1. 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.
2. 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.
3. 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.
4. 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.

中文翻译：

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从经验数据推断竞争结果，排名和不及物性：不同方法的比较

1. 从经验数据推断成对竞争结果（PCO）和多物种竞争排名和不及物性对于评估竞争如何塑造植物群落至关重要。已经使用了三类方法，它们在理论背景和数据要求上有所不同：（a）理论上合理的基于共存理论的方法，（b）基于索引的方法，以及（c）“从模式进行处理”的方法。但是，它们之间的关系在很大程度上是未知的。
2. 在这项研究中，我们通过明确比较三个类别的三个代表来探索三个类别之间的关系：（a）相对适应性差异（RFD），（b）相对产量（RY）和（c）逆向工程方法（RE） ）。具体来说，我们首先使用Lotka-Volterra竞争模型进行了理论分析，以探讨它们之间的理论联系。其次，我们使用来自八个野草多年生植物的长期田间试验和短期温室试验的数据来验证理论结果。
3. 理论分析表明，应用平衡数据的RY或RE分别表示与RFD等效或非常相似的PCO，但随着数据远离平衡，这些关系变得更弱或不存在。与此相符，随着群落变得更加接近平衡，在田间实验中，RY和RE均与RFD收敛，从而表明PCO随着时间的推移而变化。而且，温室PCO（远未达到平衡）仅与早年而非后期的田间PCO相似。不及物性的推论更具挑战性，因为即使在类似竞争者之间进行很小的竞争性转移，它也可能被改组。例如，通过三种方法推断出的场不及物性差异很大：RFD未检测到不及物性；用RY和RE检测到的不及物性相关性很差，
4. 我们的发现极大地帮助了使用不同方法进行研究的比较和归纳。对于将来的研究，如果可以获得平衡数据，则可以用RY或RE推断PCO和多物种竞争等级。如果不是，则应将RFD应用于密度梯度或时间序列数据。平衡可以通过T检验或标准偏差进行评估。为了可靠地推断出不传递性，人们需要一种高质量的数据才能首先准确地推断出PCO，尤其是在类似竞争对手中。