dc=4 is the upper critical dimension for the Bak-Sneppen model

Numerical results are presented indicating d(c) = 4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746 (1998)] that placed d(c) as high as d = 8. In particular, we find that avalanches are compact for all dimensions d less than or equal to 4 and are fractal for d > 4. Under those conditions, scaling arguments predict a d(c) = 4, where hyperscaling relations hold for d less than or equal to 4. Other properties of avalanches, studied for 1 less than or equal to d less than or equal to 6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.