Parameter redundancy in Type III functional response models with consumer interference

Abstract

The consumption rate is a process critically important for the stability of consumer-resource systems and the persistence, sustainability and biodiversity of complex food webs. Its mathematical description in the form of functional response equations is a key problem for describing all trophic interactions. Because some of the functional response models used in this study presented redundancy between its parameters two methods were used to check for parameter redundancy: the Hessian matrix calculation using automatic differentiation (AD) which calculates derivatives numerically, but does not use finite differences, and the symbolic method that calculates a derivative matrix and its rank. In this work, we found that the models that better describe the functional response of a rotifer is consumer dependant even at low consumer densities, but their parameters can not be estimated simultaneously because parameter redundancy. This means that fewer parameters or parameter combination can be estimated than the original number of parameters in the models. Here, the model parameters that incorporate intraspecific competition by interference in the consumer-resource interaction are not identifiable, suggesting that this problem may be more widespread than is generally appreciated in the literature of food webs. Including knowledge on competitive interactions in current model predictions will be a necessity in the next years for ecology as ecological models are getting more complex and more real. Identifiability of biological parameters in nonlinear ecological models will be an issue to consider.