# ibs results show that changes in the G-matrix orientation (A) underlie the direction of branching (B, C).

Panels **A** and **B** correspond to 500 ibs replicates approaching the branching point from direction −3*π*/4 (i.e., from the bottom-left of the phenotype space). **A**: as the population approaches the branching point, the population’s phenotypic distribution becomes elongated along the direction that is perpendicular to movement. (In this case, the **G**-matrix orientation distribution becomes peaked at 3*π*/4, consistent with the second and third panels in Fig 4C.) **B**: Although there is high stochasticity, the **G**-matrix orientation prior to the onset of branching predicts the eventual direction of branching. The orange line and yellow confidence bands result from a linear regression modified to take into account the circular variable space. **C**: All else being equal, different **G**-matrix orientations cause different directions of branching. Each dark histogram shows the branching direction of 600 ibs replicates initialized at the branching point, with individuals drawn from a bivariate normal distribution with a positive (top) or negative (bottom) Pearson correlation coefficient (*ρ*). The light histograms are a mirror copy of the same data and are included for ease of visual interpretation. Parameters: *n* = 10, 000; *σ* = 2.5 × 10^{−5}; for more parameters and details see Appendix A in S1 Text.