In order to study the genetic mechanism under biological competition, a genome-wide association study (GWAS) is conducted on the two interactive bacterial species using experimental data. The growth in numbers of both E.coli and S.aureus has two stages: a fast-growing stage that is close to an exponential growth, and a stable stage when the numbers vibrate around a fixed value. The model describing such growing processes is a combination of the Lotka-Volterra differential equation system and a non-parametric vibration part. A generalized profiling procedure is used to detect significant SNP pairs (one from E.coli and the other from S.aureus) that are associated with the competition between two bacterial species.