Kaufman and percolation

To make a convincing argument, Kaufman takes the super macro-biological point of view which involves, not the study of fitness in specific phenotypical traits, but fitness based on the interrelatedness of potentially infinitely many phenotypical traits. This is not a new point of view; Dawkins[17] has suggested, from this point of view, several strategies used by genotypes and phenotypes that influence each other through a complex ecological web. The novelty of Kaufman's approach lies in his wanting to demonstrate that the interconnectivity of phenotypes give rise to emergent features that constitute evolutionary novelties. He suggests two computer models, one of which is not unlike the Ising model that is discussed in this thesis.

The random nk boolean network treats an organism or genome as a composite system with n constituents that are regulated through k other elements. A constituent n has two possible states determined by its relationship to the states of its k connections, at a preceding moment. This kind of model is usually referred too, in physics, as percolation. Percolation leads to a second order phase transition. Both concepts will be described in more detail in subsequent chapters. Kaufman suggests that, in the face of limited resources, a strategy for minimizing cost and maximizing benefits can imply spontaneous order that will stabilize particular phenotypical or genotypical features in organisms. This point of view implies that,

1.

profound structural changes may occur in fairly short periods of time, compared to the usual assumption that novelties are resultant and require lengthy time scales to occur,

2.

that novelties are not necessarily the result of selective pressures of the kinds described by Darwin,

3.

that the implication of infinite connectivity between and within organisms increases the complexity of systems to a point in which it is difficult to establish any kind of discreteness in a description of particular phenotypes and genotypes.

Moreover phase transition seems to offer a description that convincingly reconciles micro-observations in the study of genotypes and macro-observations in the study of phenotypes as it describes how phenotypical traits can influence micro-structures in fundamental ways and how the interactions in micro-structures give rise to radically different features from the ones that define any individual micro-constituent.

Phase transitions may have been first adequately described in statistical physics, but the feature of spontaneous structural changes in overall systems broadly applicable. Kaufman understands its repercussions in biological fields; however biology is not the only field to benefit from this approach. Economics also turns to statistical physics to model economical trends.