The effect of molecular abundance variations on optical depth and intensity. Left: Modeled CO optical depth as a function of CO intensity for x_CO = 1.4 × 10⁻⁵ (green contours) x_CO = 1.4 × 10⁻⁴ (blue contours) x_CO = 1.4 × 10⁻³ (orange contours). Left center: Modeled HCN optical depth as a function of HCN intensity for x_HCN = 10⁻⁹ (brown contours), x_HCN = 10⁻⁸ (red contours), and x_HCN = 10⁻⁷ (purple contours). Right center: Modeled HCN/CO intensity ratio as a function of CO optical depth for varying CO abundance. The HCN intensities are for x_HCN = 10⁻⁸. Right: Modeled HCN/CO intensity ratio as a function of CO optical depth for varying HCN abundance. The CO intensities are for x_CO = 1.4 × 10⁻⁴. Ten contours are drawn in even steps from the 16th to 100th percentile. Contours are shown in the right two panels for our sample of galaxies and the EMPIRE sample as the solid black and dashed black contours, respectively.