## DSS ax KS S X0 S20

As with the Michaelis-Menton equation, the integrated form of Monod kinetics cannot be solved for St, but can be solved for t, and then the substrate concentration can be determined iteratively.

While apparently complex, Monod kinetics can be simplified under certain conditions to yield each of the kinetic equations described above. Table 16.1 summarizes the various kinetic equations and the conditions under which they will occur. For instance, when the initial concentration of microbial biomass is much greater than the initial substrate concentration (e.g., X0 >> S0), then the term (S0 + X0 - S) in the Monod equation can be approximated to X0 and the Monod equation is simplified to the Michaelis-Menton equation used to describe enzyme kinetics.

modeling the dynamics of decomposition and nutrient transformations

Models can be used to gain an understanding of the processes and controls involved in nutrient cycles, to generate data on the size of various pools and the rates at which nutrients are transformed, and to make predictions when experiments are inappropriate. While conceptual models may be sufficient for the first task, only quantitative models can achieve the latter tasks. Quantitative models of SOM and nutrient dynamics are attempts to describe soil biological processes rather than strictly mathematical expressions and statistical procedures used to find best-fitting curves. Fitting model equations to carbon and nutrient mineralization curves provides estimates of the amount of mineralized product released (e.g., CO2) and the rate at which the product (e.g., NO-) is made available to plants. Models range from single-equation kinetic representations such as those outlined above to large mechanistic models that account for many components of an ecosystem and require computers for generating the results.

TABLE 16.1 The Monod Kinetic Equation, Its Simplifications, and the Conditions under Which the Simplifications Can Be Made

Condition Outcome

Kinetics Differential form

Integrated form

Solve for S?

Exponential dS _

Logistic dS ßmaxS

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