Quantitative description of steady state, nutrient‐saturated algal growth, including adaptation

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Abstract
Steady state, nutrient‐saturated phytoplankton growth can be quantitatively described by four equations: an empirical equation relating growth rate µ8 to absorbed irradiance ξ; a different equation relating µ8 and ξ derived from the empirical equation relating instantaneous rate of gross photosynthesis to irradiance; an empirical equation relating the respiratory rate constant Rp to growth rate; and an equation stating the approximate constancy of the ratio ξp/θ of the light saturation parameter ξp of the photosynthetic light curve and the C:Chl a quotient θ. The equations involve eight constant parameters which were evaluated for Chlorella pyrenoidosa from data in the literature. The four equations do not incorporate an empirical description of the adaptive parameter functions ξp(µ8) or θ(µ8). However, the equations can be solved simultaneously to obtain these functions. The derived functions agree with the experimental ones for C. pyrenoidosa. Since the equations not only describe respiration and the light curves of growth and photosynthesis, but also predict ξp and θ, they constitute an improved model of nutrient‐saturated algal growth: given any irradiance, the equations predict µ8, Rp, ξp, and θ and the specific light curve of photosynthesis. The model provides a necessary foundation for subsequent description of nutrient‐limited growth in culture and in nature.

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