  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.
