The Influence of Branch Order on Optimal Leaf Vein Geometries: Murray’s Law and Area Preserving Branching
Figure 4
Box and whisker plot of the distribution of area ratios as a function of node order.
Within each box, the central red mark is the median value, the box edges represent the 25th and 75th percentiles, the whiskers extend to the most extreme data points not considered outliers, and outliers (red plus symbols) are plotted individually. Outliers are considered those values which are larger than P75 + 1.5(P75-P25) or smaller than P25 - 1.5(P75-P25), where P75 and P25 are the 75th and 25th percentiles, respectively [53]. We classify data points as outliers only for the purposes of visualization; no data points were removed from our analyses. The red and black dashed lines are the expectations from Murray’s law and elastic similarity, respectively. Note that for vein orders 1-4 agreement with the expectation for Murray’s law is strong, but begins to depart as branch order increases, moving closer to the expectation for area-preserving branching. Note that in contrast to the convention used by leaf anatomists, here first order veins are the smallest, “terminal” veins in the network (see Methods).