March 19, 1998 NCEAS Working Group Report.

"Investigating alternative land use/habitat conservation strategies using GIS and optimization modeling"
July 1996-August 1998
Co-investigators: Michael Gilpin, Peter Stine, Richard Church, Ross Gerrard

The focus of our project is on creation of new modeling tools, particularly optimization methods, to approach land use decisions with respect to habitat conservation goals and the realities of economic development. Our study site is the Eastern Alameda-Contra Costa Biodiversity Study Area in northern California, east of San Francisco Bay and comprising 228,000 acres. The land cover in the area is roughly two-thirds annual grassland and one-fifth oak woodland, with the remainder in agriculture, urban, and shrubland, and wetlands. We have a working group of 8-10 persons involved, including participants from academia, county planning and regional park agencies, California Department of Fish and Game, and USGS Biological Resources Division.

We were fortunate to start the project with rather complete GIS-based landscape and habitat information on eastern Alameda and Contra Costa Counties put together by the consulting company of Jones and Stokes (and later augmented by us). In addition, we knew of a variety of algorithmic approaches to reserve design and selection, all of which had some kind of recognizable deficiency. Our task was to see whether we could, in the context of real data, improve the logic of reserve optimization.

We commenced in the summer of 1996 with a scoping meeting attended by all of the original 10 group members. Soon, however, a core group of Richard Church (Geography, UC Santa Barbara), Ross Gerrard (NCEAS postdoc), Stine and Gilpin, having acquainted ourselves with weaknesses in previous approaches, started to fashion an alternative approach that better fitted the underlying biology.

Rick Church noted that the existing approaches to reserve optimization invariably work with spatial units (building blocks) that are not, of themselves, very biological. They are almost always square in shape, and they are typically of a scale that does not often accord with anything of biological significance. Rather, the scale accords itself with something relevant to the GIS input. Sometimes these units of the optimization are too big. They might be 15 minute topographic sections, or entire drainages (which might be polygons rather than squares). Such large units typically contain a multidimensional vector of optimizable entities, usually in the form of a binary presence/absence vector. By adding together a few such units, it is often possible to obtain at least one kind of each entity from the required list. However, the distribution and abundance of the entities within the unit is very seldom spatially resolved. This leads to the problem that the "solution" for one entity might be overly generous, while the for a second it might be less than viable.

When the cells for optimization are small, e.g., on the range of a hectare, there are some different problems. For one thing, the underlying computations involved in the optimization approach might become prohibitively large.

But Church and Gerrard recognized a different problem. An optimization proceeds under a set of constraints. The more constraints, the more computationally complex the problem. Furthermore, some constrains are conditional, making it difficult simply to write them down. Consider the kit fox, which we had to deal with in our real world situation. Our minimum map unit is a square cell, 200 meters on a side. A territory for a kit fox pair might be as large as 4 square miles. Optimization necessarily has to deal with integer numbers of kit fox territories, each of which has to be rational given the underlying habitat suitabilities. Writing this into a linear programming model is almost fundamentally intractable.

If we could pre-solve the problem to be based on reasonable biological entities, we could then use more straightforward optimization techniques, such as discrete linear programming, to build a composite solution. It is this novel insight that we have been pursuing these last many months. And on it we have made considerable progress.

We started with the kit fox. The kit fox is recognized as an appropriate "umbrella" species for the grassland habitat in the area (two-thirds of the study region). It has the greatest spatial requirement of any grassland species, requiring patches four square miles in size. In addition, it is a federally listed endangered species and thus must be considered in land use planning decisions as growth pressures mount and the possibility of an area-wide multi-species Habitat Conservation Plan looms. It is with the kit fox that we have made our initial progress. We shall follow this with other elements of Alameda and Contra Costa biodiversity.

The first step was to evaluate the 4 hectare cells from the standpoint of suitability to a pair of kit foxes. This evaluation had both an intrinsic and a contextual component. To base our analysis on sound footing, Stine enlisted several kit fox experts for help in delineating fundamental kit fox habitat requirements. Individuals who assisted included Sheila Larson and Heather Bell (U.S. Fish and Wildlife Service), Linda Spiegel (California Energy Commission), Kevin Hunting (California Department of Fish and Game), and also Kathy Ralls and Patrick Kelly, who lead another NCEAS team. With Gerrard acting as main GIS analyst, our core team produced a grid-based depiction of the landscape evaluated from the standpoint of kit fox territory suitabilities. Extensive development of appropriate GIS data structures and operations, particularly in GRID, were necessary to derive this "total habitat values" raster datalayer pertaining to the kit fox.

