There are several models for the evolutionary process forming a species tree. We examine the Birth-and-Death model (BDM), the Proportional-to-Distinguishable Arrangements (PDA) model, the Kirkpatrick and Slatkin (KS) model, the Beta- Splitting (BS) model and a model where birth rates evolve according to a Geometric Brownian Motion Process (GBM). For testing and calibrating the models, we evaluate tree topologies from TreeBASE and a large tree provided by the Tree of Life project. In a simulation we compare the distribution of tree topologies generated by the models with tree topologies of observed trees. For describing the distribution of topologies we use the tree imbalance statistics B1, Colless'C and Shao and Sokal's N, and calculate the maximum-likelihood estimate of $β$from the BS model. Further we explore the splitting pattern of the generated trees. From the observed trees we show that trees generated by the BDM are too balanced and trees generated by the PDA model are too imbalanced. The BS model with $β$= - 1, the KS model with ratio 1:2 and an adjusted GBM model represent better fitted models for reproducing the imbalance in observed tree topologies.