  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.
