Modeling fish biomass structure at near pristine coral reefs and degradation by fishing

Inverted biomass pyramids (IBPs) seem to be extremely rare in natural communities. Until recently, the only examples have been in freshwater and marine planktonic communities. In 2002 and 2008, investigators documented inverted biomass pyramids for nearly pristine coral reef ecosystems within the NW Hawaiian islands and the Line Islands, where apex predator abundance comprises up to 85% of the fish biomass. Large predator:prey biomass ratio seems to be a signature of nearly pristine coral reefs. While the mechanism responsible for the IBP for homogeneously mixed planktonic communities seems to be well understood, this mechanism is not strictly applicable to nearly pristine coral reefs where much of the prey use coral as refuge and are inaccessible to the predators. We construct a mathematical model with an explicit refuge to illustrate a new biologically plausible mechanism that can explain stable IBPs in nearly pristine coral reefs. New modeling components include a refuge of explicit size, a refuge size dependent functional response, and refuge size dependent prey growth rate. Utilizing realistic life history parameters of coral reef fishes, our model exhibits a stable inverted biomass pyramid. We prove that all fishing decreases the biomass ratio and sufficiently strong fishing transforms the inverted biomass pyramid to be bottom heavy. Finally we use our model to test the conjecture that pristine coral reefs will rebound faster from environmental shocks and find that it is not always true.