Are critical phenomena relevant to large-scale evolution?

Recent theoretical studies, based on the theory of self-organized critical systems, seem to suggest that the dynamical patterns of macroevolution could belong to such class of critical phenomena. Two basic approaches have been proposed: the Kauffman-Johnsen model (based on the use of coupled fitness landscapes) and the Bak-Sneppen model. Both are reviewed here. These models are oversimplified pictures of biological evolution, but the (possible) validity of them is based on the concept of universality, i.e. that apparently very different systems sharing some few common properties should also behave in a very similar way. In this paper we explore the current evidence from the fossil record, showing that some properties that are suggestive of critical dynamics would also be the result of random phenomema. Some general properties of the large-scale pattern of evolution, which should be reproduced by these models, are discussed.