Reconstructing minimal length tree branch systems from leaf positions

We present a method to infer a straight-lines tree branch system from a given set of leaf positions and average branching angles. Among an extensive set of possible branch systems constructed in the process, we choose the one featuring the shortest total length, following an optimality hypothesis by Leopold (1971). The approach is illustrated using empirical low-order skeletons from European beech. Our method further allows to assess, for a given species or individual tree, to what extent its branching pattern accords to Leopold's hypothesis, which we argue to be the case for beech. While yet facing issues of computational intensity for too many leaves, the method can furthermore be used to complement existing tree structure reconstruction methods that otherwise require a rudimentary skeleton as manual input.