title: Probability bounds analysis for nonlinear population ecology models.
abstract: Mathematical models in population ecology often involve parameters that are empirically determined and inherently uncertain, with probability distributions for the uncertainties not known precisely. Propagating such imprecise uncertainties rigorously through a model to determine their effect on model outputs can be a challenging problem. We illustrate here a method for the direct propagation of uncertainties represented by probability bounds though nonlinear, continuous-time, dynamic models in population ecology. This makes it possible to determine rigorous bounds on the probability that some specified outcome for a population is achieved, which can be a core problem in ecosystem modeling for risk assessment and management. Results can be obtained at a computational cost that is considerably less than that required by statistical sampling methods such as Monte Carlo analysis. The method is demonstrated using three example systems, with focus on a model of an experimental aquatic food web subject to the effects of contamination by ionic liquids, a new class of potentially important industrial chemicals.
authors.affiliation: Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556, USA.
authors.forename: Joshua A
authors.initials: JA
authors.lastname: Enszer
authors.affiliation: Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556, USA.
authors.forename: D
authors.initials: D
authors.lastname: Andrei Măceș
authors.affiliation: Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556, USA. Electronic address: markst@nd.edu.
authors.forename: Mark A
authors.initials: MA
authors.lastname: Stadtherr
mesh_terms: D000818:Animals; D017753:Ecosystem; D020387:Food Chain; D055641:Mathematical Concepts; D008954:Models, Biological; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D011336:Probability
keywords: Food webs; Ionic liquids; Nonlinear dynamics; Parameter uncertainty; Population ecology; Probability distributions