= Solution
The <asymptotic normality of the Watterson estimator> gives approximate standard error $\sqrt{\theta/\log n}$. Thus \b[precision at a fixed nonrecombining locus improves only logarithmically with sample size]. To halve the asymptotic standard error, one needs $\log n'\simeq4\log n$, or roughly $n'=n^4$, rather than four times as many sampled chromosomes.
For large samples and positive $\widehat\theta$, a plug-in <normal approximation> gives $\widehat\theta\pm1.96\sqrt{\widehat\theta/\log n}$ as an approximate 95% <confidence interval>. At low mutation counts it can perform poorly or give a negative endpoint; the exact count model is then preferable. Multiple independent, comparable loci can provide additional independent information, whereas tightly linked chromosomes still share the random ancestry at one locus. <Genetic recombination>, nonneutral evolution and changing population size require corresponding changes to the model.
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