Data from: Cyclic population dynamics and density-dependent intransitivity as pathways to coexistence between co-occurring annual plants

1. Recent studies have brought renewed attention to the importance of complex species interactions - notably intransitive interactions - to patterns of plant community diversity. One underappreciated avenue through which intransitivity can occur is through cyclic population dynamics. Though such cyclic intransitive relationships have been extensively studied in predator-prey systems, evidence of their importance in competitive communities, notably plant communities, is more limited. Most studies of coexistence in plant communities assume fixed-point coexistence even while utilizing models that allow for cyclic population dynamics. 2. In this paper, we explore the potential for density-dependent, cyclic population dynamics and intransitivity in a model for annual plants. We then examine how these density-dependent cycles impact mutual invasibility and ultimately stable coexistence between plant species pairs. We do this using data collected from four co-occurring annual plant species living in natural wildflower communities in SW Western Australia. To maximize the number of biologically plausible pathways by which coexistence mediated by density-dependent cyclic intransitivity can occur, we use an annual plant model that allows for competitive direct interactions, facilitative direct interactions, and higher-order interactions between species. 3. Results from our empirically-parameterized model suggest that monocultures of all four focal species can have cyclic solutions with periodicity greater than 1 under sunny ("open") or shaded field conditions. Cyclic patterns drive variation in annual abundance patterns, with stable solutions for persistent monocultures and invasibility potential (the capacity of one population to invade another) common. Mutual invasibility in the face of cyclic population dynamics was found for just one of six species pairs, only under open environmental conditions. Our results illustrate the potential for cyclic intransitivity to both drive and prevent stable coexistence in environmentally heterogeneous biological communities. 4. Synthesis. We provide analytical and empirical evidence that coexistence in competitive communities (annual plants) can be achieved under non-equilibrium circumstances, through density-dependent cyclic intransitivity. Our results suggest that cyclic population dynamics may be common and important for coexistence dynamics in some types of communities. In such communities, the exploration of stable coexistence should therefore include consideration of cyclic as well as fixed-point equilibria for maximal accuracy.