Fitting functional responses: Direct parameter estimation by simulating differential equations

Abstract

The 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 to predict, for example, the efficiency of biocontrol agents, population dynamics, food web structure, and subsequently biodiversity, a trustworthy parameter estimation method is highly important for scientists using this framework. Classical approaches for estimating functional response parameters lack flexibility and often only provide approximations of the correct parameters. Here, we combined ordinary differential equation (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. We found that for classical functional response models, such as the frequently used type II and type III functional responses, the established fitting methods are reliable. However, by using more complex and flexible functional responses, our new method outperforms the traditional methods. Additionally, our method allows the incorporation of side effects such as resource growth and background mortality. Our method will enable researchers from different scientific fields who are measuring functional responses to calculate more accurate parameter estimates. These estimates will enable community ecologists to parameterize their models more precisely, thus allowing a deeper understanding of complex ecological systems, and will increase the quality of ecological prediction models.

Consistent temperature dependence of functional response parameters and their use in predicting population abundance

“…To account for natural prey mortality, we numerically integrated prey decline in the predator-free controls over the experimental duration (t = 1 day), as per Rosenbaum and Rall (2018), using the following equation:…”

“…We used the R package odeintr to solve the ordinary differential equation for natural mortality, as described in Rosenbaum and Rall (2018). The point estimates for the free parameters in the model were obtained by maximum likelihood using the 'mle2' function with 'method = "L-BFGS-B"' from the R package bbmle.…”

Data paper: FoRAGE (Functional Responses from Around the Globe in all Ecosystems) database: a compilation of functional responses for consumers and parasitoids

“…To obtain parameter estimates and confidence intervals, we used the medians and 95% quantiles of the bootstrapped parameter distributions, respectively. We did not account for prey or predator population growth in the fitting procedure (Rosenbaum and Rall, 2018), although most experiments were conducted for periods precluding changes in prey or predator through reproduction.…”

Towards a mechanistic understanding of individual‐level functional responses: Invasive crayfish as model organisms

“…As basic functional response model, we used the Royama-Rogers random predator equation (Rogers, 1972;Royama, 1971) which is an extension of Holling's (1959b) disc equation (Equation 1) and accounts for prey depletion. For this model, we used the notation derived by Rosenbaum and Rall (2018):…”