Reese G R, Reese A A, Mathison G W, Okine E K, McDonald A D
Department of Animal Science, University of Alberta, Edmonton, Canada.
J Anim Sci. 1995 Jan;73(1):177-90. doi: 10.2527/1995.731177x.
The Poisson process, the simplest stochastic flow process, was used to develop a multicompartment model of ruminant digesta flow with Gamma distributed retention times. Although mathematically the model is a generalization of many previously published models, the physiological model differs substantially in asserting that the distributed delay time and the exponential rate (scale) parameters, including the scale parameter of the Gamma distribution, are determined by total digesta flow, and thus invariant with respect to the fraction marked. The shape factor of the Gamma distribution is shown to be sufficient to explain the difference between markers in rate of marker excretion. Consequently, the parameters of multiple markers can be simultaneously estimated with the constraint that the exponential scale parameters and the delay time are invariant with respect to marker. This constraint leads to a measure of pure error to strengthen statistical tests for model rejection. Steady-state digesta retention time is estimated from the transient marker retention parameters, eliminating the necessity of speculating on what fraction of digesta the marked fraction represents. Tests of various models, using simulations and animal experiments indicate that, even if a model is correct, it is not possible to obtain reliable parameter estimates by fitting to a single marker. Even with multiple markers some caution must be used in interpreting parameter estimates derived from least squares fitting.
泊松过程是最简单的随机流动过程，被用于建立一个具有伽马分布停留时间的反刍动物消化物流动的多隔室模型。尽管从数学角度来看，该模型是许多先前发表模型的推广，但该生理模型在断言分布延迟时间和指数速率（尺度）参数（包括伽马分布的尺度参数）由总消化物流量决定，因此相对于标记部分是不变的这一点上有很大不同。伽马分布的形状因子被证明足以解释标记物排泄速率中标记物之间的差异。因此，多个标记物的参数可以在指数尺度参数和延迟时间相对于标记物不变的约束下同时估计。这种约束导致了一种纯误差度量，以加强对模型拒绝的统计检验。稳态消化物停留时间由瞬态标记物保留参数估计得出，从而消除了推测标记部分占消化物的比例的必要性。使用模拟和动物实验对各种模型进行的测试表明，即使模型正确，通过拟合单个标记物也不可能获得可靠的参数估计。即使使用多个标记物，在解释从最小二乘拟合得出的参数估计时也必须谨慎。
