Abstract
A combined model of a lactation curve was conceived for evaluating meteorological effects on milk production. The model was written as follows: y=b0+ b(e-t/c-e-t/ac)+b1u1/2d3/2(Tb-Tn)+b2Dd, where y was the milk yield of t-th day after partum. The first term b0 was a constant minimized to zero. The second term was just the vibration model (HAYASHI et al., 1986) containing three lactation parameters a, b and c. The third term was heat-loss model which explained short-term variation in milk yield by heat transfer from cow body to air, where u in the third term was average wind velocity (m/sec) of t-th day, and d was the radius of an imaginary ball when the cow was considered to be a large ball of density 1.0 for simplification. It was proven that wind velocity was effective for heat transfer in the form of 1/2 power. Tb and Tn in the third term were the subject cow's body temperature and average air temperature of t-th day. Dd in the fourth term revealed a variable of milk yield depression for drying in terminal lactation.
In the combined model, b0, b, a, c, b1u and b2 were unknown. The iterative method was performed to estimate parameters a and c. Other parameters b0, b, b1u and b2 were estimated via the multiple regression method. Controlled data of sixty-five lactations were analyzed by fitting the combined model. Meteorological data for wind velocity and air temperature at all times were supported by AMeDAS: Automated Meteorological Data Acquisition System.
A comparison was made of the fitness for lactation data of the three models which were WOOD'S formula, the vibration model and the present combined model. The multiple correlations of the three models were ranked as combined model>vibration model>WOOD's formula. The slopes of partial regression coefficient b in the combined model were significant (P<0.01) in all cases. Also the slopes of b2 which was the coefficient of the term for drying off, were significant (P<0.01) in most cases. The slopes of coefficient b1u in heat-loss model were significant (P<0.01 or P<0.05)in many cases, although the slopes of b1u centering around the value of 0.038 were scattered in plus or minus ranges. A positive significant correlation between parameter a and average air temperature during lactation, and a negative significant correlation between parameter c and average air temperature were shown. The correlations between lactation parameters and average air temperature indicated that the shape of the lactation curve was affected by average air temperature. Ultimately, the rise in average air temperature induced the delay of milk-yield elevation in the early stages of lactation, and induced acceleration of the milk-yield depression after peak lactation.
