Modeling inverted biomass pyramids and refuges in ecosystems

Although the existence of robust inverted biomass pyramids (IBPs) seems paradoxical, they are well known to exist in planktonic communities, and have recently been discovered in pristine coral reefs and in a reef off the North Carolina coast. Understanding the underlying mechanisms which produce inverted biomass pyramids provides new ecological insights. Some ecologists hypothesize that "the high growth rate of prey and low death rate of predators" causes IBPs. However, we show this is not always the case (see Sections 3.1 and 4). We devise predator-prey models to describe three mechanisms that can lead to IBPs: (1) well-mixed populations with large prey turn-over rate, (2) well-mixed populations with prey immigration, and (3) non-mixed populations where the prey can hide in refuges. The three models are motivated by the three ecosystems where IBPs have been observed. We also devise three refuge mediated models, with explicit refuge size, which incorporate different prey responses in the refuge, and we discuss how these lead to IBPs.