Fig. 3. K function analysis showing the extent to which cases of chronic bee paralysis are clustered spatially for all years (2007–2017).

The observed $\widehat{k}$ (black line) represents a mean count of the number of chronic bee paralysis cases within fixed distances of cases (x axis). Higher values of $\widehat{k}$ show stronger clustering. Upper and lower 95% confidence intervals are shown for estimates of $\widehat{k}$ derived by allocating cases to randomly selected apiary sites and repeating 20 times (blue lines). Since the observed $\widehat{k}$ values (black line) are substantially greater than those derived from random resampling at all distances, we can conclude that cases of chronic bee paralysis are nearer to each other than we would expect by chance and therefore clustered. Note that the calculation of $\widehat{k}$ also includes an adjustment for coastal edge effects.