In this talk, we study dynamics of the modified Rosenzweig-MacArthur equation in constant and changing environments. We first provide a more easily verifiable classification to determine the types and codimension of nilpotent singularities in a general planar system. Second, by using some algebraic and symbolic computation methods, we show that the highest codimension of a nilpotent focus is 4 and the modified RM equation can exhibit nilpotent focus bifurcation of codimension 4. Finally, we give a brief introduction of three other modified Rosenzweig-MacArthur equations.