Roger L. Slothower, Paul A. Schwarz, and Kevin M. Johnston

Some Guidelines For Implementing Spatially Explicit, Individual-Based Ecological Models Within Location-Based Raster GIS.

ABSTRACT

There is growing interest in using raster GIS to model dynamic spatial processes. Moreover, individual-based modeling is an increasingly common aproach to modeling spatially explicit ecological processes. We consider several issues that are critical to implementing individual-based models within raster GIS. These issues are: 1) defining the individual in terms of raster GIS grid cells; 2) defining the spatial neighborhood surrounding the individual; and 3) defining the rules that govern the dynamics of the individual. We also discuss how these issues are used in the modeling of several spatially explicit ecological processes: animal movement, plant competition, and landscape change.

INTRODUCTION

Although many ecologists have embraced GIS for managing, analyzing, and displaying spatial data, fewer ecologists are using GIS for modeling dynamic ecological processes. However, there is growing interest among ecologists and many others in using GIS for dynamic modeling witness this conference and the previous two NCGIA-sponsored conferences. While much of the interest in dynamic modeling using GIS has focused on better integration between simulation models and GIS software (e.g., Hunsaker et al. 1993), there is also growing interest in developing dynamic models within GIS (e.g., Ball 1994, Burrough 1993, Maidment 1993b). GIS and raster GIS software in particular posses many desirable features for developing data-intensive simulation applications, and raster GIS packages are rapidly evolving as generic application development environments for developing spatially explicit models. This paper presents and discusses several issues that are critical to the implementation within raster GIS of a class of ecological models known as individual-based models. In addition, this paper considers how these issues relate to the modeling of three broad classes of spatial processes through examples from the ecological literature: namely animal movement, plant competition, and landscape change. The authors acknowledge that some of these issues have been presented elsewhere, but to the best of authors' knowledge, this is the first summary of these issues and their relevance to modeling within raster GIS.

BACKGROUND

Individual-based models

There are several different approaches to the modeling of spatially explicit ecological phenomena. These approaches, such as reaction-diffusion models and patch models, have been reviewed recently emphasizing plant populations and communities by Czaran and Bartha (1992) and animal populations by Dunning et al. (1995). One modeling approach that has growing interest is the so-called individual-based approach. Individual-based models (IBMs) are organism-based models capable of modeling variation among individuals and interaction between individuals. The use of the individual-based modeling approach by ecologists has become more widespread following the publication of an influential paper by Huston et al (1988). This approach, as discussed by Huston et al. (1988), DeAngelis et al. 1992, and more recently by Judson (1994), acknowledges two fundamental biological principles. The first principle is that individual organisms are behaviorally and physiologically distinct because of genetic and environmental influences. The second principle is that interactions between individuals are inherently localized, i.e., organisms are influenced mostly by nearby organisms.

Although the simulation of many individual organisms can be expensive computationally, often the individual calculations themselves are relatively simple. This simplicity results from the fact that individuals usually interact according to a sequence of basic rules (Huston et al. 1988). These rules, when applied iteratively to many individuals over time, are capable of generating phenomenologically realistic and complex behavior (DeAngelis et al 1986, Huston et al 1988). These relatively simple rules can usually be expressed as algebraic statements which minimize the need for more complex mathematical operations that are associated with other modeling approaches involving differential equations. These simple algebraic statements can be translated readily into the command syntax of many raster GIS packages.

Raster GIS

A raster GIS models space by tessellating it into regular, discrete locations and assigning attributes to each location. The most common tessellation employed by raster GIS software is the square. An individual square cell can be viewed as a unique location within the tessellation or grid. While the grid itself may be georeferenced according to some coordinate system, space within a grid is implicit and is relative to the origin of the grid. Spatial information about a phenomenon is stored for each individual cell, and different phenomena can be stored as separate grids. Most operations in raster GIS process each cell in a grid sequentially and may involve one or more grids.

