To accurately explore the interaction mechanism between Escherichia coli and Staphylococcus aureus, we designed an ecological experiment to monoculture and co-culture E. coli and S. aureus. We co-cultured 45 strains of E. coli and S. aureus, as well as each species individually to measure growth over 36 h. We implemented a genome wide association study (GWAS) based on growth parameters (λ, R, A and s) to identify significant single nucleotide polymorphisms (SNPs) of the bacteria. Three commonly used growth regression equations, Logistic, Gompertz, and Richards, were used to fit the bacteria growth data of each strain. Then each equation's Akaike's information criterion (AIC) value was calculated as a commonly used information criterion. We used the optimal growth equation to estimate the four parameters above for strains in co-culture. By plotting the estimates for each parameter across two strains, we can visualize how growth parameters respond ecologically to environment stimuli. We verified that different genotypes of bacteria had different growth trajectories, although they were the same species. We reported 85 and 52 significant SNPs that were associated with interaction in E. coli and S. aureus, respectively. Many significant genes might play key roles in interaction, such as yjjW, dnaK, aceE, tatD, ftsA, rclR, ftsK, fepA in E. coli, and scdA, trpD, sdrD, SAOUHSC_01219 in S. aureus. Our study illustrated that there were multiple genes working together to affect bacterial interaction, and laid a solid foundation for the later study of more complex inter-bacterial interaction mechanisms.