Quantitative histomorphometric studies of the dynamics of growth and development of pancreatic islets in normal and pathological states pose substantial methodological and conceptual problems. We address these problems with the geometry of random fractals, and apply our methods to the analysis of islet regeneration in the alloxan-treated guinea-pig. In both experimental islet-regenerated and control animals, islet centres are found to cluster in similar fractal subsets of dimension strictly less than 3, in agreement with the postulated origin of islets along a system of ductules, and suggesting that regeneration follows the same mathematical dynamics as original islet formation.

Random matrices have been widely studied as neutral models for the stability of large systems. However, ecosystems frequently display both a hierarchical trophic organization and organization into a family of loosely coupled subsystems. It is shown that systems with these features have lower Lyapunov stability than corresponding random systems. Thus ecosystems organization arises from other biological and physical factors. Moreover, the simulation methods presented here can be readily used to determine the effect of system structure on neutral models for other similarly complex systems.

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