  The classic Rosenzweig-MacArthur predator-prey model has been shown to
exhibit, like other coupled nonlinear ordinary differential equations (ODEs)
from ecology, worrying sensitivity to model structure. This sensitivity
manifests as markedly different community dynamics arising from saturating
functional responses with nearly identical shapes but different mathematical
expressions. Using a stochastic differential equation (SDE) version of the
Rosenzweig-MacArthur model with the three functional responses considered by
Fussman & Blasius (2005), I show that such sensitivity seems to be solely a
property of ODEs or stochastic systems with weak noise. SDEs with strong
environmental noise have by contrast very similar fluctuations patterns,
irrespective of the mathematical formula used. Although eigenvalues of
linearised predator-prey models have been used as an argument for structural
sensitivity, they can also be an argument against structural sensitivity. While
the sign of the eigenvalues' real part is sensitive to model structure, its
magnitude and the presence of imaginary parts are not, which suggests
noise-driven oscillations for a broad range of carrying capacities. I then
discuss multiple ways to evaluate structural sensitivity in a stochastic
setting, for predator-prey or other ecological systems.
