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ABSTRACT Past work has shown that group formation in foraging animals aids in resource acquisition and reduces the number of interactions with predators. However, group formation can also increase competition for resources among group members. Here, we model how the individual costs and benefits of group formation drive group size. Our model predicts that when competition for resources occurs within and between groups, forager group size will exhibit a one‐third power‐law relationship with population abundance. However, if groups form due to intragroup competition and predation, we predict either a one‐half power‐law relationship with population abundance or a constant group size depending on the coupling between predator and prey. Using empirical data on group foraging birds and ungulates, we found a scaling relationship consistent with the one‐third power‐law, suggesting that hierarchical competition drives the average group size. Our results support work highlighting the importance of density‐dependent group formation in maintaining population stability. 

Understanding how populations respond to increasingly variable conditions is a major objective for natural resource managers forecasting extinction risk. The lesson from current modelling is clear: increasing environmental variability increases population abundance variability. We show that this paradigm fails to describe a broad class of empirically observed dynamics, namely endogenously driven population cycles. In contrast to the dominant paradigm, these populations can exhibit reduced long-run population variance under increasing environmental variability. We provide evidence for a mechanistic explanation of this phenomenon that relies on how stochasticity interacts with long transient dynamics present in the deterministic cycling model. This interaction stands in contrast to the often assumed additivity of stochastic and deterministic drivers of population fluctuations. We show evidence for the phenomenon in two cyclical populations: flour beetles and Canadian lynx. We quantify the impact of the phenomenon with new theory that partitions the effects of nonlinear dynamics and stochastic variation on dynamical systems. In both empirical examples, the partitioning shows that the interaction between deterministic and stochastic dynamics reduces the variance in population size. Our results highlight that previous predictions about extinction under environmental variability may prove inadequate to understand the effects of climate change in some populations.