Three sources and three constituents of the formalism for a population with discrete age and stage structures

To construct a dynamic model for a population of plants which differ in their chronological age and ontogenetic stage, a formalism is proposed which is distinct from a matrix description suggested earlier for populations whose individuals are classified with respect to two bases. The formalism is realized for a population of woodreed Calamagrostis canescens, a perennial species dominating in the grass layer of felled forest areas, and the model projection matrix is constructed as a set of 21 demographic and ontogenetic parameters. Characteristic properties of the matrix are investigated in the general case; an expression is deduced for the reproductive potential of a population with given parameters. It is shown that the equilibrium age-stage structure may lose “left-sidedness of the age spectrum”, a property that is traditionally checked in observations.