State Key Laboratory of Grassland and Agro-Ecosystems, School of Life Science and of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People's Republic of China.
Proc Natl Acad Sci U S A. 2012 Sep 25;109(39):15823-8. doi: 10.1073/pnas.1210955109. Epub 2012 Aug 13.
We introduce a theoretical framework that predicts the optimum planting density and maximal yield for an annual crop plant. Two critical parameters determine the trajectory of plant growth and the optimal density, N(opt), where canopies of growing plants just come into contact, and competition: (i) maximal size at maturity, M(max), which differs among varieties due to artificial selection for different usable products; and (ii) intrinsic growth rate, g, which may vary with variety and environmental conditions. The model predicts (i) when planting density is less than N(opt), all plants of a crop mature at the same maximal size, M(max), and biomass yield per area increases linearly with density; and (ii) when planting density is greater than N(opt), size at maturity and yield decrease with -4/3 and -1/3 powers of density, respectively. Field data from China show that most annual crops, regardless of variety and life form, exhibit similar scaling relations, with maximal size at maturity, M(max), accounting for most of the variation in optimal density, maximal yield, and energy use per area. Crops provide elegantly simple empirical model systems to study basic processes that determine the performance of plants in agricultural and less managed ecosystems.
我们介绍了一个理论框架，用于预测一年生作物的最佳种植密度和最大产量。两个关键参数决定了植物生长的轨迹和最佳密度 N（opt），即生长中的树冠刚刚接触的地方，以及竞争：（i）成熟时的最大尺寸 M（max），由于人工选择不同的可用产品，不同品种之间存在差异；（ii）内在增长率 g，可能因品种和环境条件而异。该模型预测：（i）当种植密度小于 N（opt）时，作物的所有植物都在同一最大尺寸 M（max）下成熟，生物量产量随密度线性增加；（ii）当种植密度大于 N（opt）时，成熟时的尺寸和产量随密度的-4/3 和-1/3 次幂而降低。来自中国的田间数据表明，大多数一年生作物，无论品种和生活形式如何，都表现出相似的比例关系，最大成熟尺寸 M（max）占最佳密度、最大产量和单位面积能量利用的大部分变化。作物提供了优雅而简单的经验模型系统，可用于研究决定植物在农业和管理较少的生态系统中表现的基本过程。
