Distinguishing coalescent models - which statistics matter most?

Modelling genetic diversity needs an underlying genealogy model. To choose a fitting model based on genetic data, one can perform model selection between classes of genealogical trees, e.g. Kingmans coalescent with exponential growth or multiple merger coalescents. Such selection can be based on many different statistics measuring genetic diversity. A random forest based Approximate Bayesian Computation is used to disentangle the effects of different statistics on distinguishing between various classes of genealogy models. For the specific question of inferring whether genealogies feature multiple mergers, a new statistic, the minimal observable clade size, is introduced. When combined with classical site frequency based statistics, it reduces classification errors considerably.