The main impetus to the development of empirical modeling of lactation did Wood (1967), who suggested using the gamma function: Using model (1.7), we can consider various special cases depending on changes in values of coefficients (ai, bi) and degrees ( m, n).įor example, when for the coefficients: and for the degrees: m=1 and n=2, then from equality (1.7) follows the inverse polynomial model proposed by Nelder (1966):įor other combinations of values m and n from equation (1.7) can be easily obtained empirical model by Bianchini (1984):Īnd a number of other models (Narushin and Takma, 2003). In an effort to improve on all models that existed at the time, in the 1960s it was proposed an empirical model described by rational functions in the following form: Unfortunately, this equation does not exactly conform to the actual data. This model seems to be the first attempt to develop a model that varies both directly and exponentially with time. The first attempt to formalize the lactation curve appears to belong solely to Vučić and Bačić (1961) who developed Gaines’ model into the following form: In 1958 Fisher proposed to improve the model (1.3) in the following form, by substituting the exponential decline built into this model with a linear decline: This was followed by a relatively complex model than (1.1) introduced by Sikka (1950): This time the model made provision for the initial rise to peak production by incorporating an inclining function into the model:Īlthough this was a great improvement on their first model, later researchers such as Cobby and Le Du (1978):įound on fitting this model to lactation data of cows, that it resulted in underestimation of milk yield in mid-lactation and overestimated milk yield in late lactation. To overcome this limitation, Brody, Turner and Ragsdale presented an improved version of their model in 1924. Wood attributes this model to Gaines, but work by Gaines in this field was only published in 1927, whereas Brody et al. This model resulted in a good attempt to describe the declining phase of lactation, it was unable to model the initial rise in production to peak yield. They used the following model for this purpose: The first attempt to develop a mathematical model to describe the lactation curve was launched by Brody, Ragsdale and Turner in 1923. In all the models described it is assumed that denotes daily milk yield t, denotes time in days after parturition, and, and denote model parameters. Historical Development of Empirical Models for Lactation Process All models can be conventionally divided into three groups depending on the method of their derivation: empirical (models that have been obtained after statistical processing of results from a large amount of experimental data logical(models based on intuitive ideas fundamental to lactation curve tracing) semi-empirical (based on the principles and methods of the theory of population growth). To date, more than twenty formulas have been offered. Many authors have devoted their works to the given issue. In this paper, we present both existing and proposed lactation models. #Using apsim model for predicting yields in us fullMost of the works devoted to the lactation curve modeling in full feeding conditions are empirical or semi-empirical. As a rule, gaining a better understanding of the lactation process at the quantitative level while so doing is not pursued as a goal. Attempts at a mathematical description of this curve often endeavor to predict milk yields, dietary requirements and cash flow. Changes in daily milk yield are determined by changes in the number and activity of the cells of the mammary glands. Then follows a gradual decline up until the cow’s milk stasis in ten months after calving with a dry period of 45 days. The lactation curve for a dairy cow increases rapidly from calving until its peak. The regularity of these changes is reflected in the lactation curve. The potential milk yield of a cow during the lactation period continuously changes according to the change in its physiological state. The breeding of dairy cattle is an important component of agricultural production having a significant impact on its economic efficiency.
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