Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems

The worldwide loss of species diversity brings urgency to understanding how diverse ecosystems maintain stability. Whereas early ecological ideas and classic observations suggested that stability increases with diversity, ecological theory makes the opposite prediction, leading to the long-standing “diversity-stability debate. ” Here, we show that this puzzle can be resolved if growth scales as a sublinear power law with biomass (exponent <1), exhibiting a form of population self-regulation analogous to models of individual ontogeny. We show that competitive interactions among populations with sublinear growth do not lead to exclusion, as occurs with logistic growth, but instead promote stability at higher diversity. Our model realigns theory with classic observations and predicts large-scale macroecological patterns. However, it makes an unsettling prediction: Biodiversity loss may accelerate the destabilization of ecosystems. Editor’s summary Some of Earth’s most biodiverse ecosystems are also its most stable over time, yet ecological theory predicts that communities become less stable when more species co-occur. The most commonly used models of species coexistence are derived from the Lotka-Volterra model, which assumes that populations follow logistic growth patterns and that self-regulation is required to allow multiple species to stably coexist. Hatton et al. show that an alternative model with sublinear population growth provides nearly identical predictions to generalized Lotka-Volterra models at the population level but very different predictions for communities. Under the sublinear model, diversity promotes stability. This model is consistent with published population time series and macroecological scaling relationships. —Bianca Lopez Modeling population growth as sublinear instead of logistic predicts that ecological stability increases with diversity. INTRODUCTION The Earth’s tropical rainforests and coral reefs are a marvel of biodiversity and stability. For ecologists, however, they present a theoretical puzzle. Early ecologists believed species diversity to be a leading cause of ecological stability, which includes relative constancy in abundance and the ability to recover from disturbance. However, this view runs counter to classic theories and simple ecological models, such as the generalized Lotka-Volterra (GLV) model. The GLV model, along with Robert May’s seminal results from random matrix theory, implies that diversity should instead lead to instability. Many studies have since found factors that can extend stability to more diverse competitive communities, but theory has yet to demonstrate how diversity may be the cause of stability, producing a positive diversity-stability relationship. This disconnect between theory and observation, framed as the “diversity-stability debate,” casts doubt on ecological model predictions at a time when they are most critically needed. RATIONALE Although much theory has focused on the varied ways in which species interact with each other, we focus on the nature of population growth and the way in which a species interacts with itself. Many models, including GLV, assume that populations grow exponentially at low densities and saturate at high densities, following the logistic function. However, there is evidence from time-series analysis that many populations of mammals, birds, fish, and insects tend to follow a different trajectory, one in which the growth of populations increases with density raised to a power less than one. This “sublinear” dynamic is thus similar to the widely used Bertalanffy model of individual growth through ontogeny. Here, we contrast the competitive dynamics that result under both the logistic and sublinear growth models. We then confront sublinear model predictions with several macroecological patterns, as well as observations of community recovery from disturbance. RESULTS Although logistic and sublinear growth share similar features at the population level, they lead to opposing predictions at the community level. Whereas logistic growth of populations implies that diversity begets instability, we find that sublinear growth allows the emergence of a form of collective regulation of populations, leading to community coexistence. Furthermore, increases in diversity enhance, rather than weaken, the stability of community dynamics, reversing the classic diversity-stability relation. Our results, based on mathematical analysis and simulations, are robust to a wide range of alternative assumptions and generalized modeling frameworks. We also find that the sublinear model is consistent with several well-known macroecological patterns, recovering production-biomass scaling across ecosystems, as well as the species abundance distribution, mean-variance scaling, and size-density scaling. As such, the model allows links to be drawn among distinct patterns of abundance. Finally, unlike the GLV model, but consistent with the biodiversity-ecosystem functioning literature, our model predicts that losses in biodiversity will tend to destabilize communities and lengthen their recovery time after disturbance. CONCLUSION The alarming rate of diversity loss means that ecology is in urgent need of a theoretical framework capable of making realistic predictions. We propose that the sublinear model is a viable description of population and community dynamics, drawing an intriguing parallel with individual growth dynamics. Population time series indicate that sublinear growth appears to be a more accurate model of population dynamics than the widely used logistic function. This small difference in the form of population growth allows collective regulation, reversing the theoretical diversity-stability relation predicted by decades of competition theory. Sublinear growth implies a positive diversity-stability relation, suggesting that diversity may be, in part, the cause of stability. Our results help to clarify the origin of the diversity-stability paradox, including the implicit assumptions in May’s argument. Moreover, sublinear growth recovers common patterns of production, biomass, and abundance, offering a simple and general predictive framework. Although we still lack an understanding of the mechanistic origin of sublinear growth, our model is consistent with early ecological wisdom, modern macroecology, and what is known about some of Earth’s most cherished ecosystems. From tropical rainforests to coral reefs, some of Earth’s most diverse ecosystems are also the most stable. This staggering diversity stands in opposition to ecological theory, which for decades has predicted that diversity begets instability. We show that a small difference in how population growth is formulated can reverse these classic predictions and match theory with observation. [Photos: Rhett Butler and MPI MiS]