Ecological Processes

Although the specific spatial processes that are to be simulated are unique to each application, two common types of processes are animal movement and plant competition. Animal movement entails the transfer of an individual organism from one location to another location, and by definition, vacating the previous location. Movement entails both the movement itself as well as the perception or knowledge of space. Other ecological processes, such as foraging and dispersal, often incorporate movement. Plant competition is loosely defined to mean that the presence or proximity of one individual negatively affects the status (e.g. health or probability of success) of another individual plant.

ISSUES

In IBMs, space is continuous and location is explicit, while in raster GIS, space is discrete and location is implicit. Therefore the implementation of an IBM within raster GIS requires translating the definition of individuals, neighborhoods, and rules into the implicit locations used in raster GIS.

Defining the individual

To translate an IBM to raster GIS, it is necessary to define the individual organism in terms of a location. Defining individuals in terms of their locations was described by Molofsky (1994) as the key "trick." In their simplest form, an individual-based model simulates the actions of individual organisms and each organism interacts with others across space and through time. A state vector describing the individual organism includes explicit location coordinates. In the translation to raster GIS, the description of the individual becomes the description of the cell in which the individual organism is found. A state vector describing an individual location contains the necessary attributes to describe the contents of each cell, but in practice, each grid may represent only one attribute of the individual. The state vector now describes a cell, the location of which is implicit in the grid.

One of the defining principles of individual-based models is variation among individuals. When the individual is represented in a cell on a grid as a simple binary presence/absence, then variability between these individuals is either non-existent or must be represented within the rules as a stochastic element. True individuality exists only when the individual is represented by one or more unique values which interact with the rules of the model. It may be that the degree of individuality is determined by the range of values available for the state vector.

There are several approaches for incorporating this variation among individuals in raster GIS models. Increased variability between individuals implies more attributes for each individual, requiring a need to track these additional attributes. Various techniques can be used to keep track of these attributes: a grid for each attribute (resulting in multiple grids); a multiple attribute table that has a record for each individual; placing only similar individuals (such as an age or size class) onto the same grids; or even putting each individual onto its own grid.

It is a logical extension to also consider cases where the 'individual' represents more than one organism (Murdoch 1993). When the individual is a natural group, such as a herd (e.g., Turner 1993), stand, or family, then the rules governing the dynamics are defined in terms of the natural grouping. Aggregations such as populations and communities may not be so readily treated as individuals since the rules of the aggregation may be based on characteristics of the distribution of individuals within the group. However, an aggregation of individuals (especially plants) can often be treated as a uniform or homogeneous location (grid cell) within which the spatial interactions between individual organisms are ignored (Fahrig 1988, Hyman et al. 1991).

Defining individuals in terms of spatial locations is analogous to the modeling of particles using an Eulerian framework. Lagrangian models calculate the trajectories of masses of particles through space and time. Eulerian models, on the other hand, calculate fluxes (or movements) at fixed locations (Maidment 1993a, 1993b). In biological applications, the Lagrangian framework has been used to model the movement of individual organisms (e.g., plankton) while the Eulerian framework has been used to model density fluxes of organisms at fixed locations (Grunbaum 1994).

Defining the neighborhood

In addition to defining the individual, the zone of influence of an individual must also be defined in terms of location. The second principle of IBMs is that interactions between individuals are inherently localized, that is, organisms are influenced mostly by nearby organisms. In the translation of the IBM to raster GIS, the 'localized' area (i.e., the neighborhood) must be defined in terms of the locations which surround a given location. The influences on a location are defined by what is in the space around it.

In IBMs within raster GIS, the simplest neighborhood is one in which only the cells adjacent to the cell being processed are considered. More generally, the neighborhood can be defined as some finite, spatial domain. The definition of neighborhood can include:

The characteristics of the neighborhood need not be constant and may be a function of time or even of the individual organism. For example, different age classes, represented as separate grids, may require different size neighborhoods for a specific rule.

