qvalue and p.adjust functions Between the qvalue package and the p.adjust function, which is more appropriate to use when trying to calculate the q-values of a dataset? According to the manual for the q-value package, the q-value calculated is not an adjusted p-value which is what the p.adjust function would return. There seems to be an equal amount of people that use one or the other, but I wanted to see other opinions that could help clarify what would be most appropriate to use.
p.adjust can calculate adjusted p-values with different methods. I think you can choose Bonferroni correction and BH correction, for instance. BH correction gives you False Discovery Rate (FDR), which is one of the most commonly used I guess.

Q-value is different and cannot be calculated by p.adjust. The idea is that when you have many p-values to adjust, they form a distribution. If all p-values come from the null hypothesis, the p-value distribution is going to be uniform on [0, 1]. But usually, our p-values are a mixture of the null distribution and alternative distribution. The parameter $\pi_0$ describes the proportion of p-values (or tests) that comes from the null hypothesis. To calculated q-values, the algorithm first estimates $\pi_0$, then calculates the q-value.

Note that if you set $\pi_0=1$, which means that you believe all the p-values come from the null distribution, then q-value is equal to FDR.

I think most people do not know about the meaning and details of q-values and it might be sufficient to use BH procedure in most cases.