Light-limited growth and competition for light in well-mixed aquatic environments: An elementary model

Light is never distributed homogeneously since it forms a gradient over biomass. As a consequence, the common theories on nutrient competition are not applicable to competition for light. In this paper, we investigate a model for light-limited growth and competition among phytoplankton species in a mixed water column. The model is based on standard assumptions such as Lambert-Beer's law of light absorption, a Monod equation for carbon uptake, and constant specific carbon losses. By introducing the concept of quantum return, we show that the dynamics of growth and competition can be quantified not only in terms of depth but also directly in terms of light availability. We argue that the crucial measure for phytoplankton growth is not a ''critical depth'' but a ''critical light intensity,'' I-out*. For each species, I-out* corresponds to the equilibrium light intensity at the bottom of a water column when the species is grown in monoculture. I-out* plays a role similar to the ''critical nutrient concentration'' R* used in models of nutrient-limited growth. For a constant light supply, the species with the lowest I-out* will competitively exclude all other species. There are, however, some important differences between R* and I-out*. Whereas R* reflects both the local and the total balance between nutrient uptake and nutrient losses, I-out* only reflects the total carbon balance. Moreover, I-out* decreases with increasing light supply, whereas R* is independent of the nutrient supply. As a consequence, (1) the outcome of competition for light may depend on the light supply, (2) the compensation point is not a good predictor for the outcome of competition, (3) the resource ratio hypothesis does not apply when species compete for both nutrients and light. The outcome of competition for nutrients and light may depend on the nutrient and light supply, on the mixing depth, and on the background turbidity due to inanimate substances