How to verify error independence for ensembles in R




One of the assumptions in ensemble modelling is that the error terms of individual models are statistically independent.
How does the algo check this?Like in linear regression we can plot the residuals and see this,but how does something like an ensemble of CART’s validate this.?

In the above diagram,the errors are closely related around the intersecting regions,so an ensemble will not work quite nicely i guess.Can someone please illustrate this better.
Any links to demonstrations in R will be highly appreciated.