Innovative Applications of O.R.
Optimal design of compact and functionally contiguous conservation management areas
Introduction
In many parts of the world conservation reserves are established to protect critical habitat areas from agricultural/urban development and managed to maintain or enhance species survival chances. Due to the scarcity of financial resources, determination of the optimal amount and location of those areas is an important issue. Typically, this is done by dividing the landscape into discrete land units (sites) and selecting an optimal subset of them assuming that each site provides measurable habitat services to the targeted species. This problem is often stated as minimization of the cost of selected sites while meeting the conservation goals (e.g., minimum occurrence of each species in selected sites), or maximization of a conservation objective (e.g. number of species protected) subject to the available resource constraints (Moilanen, Wilson, and Possingham 2009). These problems were addressed initially by using heuristic approaches (e.g., Pressey et al., 1993, Pressey et al., 1997). Later, they were formulated as linear mixed-integer programs (MIP) in the framework of the set covering problem (SCP) and maximal covering problem (MCP) (Camm et al., 1996, Church and ReVelle, 1974, Church et al., 1996, Cocks and Baird, 1989, Kirkpatrick, 1983, Polasky et al., 2001, Possingham et al., 2000, C. and ReVelle, 1973, Underhill, 1994, Williams and ReVelle, 1997). Although the optimal solutions of these MIP formulations are economically efficient, they usually lack spatial coherence. This may limit the chances of inter-site dispersal and long-term survival of species within the conservation reserve areas. Also, managing a spatially coherent reserve network is more convenient and efficient than managing many sites scattered over a large area. Therefore, additional mechanisms need to be introduced in the SCP and MCP formulations to take spatial properties into account when determining the optimal site selection.
Spatial criteria in reserve site selection may take a variety of forms (Haight and Snyder, 2009, Williams et al., 2005). Most commonly used criteria include compactness (Fischer and Church, 2003, Jafari and Hearne, 2013, Önal and Briers, 2003, Tóth and McDill, 2008, Wright et al., 1983), proximity of selected sites (Briers, 2002, Dissanayake et al., 2012, Miller et al., 2009, Nalle et al., 2002, Önal and Briers, 2002, Rothley, 1999, Snyder et al., 2007, Williams, 2008), habitat fragmentation (Önal and Briers, 2005, Önal and Wang, 2008), contiguity (Cerdeira and Pinto, 2005, Cerdeira et al., 2005, Cerdeira et al., 2010, Cova and Church, 2000, Duque et al., 2011, Jafari and Hearne, 2013, Marianov et al., 2008, Önal and Briers, 2006, Tóth et al., 2009, Wang and Önal, 2011, Wang and Önal, 2013, Williams, 2001; Carvajal et al., 2013), existence of buffers and corridors (Conrad et al., 2012, Williams, 1998, Williams and ReVelle, 1996, Williams and ReVelle, 1998, Williams and Snyder, 2005), and accessibility (Önal and Yanprechaset, 2007, Ruliffson et al., 2003). Incorporating these criteria in optimum site selection requires more sophisticated and computationally complex mathematical models than the SCP and MCP formulations. Consideration of multiple attributes together increases this challenge further. This article presents a linear integer programming model to incorporate compactness and connectivity criteria simultaneously.
