Single nucleotide polymorphism (SNP) data can be used for parameter estimat
ion via maximum likelihood methods as long as the way in which the SNPs wer
e determined is known, so that an appropriate likelihood formula can be con
structed. We present such likelihoods for several sampling methods. As a te
st of these approaches, we consider use of SNPs to estimate the parameter T
heta = 4N(e)mu (the scaled product of effective population size and per-sit
e mutation rate), which is related to the branch lengths of the reconstruct
ed genealogy. With infinite amounts of data, ML models using SNP data are e
xpected to produce consistent estimates of Theta. With finite amounts of da
ta the estimates are accurate when Theta is high, but tend to be biased upw
ard when Theta is low. If recombination is present and not allowed for in t
he analysis, the results are additionally biased upward, but this effect ca
n be removed by incorporating recombination into the analysis. SNPs defined
as sites that are polymorphic in the actual sample under consideration (sa
mple SNPs) are somewhat more accurate for estimation of Theta than SNPs def
ined by their polymorphism in a panel chosen from the same population (pane
l SNPs). Misrepresenting panel SNPs as sample SNPs leads to large errors in
the maximum likelihood estimate of Theta. Researchers collecting SNPs shou
ld collect and preserve information about the mettled of ascertainment so t
hat the data can be accurately analyzed.