Combining bifurcation and sensitivity analysis for ecological models: Model analysis, and the allegory of the cave

Plato’s well-known allegory of the cave describes an observer
chained in a cave facing a blank wall on which shadows are projected of
objects that are outside the cave. Only by breaking free from the chains
can the observer submerge from the cave to see what the objects really
look like. Ecological model features compare to the objects outside
the cave in this allegory. By performing model analysis light is shed
on these features, creating projections that researchers can see. Model
analysis methodologies like bifurcation analysis and sensitivity analysis
each focus on particular model features and thus allow researchers to
uncover only part of the model behaviour. By combining methodologies
for model analysis possibilities arise for unravelling more of the model’s
behaviour, allowing researchers to ‘break free’. In this paper benefits
and issues of combining model analysis methodologies are discussed
using a case study. The case study involves three representations of
the well-known Rosenzweig-MacArthur predator-prey model, namely
the usual one where state variables and parameters have dimensions, a
dimensionless representation, and a generalized representation. Based
on the results we argue that researchers should combine bifurcation and
sensitivity analysis methodologies when analyzing ecological models.