Data from: A new non-parametric method for analyzing replicated point patterns in ecology

Most ecological studies that involve point pattern analyses are based on a single plot, which prevent the separation of the effects of various processes that could act simultaneously, as well as limiting the conclusions that can be extracted from these studies. However, considering the spatial distribution of individuals in several plots as replicates of the same process could help to differentiate its specific effects from those of other confounding processes. Thus, we introduce a new method for analyzing spatial point patterns that are replicated according to a two-factorial design. By summarizing the spatial patterns as K-functions, the proposed method computes the average K-functions for each level of the two factors (i.e., predictors) and for each combination of levels, before estimating the sum of squared deviations from the overall mean K-function. Inferences of the strength of the relationship between the predictors, their interaction, and the spatial structure are made based on a non-parametric bootstrap procedure, which considers the dependency among spatial scales. We illustrate the proposed approach based on an analysis of the effects of altitude (with two levels: low and high) and slope (with two levels: flat and steep slopes) on the spatial pattern of Croton wagneri, a dominant shrub in an Andean dry scrubland. Our method detected a significant effect of the interaction between slope and altitude, which could not have been detected using current point pattern analysis methodology. The prevalence of single-plot analysis in ecological studies may be due to a lack of familiarity with appropriate methods for replicated point patterns, as well as the greater complexity of these methods and the absence of appropriate software. Our approach can be applied to a significant number of ecological questions while maintaining a simple, understandable, and easily reportable methodological framework.

绝大多数开展空间点格局分析（point pattern analyses）的生态学研究均基于单一样地，这不仅无法区分同时作用的多种生态过程的效应，还限制了此类研究可推导的结论范围。
然而，将多个样地中个体的空间分布视为同一生态过程的重复样方，将有助于区分该过程的特异性效应与其他混杂过程的效应。
据此，本文提出一种新的空间点格局分析方法，适用于按照双因素实验设计设置重复的空间点格局数据。
该方法将空间格局归纳为K函数（K-functions），先针对双因素的每个水平（即预测变量）以及各水平的所有组合计算平均K函数，随后估算其与整体平均K函数的平方偏差总和。
基于考虑空间尺度间相关性的非参数自助法（bootstrap），可对预测变量、其交互效应与空间结构间的关联强度开展统计推断。
本文以安第斯干旱灌丛优势灌木瓦格纳巴豆（Croton wagneri）的空间格局为研究对象，分析海拔（设置低、高两个水平）与坡度（设置平缓、陡峭两个水平）对其空间格局的影响，以此演示所提方法的应用。
本方法成功检测到坡度与海拔的交互效应，而现有空间点格局分析方法无法识别此类效应。
生态学研究中单一样地分析方法仍占主流，其原因可能在于研究者对适用于重复点格局数据的分析方法不够熟悉，同时此类方法复杂度更高且缺乏配套的专业软件。
本方法既可适配大量生态学研究问题，又具备逻辑简洁、易于理解且便于报告的方法论框架。