Organisms consist of several genetic factors differing between species. However, the evolutionary effects of gene interactions on the evolutionary rate, adaptation, and divergence of organisms remain unknown. In a previous study, the 2-dimensional genetic algorithm (2DGA) program, including a gene interaction parameter, could simulate punctuated equilibrium under the disparity mode. Following this, we verified the effect of the number of gene interactions (gene cluster size) on evolution speed, adaptation, and divergence using the advanced 2DGA program. In this program, the population was replicated, mutated, and selected for 200,000 generations, and the fitness score, divergence, number of population, and genotype were output and plotted. The genotype data were used for evaluating the phylogenetic relations among the population. The gene cluster size 1) affected the disparity and parity mutagenesis modes differently, 2) determined the growth/exclusion rate and error threshold, and 3) accelerated or decelerated the population's speed of evolutionary advancement. In particular, when the gene cluster size expanded, the rate of increase in fitness scores decreased independently of the mutation rate and mode of mutation (disparity mode/parity mode). The mutation rate at the error threshold was also decreased by expanding the gene cluster size. Dendrograms traced the genotypes of the simulated population, indicating that the disparity mode caused the evolutionary process to enter 1) a stun mode, 2) an evolution mode, or 3) a divergence mode based on the mutation rate and gene cluster size, while the parity mode did not cause the population to enter a stun mode. Based on the above findings, we compared the predictions of the present study with evolution observed in the laboratory or the natural world and the processes of ongoing virus evolution, suggesting that our findings possibly explained the real evolution.