title: Fixed point sensitivity analysis of interacting structured populations.
abstract: Sensitivity analysis of structured populations is a useful tool in population ecology. Historically, methodological development of sensitivity analysis has focused on the sensitivity of eigenvalues in linear matrix models, and on single populations. More recently there have been extensions to the sensitivity of nonlinear models, and to communities of interacting populations. Here we derive a fully general mathematical expression for the sensitivity of equilibrium abundances in communities of interacting structured populations. Our method yields the response of an arbitrary function of the stage class abundances to perturbations of any model parameters. As a demonstration, we apply this sensitivity analysis to a two-species model of ontogenetic niche shift where each species has two stage classes, juveniles and adults. In the context of this model, we demonstrate that our theory is quite robust to violating two of its technical assumptions: the assumption that the community is at a point equilibrium and the assumption of infinitesimally small parameter perturbations. Our results on the sensitivity of a community are also interpreted in a niche theoretical context: we determine how the niche of a structured population is composed of the niches of the individual states, and how the sensitivity of the community depends on niche segregation.
authors.affiliation: Department of Ecology and Evolutionary Biology, University of Michigan, 830 North University, Ann Arbor, MI 48109-1048, United States. Electronic address: dysordys@umich.edu.
authors.forename: György
authors.initials: G
authors.lastname: Barabás
authors.affiliation: Department of Biological Physics, Eötvös Loránd University, Pázmány Péter sétány 1A, H-1117, Budapest, Hungary. Electronic address: geza.meszena@elte.hu.
authors.forename: Géza
authors.initials: G
authors.lastname: Meszéna
authors.affiliation: Department of Ecology and Evolutionary Biology, University of Michigan, 830 North University, Ann Arbor, MI 48109-1048, United States. Electronic address: aostling@umich.edu.
authors.forename: Annette
authors.initials: A
authors.lastname: Ostling
mesh_terms: D008962:Models, Theoretical; D011157:Population Dynamics
keywords: Coexistence; Matrix models; Robustness