Similarity of general population matrices and pseudo-Leslie matrices

TL;DR

This paper establishes a similarity transformation between complex population models and a simplified pseudo-Leslie model, highlighting computational advantages and differences in entropy despite similar growth ratios.

Contribution

It introduces a similarity transformation linking general population matrices to pseudo-Leslie matrices, enabling easier computations and analyzing entropy differences.

Findings

Pseudo-Leslie matrices can decompose into a row and a subdiagonal matrix.

Solutions using Leslie matrices are computationally efficient.

Kolmogorov-Sinai entropies differ between Lefkovitch and Leslie models with the same growth ratio.

Abstract

A similarity transformation is obtained between general population matrices models of the Usher or Lefkovitch types and a simpler model, the pseudo-Leslie model. The pseudo Leslie model is a matrix that can be decomposed in a row matrix, which is not necessarily non-negative and a subdiagonal positive matrix. This technique has computational advantages, since the solutions of the iterative problem using Leslie matrices are readily obtained . In the case of two age structured population models, one Lefkovitch and another Leslie, the Kolmogorov-Sinai entropies are different, despite the same growth ratio of both models. We prove that Markov matrices associated to similar population matrices are similar.