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 th at are often supplied front below. In poorly mixed water columns, algae can be heterogeneously distributed, with thin layers of biomass found on the s urface, at depth, or on the sediment surface. Here, we show that these patt erns can result from intraspecific competition for light and nutrients. Fir st, we present numerical solutions of a reaction-diffusion-taxis model of p hytoplankton, 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 phytoplankt on as the strategy. The evolutionarily stable strategy is the depth at whic h the phytoplankton are equally limited by both resources, as long as the l ayer 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 s upply. For low nutrient levels, low background attenuation, and shallow wat er columns, a benthic layer occurs; for intermediate nutrient levels in dee p water columns, a deep chlorophyll maximum occurs; and for high nutrient l evels, a surface scum occurs. These general patterns are in agreement with field observations. Thus. this model can explain many patterns of algal dis tribution found in poorly mixed aquatic ecosystems.