The RSN formulation of Equations 4.1 and 8.1 incorporate the classical competition, predation, and logistic equations of ecology, plus mutualistic and orthologistic equations that are not part of the classical set. For this, the parameters can remain constant.
But they are not constant in all cases. Volterra (1928) considered parameters that vary through time, but more generally the parameters can be functions of population density as well. In this way the RSN formulation can be extended to cover not just the classical equations of ecology and related equations, but any equations of ecology whatever, as with Equation 4.3, proposed by Kolomogorov.