title: A new hypervolume approach for assessing environmental risks.
abstract: Assessing risks of uncertain but potentially damaging events, such as environmental disturbances, disease outbreaks and pest invasions, is a key analytical step that informs subsequent decisions about how to respond to these events. We present a continuous risk measure that can be used to assess and prioritize environmental risks from uncertain data in a geographical domain. The metric is influenced by both the expected magnitude of risk and its uncertainty. We demonstrate the approach by assessing risks of human-mediated spread of Asian longhorned beetle (ALB, Anoplophora glabripennis) in Greater Toronto (Ontario, Canada). Information about the human-mediated spread of ALB through this urban environment to individual geographical locations is uncertain, so each location was characterized by a set of probabilistic rates of spread, derived in this case using a network model. We represented the sets of spread rates for the locations by their cumulative distribution functions (CDFs) and then, using the first-order stochastic dominance rule, found ordered non-dominant subsets of these CDFs, which we then used to define different classes of risk across the geographical domain, from high to low. Because each non-dominant subset was estimated with respect to all elements of the distribution, the uncertainty in the underlying data was factored into the delineation of the risk classes; essentially, fewer non-dominant subsets can be defined in portions of the full set where information is sparse. We then depicted each non-dominant subset as a point cloud, where points represented the CDF values of each subset element at specific sampling intervals. For each subset, we then defined a hypervolume bounded by the outermost convex frontier of that point cloud. This resulted in a collection of hypervolumes for every non-dominant subset that together serve as a continuous measure of risk, which may be more practically useful than averaging metrics or ordinal rank measures. Overall, the approach offers a rigorous depiction of risk in a geographical domain when the underlying estimates of risk for individual locations are represented by sets or distributions of uncertain estimates. Our hypervolume-based approach can be used to compare assessments made with different datasets and assumptions.
authors.affiliation: Natural Resources Canada, Canadian Forest Service, Great Lakes Forestry Centre, 1219 Queen Street East, Sault Ste. Marie, ON, P6A 2E5, Canada. Electronic address: denys.yemshanov@canada.ca.
authors.forename: Denys
authors.initials: D
authors.lastname: Yemshanov
authors.affiliation: USDA Forest Service, Southern Research Station, Eastern Forest Environmental Threat Assessment Center, 3041 East Cornwallis Road, Research Triangle Park, NC, 27709, USA.
authors.forename: Frank H
authors.initials: FH
authors.lastname: Koch
authors.affiliation: Natural Resources Canada, Canadian Forest Service, Great Lakes Forestry Centre, Sault Ste. Marie, ON, Canada.
authors.forename: Bo
authors.initials: B
authors.lastname: Lu
authors.affiliation: Natural Resources Canada, Canadian Forest Service, Great Lakes Forestry Centre, Sault Ste. Marie, ON, Canada.
authors.forename: Ronald
authors.initials: R
authors.lastname: Fournier
authors.affiliation: USDA Animal and Plant Health Inspection Service, Centre for Plant Health Science and Technology, Plant Protection and Quarantine, Fort Collins, CO, USA.
authors.forename: Gericke
authors.initials: G
authors.lastname: Cook
authors.affiliation: Natural Resources Canada, Canadian Forest Service, Great Lakes Forestry Centre, Sault Ste. Marie, ON, Canada.
authors.forename: Jean J
authors.initials: JJ
authors.lastname: Turgeon
mesh_terms: D000818:Animals; D004777:Environment; D005843:Geography; D006801:Humans; D008962:Models, Theoretical; D018570:Risk Assessment; D035501:Uncertainty
keywords: Asian longhorned beetle; Environmental risks; Hypervolume; Invasive species; Non-dominant set; Stochastic dominance; Uncertainty