Recommendations for the formulation of grazing in marine biogeochemical and ecosystem models

For nearly a century, functional reizes beingponse 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 considered. In models, which must represent the mean state of different functional groups, size spectra or in many cases the entire zooplankton community, 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 less sensitive to it's 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 models, 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 population and ecosystem models that use functional response curves.