Lesnoff, M.; Ezanno, P.; Caswell, H. Sensitivity analysis in periodic matrix models: a postscript to Caswell and Trevisan. (English) Zbl 1073.91062 Math. Comput. Modelling 37, No. 9-10, 945-948 (2003). Summary: Periodic matrix population models are a useful approach to modelling cyclic variations in demographic rates. H. Caswell and M. L. Trevisan [Sensitivity analysis of periodic matrix models, Ecology 5, 1299–1303 (1994)] introduced the perturbation analysis (sensitivities and elasticities) of the per-cycle population growth rate for such models. Although powerful, their method can be time-consuming when the dimension of the matrices is large or when cycles are composed of many phases. We present a more efficient method, based on a very simple matrix product. We compared the two methods for matrices of different sizes. We observed a reduction in calculation time on the order of 24% with the new method for a set of 26 within-year Leslie matrices of size \(287 \times 287\). The time saving may become particularly significant when sensitivities are used in Monte Carlo or bootstrap simulations. Cited in 3 Documents MSC: 91D20 Mathematical geography and demography Keywords:Sensitivity; Elasticity; Periodic matrix models; Population dynamics; Population; growth rate PDFBibTeX XMLCite \textit{M. Lesnoff} et al., Math. Comput. Modelling 37, No. 9--10, 945--948 (2003; Zbl 1073.91062) Full Text: DOI References: [1] Caswell, H.; Trevisan, M. C., Sensitivity analysis of periodic matrix models, Ecology, 75, 5, 1299-1303 (1994) [2] Caswell, H., Matrix Population Models. Construction, Analysis and Interpretation (2001), Sinauer: Sinauer Sunderland, MA [3] Skellam, J. G., (Proceedings of the 5th, Berkeley Symposium on Mathematical Statistics and Probability, Volume 4 (1966)) [4] Caswell, H., Matrix Population Models. Construction, Analysis and Interpretation (1989), Sinauer: Sinauer Sunderland, MA [5] Magnus, J. R.; Neudecker, H., Matrix Differential Calculus with Applications in Statistics and Econometrics (1995), Wiley: Wiley Chichester [6] Lesnoff, M.; Lancelot, R.; Tillard, E.; Dohoo, I. R., A steady-state approach of benefit-cost analysis with a periodic Leslie-matrix model. Presentation and application to the evaluation of a sheep-diseases preventive scheme in Kolda, Senegal, Prev. Vet. Med., 46, 2, 113-128 (2000) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.