Fitting functional responses: Direct parameter estimation by simulating differential equations

TY - JOUR

T1 - Fitting functional responses: Direct parameter estimation by simulating differential equations

AU - Rosenbaum, Benjamin

AU - Rall, Björn Chr.

N1 - 6543, AqE,TE; Data archiving: data archived in Dryad

PY - 2018

Y1 - 2018

N2 - 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.2 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.3. 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.4. 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.

AB - 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.2 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.3. 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.4. 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.

KW - international

U2 - 10.1111/2041-210X.13039

DO - 10.1111/2041-210X.13039

M3 - Article

SN - 2041-210X

VL - 9

SP - 2076

EP - 2090

JO - Methods in Ecology and Evolution

JF - Methods in Ecology and Evolution

IS - 10

ER -