Ecological Modelling 221 (2010) 2243–2250 Contents lists available at ScienceDirect Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel Mathematical problem definition for ecological restoration planning Marissa F. McBride a,∗ , Kerrie A. Wilson b , Jutta Burger c , Yi-Chin Fang c , Megan Lulow c , David Olson c,d , Mike O’Connell c , Hugh P. Possingham b a University of Melbourne, School of Botany, Melbourne, Victoria 3010, Australia b University of Queensland, School of Biological Sciences, St. Lucia, Queensland 4072, Australia c Irvine Ranch Conservancy, 4727 Portola Parkway, Irvine, CA 92620-1914, USA d Conservation Earth Consulting, 4234 McFarlane Avenue, Burbank, CA 91505, USA article info Article history: Received 12 November 2009 Received in revised form 22 April 2010 Accepted 23 April 2010 Available online 30 June 2010 Keywords: Ecological restoration Restoration priorities Decision theory Conservation planning Ecological thresholds Ecosystem management abstract Ecological restoration is an increasingly important tool for managing and improving highly degraded or altered environments. Faced with a large number of sites or ecosystems to restore, and a diverse array of restoration approaches, investments in ecological restoration must be prioritized. Nevertheless, there are relatively few examples of the systematic prioritization of restoration actions. The development of a general theory for ecological restoration that is sufficiently sophisticated and robust to account for the inherent complexity of restoration planning, and yet is flexible and adaptable to ensure applicability to a diverse array of restoration problems is needed. In this paper we draw on principles from system- atic conservation planning to explicitly formulate the ‘restoration prioritization problem’. We develop a generalized theory for static and dynamic restoration planning problems, and illustrate how the basic problem formulation can be expanded to allow for many factors characteristic of restoration problems, including spatial dependencies, the possibility of restoration failure, and the choice of multiple restora- tion techniques. We illustrate the applicability of our generic problem definition by applying it to a case study – restoration prioritization on The Irvine Ranch Natural Landmark in Southern California. Through this case study we illustrate how the definition of the general restoration problem can be extended to account for the specific constraints and considerations of an on-the-ground restoration problem. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Ecological restoration, the process of “assisting the recovery of an ecosystem that has been degraded, damaged, or destroyed” (e.g. Hobbs and Cramer, 2008), is an increasingly important tool for delivering a diverse range of conservation outcomes (Dobson et al., 1997; Young, 2000). Restoration is used extensively for: sta- bilising degraded soils, returning biodiversity and habitat values to a landscape, reducing poverty and sequestering carbon diox- ide from the atmosphere (Jordan et al., 1988; Dobson et al., 1997; Lamb et al., 2005; Hobbs and Cramer, 2008). Regardless of its util- ity, the assisted restoration of habitat is characteristically time- and resource-intensive (Noss et al., 2009). While ecological restoration may be achieved with limited financial outlay (through, for exam- ple, the implementation of prescribed burning or the removal of introduced grazers), it can also entail costly reintroductions of rare species, replanting of diverse plant communities, and/or the cre- ation of specific ecological niches (Hobbs and Norton, 1996). Some landscapes may have the capacity to passively restore or naturally ∗ Corresponding author. Tel.: +61 3 8344 3305; fax: +61 3 9348 1620. E-mail address: m.mcbride@pgrad.unimelb.edu.au (M.F. McBride). regenerate, but others may fail to fully regain their natural biodi- versity and ecological integrity without active intervention (McIver and Starr, 2001). The likelihood of a successful outcome may also be linked to the cost and relative intensity of the restoration activ- ity selected (Dorrough et al., 2008). In such situations and when resources are limited, decisions about which areas to restore, when, and what restoration techniques to use must be made (Hyman and Leibowitz, 2000; Beechie et al., 2008). Previous examples of priority setting for restoration have tended to be based on scoring or rank- ing methods, or on expert opinion (O’Neill et al., 1997; McAllister et al., 2000; Cipollini et al., 2005; Petty and Thorne, 2005) although there are an increasing number of examples of the use of system- atic techniques to prioritize areas for restoration to achieve a range of objectives (Crossman et al., 2007; Bryan and Crossman, 2008; Crossman and Bryan, 2009). Regardless of the solution method, the process of restoration planning needs to be underpinned by a well- defined problem (Possingham, 2001). This problem definition must be sufficiently sophisticated and robust to account for the inherent complexity of ecological restoration, but also flexible enough to ensure applicability to a diverse array of restoration problems. To some extent a framework for restoration planning already exists in the considerable body of research focused on the design of protected area networks, commonly referred to as systematic con- 0304-3800/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2010.04.012