We consider a class of models that generalizes the Bak Sneppen model that can be used to study evolution. Agents with random fitnesses are located at the vertices of a graph $G$. At every time-step the agent with the worst fitness emph{and its neighbors on $G$} are replaced by new agents with random fitnesses. By using Order Statistics and Dynamical Systems, we succeeded in solving a number of questions about how the distribution of the fitnesses evolves under this process. In particular we can prove that for the models that describe in-species evolution, all initial conditions converge to a (not necessarily unique) discrete measure. In contrast for models that describe speciation, every initial probability measure will converge to a (unique) absolutely continuous measure. The conclusion is that in-species evolution can optimize fitness but all agents tend to become identical (no diversity). Speciation on the other hand also improves fitness a little less dramatically, but diversity is retained: a range of fitnesses is preserved. This is a preliminary report of research in progress. Joint work with F. J. Prieto(Univ Carlos III, Madrid, Spain) and M. Orhai (Portland State University).