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

Steady state, nutrient-saturated phytoplankton growth can be quantitatively described by four equations: an empirical equation relating growth rate ~1, to absorbed irradiance [; a different equation relating b and 4 derived from the empirical equation relating instantaneous rate of gross photosynthesis to irradiance; an empirical equation relating the respiratory rate constant R, to growth rate; and an equation stating the approximate constancy of the ratio &JO of the light saturation parameter & of the photosynthetic light curve and the C:Chl a quotient 8. The equations involve eight constant parameters which were evaluated for Chlorella pyrenoidosa from data in the literature. The four equations do not incorporate an cmpirical description of the adaptive parameter functions &&) or @(CL,). 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 &, and 8, they constitute an improved model of nutrient-saturated algal growth: given any irradiance, the equations predict 11.8, R,, &,, and 8 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. Accurate description of the effects of temperature, illumination, and nutrient concentration on phytoplankton growth is an important goal of algal physiology and a necessary element of a theory of growth in lakes and seas. The subject of this paper is an improved description of the effect of varying illumination on the properties of algae undergoing steady state growth, at constant temperature in the presence of saturating concentrations of CO, and other nutrients. Such growth may be termed “nutrient saturated.” Practical criteria of nutrient saturation are concentrations in culture at least lOOfold larger than the half-saturating concentrations (K,) for growth; commonly used culture media containing 300 PM CO, (corresponding to 0.5% CO, in air) and 500 PM nitrogen and phosphorus meet or exceed this standard. Various aspects of nutrient-saturated growth of a number of species have been reported (e.g. Eppley and Dyer 1965; Jitts et al. 1964; Smayda 1969; Thomas 1966; Eppley and Sloan 1966; Eppley and Coatsworth 1966). The most comprehensive characterization of a single species is contained in the studies of Phillips (1953), Phillips and Myers (195444 and Myers and Graham (1971). Their work, carried out with Chlorella pyrenoidosa grown in a turbidostat, included measurement of the light curve of growth, and, for samples grown at different rates under different irradiances, determinations of chlorophyll content, dark respiration, and the light curve of instantaneous gross photosynthesis. Cell number, size, density, and dry weight were also determined. The value of these data is enhanced by careful descriptions of optical geometry and of spectral and total irradiance; as a result the irradiances on cells in culture and in photosynthesis measurements can be calculated rather accurately. In a previous theory of nutrient-saturated growth in mixed layers (Bannister 1974b), my description of basic algal properties consisted of certain constants (e.g. the quantum yield of photosynthesis +,,, and the algal extinction coefficient k,), values of which were roughly estimated; the equation of Smith (1936) for the light curve of photosynthesis; and graphical functions, derived from the data of Myers and Graham (1971), representing the growth rate dependences of the three adaptive parameters (respiratory rate