Smith David F
Division of Fisheries and Oceanography, C.S.I.R.O., 2230, Cronulla, N.S.W., Australia.
Oecologia. 1974 Jun;16(2):107-117. doi: 10.1007/BF00345576.
Although the linear relationships characterizing an ecosystem, e.g., nutrient fluxes and pathways of energy flow, may be obtained experimentally or known a priori, these alone are insufficient to yield a model which behaves realistically; the non-linear relationships between system variables must also be incorporated. However, even though a non-linear relationship between two system variables is suspected there exists no formal approach whereby one might experimentally verify the presence of such a non-linear relation, assess the magnitude of its influence, and formulate the relation in a functional notation suited to incorporation into the system model.In this paper it is shown that for those systems amenable to kinetic tracer incorporation experiments it is possible to estimate a parameter which quantitatively states the effect of a non-linear relationship between the two system variables.The approach requires that some one variable of the system is capable of being maintained at a constant value during the course of a tracer kinetic incorporation experiment; i.e., may be employed as an independent variable. A set of experiments is conducted in which a single component of the system is labelled and the time-varying radioactivities of the remaining system components are measured as are the component values themselves. The experiments differ only in the value at which the independent system variable is maintained. From each experiment, one obtains a set of time-varying curves of component radioactivities which are resolved into sums of exponentials by a global fitting strategy. The component values and the exponents obtained in the set of experiments provide the data required to estimate the non-linear system parameter.To demonstrate the validity of this approach tracer kinetic experiments were simulated for two different cases. The models employed in each of the simulated cases were identical in all respects but one. In one case the model system contained a non-linear relationship in the form of a negative feedback loop. In the other case, the model lacked this non-linearity.The proposed analysis was applied to both cases and yielded the parameter values consistent with each case. Thus the analysis is capable of demonstrating the absence of a non-linear relationship presumed to exist between system components.
尽管表征生态系统的线性关系，例如养分通量和能量流动途径，可以通过实验获得或事先已知，但仅这些不足以产生一个行为逼真的模型；系统变量之间的非线性关系也必须纳入其中。然而，即使怀疑两个系统变量之间存在非线性关系，也不存在一种正式方法可以通过实验验证这种非线性关系的存在、评估其影响程度，并以适合纳入系统模型的函数形式来表述这种关系。本文表明，对于那些适合进行动力学示踪剂掺入实验的系统，有可能估计一个参数，该参数定量地表明两个系统变量之间非线性关系的影响。该方法要求在示踪剂动力学掺入实验过程中，系统的某个变量能够保持恒定值；即可以用作自变量。进行一组实验，其中系统的单个组分被标记，并测量其余系统组分随时间变化的放射性以及组分值本身。这些实验仅在保持独立系统变量的值方面有所不同。从每个实验中，可获得一组组分放射性随时间变化的曲线，通过全局拟合策略将其分解为指数之和。在这组实验中获得的组分值和指数提供了估计非线性系统参数所需的数据。为了证明这种方法的有效性，对两种不同情况进行了示踪剂动力学实验模拟。在每个模拟案例中使用的模型在所有方面都相同，只有一点不同。在一种情况下，模型系统包含一个以负反馈回路形式存在的非线性关系。在另一种情况下，模型缺乏这种非线性。将所提出的分析应用于这两种情况，得到了与每种情况一致的参数值。因此，该分析能够证明假定存在于系统组分之间的非线性关系不存在。
