Department of Ecology and Evolution, Stony Brook University, 650 Life Sciences Building, Stony Brook, New York, 11794, USA.
Ecology. 2017 Jul;98(7):1764-1770. doi: 10.1002/ecy.1877. Epub 2017 Jun 14.
Analyses of point process patterns and related techniques (e.g., MaxEnt) make use of the expected number of occurrences per unit area and second-order statistics based on the distance between occurrences. Ecologists working with point process data often assume that points exist on a two-dimensional x-y plane or within a three-dimensional volume, when in fact many observed point patterns are generated on a two-dimensional surface existing within three-dimensional space. For many surfaces, however, such as the topography of landscapes, the projection from the surface to the x-y plane preserves neither area nor distance. As such, when these point patterns are implicitly projected to and analyzed in the x-y plane, our expectations of the point pattern's statistical properties may not be met. When used in hypothesis testing, we find that the failure to account for the topography of the generating surface may bias statistical tests that incorrectly identify clustering and, furthermore, may bias coefficients in inhomogeneous point process models that incorporate slope as a covariate. We demonstrate the circumstances under which this bias is significant, and present simple methods that allow point processes to be simulated with corrections for topography. These point patterns can then be used to generate "topographically corrected" null models against which observed point processes can be compared.
点过程模式及其相关技术（例如，最大熵）的分析利用了单位面积上的预期发生次数和基于发生之间距离的二阶统计量。研究点过程数据的生态学家通常假设点存在于二维 x-y 平面或三维体积内，但实际上许多观察到的点模式是在三维空间内的二维表面上生成的。然而，对于许多表面，例如景观的地形，从表面到 x-y 平面的投影既不保留面积也不保留距离。因此，当这些点模式被隐含地投影到 x-y 平面并在其中进行分析时，我们对点模式统计性质的期望可能无法得到满足。在假设检验中，我们发现，如果不考虑生成表面的地形，可能会使统计检验产生偏差，从而错误地识别聚类，并且，可能会使包含坡度作为协变量的非均匀点过程模型中的系数产生偏差。我们演示了这种偏差显著的情况，并提出了简单的方法，允许对点过程进行模拟，以纠正地形的影响。然后，可以使用这些点模式生成“地形校正”的零模型，以与观察到的点过程进行比较。
