Much of biological thinking starts with the view that, given enough time, anything can evolve. We think that it is more fruitful to delineate first the forbidden states of ecology and evolution—“forbidden” not because they cannot occur, but because they cannot last. Our hypothesis is that much of the structure and stability of biodiversity seen at the macro level is the result of an ongoing process of selective elimination of unstable configurations. Selective elimination processes are powerful non-adaptive evolutionary forces, and they are not specific to biological systems. The evolution of the planetary system or, for example, of the rings of Saturn has been driven by the elimination of many physical bodies. The elimination processes in biology are different only in that the forces of evolution continually generate biological systems that approach or transgress eliminative boundaries, and thus elimination is a never-ending process. Various observed macroscopic ecological laws can be explained by the mathematical conditions of stability in systems of interacting species. This is a fruitful approach that was initiated by Robert May in the 1970s and has been attracting more attention in the last decade.