What are the practical differences between the Benjamini & Hochberg (1995) and the Benjamini & Yekutieli (2001) false discovery rate procedures? My statistics program implements both the Benjamini & Hochberg (1995) and Benjamini & Yekutieli (2001) false discovery rate (FDR) procedures.  I have done my best to read through the later paper, but it is quite mathematically dense and I am not reasonably certain I understand the difference between the procedures.  I can see from the underlying code in my statistics program that they are indeed different and that the latter includes a quantity q that I have seen referred to in regards to FDR, but also don't quite have a grasp of.
Is there any reason to prefer the Benjamini & Hochberg (1995) procedure versus the Benjamini & Yekutieli (2001) procedure?  Do they have different assumptions?  What are the practical differences between these approaches?
Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B, 57, 289–300.
Benjamini, Y., and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics 29, 1165–1188.
The 1999 paper referenced in the comments below: Yekutieli, D., & Benjamini, Y. (1999). Resampling-based false discovery rate controlling multiple test procedures for correlated test statistics. Journal of Statistical Planning and Inference, 82(1), 171-196.
 A: Benjamini and Hochberg (1995)  introduced the false discovery rate. Benjamini and Yekutieli (2001)  proved that the estimator is valid under some forms of dependence.  Dependence can arise as follows. Consider the continuous variable used in a t-test and another variable correlated with it; for example, testing if BMI differs in two groups and if waist circumference differs in these two groups. Because these variables are correlated, the resulting p-values will also be correlated. Yekutieli and Benjamini (1999) developed another FDR controlling procedure, which can be used under general dependence by resampling the null distribution. Because the comparison is with respect to the null permutation distribution, as the total number of true positives increases, the method becomes more conservative.  It turns out that BH 1995 is also conservative as the number of true positives increases. To improve this, Benjamini  and Hochberg (2000)  introduced the adaptive FDR procedure. This required estimation of a parameter, the null proportion, which is also used in Storey's pFDR estimator.  Storey gives comparisons and argues that his method is more powerful and emphasizes the conservative nature of 1995 procedure.  Storey also has results and simulations under dependence. 
All of the above tests are valid under independence. The question is what kind of departure from independence can these estimates deal with. 
My current thinking is that if you don't expect too many true positives the BY (1999) procedure is nice because it incorporates distributional features and dependence. However, I'm unaware of an implementation. Storey's method was designed for many true positives with some dependence. BH 1995 offers an alternative to the family-wise error rate and it is still conservative. 
Benjamini, Y and Y Hochberg. On the Adaptive Control of the False Discovery Rate in Multiple Testing with Independent Statistics. Journal of Educational and Behavioral Statistics, 2000.
