Multiscaled randomness: A possible source of 1/f noise in biology

Jeffrey M. Hausdorff and C.-K. Peng

Phys Rev E 1996;54:2154-2157

We evaluate the possibility that the 1/f fluctuations observed in many biological time series result simply from the fact that biological processes have many inputs with differing time scales. We present a stochastic model whose output is the summation of multiple random inputs (i.e., different regulatory mechanisms). We derive the conditions under which the model reproduces the complex fluctuations and 1/f scaling observed in biological systems. Simulations demonstrate that if model parameters are unconstrained, the likelihood of generating 1/f noise is quite small. Thus, while the model can be used to generate 1/f beta noise with various scaling exponents, it is unlikely that the 1/f behavior observed in many biological systems is due only to the fact that these systems are regulated by many different inputs acting on different time scales.

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