Asymmetry of configuration space induced by unequal crossover: Implications for a mathematical theory of evolutionary innovation

Evolution can be regarded as the exploration of genetic or morphological sl ate space by populations. In traditional models of population and quantitat ive genetics, the state space can be formally represented as a configuratio n space with clearly defined concepts of neighborhood and distance, defined by the action of variational operators such as mutation and/or recombinati on. In this paper, we describe a process where no genetic configuration spa ce closure (and hence, no non-arbitrary notion of distance and neighborhood ) exists. The process is gene duplication by means of unequal crossover, wh ich we regard as an example of an "innovation" process that changes the sta te space of the system rather than exploring a closed state space. We asser t that such processes are qualitatively distinct from representations of th e adaptation process, which occur on regular configuration spaces.