What are the implications for training a Tree Ensemble with highly biased datasets?
I would recommend training on more balanced subsets of your data. Training random forest on sets of randomly selected positive example with a similar number of negative samples. In particular if the discriminative features exhibit a lot of variance this will be fairly effective and avoid over-fitting. However in stratification it is important to find balance as over-fitting can become a problem regardless. I would suggest seeing how the model does with the whole data set then progressively increasing the ratio of positive to negative samples approaching an even ratio, and selecting for the one that maximizes your performance metric on some representative hold out data. 

This paper seems fairly relevant http://statistics.berkeley.edu/sites/default/files/tech-reports/666.pdf it talks about a weighted Random Forest which more heavily penalizes misclassification of the minority class.