Quantitative theory for nutrient element ratios

The relationship between nutrients and the growth of populations of microorganism can be described in three ways. The simplest theory is the one developed for organic-carbon-limited bacterial growth by Monod (1942) and popularised for application to phytoplankton by Dugdale (1967). In this MONOD theory, the rate of uptake of dissolved nutrient (per unit biomass) depends on ambient concentration S  

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). 

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  

The quota can vary between a minimum content kQ and a maximum 2max, and p is 1 for a limiting nutrient and greater than 1 otherwise. The ratio 2max/fcg determines a population s storage capacity for a given nutrient. The ratio k-Qp/ko helps to determine relative limitation by nutrients j1 and j2. For example, Sji/Sj2 kQi jl/kQi j2 may indicate that nutrient j1 limits species i, although as Box 1 shows, other factors also play a part. 

Given such interpretational difficulties, which add errors to those given in the tables, only a few generalisations can be reliably drawn  

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