Abstract
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 worse 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 provide a theoretical demonstration that the additivity of threats can change with different magnitudes of threat impacts. 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 two threats, and the population parameter that is impacted by each threat. In our model specifically, when multiple threats impact the growth rate of a population, they display superadditive dynamics at low magnitudes of threat impacts. In contrast, threats that impact the carrying capacity of the environment are always additive or subadditive. These dynamics can be understood by reference to the curvature of the relationship between a given parameter (e.g., growth) and equilibrium population size. Our results suggest that management actions can achieve amplified benefits if they target threats that affect the growth rate, and low-magnitude threats, since these will be in a superadditive phase. More generally, our results suggest that cumulative impact theory should focus on the magnitude of the impact on the population parameter, and should be cautious about attributing additive dynamics to particular threat combinations.
