Does feature selections matter to Decision Tree algorithms? 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?
For ensembles of decision trees, feature selection is generally not that important. During the induction of decision trees, the optimal feature is selected to split the data based on metrics like information gain, so if you have some non-informative features, they simply won't be selected. 

Feature selection can still be important for small datasets, where spurious relationships between features and class labels are more commonly seen. 

As a side note: it's common practice to remove some features from datasets for all learning algorithms, like ID fields. These features are especially bad for decision trees, as they usually end up being the feature with the highest information gain (and therefore selected to be split on) while actually containing no generalisable information. So in this way, feature selection can be useful when using decision trees, although it's arguable that the ID field should be considered a feature in the first place.