Evolvability of graph- and Vector Field Embryogeny representations

Most developmental representations for design optimization with evolutionary computation that have been described in the literature are graph-based mimicking the interactions observed in biological gene regulatory networks. Alternative methods that directly manipulate the dynamical control system for developmental processes have been termed Vector Field Embryogeny (VFE) and have been applied successfully to cell differentiation. In this paper, we compare the evolvability of graph-based and vector field representations for controlling developmental processes. Inspired by the notion of strong causality in evolutionary strategies, we measure the covariance between genotype and phenotype changes for both representations. Furthermore, we propose a measure to characterize the representational power of both methods. If we compare VFE and graph-based representations with similar representational power, we notice that the covariance measure and therefore, the expected evolvability of VFE is higher. We also observe that the representational power of both methods decreases with increasing degree of freedom. We speculate that the reason for this could be the increased probability of the occurrence of strong point attractors.