Evolvability via the Fourier transform

• Authors: Loizos Michael
• Venue: Theoretical Computer Science
• Year: 2012

The evolvability framework is a computational theory proposed by Valiant as a quantitative tool for the study of evolution. We explore in this work a natural generalization of Valiant's framework: an organism's genome is regarded as representing the Fourier spectrum of a real-valued function that the organism computes. A performance function is suggested that averages in a certain way the organism's responses over the distribution of its experiences. We show that this generalization supports the existence of an efficient, conceptually simple and direct evolutionary mechanism. More concretely, we consider the case where the ideal behavior that an organism strives to approximate is encoded by some decision list, and establish the evolvability of decision lists with respect to the suggested performance metric, over the uniform probability distribution. In accordance with biological evidence on how genomes mutate, the evolutionary mechanism we propose performs only simple operations on the organism's genome to obtain mutated genomes. The surviving genome is selected greedily among genomes in the current generation based only on performance. A sustained performance improvement is ensured, at a fixed and predictable rate across generations, and a highly fit genome is evolved in a number of generations independent of the size of the ideal function, and determined only by the required approximation degree. Furthermore, the size of the genome grows logarithmically in the number of environmental attributes. None of these rather stringent, and presumably biologically desirable properties are enforced by the baseline evolvability framework, nor are these properties possessed by other early evolvability results.