To examine if selective pressure between the seven groups of TPSs genes would change, the likelihood ratio tests of positive selection were used via the ML methods as well as codon substitution models (Yang, 1998; Yang and Bielawski, 2000; Yang et al., 2012). Two tests were performed during the analysis process. First, models M0 and M3 were compared in order to assess whether dN/dS ratio variations existed among codon positions below each group. On the whole, the maximum likelihood estimates of dN/dS values as for groups under model M0 were close to zero, with three exceptions of Arabidopsis TPS genes in group I-2. This implied that the principal force which acting on the evolution of TPS family was purifying selection (Table 3). It is obvious that although the majority of protein residues are heavily dependent on constant purifying selection, some sites are also being impacted by positive selection. Positive selection is an important adaption mechanism; thus, sites under positive selection pressure may have sped up functional divergence of TPS; in this case it would allow the plants to adjust to its environment. The results we get are in accordance with this conclusion. As the statistical differences of log likelihood between model M0 and M3 were significant for all groups, it suggests that the overall selective constraint levels varied across the TPS family group lineages. Secondly, the LRT which is applied to compare data fit to models M7 vs. M8 was used to determine whether positive selection promoted divergence of TPS family below groups or not. Two groups (group I-1 and II-2) of the 7 groups analyzed, were believed to have undergone positive selection, because they satisfied that (1) an estimate of ω > 1 under M8, (2) sites identified to be under positive selection, and (3) a significant LRT. This result suggests that positive selection contributed to the evolution of genes in these groups. When the LRT suggested positive selective action had occurred, positively selected sites are identified under model M8 using Bayesian method (Nielsen and Yang, 1998; Yang and Bielawski, 2000). We found 31 and 4 positively selected sites in subgroup I-1 and II-2, respectively.