An overview of a general approach for mathematical modeling of evolving heterogeneous
populations using a wide class of selection systems and replicator equations (RE) is
presented. The method allows visualizing evolutionary trajectories of evolving
heterogeneous populations over time, while still enabling use of analytical tools of
bifurcation theory. The developed theory involves introducing escort systems of auxiliary
“keystone" variables, which reduce complex multi-dimensional inhomogeneous models to
low dimensional systems of ODEs that in many cases can be investigated analytically. In
addition to a comprehensive theoretical framework, a set of examples of the method’s
applicability to questions ranging from preventing the tragedy of the commons to cancer
therapy is presented.