Recombination Spaces, Metrics, and Pretopologies

The topological features of genotype spaces given a genetic operator have a substantial impact on the course of evolution. We explore the structure of the recombination spaces arising from five different unequal crossover models in the context of pretopological spaces. We show that four of the models are incompatible with metric distance measures due to a lack of symmetry.

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 state space by populations. In traditional models of population and quantitative genetics, the state space can be formally represented as a configuration space with clearly defined concepts of neighborhood and distance, defined by the action of variational operators such as mutation and/or recombination. In this paper, we describe a process where no genetic configuration space closure (and hence, no non-arbitrary notion of distance and neighborhood) exists. The process is gene duplication by means of unequal crossover, which we regard as an example of an “innovation” process that changes the state space of the system rather than exploring a closed state space. We assert that such processes are qualitatively distinct from representations of the adaptation process, which occur on regular configuration spaces.