Defining the rules

The third issue to be considered is the definition of the rules governing an individual's behavior in terms of location. In an IBM, rules describe the dynamics of the individual and are dependent on the definition of both the individual and the neighborhood. These rules may be deterministic or stochastic. In raster GIS, rules are implemented as spatial operations. The types of operations available raster GIS are well described elsewhere (see Berry 1993, Tomlin 1990). The spatial extent of the operations can generally be associated with the classes of neighborhoods described above. A single ecological process may require several spatial rules. Movement, for example, requires at least two rules, one assessing the neighborhood it can perceive (or have knowledge of), and the other actually performing the move.

Time can be modeled as discrete or continuous in a discrete space system. In continuous time, an ecological rule is applied to an arbitrary location and the subsequent application of any rule recognize the results of all previously applied rules at all locations. In discrete time, the rule is applied to all locations 'simultaneously' without recognizing the changes made in adjacent cells. Raster GIS is well suited for discrete time modeling.

One important part of defining rules in raster GIS is an understanding the operations which are currently available. The current technology of raster GIS uses procedures which process each cell of the grid sequentially. Each cell becomes the focus cell, calculations based on an appropriate neighborhood are performed on that focus cell, and the state vector describing the cell is updated. The focus is then moved to the next cell and the calculations are repeated. Consequently, only the state of the focus cell is updated. If the value of a cell is going to change, it can only be changed when that cell is the focus cell. Thus, operations are based on the "focus" of any interaction. This requires a switch from calculating how a cell affects its neighbors to how a "focus" cell is affected by its neighbors. As an example of the two orientations, a tree conceptually disperses seeds to many locations, but raster GIS requires calculating, at each location, the trees that are contributing seeds to that location. This switch requires an inversion of the neighborhood. In an individual organism model, the neighborhood for a seed shadow may be to the southwest of a tree. In the raster GIS, that neighborhood will be inverted to reflect that the major seed input to the focus cell are the trees to the northeast.

It should be emphasized that this "focus" cell restriction may only be a technological limitation of the currently available operations in raster GIS software. The authors believe this to be an artifact of the ease of processing and contributions from the remote sensing field where symmetrical convolution filters were incorporated from electrical engineering (William Philpot, pers.comm.). There may be no reason why processing algorithms could not be written that permit writing to any cell in the grid regardless of the current focus.

DISCUSSION

Movement of animals and competition between plants are two examples of spatial ecological processes which can be modeled as IBMs in raster GIS. A discussion of known applications can provide insight into how the three implementation issues described above are critical to how models are implemented. There are only a few examples of IBMs which model these processes within raster GIS (e.g. Johnston 1992, Rechel 1992). Consequently, this discussion relies on examples from the ecological literature which illustrate the issues presented above.

Some ecological modelers use cellular automata as a modeling approach. Cellular automata are conceptually related to raster GIS in that individuals are placed on a of square grid and the rules are usually implemented within a neighborhood of adjacent cells. Generally, the rules model the transition between states for an individual and are only dependent on the previous state of the individual and the other individuals in the neighborhood, although many of the ecological applications loosen that definition to include a wider range of independent variables (e.g., Ellison and Bedford 1995). Itami (1994) argues that cellular automata models are a logical extension of raster GIS and has developed a specialized GIS for performing cellular automata simulations, as have Theobald and Gross (1994). An alternative to raster GIS and cellular automata is the development of an application-specific system for modeling ecological processes, as seen in the work of Turner et al. (1993). Such systems tend to be application-specific but are often less flexible than the more generic raster GIS packages.

Animal movements

Johnston (1992) builds a predator/prey model which demonstrates that movement includes both a perception neighborhood and a movement neighborhood. The model contains four different sub-models; deer browsing, deer escaping, hunter movement and hunter shooting. The browsing deer has a neighborhood of the adjacent cells in which the rules of interaction (i.e., perception of food resources) and the rules of movement are applied. The hunted deer has a neighborhood in a 3 cell radius (apparently about 37 cells) in which hunters can be perceived. The hunter has a neighborhood of the adjacent cells for perception of the habitat and movement, but has the larger 3 cell radius for perception of deer and shooting.

