A class of statistical tests based on molecular polymorphism data is s
tudied to determine size and power properties. The class includes TAJI
MA's D statistic as well as the D and F* tests proposed by FU and LI.
A new method of constructing critical values for these tests is descr
ibed. Simulations indicate that TAJIMA's test is generally most powerf
ul against the alternative hypotheses of selective sweep, population b
ottleneck, and population subdivision, among tests within this class.
However, even TAJIMA's test can detect a selective sweep or bottleneck
only if it has occurred within a specific interval of time in the rec
ent past or population subdivision only when it has persisted for a ve
ry long time. For greatest power against the particular alternatives s
tudied here, it is better to sequence more alleles than more sites.