Hi,

Tajima's D indicates whether there is an over(under) representation of rare alleles by comparing two theta estimators derived from a sequence alignment. The first estimator is based on the number of polymorphic sites while the other is based on the average distance between two sequences. If you consider an allele A1 presents in half the population and an allele A2 present in only one individual, A1 and A2 have the same impact on the first theta estimator (number of polymorphic sites) but different impact on the second estimator (average distance between two sequences).

it's quite hard to further explain these concepts with only text and no blackboard...

But I think that you could find the following video quite useful to better understand the fundament of this test:

http://www.youtube.com/watch?v=wiyay4YMq2A

The interpretation of Tajima's D test/value is not obvious since different scenarios can lead to comparable over(under) representation of rare alleles (e.g. variation of selective pressure vs variation of effective population size). Concerning this point, and the interpretation of other tests you mentioned, you may be interested by the following paper:

http://www.nature.com/nrg/journal/v4/n2/fig_tab/nrg999_F2.html

http://www.nature.com/nrg/journal/v4/n2/fig_tab/nrg999_T1.html

I hope this will help,