Superlinear intraspecific or sublinear interspecific interactions enhance species coexistence with a tipping point effect of population scale

Species coexistence is fundamental to the maintenance of biodiversity and the provision of ecosystem services in nature. The generalized Lotka–Volterra models (GLV) are widely used to study species coexistence, but they are insufficient to explain the observed relationship between diversity and stability in multi–species systems. Recently, density–dependent nonlinear species interactions have been shown to enhance community stability, but how sub–/super–linear interactions affect species coexistence remains underinvestigated. In this study, we analyzed the effects of sub– and super–linear interactions on the stability of species coexistence in 2–species models by modifying the conventional GLV models. Our results indicate that the stability condition for sub– and super–linear interaction models depends on the carrying capacity ( K ), interaction coefficient ( b ), and interaction power coefficient ( a ). In our model, superlinear ( a > 1 ) intraspecific or sublinear (0 < a < 1 ) interspecific interactions are generally beneficial to species coexistence with a much larger stability range than the conventional GLV models; hyperstability was observed in modified GLV mutualistic models. However, K has a tipping–point effect at K = 1, reversing the stability effect of a . Our studies highlight the significance of nonlinear interactions and the carrying capacity as tipping points in shaping species coexistence and community stability, and warrant further investigation, particularly by validating the models with empirical data.