Superadditive and subadditive dynamics are not inherent to the types of interacting threat

Species and ecosystems usually face more than one threat. The damage caused by these multiple threats can accumulate nonlinearly: either subadditively, when the joint damage of combined threats is less than the damages of both threats individually added together, or superadditively, when the joint damage is greater than the two individual damages added together. These additivity dynamics are commonly attributed to the nature of the threatening processes, but conflicting empirical observations challenge this assumption. Here, we use a theoretical model to demonstrate that the additivity of threats can change with different magnitudes of threat impacts (effect of a threat on the population parameter, like growth rate). We use a harvested single-species population model to integrate the effects of multiple threats on equilibrium abundance. Our results reveal that threats do not always display consistent additive behavior, even in simple systems. Instead, their additivity depends on the magnitudes of the impacts of two threats, and the population parameter that is impacted by each threat. In our model specifically, when multiple threats have a low impact on the growth rate of a population, they display superadditive dynamics. In contrast, threats that impact the species' carrying capacity are always additive or subadditive. These dynamics can be understood by reference to the curvature of the relationship between a given population parameter (e.g., growth) and equilibrium population size. Our results suggest that management actions can achieve amplified benefits if they target low-amplitude threats that affect the growth rate, since these will be in a superadditive phase. More generally, our results suggest that cumulative impact theory should focus more than previously on the magnitude of the impact on the population parameter, and should be cautious about attributing additive dynamics to particular threat combinations.