Connectivity is an important factor for efficient functioning of conservation reserves. A well-connected reserve network1 allows the species to utilize all the resources available in the reserve and increases the likelihood of species survival and ability to colonize suitable habitat areas. This depends not only on the habitat characteristics of an individual reserve site, but also on the characteristics of the neighboring reserve sites (Van Teeffelen et al., 2006). Connectivity is approached in different ways. Metapopulation connectivity deals with spatially separated but interacting local populations in the reserve network (Hanski, 1999, Moilanen and Hanski, 1998, Moilanen and Hanski, 2001). Landscape connectivity, on the other hand, deals with the degree to which the landscape facilitates movement of species within reserves. Landscape connectivity can be achieved either by structural connectivity (or physical contiguity) that allows species to dwell in the reserve without having to get out of the protected area, or functional connectivity which deals with the degree to which a reserve facilitates species’ capability to move within the reserve (Bunn et al., 2000, Taylor et al., 2006, Taylor et al., 1993, Tischendorf and Fahrig, 2000, Urban and Keitt, 2001). A structurally connected reserve may not necessarily be functionally connected if physical characteristics of some sites impede movement within or between the reserved areas (e.g. presence of steep rocky terrains or water bodies, lack of sufficient vegetation or forest cover). Although the importance of functional connectivity has been widely acknowledged, a generally agreed upon operational definition of the concept is not yet available (Bélisle, 2005, Kadoya, 2009). Incorporating these two connectivity criteria in site selection may lead to dramatically different configurations. For instance, minimization of the reserve size along with the physical contiguity requirement may lead to an elongated, narrow and winding reserve configuration containing the best available but spatially dispersed sites (see, for instance, Cerdeira et al., 2005, Önal and Briers, 2006; Williams & Snyder, 2005 ). This would increase the likelihood of species’ exposure to unfavorable conditions within and outside the reserve area and may not work effectively if the individuals tend to roam around or move in random directions. A contiguous reserve configuration may include poor quality sites just to obtain physical connections (bridges) between good habitats. Such a reserve would not be functionally connected if the targeted species do not have the capability to cross those bridging sites. Therefore, in essence the reserve would consist of multiple ‘functionally detached’ sub-reserves some of which may not be large enough to provide adequate habitat services for a minimum viable population of the target species. On the other hand, a functionally connected reserve may not be structurally connected if the species (e.g. birds, butterflies) can crossover between closest, but not necessarily adjacent areas in the reserve. In many cases a network of multiple connected reserves is a preferred configuration than a single large connected reserve to safeguard against catastrophic events such as fire, diseases, etc.2 In this article we address these issues and present a linear integer programming model to determine an optimal compact and connected reserve network configuration where connectivity can be enforced in the form of structural connectivity and/or functional connectivity. We apply this approach to the protection of a ground-bound species where compactness, structural connectivity, and functional connectivity must be enforced together.
Section snippets
Problem description
Many rare, threatened, and endangered species in the U.S. are found within the boundaries or in the vicinity of military installations (Flather et al., 1994, Flather et al., 1998, Stein et al., 2008).3 The Department of Defense (DoD) allocates a significant amount of capital, human
The model
To address the issues described above we first partition the area considered for development of a conservation reserve5 into disjoint spatial units (e.g., a uniform square grid cover6
Computational efficiency
In general, discrete optimization models are difficult to solve, even in the linear MIP case, when a large number of constraints and discrete variables is involved. Therefore, the usefulness of the MIP formulation presented above may be an issue in large-scale reserve selection models. In this section, we test the computational efficiency of our formulation against two alternative contiguity and compactness formulations presented by Duque et al. (2011) and Jafari and Hearne (2013). In the
An empirical application
We present an empirical application of the model described by (1)–-(8), with and without incorporation of the habitat-adjusted distances given by (9), to select the best conservation management areas (CMA) for a keystone species, the Gopher Tortoise (GT), in Ft. Benning, Georgia. Over the past decades, the GT population in several southeastern states declined substantially (estimated as 80 percent) due to the loss of suitable habitats resulting from agricultural and urban development (BenDor,
Results and discussion
We first found the optimum spatially unrestricted selection of GT habitat sites, namely the minimum number of sites that collectively provide 20,000 units of habitat suitability.14 This solution is displayed in Fig. 5a. As expected and stated at the outset, this selection includes a highly scattered subset of sites which have highest habitat suitability. Clearly this selection is not a meaningful CMA
Concluding remarks
This article presented a linear integer programming formulation to incorporate reserve compactness and landscape connectivity as spatial criteria in reserve site selection. Compactness is achieved by minimizing the sum of pairwise distances between all sites assigned to a reserve and a central site of that reserve, both determined by the model simultaneously. The model includes an explicit constraint to achieve spatial contiguity, namely if a site is to be selected an adjacent site closer to
Acknowledgments
This research was partially supported by the ERDC-CERL Project no. W81EWF-7204-6330, CREES Project no. ILLU 05-0361, and National Natural Science Foundation of China (71202096).
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2022, Computers, Environment and Urban SystemsCitation Excerpt :Some have approached this using proxy approaches and measures, such as compactness suggested by Wright et al. (1983), Fischer and Church (2003) and Ligmann-Zielinska, Church, and Jankowski (2008). Specifically, compactness is the idea of being mutually interconnected, or circle like, where a measure is applied to selected land units, such as Wright et al. (1983) minimizing the total exterior perimeter, Onal, Wang, Dissanayake, and Westervelt (2016) relying on total weighted distance centrality and Validi, Buchanan, and Lykhovyd (2022) using moment-of-inertia. Researchers have used heuristic techniques to find patches, reflected in the work of Brookes (1997), Church et al. (2003) Duh and Brown (2007), Cao, Huang, Wang, and Lin (2012), Li, Church, and Goodchild (2014), Li and Parrott (2016), Ager et al. (2016) and Feng, Liu, and Tong (2018).