Fig. S3 . Elevation map showing variation of the minimum BaMwidth (red line) under different sea-level scenarios. Pink lines denote contours at specified elevation/bathymetry.
Once depth-width data had been collected, we used an ensemble of polynomial fits to create a smooth model for width under different sea-level conditions. The final polynomial model was selected based on three criteria: 1) no width-depth inversions were detected (i.e., with increased depth, BaMwidth must decrease); 2) a p-value of <0.05 and R2 value >0.95 was achieved; and 3) our current measured width of the Strait (25.6 ± 0.225 km) must fall within the 95% confidence intervals of the polynomial model. We chose a 3-order polynomial fit. While 4-6 order fits provided higher R2 values, these resulted in substantial width-depth inversions (i.e., as sea-levels decreased, at points BaMwidth increased) when combined with the RSL. The resultant formula of the fit (Fig. S4A) was combined with the RSL Probability Maximum curve and 95% confidence intervals (Grant et al., 2012, 2014) to provide models for the minimum BaMwidthat 0.125 kyr intervals over the last 130 ka BP. Our modelled BaMwidth at 0 ka BP (30.15 +4.88/-4.26 km) is slightly greater than our measured width (25.6 ± 0.225 km). (fig. 4). We relate this to two complications: 1) the complex elevation and bathymetry of the Bab-al-Mandab area (sudden changes in elevation gradients) which the smooth polynomial fit does not easily detect (Fig. S4A), and 2) the RSL slightly overpredicts present sea-levels by ~1.7 m. However, uncertainties of the measured width (25.6 ± 0.225 km) and modelled width (30.15 +4.88/-4.26 km) overlap, and the measured width falls within the 95% confidence intervals of the polynomial fit. Additionally, the chosen polynomial fit slightly underestimates contour distance at +10 m, meaning that the reconstructed BaMwidth is slightly conservative to sea-level increases during early MIS 5e.