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Sensitivity analysis in periodic matrix models: a postscript to Caswell and Trevisan. (English) Zbl 1073.91062

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.

MSC:

91D20 Mathematical geography and demography
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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
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