of MD on milk production. Milk production data were fitted with the nonlinear MilkBot lactation model, and health records were used to classify cows as healthy (H), affected by one MD (MD), or by multiple MD (MD+). The final data set contained 1,071 H, 348 MD, and 136 MD+ cows, with distinct incidences of 3.7% twinning, 4.8% milk fever, 3.6% retained placenta, 15.4% metritis, 8.3% ketosis, 2.0% displaced abomasum, and 3.7% mastitis in the first 30 DIM. The model containing all healthy and diseased cows showed that lactations classified as H had milk production that increased faster (lower ramp) and also declined faster (lower persistence) compared with cows that encountered one or more metabolic problems. The level of production (scale) was only lowered in MD+ cows compared with H and MD cows. Although the shape of the lactation curve changed when cows encounter uncomplicated (single) MD or complicated MD (more than one MD), the slower increase to a lower peak seemed to be compensated for by greater persistency, resulting in the overall 305-d milk production only being lowered in MD+ cows. In the individual disease models, specific changes in the shape of the lactation curve were found for all MD except twinning. Milk fever, retained placenta, ketosis, and mastitis mainly affected the lactation curve when accompanied by another MD, whereas metritis and displaced abomasum affected the lactation curve equally with or without another MD. Overall, 305-d milk production was decreased in complicated metritis (10,603 ± 50 kg vs. 10,114 ± 172 kg). Although care should be taken in generalizing conclusions from a highly specialized transition management facility, the current study demonstrated that lactation curve analysis may contribute substantially to the evaluation of both short- and long-term effects of metabolic diseases on milk production by detecting changes in the distribution of production that are not apparent when only totals are analyzed.

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.

The aim of this study was to identify genomic regions associated with 305‐day milk yield and lactation curve parameters on primiparous (n = 9,910) and multiparous (n = 11,158) Holstein cows. The SNP solutions were estimated using a weighted single‐step genomic BLUP approach and imputed high‐density panel (777k) genotypes. The proportion of genetic variance explained by windows of 50 consecutive SNP (with an average of 165 Kb) was calculated, and regions that accounted for more than 0.50% of the variance were used to search for candidate genes. Estimated heritabilities were 0.37, 0.34, 0.17, 0.12, 0.30 and 0.19, respectively, for 305‐day milk yield, peak yield, peak time, ramp, scale and decay for primiparous cows. Genetic correlations of 305‐day milk yield with peak yield, peak time, ramp, scale and decay in primiparous cows were 0.99, 0.63, 0.20, 0.97 and −0.52, respectively. The results identified three windows on BTA14 associated with 305‐day milk yield and the parameters of lactation curve in primi‐ and multiparous cows. Previously proposed candidate genes for milk yield supported by this work include GRINA, CYHR1, FOXH1, TONSL, PPP1R16A, ARHGAP39, MAF1, OPLAH and MROH1, whereas newly identified candidate genes are MIR2308, ZNF7, ZNF34, SLURP1, MAFA and KIFC2 (BTA14). The protein lipidation biological process term, which plays a key role in controlling protein localization and function, was identified as the most important term enriched by the identified genes.

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