Inferring competitive outcomes, ranks and intransitivity from empirical data: A comparison of different methods

The inference of pairwise competitive outcomes (PCO) and multispecies competitive ranks and intransitivity from empirical data is essential to evaluate how competition shapes plant communities. Three categories of methods, differing in theoretical background and data requirements, have been used: (a) theoretically sound coexistence theory‐based methods, (b) index‐based methods, and (c) ‘process‐from‐pattern’ methods. However, how they are related is largely unknown.
In this study, we explored the relations between the three categories by explicitly comparing three representatives of them: (a) relative fitness difference (RFD), (b) relative yield (RY), and (c) a reverse‐engineering approach (RE). Specifically, we first conducted theoretical analyses with Lotka–Volterra competition models to explore their theoretical linkages. Second, we used data from a long‐term field experiment and a short‐term greenhouse experiment with eight herbaceous perennials to validate the theoretical findings.
The theoretical analyses showed that RY or RE applied with equilibrium data indicated equivalent, or very similar, PCO respectively to RFD, but these relations became weaker or absent with data further from equilibrium. In line with this, both RY and RE converged with RFD in indicating PCO over time in the field experiment as the communities became closer to equilibrium. Moreover, the greenhouse PCO (far from equilibrium) were only similar to the field PCO of earlier rather than later years. Intransitivity was more challenging to infer because it could be reshuffled by even a small competitive shift among similar competitors. For example, the field intransitivity inferred by three methods differed greatly: no intransitivity was detected with RFD; intransitivity detected with RY and RE was poorly correlated, changed substantially over time (even after equilibrium) and failed to explain coexistence.
Our findings greatly help the comparison and generalization of studies using different methods. For future studies, if equilibrium data are available, one can infer PCO and multispecies competitive ranks with RY or RE. If not, one should apply RFD with density gradient or time‐series data. Equilibria could be evaluated with T tests or standard deviations. To reliably infer intransitivity, one needs high quality data for a given method to first accurately infer PCO, especially among similar competitors.

从经验数据中推断成对竞争结局（pairwise competitive outcomes, PCO）、多物种竞争等级与不可传递性，是解析竞争如何塑造植物群落的核心环节。当前已发展出三类基于不同理论背景与数据需求的研究方法：(a) 基于严谨共存理论的方法，(b) 基于指数的方法，以及(c) 「格局-过程」反推方法。但目前学界对这三类方法间的内在关联仍知之甚少。
本研究选取三类方法的典型代表——(a) 相对适合度差异（relative fitness difference, RFD）、(b) 相对产量（relative yield, RY）以及(c) 逆向工程方法（reverse‐engineering approach, RE），通过系统性对比三者以解析其内在关联。具体而言，研究首先借助洛特卡-沃尔泰拉竞争模型开展理论分析，以明确三类方法的理论关联；其次，依托包含8种多年生草本植物的长期野外实验与短期温室实验所获数据，对理论分析结果进行验证。
理论分析结果显示：当使用平衡态数据时，RY与RE分别得到的PCO与RFD结果等价或高度相似；但当数据偏离平衡态程度越高，这类关联便会逐渐减弱甚至消失。与此一致，野外实验中随着植物群落逐步趋近平衡态，RY与RE在推断PCO时的结果会逐渐与RFD趋于一致。此外，温室实验（群落远未达到平衡态）得到的PCO仅与野外实验早期年份的PCO相似，而非后期年份。不可传递性的推断则更具挑战性：即使相似物种间出现微小的竞争偏移，都可能改变不可传递性的格局。举例而言，三类方法推断得到的野外群落不可传递性结果差异显著：RFD未检测到任何不可传递性；RY与RE检测到的不可传递性相关性极低，且随时间（甚至在达到平衡后）发生剧烈变化，同时无法解释群落共存现象。
本研究结果可为采用不同方法的相关研究的对比与推广提供重要支撑。针对未来研究：若可获取平衡态数据，可通过RY或RE推断PCO与多物种竞争等级；若无法获取平衡态数据，则应结合密度梯度数据或时间序列数据使用RFD。群落是否达到平衡态可通过T检验或标准差进行评估。若要可靠推断不可传递性，则需针对所选用的方法获取高质量数据，以首先精准推断PCO，尤其是相似物种间的竞争结局。