  We investigate a class of models related to the Bak-Sneppen model, initially
proposed to study evolution. The BS model is extremely simple and yet captures
some forms of "complex behavior" such as self-organized criticality that is
often observed in physical and biological systems.
  In this model, random fitnesses in $[0,1]$ are associated to agents located
at the vertices of a graph $G$. Their fitnesses are ranked from worst (0) to
best (1). At every time-step the agent with the worst fitness and some others
\emph{with a priori given rank probabilities} are replaced by new agents with
random fitnesses. We consider two cases: The \emph{exogenous case} where the
new fitnesses are taken from an a priori fixed distribution, and the
\emph{endogenous case} where the new fitnesses are taken from the current
distribution as it evolves.
  We approximate the dynamics by making a simplifying independence assumption.
We use Order Statistics and Dynamical Systems to define a \emph{rank-driven
dynamical system} that approximates the evolution of the \emph{distribution} of
the fitnesses in these rank-driven models, as well as in the Bak-Sneppen model.
For this simplified model we can find the limiting marginal distribution as a
function of the initial conditions. Agreement with experimental results of the
BS model is excellent.