The habitat value grid was passed to Mike Gilpin, who created a technique and associated computer code to construct acceptable kit fox territories on the habitat values grid. Gilpin produced a model that from any initial start cell (e.g., the den of a kit fox pair) produces a minimal territory, which we term a patch. This is performed with a kind of fuzzy optimization. Since single cell suitability indices are integers running from -6 to 6, there are normally multiple equivalent solutions to the single pair territory problem. In principle, Gilpin's algorithm can find all of them. The important thing, however, is to find several. This optimization model has a number of control parameters that govern the shape and the location of the edge of the territory. Once completed, Gilpin passed his codes to Gerrard, who ran them to create numerous patches starting from many different seed cells. In this way, we generate a set of candidates that liberally samples the potential habitat available for the kit fox. At this point, there is a technical hurdle in that the set of patches must be imported into the GIS environment for display and further analysis. Due to the large number and variety of patches, it was necessary to invest considerable effort in specialized GIS codes that provide menu-driven access to any patch a user desires to inspect.

While Gilpin was pursuing the generation of appropriate territories, Gerrard and Stine were attempting to grasp the socioeconomic side of the landscape. To this end, we applied GIS data on zoning, proximity to urban limit lines, presence of planned or pending development projects, public vs. private ownership, etc. to manufacture another grid datalayer reflecting the difficulty of conserving land, or the "cost" of placing it in protected status.

Our approach to making land use prescriptions is an attempt to integrate the biology of the problem, represented by the kit fox habitat patches, with the socioeconomics of the problem, represented by the derived cost surface. Ideally, we could conserve sufficient kit fox or other habitat by acquiring only "cheap" land. Unfortunately, this is probably not the case, at least if habitat sufficient to allow the species to persist long-term is to be acquired. Realizing the inevitable conflict between the two issues, what we are interested in is minimizing that conflict by minimizing the "cost" or conservation resistance of a set of kit fox habitat patches. To accomplish this, we have a mathematical formulation, known as an integer programming model, that selects a specified number of animal territories to minimize conflict with competing land uses. Writing such a model is not a simple exercise and is mostly the work of Rick Church of our team, who specializes in spatial optimization. Our optimization model represents an end product; it is the long-term purpose behind the creation of the habitat value map, the patches, and the cost map.

Solving the optimal patch siting model entails several steps. A large number of patches are candidates that could be selected - this ensures that all potential areas are eligible for consideration. However, we cannot allow two patches to inhabit the same area or substantially the same area, which they likely would as they "compete" with each other to be located in "cheap" areas. This means that the GIS must be utilized to evaluate the overlap of all patch pairs. Patch pairs that overlap too much cannot simultaneously be selected, necessitating a specialized "anti-overlap" constraint in the optimization model. Another major step required for the optimization is to differentiate patches, nominally all equivalent, by other relevant measures such as shape. In an area pockmarked with different habitats, a patch will be composed of cells that give it a more elongated shape than in an area that is exclusively open grassland. We use the GIS to calculate perimeter/area ratio for each patch, and discriminate in the optimization between the cheapest patches and the most compact patches. In this way we can conduct a truly multi-objective analysis that reveals the tradeoffs between patch cost and shape, as well as the number of patches selected.

After a year and a half, we have substantially completed the single-species optimization analysis that we set out to do. Our future efforts will be substantially facilitated by NCEAS' recent acquisition of the Cplex mathematical programming software, running on a four-processor Silicon Graphics computer since early March 1998 at the Center. Previously, we were limited to an older Sun Sparc10 workstation provided courtesy of Rick Church. We are currently gathering biological input for at least one additional species and are developing a second major optimization model that will solve the problem for two species and hopefully identify fruitful opportunities for conserving multiple habitats within the same reserve sites. We at this point envision submitting for publication a manuscript on the GIS grid analysis that produced the kit fox habitat values, a manuscript on the generation of patches, a manuscript on the optimal patch selection model, and an overview paper. This forecast is a minimum and does not include expected papers dealing with multi-species applications.

We have so far done all of our work with the end user in mind. All of our work returns graphical feedback. Thus, conservation decisionmakers will be able to review our work to check the logic, and, more importantly, to input their own values for some of the parameters.

We believe our project is an important synthesis that could not have been done in any way other than with NCEAS support. Our core group, having gotten familiar with one another in several face to face sessions, has been able to sustain progress while working in an Internet collaboration. Our web site not only documents our approach, it has proved the focus and forum for our intellectual discussions.