DROOP model

The second level, or cell-quota theory, allows organisms to vary their content of nutrient Q (and hence their yield of biomass from assimilated nutrient). It is increasingly referred to as the DROOP model after one of its authors (Droop, 1968, 1983). In principle, the quota should be defined as the ratio of nutrient to biomass (Droop, 1979) and will here be understood as the population (atomic) ratio of the nutrient element to carbon. A simplified version of the theory and some deductions from it, is given in Box 1 (refer page 348). The key equation (ignoring physical transports) is ... 

Droop, M.R. (1983) 25 years of algal growth kinetics - a personal view. Botanica Marina, 26, 99-112. Ducobu, H., Huisman, J., Jonker, R.R. and Mur, L.R. (1998) Competition between a prochlorophyte and a cyanobacterium under various phosphorus regimes Comparison with the Droop model. 

Table 16.4 shows a model for primary production that distinguishes uptake and growth. An important example of such a model is that of Droop (1973). Differential equations for this model are formulated in a more convenient way inDucobu etal. (1998) and Ahn et al. (2002). The rate expressions given in Table 16.4 are from the Droop model. The dependence on environmental factors other than concentrations of phosphate and algae is absorbed by the variables u and x. This includes switching between... 

Sommer, U. (1991). A comparison of the Droop and Monod models of nutrient Hmited growth applied to natural populations of phytoplankton. Funct. Ecol. 5, 535—544. 

The scaling factor of a m.p. sequence depends on p (Haeberlen, 1976). A variation of p during the sequence therefore causes a chirp of each resonance. Our simulation program allows us to quantify this effect also. In Fig. 10 we show a simulated BR-24 spectrum of our model system that assumes an exponential power droop that amounts to no more than a 1% decrease of p after 100 BR-24 cycles, that is, after 2400 pulses. Note the asymmetry of the lines and the wiggles at their feet that are indicative of the chirp. In Section IV we present experimental m.p. spectra that display exactly these features. 

The crucial parameters are the concentration ks at which uptake is half of the maximum rate and the fixed ratio (or yield) q l at which nutrient is converted to biomass. The yield may be the Redfield ratio or some other optimum composition. Tilman etal. (1982) used the model to show how freshwater phytoplankters of different optimum composition or different half-saturation concentrations, might succeed to different extents depending on the ambient ratios of nutrient elements. Although the assumption of constant yield may be appropriate for pelagic heterotrophs, it is now seen to be too simple for accurate prediction of the growth of phytoplankters (Droop, 1983 Sommer, 1991 Ducobu etal., 1998). 

Droop, M.R. (1973) Some thoughts on nutrient limitation in algae. Journal of Phycology, 9, 264—272. Droop, M.R. (1979) On the definition of X and of Q in the Cell Quota model. Journal of Experimental Marine Biology and Ecology, 39, 203. 

Tett, P. and Droop, M.R. (1988) Cell quota models and planktonic primary production, in Handbook of Laboratory Model Systems for Microbial Ecosystems, vol. 2 (ed. J.W.T. Wimpenny), CRC Press, Florida, pp. 177-233. 

Most models of algal growth combine the steps of nutrient uptake into the cell and growth on intracellular nutrients into a single step of uptake and growth. In the models that separate those two steps for phosphorus (e.g. Droop, 1973, 2003), an intracellular phosphorus pool must be included, in addition to the phosphorus that is part of the organic molecules. We denote the mass fraction of intracellular phosphorus contained in nutrient storage pools as... 

Droop, M.R. (2003) In defence of the cell quota model of micro-algal growth. Journal of Plankton Research 25, 103-107. 

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