In a simulation model of foraging behavior, Turner and others (1993) develop an application-specific system in which the individual being modeled is a group of ungulates. With a common perception neighborhood, two different movement neighborhoods are compared; a 1-cell neighborhood and a maximum-forage or maximum-distance-per-day neighborhood. The rules for determining the movement are designed to assess the importance of proximity and quantity of food resources in the four cardinal directions within the perception neighborhood.

Plant competition

In Colasanti and Grime's (1993) cellular automaton model of competition between three generic plant types (ruderal, competitive, and stress tolerator), the individual is defined as a single plant and the neighborhood is composed of the four adjacent cells. The rules model indirect competition as a Markov chain enhanced to include spatial proximity and the resource status of neighboring plants. Silvertown et al. (1992) also use cellular automata to model competitive interactions among five grass species. They also defined simple individuals, simple neighborhoods, and Markovian-type rules for modeling direct competition. In each of these examples, simple models provided significant insight into plant competition.

Landscape change models

Although not defined in terms of individual organisms, landscape change models can be discussed in terms of the issues presented above. Baker (1989) places landscape change models on a continuum of increasing spatial explicitness, culminating in a landscape "element model, in which change in individual landscape elements is modeled" (p. 121). Although Baker explicitly distinguishes these from individual organism models, he acknowledges that they are analogous to individual-based models but from a landscape perspective, that is, the same techniques presented above for individual-based models might also be applied to address questions focused on how landscapes change. The simulation by Turner (1988) of landscape change in Georgia is setup such that cells are arbitrary land uses, the neighborhoods are adjacent cells, and the rules are based on spatially-influenced transition probabilities. Although Turner's individuals are not organisms, the neighborhood and the rules are similar to those in the competition model of Colasanti and Grimes (1992). Ratz (1995) studied the influence of fire on boreal forest succession in which the "individual" was defined as a 4 ha forest stand, the neighborhood was composed of the four adjacent cells, and the rules were governed by stand's susceptibility to burning. While simple in nature, Ratz (1995) concluded that the dynamics of his model were consistent with empirical evidence.

Other considerations

Although raster GIS offers many attractive features as a spatial modeling environment, such as data management, spatial analysis and visualization, it has yet to reach its full potential. Burrough (1992) has argued that the current GIS data structures are too simplistic and that more sophisticated structures are needed. Moreover, the historical emphasis of GIS as a spatial database management system requires that the results of each spatial operation be verified and stored back in the database. Consequently, this imposes severe performance penalties when rapidly updating the database as required for dynamic process modeling. However, the development of GIS software that allows for the updating of grids that are stored in memory and are only stored back to disk when needed may help to reduce this performance penalty. In addition, boundary conditions are an important part of most spatially explicit models because they control edge effects, and the modeling of boundary conditions within raster GIS is often awkward or difficult. Finally, much of the terminology of GIS can be traced to its origins in geography which may not be familiar to ecologists, thus making GIS more difficult to use. Better user interfaces may rectify this thus make GIS packages easier to use. Many of these considerations are being addressed elsewhere during this conference. However, the authors believe that raster GIS is a viable development environment for ecological models because raster GIS is widely used to maintain ecological information, the command syntax is familiar to those ecologists already using GIS, and it includes many spatial operations that are useful for dynamic modeling.

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AUTHORS

Roger L Slothower
Department of Natural Resources
Cornell University
Ithaca, NY 14853
rs26@cornell.edu

Paul A. Schwarz
Cornell Theory Center
Ithaca, NY 14853-3801
schwarz@tc.cornell.edu

Kevin M. Johnston
Environmental Systems Research Institute, Inc
Oakham, MA 01068
kjohnston@esri.com

SF23 1/5/96 1600