Top-down origins of the predator-prey power law?

Abstract

The ratio of predator-to-prey biomass density is not constant along ecological gradients: denser ecosystems tend to have fewer predators per prey, following a scaling relation known as the "predator-prey power law". The origin of this surprisingly general pattern, particularly its connection with environmental factors and predator-prey dynamics, is unknown. Here, we explore some ways that a sublinear predator-prey scaling could emerge from density-dependent interactions among predators and between predators and prey (which we call a top-down origin), rather than among prey (bottom-up origin) as proposed in Hatton et al. (2015). We combine two complementary theoretical approaches. First, we use phenomenological differential equations to explore the role of environmental parameters and dynamical properties in controlling the predator-prey ratio. Second, we simulate an agent-based model with tunable predator self-regulation to investigate the emergence of predator-prey scaling from plausible microscopic rules. While we cannot rule out alternative explanations, our results show that density-dependent mechanisms relative to predation and intraspecific predator interactions, including prey saturation, predator interference, and predator self-regulation, offer potential explanations for the predator-prey power law.