Complexity, contingency, and criticality.

Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or "punctuations" of all sizes. In the critical state, events which would otherwise be uncoupled become correlated. The apparent, historical contingency in many sciences, including geology, biology, and economics, finds a natural interpretation as a self-organized critical phenomenon. These ideas are discussed in the context of simple mathematical models of sandpiles and biological evolution. Insights are gained not only from numerical simulations but also from rigorous mathematical analysis.

Contrasting complexity of two rust resistance loci in flax.

DNA probes from the L6 rust resistance gene of flax (Linum usitatissimum) hybridize to resistance genes at the unlinked M locus, indicating sequence similarities between genes at the two loci. Genetic and molecular data indicate that the L locus is simple and contains a single gene with 13 alleles and that the M locus is complex and contains a tandem array of genes of similar sequence. Thus the evolution of these two related loci has been different. The consequence of the contrasting structures of the L and M loci on the evolution of different rust resistance specificities can now be investigated at the molecular level