树木尺寸分布作为进化主方程的平稳极限
Tree size distribution as the stationary limit of an evolutionary master equation
AI总结：
本文通过分析中欧森林数据，提出一种进化主方程模型，其平稳解为Gamma分布，可描述树木尺寸分布，并仅用两个拟合参数，同时表明该统计可用于推断林地自然度。
摘要：
在温带成熟森林中，特定落叶树种直径分布可由Gamma分布良好近似。我们通过分析中欧成熟半自然林和古老传统管理的林地-牧场中的落叶树尺寸数据，为该猜想提供了新的实验证据。当树木尺寸按样本均值归一化时，这些分布函数坍缩为通用形状。我们采用一种新颖的进化主方程来模拟观测到的分布。该模型包含三个概率过程：树木生长、死亡和多样化。通过使用简单且现实的状态依赖核函数描述生长和重置速率，并假设多样化引起的乘性稀释，主方程的平稳解产生了实验观测到的Gamma分布。该模型在表述上允许解析紧凑解，且仅有两个拟合参数，其值与生长和重置过程的实验数据一致。我们的结果还表明，树木尺寸统计可用于推断林地自然度。
英文摘要：
The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data in mature semi-natural forest and ancient, traditionally managed wood-pasture from Central Europe. These distribution functions collapse on a universal shape if the tree sizes are normalized to the mean value in the considered sample. A novel evolutionary master equation is used to model the observed distribution. The model incorporates three probabilistic processes: tree growth, mortality and diversification. By using simple, and realistic state dependent kernel functions for the growth and reset rates together with an assumed multiplicative dilution due to diversification, the stationary solution of the master equation yields the experimentally observed Gamma distribution. The model as it is formulated allows analytically compact solution and has only two fitting parameters whose values are consistent with the experimental data for the growth and reset processes. Our results suggest also that tree size statistics can be used to infer woodland naturalness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
