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		2.5.16— Biological Implications of the Strengths and Weakness in Analyzing Data

		1— Methods of Analysis

		Some biological data look as if they were generated by random mechanisms. We now know that deterministic, chaotic mechanisms can also generate data that look as if they were generated by random mechanisms. There are now methods to analyze biological data to determine if they were generated by a random or a deterministic mechanism. If the data were generated by a deterministic mechanism, then we may be able to understand and even control that biological process.

		We have shown that measures that can tell us if the data were generated by a random or a deterministic process are: the fractal dimension of the phase space set, the bifurcation sequence, the average trajectories in small regions of the phase space, and the use of surrogate data sets. Additional measures include: the Liapunov exponents (how fast trajectories separate from each other in phase space and thus a direct measure of the sensitivity to initial conditions), nonlinear prediction (a deterministic relationship can predict subsequent values in the time series), and the kneading sequence of the symbolic dynamics (deterministic relationships in the trajectories).

		2— Experimental Considerations

		Many of these methods of analysis require lots of data. It is not clear how to maintain a living, biological system under constant conditions long enough to record this amount of data.

		Because of the problems in using these methods to analyze data, it is best if the experimental system can serve as its own control, that is, to design the experiment with a control parameter so that the behavior of the system, such as chaotic or non-chaotic, depends on the value of the control parameter. The results of the analysis of the different behaviors can then be compared to each other. This is a more reliable way to identify a chaotic system than one uncontrolled measurement of the fractal dimension of the phase space set.

 

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