Combining bifurcation and sensitivity analysis for ecological models

Abstract

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.