Infinite series of exact equations in the Bak-Sneppen model of biological evolution

We derive an infinite series of exact equations for the Bak-Sneppen (BS) model in arbitrary dimensions. These equations relate different moments of temporal duration and spatial size of avalanches. We prove that the exponents of the BS model are the same above and below the critical point, and express the universal amplitude ratio of the avalanche spatial size in terms of the critical exponents. The equations uniquely determine the shape of the scaling function of the avalanche distribution. It is shown that in the BS model in arbitrary dimensions there is only one independent critical exponent.