Theoretical and experimental research studies have shown that ecosystems governed by nontransitive competition networks tend to maintain high levels of biodiversity. The theoretical body of work, however, has mainly focused on competition networks in which the outcomes of competition events are predetermined and hence deterministic, and where all species are identical up to their competitive relationships, an assumption that may limit the applicability of theoretical results to real-life situations. In this paper, we aim to probe the robustness of the link between biodiversity and non-transitive competition by introducing a three-dimensional winning probability parameter space, making the outcomes of competition events in a three-species in silico ecosystem uncertain. While two degenerate points in this parameter space have been the subject of previous studies, we investigate the remaining settings, which equip the species with distinct competitive abilities. We find that the impact of this modification depends on the spatial dimension of the system. When the system is well mixed, it collapses to monoculture, as is also the case in the non-transitive deterministic setting. In one dimension, chaotic patterns emerge, which tend to maintain biodiversity, and a power law relates the time that species manage to coexist to the degree of uncertainty regarding competition event outcomes. In two dimensions, the formation of spiral wave patterns ensures that biodiversity is maintained for moderate degrees of uncertainty, while considerable deviations from the non-transitive deterministic setting have strong negative effects on species coexistence. It can hence be concluded that non-transitive competition can still produce coexistence when the assumption of deterministic competition is abandoned. When the system collapses to monoculture, one observes a "survival of the strongest" law, as the species that has the highest probability of defeating its competitors has the best odds to become the sole survivor. Published by AIP Publishing. https://doi.org/10.1063/1.5046795One of the main enigmas in ecology concerns biodiversity is: How do species manage to coexist? The intricate structures found in ecological interaction networks, i.e., graphs summarizing competitive, mutualistic, predatory, or parasitic relationships among species, have been pinpointed as a possible answer to the biodiversity conundrum, as they allow for the coexistence of a large variety of species. In particular, the merits of cyclic competition as a mechanism supporting coexistence have been studied extensively from a theoretical and experimental point of view. Species constituting a community governed by such a cyclic competition network compete with each other much like rock, paper, and scissors do in the popular children's game. Theoretical research has shown that this behavior results in the formation of spatial patterns, which allows all species to coexist. These findings, however, are based on the assumption that the outcome of a competition event is p...
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