Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA.
Proc Natl Acad Sci U S A. 2010 Jul 20;107(29):12777-81. doi: 10.1073/pnas.1008257107. Epub 2010 Jul 6.
A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population dynamics and genetics, where it originated. Here we demonstrate that the GFE can also be useful in other fields, specifically in chemistry, with models of two chemical reaction systems for which the mechanisms and rate coefficients correspond reasonably well to experiments. A bad fit of the GFE can be a sign of high levels of measurement noise; for low or moderate levels of noise, fulfillment of the GFE is not degraded. Hence, the GFE presents a noise threshold that may be used to test the validity of experimental measurements without requiring any additional information. In a different approach information about the system (model) is included in the calculations. In that case, the discrepancy with the GFE can be used as an optimization criterion for the determination of rate coefficients in a given reaction mechanism.
广义 Fisher 方程（GFE）将内禀增长率平均值的时间导数与其方差联系起来。GFE 是一个精确的数学结果，已被广泛应用于起源于种群动力学和遗传学领域。在这里，我们证明了 GFE 也可以在其他领域，特别是在化学中有用，我们对两个化学反应系统的模型进行了演示，这些模型的机制和速率系数与实验相当吻合。GFE 的拟合不佳可能是测量噪声水平高的标志；对于低或中等水平的噪声，GFE 的满足程度不会降低。因此，GFE 提出了一个噪声阈值，可用于在不要求任何其他信息的情况下测试实验测量的有效性。在另一种方法中，系统（模型）的信息包含在计算中。在这种情况下，与 GFE 的差异可以用作确定给定反应机制中速率系数的优化标准。
