Desharnais Robert A, Costantino R F, Cushing J M, Henson Shandelle M, Dennis Brian, King Aaron A
Ecol Lett. 2006 May;9(5):537-47. doi: 10.1111/j.1461-0248.2006.00903.x.
A scaling rule of ecological theory, accepted but lacking experimental confirmation, is that the magnitude of fluctuations in population densities due to demographic stochasticity scales inversely with the square root of population numbers. This supposition is based on analyses of models exhibiting exponential growth or stable equilibria. Using two quantitative measures, we extend the scaling rule to situations in which population densities fluctuate due to nonlinear deterministic dynamics. These measures are applied to populations of the flour beetle Tribolium castaneum that display chaotic dynamics in both 20-g and 60-g habitats. Populations cultured in the larger habitat exhibit a clarification of the deterministic dynamics, which follows the inverse square root rule. Lattice effects, a deterministic phenomenon caused by the discrete nature of individuals, can cause deviations from the scaling rule when population numbers are small. The scaling rule is robust to the probability distribution used to model demographic variation among individuals.
生态理论的一个标度律虽被认可但缺乏实验验证，即由于人口统计学随机性导致的种群密度波动幅度与种群数量的平方根成反比。这一假设基于对呈现指数增长或稳定平衡的模型的分析。我们使用两种定量方法，将该标度律扩展到种群密度因非线性确定性动态而波动的情况。这些方法应用于在20克和60克栖息地均呈现混沌动态的赤拟谷盗种群。在较大栖息地培养的种群呈现出确定性动态的一种澄清，遵循平方根反比律。晶格效应是由个体的离散性质引起的一种确定性现象，当种群数量较小时，可能导致偏离标度律。标度律对于用于模拟个体间人口统计学变异的概率分布具有稳健性。
