On the structural complexity of simple biosystems

PERSPECTIVE METAZOAN COMPLEXITY AND EVOLUTION: IS THERE A TREND?

The notion that complexity increases in evolution is widely accepted, but the best-known evidence is highly impressionistic. Here I propose a scheme for understanding complexity that provides a conceptual basis for objective measurement. The scheme also shows complexity to be a broad term covering four independent types. For each type, I describe some of the measures that have been devised and review the evidence for trends in the maximum and mean. In metazoans as a whole, there is good evidence only for an early-Phanerozoic trend, and only in one type of complexity. For each of the other types, some trends have been documented, but only in a small number of metazoan subgroups.

Stochastic approaches in phyllotaxis

Theoretical models of phyllotaxis are based on geometric regularities appearing at the level of the shoot apical meristem (SAM). However, one cannot forget the presence of perturbed patterns in many plants. Disorganized patterns found in mutants of Arabidopsis and Antirrhinum bring new theoretical problems that cannot be solved by using models developed to analyse regular phyllotactic patterns. One way to take into account the perturbed patterns is to use a probabilistic approach to phyllotaxis. This review will focus mainly on recent probabilistic approaches that can be used to analyse perturbed patterns found in the plant kingdom in general and in phyllotactic mutants in particular. More precisely, it will be shown how probabilistic approaches can be used to determine the degree of order of phyllotactic patterns. By using particular tests, it is possible to statistically differentiate between whorled and distichous patterns (aggregated dispersion), spiral patterns (uniform dispersion), and random patterns (random dispersion). The elaboration of a general probabilistic model of phyllotaxis represents a new challenge for both theoretical and experimental research.