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 efficient approach to measure the extinction risk of an ecosystem as a whole is to quantify the phase synchrony among the co-habiting species populations. Generally, in models describing population dynamics of ecosystems, both trophic and non-trophic inter-species interactions are classified as two-species interactions. This approach contradicts the fact that several species living in close proximity 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 and their effect on phase synchronization of populations need to be investigated. In this study, we model a species-rich ecosystem as a multi-node complex ecological network and examine the phase dynamics of the total species 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 commensalist/mutualist (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. We investigate the effects of both higher-order coupling and asymmetry on the phase synchronization of the ecological network as a whole. Our findings demonstrate that higher-order interactions above a threshold amplitude result in a transition from synchronous to asynchronous dynamics of the ecosystem. Further, we find that increase in the size and diversity of the ecosystem lead to increased threshold higher order coupling required to reach asynchronous dynamics, though eventually it happens. We also demonstrate that the asynchrony in dynamics induced by higher-order interactions, is further promoted by high asymmetry among the individual nodes. Notably, negative inter-species interactions, if existing to a high degree also induce asynchrony in the system. However, the size of the network also plays a role in deciding the threshold value of higher order coupling required to induce asynchrony.