Assumptions of the model. We used surrounding gene exons as reference. We assumed the substitution rate relative to those exons would not change too much if no selection pressures affect this region. For test sequence, we defined three constant substitution rates on the species tree, to test the rate change at two time point: inversion and emergence of Pldi-Ak158810 transcription. (a) Red lines represent for substitutions after gene birth, at rate r2; green lines represent for substitutions after two observed inversion, and before gene birth, at rate r1; black lines represent for substitutions before inversion, at rate r0. We were concerned about the rate change relative to surrounding gene exons, all the rates were normalized by the variable reference rate rR. (b-d) raverXY were calculated by dividing test sequence XY distance by reference XY distance, which indicates a relative substitution rate on the bold path; three raverXY will be similar if substitution rates do not vary significantly in three stages.