Exploring the performance of intransitivity indices in predicting coexistence in multispecies systems

Abstract Recent evidence suggests that intransitive competition (as in the game “rock‐paper‐scissors,” and in contrast to transitive or hierarchical competition) may be common in natural plant communities. This is important as theoretical analyses indicate that intransitivity promotes species coexistence. However, while intransitivity is common, competitive relationships among many species in communities may vary from transitive to highly intransitive. With increasing numbers of species, variation in competitive interrelationships among species can take on vastly more variable topologies. Consequently, several indices can be used to capture topological variation that is relevant to the prediction of species coexistence. Different indices capture different elements of topological variation. In addition, evidence indicates that these indices vary in their capacity to predict coexistence, and that variation not captured by these indices also contributes to variation in species coexistence. We used aspatial and spatial competition models to explore how well different indices (Slater's i , Kendall and Babington Smith's d , Monsuur and Storcken's ν, Bezembinder's ρ and Bezembinder's δ′, plus two binary indices we call “unbeatability” [ u ] and “always‐beatability” [ a ]) predict coexistence under the full spectrum of competitive tournament topologies for three to eight species, and a large sample of existing tournament topologies for nine species. All indices explored were generally better at predicting short‐term coexistence (i.e. the number of generations until the first extinction) compared to long‐term coexistence (i.e. generations until monoculture or long‐term species richness in aspatial and spatial models respectively). Indices also differed in performance: Kendall and Babington Smith's d (a measure of the number intransitive cycles among an assemblage's three‐species subsets that has also been reformulated as the relative intransitivity index) was the best predictor of short‐term coexistence; in terms of long‐term coexistence, the best predictor was typically d or u , the latter indicating the presence or absence of a species capable of outcompeting all its competitors. Synthesis . The indices employed here capture different elements of topological variation. Existing indices that capture aspects of intransitive competition vary in their capacity to predict coexistence in competition models. The more continuous nature of Kendall and Babington Smith's d index likely contributed to its robust performance; likewise, the ability of unbeatability to detect intransitivities involving the strongest competitors helps explain its success.

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