Susceptibility to common human diseases such as cancer is influenced by many genetic and environmental factors that work together in a complex manner. The state of the art is to perform a genome-wide association study (GWAS) that measures millions of single-nucleotide polymorphisms (SNPs) throughout the genome followed by a one-SNP-at-a-time statistical analysis to detect univariate associations. This approach has identified thousands of genetic risk factors for hundreds of diseases. However, the genetic risk factors detected have very small effect sizes and collectively explain very little of the overall heritability of the disease. Nonetheless, it is assumed that the genetic component of risk is due to many independent risk factors that contribute additively. The fact that many genetic risk factors with small effects can be detected is taken as evidence to support this notion. It is our working hypothesis that the genetic architecture of common diseases is partly driven by non-additive interactions. To test this hypothesis, we developed a heuristic simulation-based method for conducting experiments about the complexity of genetic architecture. We show that a genetic architecture driven by complex interactions is highly consistent with the magnitude and distribution of univariate effects seen in real data. We compare our results with measures of univariate and interaction effects from two large-scale GWASs of sporadic breast cancer and find evidence to support our hypothesis that is consistent with the results of our computational experiment.

Recombination is a commonly used genetic operator in artificial and computational evolutionary systems. It has been empirically shown to be essential for evolutionary processes. However, little has been done to analyze the effects of recombination on quantitative genotypic and phenotypic properties. The majority of studies only consider mutation, mainly due to the more serious consequences of recombination in reorganizing entire genomes. Here we adopt methods from evolutionary biology to analyze a simple, yet representative, genetic programming method, linear genetic programming. We demonstrate that recombination has less disruptive effects on phenotype than mutation, that it accelerates novel phenotypic exploration, and that it particularly promotes robust phenotypes and evolves genotypic robustness and synergistic epistasis. Our results corroborate an explanation for the prevalence of recombination in complex living organisms, and helps elucidate a better understanding of the evolutionary mechanisms involved in the design of complex artificial evolutionary systems and intelligent algorithms.

In gene regulatory circuits, the expression of individual genes is commonly modulated by a set of regulating gene products, which bind to a gene's cis -regulatory region. This region encodes an input-output function, referred to as signal-integration logic, that maps a specific combination of regulatory signals (inputs) to a particular expression state (output) of a gene. The space of all possible signal-integration functions is vast and the mapping from input to output is many-to-one: For the same set of inputs, many functions (genotypes) yield the same expression output (phenotype). Here, we exhaustively enumerate the set of signal-integration functions that yield identical gene expression patterns within a computational model of gene regulatory circuits. Our goal is to characterize the relationship between robustness and evolvability in the signal-integration space of regulatory circuits, and to understand how these properties vary between the genotypic and phenotypic scales. Among other results, we find that the distributions of genotypic robustness are skewed, so that the majority of signal-integration functions are robust to perturbation. We show that the connected set of genotypes that make up a given phenotype are constrained to specific regions of the space of all possible signal-integration functions, but that as the distance between genotypes increases, so does their capacity for unique innovations. In addition, we find that robust phenotypes are (i) evolvable, (ii) easily identified by random mutation, and (iii) mutationally biased toward other robust phenotypes. We explore the implications of these latter observations for mutation-based evolution by conducting random walks between randomly chosen source and target phenotypes. We demonstrate that the time required to identify the target phenotype is independent of the properties of the source phenotype.