Accounting for Intrapopulation Variability in Biogeochemical Models Using Agent-Based Methods

Abstract

Present biogeochemical models typically use a lumped-system (population-level) modeling (LSM) approach that assumes average properties of a population within a control volume. For modern models that formulate phytoplankton growth as a nonlinear function of the internal nutrient (e.g., Droop kinetics), this averaging assumption can introduce a significant error. Agent-based (individual-based) modeling (ABM) is an alternative approach that does not make the assumption of average properties. This paper presents a new agent-based phytoplankton model called iAlgae. The model is contrasted to a conventional lumped-system model, constructed based on identical underlying sub-models of nutrient uptake (including luxury uptake) and growth (cell quota, Droop model). The two models are validated against laboratory data and applied to a realistic scenario, consisting of a point source nutrient discharge into a river. For the realistic scenario, the ABM-predicted phytoplankton bloom is significantly lower than the LSM-predicted one, which is due to the intrapopulation distribution in cell quotas (due to different life histories of individuals) and nonlinearity of the growth rate model. In the ABM, a fraction of the population accumulates nutrients in excess of their immediate growth requirement (luxury uptake), leaving less for the remainder. Because the model is nonlinear, this results in a suboptimal (from a population perspective) utilization of nutrient and a lower population-level growth rate, compared to the case of no intrapopulation variability assumed by the LSM model. In general, the ABM and LSM approaches can produce significantly different results when incompletely mixed conditions lead to intrapopulation variability in cell properties (i.e., cell quota) and the model equations are nonlinear.