Insights of Global Sensitivity Analysis in Biological Models with Dependent Parameters

Abstract

Global sensitivity analysis (GSA) has become an important tool in the modeling process of biological phenomenon to determine how the uncertainty of model inputs influences the model response. Usually, GSA methods assume the independence of input distributions and several heuristics for model design were defined to improve models’ design and parametrization (Cariboni et al. in Ecol Model, 203(1–2):167–182, 2007). However, recent developments of GSA with dependent inputs suggest reconsidering them from another perspective. In particular, Sobol’s indices were generalized to dependent inputs by explicitly dissociating structural and correlation influence on model outputs (Li et al. in J Phys Chem A, 114(19):6022–6032, 2010). This study considers the prey–predator model, Lotka–Volterra, and the individual plant growth model, Sunflo, to illustrate these new indices and aims to confront them to usual heuristics. The introduction of parameters’ dependence was managed with copulas’ theory, and generalized Sobol’s indices were estimated with the hierarchically orthogonal Gram–Schmidt procedure (Chastaing et al. in J Stat Comput Simul, 85(7):1306–1333, 2015). Strong changes were observed due to the introduction of parameters’ dependence, but classical heuristics remain consistent in the generalized framework. Although additional studies are essential to define more precisely these new heuristics, generalized Sobol’s indices are a promising statistical tool for deepening the understanding of biological model behavior. Supplementary materials accompanying this paper appear online.