Recommendations for the Formulation of Grazing in Marine Biogeochemical
and Ecosystem Models
Anthony Richardson
Commonwealth Scientific and Industrial Research Organisation (CSIRO) Oceans and Atmosphere, BioSciences Precinct (QBP), St Lucia, Queensland, Australia, Commonwealth Scientific and Industrial Research Organisation (CSIRO) Oceans and Atmosphere, BioSciences Precinct (QBP), St Lucia, Queensland, Australia, Commonwealth Scientific and Industrial Research Organisation (CSIRO) Oceans and Atmosphere, BioSciences Precinct (QBP), St Lucia, Queensland, Australia
Author ProfileAbstract
For nearly a century, the functional response curves, which describe how
predation rates vary with prey density, have been a mainstay of
ecological modelling. While originally derived to describe terrestrial
interactions, they have been adopted to characterize aquatic systems in
marine biogeochemical, size-spectrum, and population models. However,
marine ecological modellers disagree over the qualitative shape of the
curve (e.g. Type II vs. III), whether its parameters should be
mechanistically or empirically defined (e.g. disk vs. Michaelis-Menten
scheme), and the most representative value of those parameters. As a
case study, we focus on marine biogeochemical models, providing a
comprehensive theoretical, empirical, and numerical road-map for
interpreting, formulating, and parameterizing the functional response
when used to prescribe zooplankton specific grazing rates on a single
prey source. After providing a detailed derivation of each of the
canonical functional response types explicitly for aquatic systems, we
review the literature describing their parameterization. Empirical
estimates of each parameter vary by over three orders of magnitude
across 10 orders of magnitude in zooplankton size. However, the strength
and direction of the allometric relationship between each parameter and
size differs depending on the range of sizes being considered. In
models, which must represent the mean state of different functional
groups, size spectra or in many cases the entire ocean’s zooplankton
population, the range of parameter values is smaller, but still varies
by two to three orders of magnitude. Next, we conduct a suite of 0-D NPZ
simulations to isolate the sensitivity of phytoplankton population size
and stability to the grazing formulation. We find that the disk
parameterizations scheme is much less sensitive to it parameterization
than the Michaelis-Menten scheme, and quantify the range of parameters
over which the Type II response, long known to have destabilizing
properties, introduces dynamic instabilities. Finally, we use a simple
theoretical model to show how the mean apparent functional response,
averaged across sufficient sub-grid scale heterogeneity diverges from
the local response. Collectively, we recommend using a type II disk
response for models with smaller scales and finer resolutions but
suggest that a type III Michaelis-Menten response may do a better job of
capturing the complexity of all processes being averaged across in
larger scale and coarser resolution modal, not just local consumption
and capture rates. While we focus specifically on the grazing
formulation in marine biogeochemical models, we believe these
recommendations are robust across a much broader range of ecosystem
models.