Evidence for conformal invariance of crop yields
Evidence for conformal invariance of crop yields
复制标题
作物产量保形不变性的证据
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
D. Clifford
中科院分区：
文献类型：
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作者：
P. McCullagh;D. Clifford
本文旨在研究农作物产量空间相关性的本质。重点主要是自然或非人为的空间变化，无法用地形、品种或处理效果或农业实践来解释的模式。共形不变性意味着平稳性和各向同性，也决定了空间相关性的衰减速率。由此产生的高斯模型进行了实证研究，看看它是否令人满意地描述了各种作物的田间试验中观察到的空间相关性的模式。通过将该定律嵌入到一个更大的统计模型中，即白色噪声与具有范围参数λ−1和平滑度参数ν的Matérn类的卷积，并通过收集足够范围和数量的数据，对模型预测进行了测试。25个作物产量的例子进行了研究，包括谷物，块根作物和其他蔬菜，坚果，柑橘和苜蓿产量。在典型的现场试验的规模，我们发现，非人为的变化是合理的接近各向同性。此外，我们发现一致的证据表明，范围参数往往是大的，平滑参数小。范围参数的大值证实了Fairfield Smith（Fairfield Smith 1938 J. Agric. Sci. 28，1-23），他发现农业过程中的空间相关性随着距离的增加而减少，但速度比指数慢。平滑度参数的小值意味着，根据Matérn标准，农业过程是粗糙的。对于所研究的每一个例子，极限模型与完整模型一样拟合数据，与保形模型的假设（λ，ν）=（0，0）在所有季节的所有作物的合理一致。
The aim of this paper is to study the nature of spatial correlation of yields of agricultural crops. The focus is primarily on natural or non-anthropogenic spatial variation, patterns that cannot be explained by topography, by variety or treatment effects, or by agricultural practices. Conformal invariance implies stationarity and isotropy, and also determines the rate of decay of spatial correlations. The resulting Gaussian model is studied empirically to see whether it describes satisfactorily the pattern of spatial correlations observed in field trials of various crops. By embedding the law in a larger statistical model, a convolution of white noise and the Matérn class having a range parameter λ−1 and a smoothness parameter ν, and by gathering data of sufficient range and quantity, the model predictions were tested. Twenty-five examples of crop yields are studied, including cereals, root crops and other vegetables, nut, citrus and alfalfa yields. At the scale of typical field trials, we find that non-anthropogenic variation is reasonably close to isotropic. Furthermore, we find consistent evidence that the range parameter tends to be large and the smoothness parameter small. The large value of the range parameter confirms Fairfield Smith (Fairfield Smith 1938 J. Agric. Sci. 28, 1–23), who found that spatial correlation in agricultural processes decreases with distance, but at a slower rate than exponential. The small value of the smoothness parameter means that, by Matérn standards, agricultural processes are rough. For each of the examples studied, the limiting model fits the data just as well as the full model, in reasonable agreement with the hypothesis of the conformal model that (λ, ν)=(0, 0) for all crops in all seasons.