Non-stationarity of tree branching patterns and bifurcation ratios

Branching patterns in organisms have been analysed by using branch ordering and bifurcation ratio techniques originally developed by geomorphologists to study stream drainage patterns. An underlying assump­tion of these methods is that branching patterns are stationary across boundaries of scale so that a subsample will accurately model a larger structure. This assumption of stationarity is not generally valid for tree branching patterns. Data from four species reveal two specific patterns of non-stationarity that are directly related to morphological patterns of shoot development. Average bifurcation ratios appear to be inappropriate descriptions of tree branching patterns, since they are based solely on relative branch position and ignore biologically important details of form and development. ‘Certain assumptions are liable, through long usage, to become part of the recognized currency of thought, although most of those who employ them have never made any effort to test their validity.’ Agnes Arber, 1933