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Reply to Carreira-Perpiñán and Goodhill

Although mathematical arguments certainly have a place in biology, we think it is inappropriate to apply, as do Carreira-Perpiñán and Goodhill (hereafter CP&G, 2002), the standards of proof required in mathematics to the acceptance or rejection of scientific hypotheses. To give some examples, showing that data are well described by a linear model does not rule out an infinity of other possible models that might give better descriptions of the data. Proving in a mathematical sense that the linear model was correct would require ruling out all other possible models, a hopeless task. Similarly, to demonstrate that two DNA samples come from the same individual, it is sufficient to show a match between only a few regions of the genome, even though there remains a very large number of additional comparisons that could be done, any one of which might potentially disprove the match. This is unacceptable in mathematics, but in the real world, it is a perfectly reasonable basis for belief. Hypothesis testing in science, unlike mathematics, proceeds by taking a hypothesis for which there is usually some good a priori basis. Tests are then applied with the aim of getting results that are either consistent or inconsistent with the null hypothesis. In the present case, it is important to