Comments on the discrete matrix model of population dynamics

Abstract

This paper exa mines several aspects of the discrete matrix model of population trans ition. Certain appropriate applications of matrix theory and exploita tion of the s pec ifi c form of the model s hould serve to enhance its already well-developed s tatus. The aspects dealt wit h in clude (1) a simplification of the Perron-Frobe nius theory; (2) row and co lumn sum bounds on maximal e igenvalues; (3) relations between osciUations in a population and the remaining e ige nvalues; (4) implications of stab ility for th e transition matrix; and (5) relation s between characte ri s ti c quantities of a sta bl e population.