When can we trust our model predictions? Unearthing structural sensitivity in biological systems

Abstract

It is well recognized that models in the life sciences can be sensitive to small variations in their model functions, a phenomenon known as 'structural sensitivity'. Conventionally, modellers test for sensitivity by varying parameters for a specific formulation of the model functions, but models can show structural sensitivity to the choice of functional representations used: a particularly concerning problem when system processes are too complex, or insufficiently understood, to theoretically justify specific parameterizations. Here we propose a rigorous test for the detection of structural sensitivity in a system with respect to the local stability of equilibria, the main idea being to project infinite dimensional function space onto a finite dimensional space by considering the local properties of the model functions. As an illustrative example, we use our test to demonstrate structural sensitivity in the seminal Rosenzweig-MacArthur predator-prey model, and show that the conventional parameterbased approach can fail to do so. We also consider some implications that structural sensitivity has for ecological modelling: we argue that when the model exhibits structural sensitivity but experimental results remain consistent it may indicate that there is a problem with the model construction, and that in some cases trying to find an 'optimal' parameterization of a model function may simply be impossible when the model exhibits structural sensitivity. Finally, we suggest that the phenomenon of structural sensitivity in biological models may help explain the irregular oscillations often observed in real ecosystems.

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

“…However, specific biological mechanisms and factors resulting in long living transients in various models using different mathematical frameworks often remain obscure (Hastings, 2004). Similarly, it remains unclear how model parameterization can affect its property to exhibit long-living transients as many widely used population dynamics models appear to be structurally unstable with regard to a small change in the constituent model functions (Fussmann and Blasius, 2005;Adamson and Morozov, 2013). In this paper our goal is to show that long-living transients mimicking complex dynamics are likely to be a common property of a conceptual, baseline single species population dynamics model.…”

Fast Sampling of Evolving Systems with Periodic Trajectories

“…This approach to predictive modelling is similar to the ideas of structural sensitivity/insensitivity considered in [2].…”

Towards developing a general framework for modelling vertical migration in zooplankton

“…For simplicity, we consider just two first leading terms A and B 1 . In the case where we can assume that all possible values of these generalized parameters belong to some rectangular domain Ω.…”

“…Having a large number of independent 'degrees of freedom' in the space of strategies, on the other hand might generally be a shortcoming for adaptation to changes in the environment since it makes such adaptation less robust to eventual errors which can be amplified due to the phenomenon known as structural sensitivity [7,1].…”