It has been argued that much of evolution takes place in the absence of fitness gradients. Such periods of evolution can be analysed by examining the mutational network formed by sequences of equal fitness, that is, the neutral network. It has been demonstrated that, in large populations under a high mutation rate, the population distribution over the neutral network and average mutational robustness are given by the principal eigenvector and eigenvalue, respectively, of the network’s adjacency matrix. However, little progress has been made towards understanding the manner in which the topology of the neutral network influences the resulting population distribution and robustness. In this work, we use numerical methods and network models to enhance our understanding of how populations distribute themselves over neutral networks. We demonstrate that, in the presence of certain topological features, the population will undergo an exploration catastrophe and become confined to a small portion of the network. These results provide insight into the behaviour of populations on neutral networks, demonstrating that neutrality does not necessarily lead to an exploration of genotype/phenotype space or an associated increase in population diversity.

Previous research has demonstrated that computational models of Gene Regulatory Networks (GRNs) can adapt so as to increase their evolvability, where evolvability is defined as a populations responsiveness to environmental change. In such previous work, phenotypes have been represented as bit strings formed by concatenating the activations of the GRN after simulation. This research is an extension where previous results supporting the evolvability of GRNs are replicated, however, the phenotype space is enriched with time and space dynamics with an evolutionary robotics task environment. It was found that a GRN encoding used in the evolution of a way-point navigation behavior in a fluctuating environment results in (robot controller) populations becoming significantly more responsive (evolvable) over time. This is as compared to a direct encoding of controllers which was unable to improve its evolvability in the same task environment.

Robustness and evolvability have traditionally been seen as conflicting properties of evolutionary systems, due to the fact that selection requires heritable variation on which to operate. Various recent studies have demonstrated that organisms evolving in environments fluctuating non-randomly become better at adapting to these fluctuations, that is, increase their evolvability. It has been suggested that this is due to the emergence of biases in the mutational neighborhoods of genotypes. This paper examines a potential consequence of these observations, that a large bias in certain areas of genotype space will lead to increased robustness in corresponding phenotypes. The evolution of boolean networks, which bear similarity to models of gene regulatory networks, is simulated in environments which fluctuate between task targets. It was found that an increase in evolvability is concomitant with the emergence of highly robust genotypes, where evolvability was defined as the populations adaptability. Analysis of the genotype space elucidated that evolution finds regions containing robust genotypes coding for one of the target phenotypes, where these regions overlap or are situated in close proximity. Results indicate that genotype space topology impacts the relationship between robustness and evolvability, where the separation of robust regions coding for the various targets was detrimental to evolvability.