Mathematical comparison and empirical review of the Monod and Droop forms for resource-based population dynamics

Almost all biological models use either the Droop or Monod form to describe the resource-basedgrowth of a living organism. Empirical evidence overwhelmingly suggests the Droop form describesdata more accurately than the Monod form, however, the Monod form is more popular due to itssimplicity. Focusing on phytoplankton, we illustrate the underlying logics behind these two formsvia conceptual comparison, experimental data validation, transient and asymptotic dynamics. Theconceptual illustration provides the primary difference in their mechanisms via a paradox. Datavalidation is tested via field and laboratory experiments. The Droop and Monod forms haveconsistent asymptotic dynamics in closed nutrient, whereas the transient dynamics are significantlydifferent when the nutrient update rate is small. In addition, we decipher Michael Droop's privatelast statements on unifying the Droop and Monod forms as well as simplifying the Droop form.This article aims to guide future model development with any resource-based growth.