TABLE OF CONTENTS The skill and innovation of experimental biologists has enabled them to obtain more and more information about their preparations. This presents a challenge to anyone who wishes to create a mathematical model or simulation of a given system. At what point does the model cease to have explanatory value, having become too complex to do anything more than simulate a variety of parameter values and initial conditions for a system? Often the models that are proposed have dozens of parameters, many of which may not be known for the particular system studied. Furthermore, the complexity of the models makes it difficult to study sensitivity to parameters and initial conditions, even on fast computers. This difficulty is magnified when the systems that are simulated are inherently stochastic, for then one can ask: How many sample paths are enough? In addition to the computational difficulties and the incomplete knowledge of parameters, there is also the issue interpreting the output of the model. Large simulations produce a tremendous amount of output, much of which is likely to be useless for the particulars of a given experiment. Finally, for many biological systems, one can only guess at the mechanism. A simulation does not tell you how dependent the behavior of a system is on the particular form of the mechanism that you have chosen. Only a detailed analysis can tell you that, and for complex models and simulations this is difficult at the very least and usually is impossible.
These...
