Tree shape statistics, particularly measures of tree (im)balance, play an important role in the analysis of the shape of phylogenetic trees. With applications ranging from testing evolutionary models to studying the impact of fertility inheritance and selection, or tumor development and language evolution, the assessment of measures of tree balance is important. Currently, a multitude of at least 30 (im)balance indices can be found in the literature, alongside numerous other tree shape statistics. This diversity prompts essential questions: How can we assist researchers to choose only a small number of indices to mitigate the challenges of multiple testing? Is there a preeminent balance index tailored to specific tasks? This research expands previous studies on the examination of index power, encompassing almost all established indices and a broader array of alternative models, such as a variety of trait-based models. Our investigation reveals distinct groups of balance indices better suited for different tree models, suggesting that decisions on balance index selection can be enhanced with prior knowledge. Furthermore, we present the \textsf{R} software package \textsf{poweRbal} which allows the inclusion of new indices and models, thus facilitating future research on the power of tree shape statistics.

翻译：树形统计量，特别是树（非）平衡性的度量，在系统发育树形态分析中扮演着重要角色。其应用范围广泛，从检验进化模型到研究繁殖力遗传与选择的影响，或肿瘤发展与语言演化，树平衡性度量的评估都至关重要。目前，文献中至少存在30多种（非）平衡性指数，以及众多其他树形统计量。这种多样性引发了一些关键问题：我们如何帮助研究人员仅选择少量指数以缓解多重检验带来的挑战？是否存在针对特定任务的卓越平衡性指数？本研究扩展了先前关于指数检验效力的研究，涵盖了几乎所有已建立的指数以及更广泛的替代模型，例如多种基于性状的模型。我们的研究表明，不同的树模型更适合使用不同类别的平衡性指数，这意味着利用先验知识可以优化平衡性指数的选择决策。此外，我们推出了R软件包poweRbal，该软件包允许纳入新的指数和模型，从而为未来树形统计量检验效力的研究提供了便利。