Even though the size of datasets in molecular analyses increased rapidly during the last years, undetected systematic errors as well as unsolved problems concerning the evaluation of data quality and adequate substitution model selection still persist. This not only hampers the correct analysis of these datasets but leads to undetectable effects in phylogenetic tree reconstruction. Model-based tree reconstruction methods like maximum likelihood estimation and Bayesian inference have become the methods of choice for reconstruction of phylogenetic trees. Although maximum likelihood methods are known to be consistent if all necessary conditions are met, it depends strongly on the quality of the multiple sequence alignment and the ability of the chosen evolutionary model to reflect the underlying historical processes. This thesis addresses the assessment of model adequacy of estimated evolutionary models to multiple sequence alignments in the light of parametric bootstrapping and aims to find new methods for detection of model misspecifications with the help of split analyses. The second chapter focuses on the influence of the number of gamma rate categories used in modelling among-site rate variation when trying to assess model adequacy using an absolute goodness-of-fit test. The analyses of simulated alignments show that the Goldmann-Cox test rejects models which were only approximated by four discrete gamma rate categories for various tree shapes and branch length setups, if they were simulated with a continuous gamma distribution. Increasing the number of discrete rate categories leads to an acceptance of model adequacy for stationary datasets and a correct detection of non-stationarity and inhomogenetity in simulated data. The results illustrate that the application of the proposed Goldmann-Cox test to evaluate model adequacy might be too strict and rigorous with empirical data, in particular for large phylogenomic datasets. Approaches such as the Goldman-Cox test evaluate the absolute fit of data and model but, do not deliver a deeper insight into the structure of the misfit. The third chapter presents the visualisation of overrepresented splits within splits graphs, which provides a good tool for gaining an overview of possible patterns and contradictory signal or noise within datasets. The analysis of these split residuals, observed by comparison to parametric bootstrap datasets based on the estimated models can help to gain a deeper insight into model adequacy. Highly overrepresented splits can give hints whether heterotachy applies or non symmetric substitution processes. The fourth chapter aims to define a new split weighting scheme by formalising aspects like 'contrast of character states' or 'character state homogeneity' within split subsets. Splits which are detected by the proposed SAMS (Splits Analysis MethodS) algorithm are re-evaluated for a more objective and formal split weighting. A comparison of the published and the new approach showed that the developed weighting scheme delivers reasonable results but needs further improvement. The development of a new GUI offers a much more capable tool to perform a split analysis and visualise the results. The shape of a visualised split spectra can indicate, whether a dataset delivers a clear split signal or if there is a lot of noise present
