Jennifer M. Arnold, Soilange Brault, and John P. Croxall. 2006. Albatross populations in peril: a population trajectory for Black-browed Albatrosses at South Georgia. Ecological Applications 16:419–432.

Appendix A. A detailed description of Matrix A and the transition equations used in the model for Black-browed Albatrosses at South Georgia.

The density-independent model is of the form

                        n_t+1  =   A n_t

where n_t and n _t+1 are vectors of the number of individuals in each of the ten stages (including four pseudostages), as indicated in Fig. 1, at years t and t+1.

The matrix A is an annual projection matrix for vector n, with the following parameterization:

The parameters of the matrix elements (indicated in the text as lower-level parameters) are defined as indicated in Table 1 of the main text. The asymptotic population rate of increase, λ, is the largest positive real eigenvalue of the A matrix.