Sensitivity analysis of periodic matrix population models

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Theoretical Population Biology 82 (2012): 329-339, doi:10.1016/j.tpb.2012.03.008.Periodic matrix models are frequently used to describe cyclic temporal variation (seasonal or interannual) and to account for the operation of multiple processes (e.g., demography and dispersal) within a single projection interval. In either case, the models take the form of peri- odic matrix products. The perturbation analysis of periodic models must trace the e ects of parameter changes, at each phase of the cycle, on output variables that are calculated over the entire cycle. Here, we apply matrix calculus to obtain the sensitivity and elasticity of scalar-, vector-, or matrix-valued output variables. We apply the method to linear models for periodic environments (including seasonal harvest models), to vec-permutation models in which individ- uals are classi ed by multiple criteria, and to nonlinear models including both immediate and delayed density dependence. The results can be used to evaluate management strategies and to study selection gradients in periodic environments.This research was supported by NSF Grant DEB-0816514, by a Research Award from the Alexander von Humboldt Foundation, and by WHOI Academic Programs Funds