Authenticity of ancient-DNA results: a statistical approach

Although there have been several papers recommending appropriate experimental designs for ancient-DNA studies, there have been few attempts at statistical analysis. We assume that we cannot decide whether a result is authentic simply by examining the sequence (e.g., when working with humans and domestic animals). We use a maximum-likelihood approach to estimate the probability that a positive result from a sample is (either partly or entirely) an amplification of DNA that was present in the sample before the experiment began. Our method is useful in two situations. First, we can decide in advance how many samples will be needed to achieve a given level of confidence. For example, to be almost certain (95% confidence interval 0.96-1.00, maximum-likelihood estimate 1.00) that a positive result comes, at least in part, from DNA present before the experiment began, we need to analyze at least five samples and controls, even if all samples and no negative controls yield positive results. Second, we can decide how much confidence to place in results that have been obtained already, whether or not there are positive results from some controls. For example, the risk that at least one negative control yields a positive result increases with the size of the experiment, but the effects of occasional contamination are less severe in large experiments.