Scale-invariant correlations in the biological and social sciences

In this opening introductory paper, we discuss the possibility that scaleinvariant correlations may be a feature of biological and possibly even social systems. We illustrate this possibility by reviewing recent work at Boston University. Speci® cally, we focus ® rst on the apparent scale-invariant correlations in non-coding deoxyribonucleic acid (DNA) and show that this feature can be used to distinguish coding and non-coding DNA. We argue that the in ̄ ating a degassed lung is characterized by a cascade of avalanches, as the airways successively open, and that distribution functions characterizing this cascade are scale invariant. Moving from the lung to the heart, we ® nd that the sequence of interbeat intervals is characterized by scale-invariant correlations in health, but not in disease. Moving from individual organs to entire organisms, we discuss recent experimental evidence that the foraging behaviour of the wandering albatross is governed by a scale-invariant Levy distribution. Finally, we enquire whether scale invariance describes not only animal behaviour but also human behaviour. To this end, we analyse data on urban growth patterns, on ® nance and on economics. For all cases, we ® nd empirical evidence of scaling behaviour. We conclude by asking why such complex systems might display scale invariance. §