The theoretical basis for estimating phytoplankton production and specific growth rate from chlorophyll, light and temperature data

Phytoplankton maximum specific growth rate, μ_max, and maximum photosynthetic quantum yield, Φ_max, can be related mathematically via the photosynthetic light curve, P(I). A model is presented in which maximum quantum yield defines the initial slope of the light curve and is assumed to be a known constant, while maximum specific growth rate defines the light-saturated region of the curve and is assumed to be a known function of temperature. The effect of introducing μ_max(T) into P(I, Φ_max) is to replace the unknown, temperature-dependent light saturation parameter with a term involving the ratio μ_max/Φ_max. The advantage of writing P(I) in terms of both μ_max and Φ_max is that those parameters are particularly well documented in the literature. Consequently, estimates of nutrient-unlimited phytoplankton growth and production rates can be based solely on the constants μ_max, Φ_max and k_c (light absorption per unit of chlorophyll) and the free variables light, temperature and chlorophyll concentration. Rate estimates appear to be accurate to within a factor of two for an extremely wide range of conditions.One particularly significant result of introducing μ_max into P(I, Φ_max) is that the carbon : chlorophyll ration, θ, appears explicitly. It is possible to derive an expression for optimum θ based on the assumption that adaptive changes in carbon/chlorophyll occur so as to maximize the specific growth rate for given conditions of light and temperature. Laboratory and field data are compiled from the literature to test the formulae presented here.