Background: Currently I'm working with my thesis project, which is to build a Tree-based ensemble methods for classification on a large data set. Before I started with modelling, I've spent a large amount of time on feature selection using correlation-based criteria to select a subset of features, so that those chosen features have high correlation with the response variable and low correlation with each other.
However, one of my supervisors questioned why I spent so much time in feature selection, as he mentioned, the decision tree algorithm can naturally select which features are most important. Later I checked book Introduction to Data Mining by Tan (2014) and it says clearly that "Feature selection occurs naturally as part of the data mining algorithm, ..., such as decision tree classifiers" . I felt a bit frustrated by spending time on feature selection. When I eventually run the models with and without feature selection, it does NOT show any significant differences between the results.
My question is: Does feature selections matter at all to Decision Tree algorithms?