Mathematical Modeling of Lactation Curves: A Review of Parametric Models
Mathematical Modeling of Lactation Curves: A Review of Parametric Models
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哺乳曲线的数学建模：参数模型回顾
DOI：
10.5772/intechopen.90253
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
N. M’Hamdi
中科院分区：
文献类型：
--
作者：
M. Bouallegue;N. M’Hamdi
牛奶产量随时间变化的数学表示是数学建模在农业中最成功的应用之一。模型提供了总结信息，这是有用的管理和育种决策。已经提出了几种经验数学函数来描述奶牛的泌乳曲线，这些函数在数学性质、参数的数量以及它们与典型泌乳模式的主要特征（如峰值产量、峰值时间和持续时间）的关系程度上不同。本文综述了用于奶牛泌乳曲线拟合的参数模型。参数模型是那些发现大量应用于拟合泌乳曲线的模型，主要是由于它们有限的数学复杂性，以及它们拟合大量曲线的能力。描述泌乳曲线的模型分为两大类：线性模型和非线性模型。非线性参数函数代表了建模泌乳曲线的首选工具，其主要目的是预测产量和描述曲线形状的参数，以及重要参数，如峰值产量和持久性。非线性模型需要迭代技术来求解。在非线性回归模型中经常使用的不同迭代方法是马夸特、牛顿、高斯和杜德。Wood模型是目前应用最广泛的参数化模型，其应用最广的一点是能直观、方便地了解模型参数与泌乳模式主曲率之间的关系。
The mathematical representation of milk production against time represents one of the most successful applications of mathematical modeling in agriculture. Models provide summary information, which is useful in making management and breeding decisions. Several empirical mathematical functions have been proposed to describe the lactation curve of dairy cattle differing in mathematical properties, in the number of parameters and in their degree of relationships with the main features of a typical lactation pattern, such as peak yield, time at peak and persistency. This review gives an overview of the parametric models used to fit of lactation curves in dairy cattle. Parametric models are those that found large application to fit the lactation curves, basically due to their limited mathematical complexity, and their abilities to fit a large kind of curves. Models to describe the lactation curve have been classified into two main groups: linear and nonlinear models. Nonlinear parametric functions have represented the preferred tools for modeling lactation curves with the main aim of predicting yields and parameters describing the shape of the curve in addition to important parameters such as peak yield and persistency. Nonlinear models need iterative techniques to be solved. Different iterative methods frequently employed in nonlinear regression models are Marquardt, Newton, Gauss and Dud. Wood model was the most popular parametric model with the largest application can be found in the immediate and easy understanding of relationships between its parameters and main curvatures of the lactation pattern.