Baker et al. reply

Although there is a tendency for our transformation to result in low R′ values for those squares where initial faecal density was low, this does not affect our results. First, this 'bias' is equivalent to a 1.2-fold difference in R′ for a 20-fold difference in initial faecal density1. Second, there was no difference between 'hunted' and 'non-hunted' squares with respect to initial faecal density, direction or magnitude of change in faecal density1. The starting conditions and pattern of change were therefore the same for hunted and non-hunted squares, and the reservations of Aebischer et al. about the transformation are unwarranted.

Our key hypothesis was that hunting with hounds (hereafter termed 'hunting') is additive to other culling practices2. Consequently, the absence of hunting during FMD would be expected to result in increased fox abundance in areas that were previously hunted. The most parsimonious way to test this hypothesis, and to remove any possibility of a transformation effect, is by using a signs test3 — this compares the number of squares in which scat density increased with the number in which it decreased, assuming a 50% chance of either event. This negates the need for a regional approach — if hunting is additive, a change of any magnitude in any region would be detected using our paired samples2.

To determine the power of this approach, we need the α-error rate (α = 0.05), the sample size (n = 157; squares with no change are excluded) and the size of the likely effect3. In previous studies4,5,6, the impact of hunting in Britain (total area, 230,367 km2) has been estimated by extrapolating kill rates per unit area to the total area covered by packs of foxhounds (145,000 km2). The proportion of land in Britain that is hunted is therefore 0.63.

Statistical power is the probability of correctly rejecting a false null hypothesis. For a two-tailed test, the minimum effect size (g) is given by: 0.63 − 0.50 = 0.13; the statistical power that corresponds to α = 0.05, n = 157 and g = 0.13 is about 0.950 (ref. 3). We therefore had a 95% chance of correctly rejecting a false null hypothesis, for a roughly 13% deviation from a probability that faecal density would increase (or decrease) in 50% of squares. The actual results showed no change (P = 0.474). The observed pattern of variation in faecal density is therefore not consistent with hunting mortality being additive. Furthermore, the small absolute changes in faecal density2 indicate minor changes in fox density. We reiterate that these results support the Committee of Inquiry into Hunting with Dogs6, which concluded that a permanent ban on hunting is unlikely to result in a dramatic increase in fox numbers.