最低限度议会法
Law of the Minimum Paradoxes
摘要：
“最小值法则”指出，增长是由最稀缺的资源（限制因素）控制的。这个概念最初应用于植物或作物生长（Justus von Liebig，1840），并得到许多实验的定量支持。提出了一些基于更复杂的“剂量-反应”曲线的推广。也有报告说，在自然和实验生态系统中违反了这一法律。我们研究了环境因素负荷下相似生物群的适应模型，并证明了违反李比希定律的适应效应。如果一个有机体在一个固定的环境中的适应性满足最小值定律，那么适应就平衡了基本因素的压力，因此违反了李比希定律。这就是最小值定律悖论：如果对于一个随机选择的“有机体-环境”对，最小值定律通常成立，那么，在一个适应良好的系统中，我们必须预期违反这一定律。对于相反的因素相互作用（一个相互放大的因素协同系统），适应导致从因素等效到较少因素的限制。为了分析适应，我们开发了一个系统的模型的基础上Selye的想法的通用适应资源（适应能源）。这些模型预测，在环境因素的负荷下，种群分为两组（阶段）：一组相关性较低，适应性较好，另一组相关性较高，属性差异较大，适应性较差。一些经验数据和跨学科的应用，计量经济学的证据进行了讨论。
英文摘要：
The "Law of the Minimum" states that growth is controlled by the scarcest resource (limiting factor). This concept was originally applied to plant or crop growth (Justus von Liebig, 1840) and quantitatively supported by many experiments. Some generalizations based on more complicated "dose-response" curves were proposed. Violations of this law in natural and experimental ecosystems were also reported. We study models of adaptation in ensembles of similar organisms under load of environmental factors and prove that violation of Liebig's law follows from adaptation effects. If the fitness of an organism in a fixed environment satisfies the Law of the Minimum then adaptation equalizes the pressure of essential factors and therefore acts against the Liebig's law. This is the the Law of the Minimum paradox: if for a randomly chosen pair "organism-environment" the Law of the Minimum typically holds, then, in a well-adapted system, we have to expect violations of this law. For the opposite interaction of factors (a synergistic system of factors which amplify each other) adaptation leads from factor equivalence to limitations by a smaller number of factors. For analysis of adaptation we develop a system of models based on Selye's idea of the universal adaptation resource (adaptation energy). These models predict that under the load of an environmental factor a population separates into two groups (phases): a less correlated, well adapted group and a highly correlated group with a larger variance of attributes, which experiences problems with adaptation. Some empirical data are presented and evidences of interdisciplinary applications to econometrics are discussed.
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