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 is unknown, as is its connection with how much it stems from environmental factors or predator-prey dynamics. Here we explore some of the ways sublinear predator-prey scaling could emerge from density-dependent interactions among predators (top-down) rather than among prey (bottom-up), 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 specific forms of predation and intra-specific predator interactions are potential mechanisms for the predator-prey power law.
