Fitting functional responses: Direct parameter estimation by simulating differential equations

Abstract

O_LIThe feeding functional response is one of the most widespread mathematical frameworks in Ecology, Marine Biology, Freshwater Biology, Microbiology and related scientific fields describing the resource-dependent uptake of a consumer. Since the exact knowledge of its parameters is crucial in order to predict, for example, the efficiency of biocontrol agents, population dynamics, food web structure and subsequently biodiversity, a trustful parameter estimation is of utmost importance for scientists using this framework. Classical approaches for estimating functional response parameters lack flexibility and can often only serve as approximation for a correct parameter estimation. Moreover, they do not allow to incorporate side effects such as resource growth or background mortality. Both call for a new method to be established solving these problems.\nC_LIO_LIHere, we combined ordinary differential equation models (ODE models), that were numerically solved using computer simulations, with an iterative maximum likelihood fitting approach. We compared our method to classical approaches of fitting functional responses, using data both with and without additional resource growth and mortality.\nC_LIO_LIWe found that for classical functional response models, like the often used type II and type III functional response, the established fitting methods are reliable. However, using more complex and flexible functional responses, our new established method outperforms the traditional methods. Additionally, only our method allows to analyze experiments correctly when resources experience growth or background mortality.\nC_LIO_LIOur method will enable researchers from different scientific fields that are measuring functional responses to estimate parameters correctly. These estimates will enable community ecologists to parameterize their models more precisely, allowing for a deeper understanding of complex ecological systems, and will increase the quality of ecological prediction models.\nC_LI