Modeling Extended Lactation Curves of Dairy Cattle: A Biological Basis for the Multiphasic Approach

Abstract

Objectives of this study are to describe the biological basis for multiphasic milk production and to propose a new empirical model for the lactation curve. To illustrate this model, we used data on 3573 first-lactation Holsteins having lactations of various lengths (285, 345, 405, 465, and 525 d) and with various days open (45, 105, 165, 225, and 285 d).The model describes an increasing first phase of milk yield and a series of decreasing phases of yield. The increasing phase, described by an increasing logistic function of time, is associated with increase in number of active mammary gland cells and increase in yield per cell. The decreasing phases, described by three decreasing logistic functions of time, are associated with decreases in cell number due to apoptosis and in yield per cell due to pregnancy. The new model isyDIM=a11+e−(DIM−c1)/b1−p2a11+(0.5e−(DIM−cmax2)/b2)2−p3a11+e−(DIM−c3)/b3−p4a1(1+0.5e−(DIM−cmax4)/b4)2,where yDIM is milk yield at each day in milk (DIM), a1 is upper level for the increasing first phase, and p2, p3, and p4 = (1−p2−p3) are proportions of a1 for the decreasing second, third, and fourth phases; b's are proportional to duration of each phase; and c's are time of maximum increase or decrease. Nonlinear regression was used to fit average milk yield for each of nine datasets, four with 180 d carried calf and five with 240 d carried calf.Average results indicated that for the first phase, upper level of milk yield was about 22kg. Duration was about 120 d, centered on time of maximum increase, which was about 11 d before calving. For the second phase (first phase of apoptosis), decrease in yield was relatively large (about 20%) and duration was relatively long (about 375 d). Time of maximum decrease was about 107 d after calving. For the third phase (pregnancy), decrease in yield was relatively small (about 6%) and duration was relatively short (about 200 d). Time of maximum decrease was about 300 d after calving. For each additional day open, time of maximum decrease increased about 1 d. For the fourth phase (second phase of apoptosis), decrease in yield was relatively large (about 74%) and duration was relatively long (about 765 d). Duration for the lactation length of 525 d was exceptionally long. Time of maximum decrease was about 382 d after calving. For each additional day of lactation, duration increased about 5.4 d and day of maximum decrease increased about 0.82 d.We believe that it is possible to model empirically standard and extended lactation curves of dairy cows, based on biological theory and predicated on the multiphasic approach. Further research to understand better the biology of extended lactations, using the proposed multiphasic model, should use planned extended lactations that are at least 525 d in milk and have at least 240 d carried calf.