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 tree balance is crucial. 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 minimize the selection of indices to mitigate the challenges of multiple testing? Is there a preeminent balance index tailored to specific tasks? Previous studies comparing the statistical power of indices in detecting trees deviating from the Yule model have been limited in scope, utilizing only a subset of indices and alternative tree models. This research expands upon the examination of index power, encompassing all established indices and a broader array of alternative 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.

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生育力遗传与选择的影响，或肿瘤发展与语言演化，树平衡性的评估都至关重要。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：我们应如何最小化指数选择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？先前比较指数在检测偏离Yule模型的树时的统计功效的研究范围有限，仅使用了部分指数和替代树模型。本研究扩展了对指数功效的考察，涵盖了所有已建立的指数以及更广泛的替代模型。我们的研究表明，不同的平衡性指数组更适合于不同的树模型，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，从而促进未来的研究。