Thoughts on the Geometry of Meso-evolution: Collecting Mathematical Elements for a Post-modern Synthesis

Metz, J.A.J. (2011). Thoughts on the Geometry of Meso-evolution: Collecting Mathematical Elements for a Post-modern Synthesis. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-11-015

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Abstract

The present chapter is complementary to the one by Warren Ewens. It contains almost no equations or genetics (or rather, both are implicitly there, but stay well hidden), fitnesses are not assumed to be constant, but keep changing (in genetical terms, selection is always seen as frequency dependent), the evolutionary path is considered as being shaped by the repeated substitution of novel mutations (as opposed to gene frequency change), and adaptive landscapes depict the fitness of potential mutant types over a space spanned by traits (instead of the mean fitness of a population over a space of gene frequencies). The reason for this difference in emphasis is that my first training is not as a mathematician or population geneticist but as a naturalist, i.e., field oriented taxonomist-ecologist, which shapes the questions that have my interest. As a consequence, within evolutionary biology I am interested primarily in meso-evolution, defined here as evolutionary changes in the values of traits of representative individuals and concomitant patterns of taxonomic diversification. This in contrast to micro-evolution, a term reserved for the changes in gene frequencies on a population dynamical time scale (the topic of Warren Ewens' chapter), and macro-evolution, a term that then can be reserved for large scale changes like anatomical innovations, where one cannot even speak in terms of a fixed set of traits. Thus meso-evolution acts on a time scale above the micro-evolutionary scale of gene substitutions but below the scale on which the intricacies of the developmental process start to have a large influence...

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