Here the relative contributions of all elements investigated to the system's ascendency can be calculated. Results will show that the system is most sensitive to the element with the slowest turnover rate. The element with the slowest turnover rate is also the element which enters the compartment in its least relative proportion. The last statement accords with Liebig's law of the minimum for which ascendency provides a theoretical basis. The same results could have been obtained by comparing elemental turnover rates of all compartments. However, ascendency provides yet another level of information, namely it identifies which source provides the limiting flow ofthe controlling element. To calculate this, the sensitivities of the individual biomasses can be expanded to include the sensitivities of the individual flows from source r to predator p. The following equation calculates the contributions of each flow:
The limiting source of the controlling element is the one which is depleted fastest in relation to its available stock, that is, the one with the highest (Trp/B,). Knowing the sensitivity of the flow for each element and compartment, it is thus possible to pinpoint nutrient limitations and the limiting flows for each compartment in the food web. In ecosystems, not all species are limited by the same nutrient. For instance when primary producers are limited by nitrogen, it does not necessarily mean that the entire food web is limited by nitrogen.
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