Asynchronous population dynamics induced by higher-order and negative asymmetric ecological interactions

Phase synchronized population dynamics of various species constituting a complex ecosystem elevates the risk of their extinction due to both environmental stochasticity and simulateneous low density fluctuations. Therefore, an extremely vital approach to measure the extinction risk of an ecosystem as a whole is to quantify the phase synchrony among the species populations co-habiting and interacting with each other in an ecosystem. Generally, in models describing population dynamics of ecosystems, both trophic and non-trophic inter-species interactions are modelled as interactions between two species. This approach contradicts the fact with such a large number of species living in close proximity, more than two species must partake in the same interaction influencing the population dynamics of each other. To address this, higher-order interactions need to be incorporated in the models describing population dynamics of an ecosystem. Consequently, their effect on phase synchronization of populations also need to be investigated. In this study, we model a species-rich ecosystem as a complex phase oscillator network and examine the phase dynamics of the total population. Each node of this network represents a constituent species, modelled as a Sakugachi-Kuramoto phase oscillator coupled non-linearly to the other nodes through both first-order and higher-order inter-species interactions. These interactions can be both mutualistic (positive) and antagonistic (negative) in nature. Along with the higher-order interactions, we also incorporate inherent asymmetry among the nodes to account for habitat heterogeneity. Further, we investigate the effects of both higher-order coupling and asymmetry on the phase synchronization of the total population. Our findings demonstrate that higher-order interactions above a threshold amplitude enforces a transition from synchronous to asynchronous dynamics of the ecosystem. Further, we find that increase in the size and diversity of the ecosystem leads to an increase in the threshold value of higher order coupling required to reach asynchronous dynamics. We also demonstrate that this higher-order induced asynchrony is further promoted by high asymmetry among the individual nodes. Importantly, negative inter-species interactions, if existing to a high degree also induce asynchrony in the system. Moreover, the size of the network also plays a role in deciding the threshold value of higher order coupling required to induce asynchrony.