An alternate approach to analyzing convergence by Leslie matrices

The process of convergence of a population vector to its stable equivalent under iteration by a Leslie matrix is analyzed. The norm mostly used is an additive norm, called the eigen‐norm. A natural convergence measure S is shown to be monotonic non‐increasing upon matrix iteration. Guaranteed rates of convergence of S for any population are described by functions F and B, and results are obtained for these functions. Analogous measures based upon concepts of spectral decompositions are considered. Corresponding results are presented, and comparisons made between these spectral measures and natural measures from a theoretical approach and from data analyses of samples of modern populations.