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.