Mathematical Modeling and Analysis of a Phytoplankton Competition Model Incorporating Preferential Nutrient Uptake

Abstract

Phytoplankton live in a complex environment with two essential resources forming various gradients. Light supplied from above is never homogeneously distributed in a body of water due to refraction and absorption from biomass present in the ecosystem and from other sources. Nutrients in turn are typically supplied from below. In poorly mixed water columns, phytoplankton can be heterogeneously distributed forming various layering patterns. We present a new reaction-diffusion-taxis model describing the vertical distribution of two phytoplankton species competing for two nutrients, one of which is assumed to be preferred. The parameter space of the model is analyzed for parameter identifiability - the ability for a parameter's true value to be recovered through optimization, and for global sensitivity - the influence a parameter has on model response. Using simulations, we exhibit evidence of thin layer formation for motile phytoplankton in poorly mixed environments. A game theoretic approximation is considered, where the depth of the phytoplankton layer is treated as the strategy the phytoplankton adopt. The evolutionary stable strategy (ESS) is the depth at which the phytoplankton are equally limited by both resources. We analytically derive the ESS of the proposed preferential uptake model along with a related two-species reaction-diffusion-taxis model which only considers one limiting nutrient.