Algal games: the vertical distribution of phytoplankton in poorly-mixed water columns

Phytoplankton often face the dilemma of living in contrasting gradients of two essential resources: light that is supplied from above and nutrients that are often supplied from below. In poorly mixed water columns, algae can be heterogeneously distributed, with thin layers of biomass found on the surface, at depth, or on the sediment surface. Here, we show that these patterns can result from intraspecific competition for light and nutrients. First, we present numerical solutions of a reaction-diffusion-taxis model of phytoplankton, nutrients, and light. We argue that motile phytoplankton can form a thin layer under poorly mixed conditions. We then analyze a related game theoretical model that treats the depth of a thin layer of phytoplankton as the strategy. The evolutionarily stable strategy is the depth at which the phytoplankton are equally limited by both resources, as long as the layer is restricted to the water column. The layer becomes shallower with an increase in the nutrient supply and deeper with an increase in the light supply. For low nutrient levels, low background attenuation, and shallow water columns, a benthic layer occurs; for intermediate nutrient levels in deep water columns, a deep chlorophyll maximum occurs; and for high nutrient levels, a surface scum occurs. These general patterns are in agreement with field observations. Thus, this model can explain many patterns of algal distribution found in poorly mixed aquatic ecosystems. The distribution of phytoplankton in lakes and oceans i