4th International Conference on Integrating GIS and Environmental Modeling (GIS/EM4):
Problems, Prospects and Research Needs. Banff, Alberta, Canada, September 2 - 8, 2000.

Modeling the propagation of land clearance using cellular automata and the implications for nature conservation

GIS/EM4 No. 93

Brett A. Bryan

Abstract

Often, little is known of the progression of land clearance in agricultural landscapes. This study uses cellular automata to model the progression of land clearance in the Mt. Lofty Ranges of South Australia. Based on a few simple rules such as the probability of land clearance and the number of neighboring cells cleared, spatially complex clearance propagation results. The end result of the cellular automata is found to closely mimic the actual historical progression. The propagation of land clearance as predicted by the cellular automata sheds light on the time since isolation of remnant habitat patches and hence, the advancement of species relaxation. This information has implications for nature conservation and restoration.

Keywords

Land clearance, propagation, cellular automata, environmental modeling, GIS, conservation, restoration.

Introduction

The distribution of remnant vegetation in the landscape is dependent upon the protection of land in nature reserves and the distribution of land clearance. Land clearance and reserve selection are often significantly influenced by the distribution of certain physical environmental properties (Pressey and Tully 1994). Without wishing to oversimplify the process, land clearance for agriculture has often targeted high productivity environments whereas low productivity environments have been avoided by clearance or targeted for reserve selection. Thus, environmental and geographical properties influence the propagation of land clearance.

Some thinkers (Goodwin 1994, Coveney and Highfield 1995) are questioning the complex nature of many processes operating in nature and tending more towards non-linear explanations and theories of self-organization. The progression of land clearance and fragmentation may also exhibit qualities of self-organization. Cellular automata are a locally-adaptive, globally evolving n dimensional array of cells which are capable of modeling self-organizing behavior in systems. Cellular automata are iterative and are based upon a set of rules involving the state of each cell and the neighborhood conditions which together define the behavior of the automaton.

In this study the propagation of land clearance in a region is modeled using cellular automata. The end result of the model (the distribution of remnant vegetation) is not important - indeed, it is already known in great detail. Rather, it is the propagation of land clearance in space and over time that are of interest in this study. The propagation of land clearance has ecological implications with respect to the time since isolation of patches and the advancement of species relaxation and implications for nature conservation and restoration.

Cellular Automata and Spatial Propagation

Initially developed by Ulam (1952) and Von Neumann (1966), cellular automata have been applied to model criticality in complex systems (Langton 1990, Packard 1988, Mitchell and others 1993; Green 1990, 1993, 1994) and in modeling spatial propagation. The latter have been less concerned with criticality but have been more interested in calibrating the spatial propagation of the model to the accurate portrayal of non-critical real-world spatial processes (e.g. Clarke and others 1994, Turner and others 1994, Hatamian 1996).

Spatial heterogeneity has been shown to affect the propagation of disturbance through a landscape (Romme 1982). Turner and others (1989) modeled the spread of disturbance across heterogeneous landscapes using percolation theory. The authors simulated disturbance as a function of the proportion of the landscape occupied by disturbance-prone habitat, the frequency (probability of initiation) and the intensity (probability of spread).

Methods

The propagation of land clearance in the Mt. Lofty Ranges (Figure 1) is modeled using cellular automata. The models involve different initial conditions of several potential settlement sites in agriculturally suitable areas. A set of simple neighborhood heuristics defines how a cell reacts to the disturbance conditions of its surroundings and the probability of clearance. In this way, a non-critical local interaction heuristic interacts with the clearance probability to recreate the process of landscape fragmentation in the Mt. Lofty Ranges. The distribution of remnant vegetation in the study area is presented in Figure 2.

Three factors are included in the model and influence the spatial propagation:

1. Initial Conditions: The geographic position of the introduction of disturbance determines from where the subsequent disturbance propagates.

2. Clearance probability: The probability that an area becomes cleared may be determined by environmental and geographic properties of the area. For example, land clearance targets the land most suitable for agriculture and avoids other areas.

3. Local Interaction: Disturbance propagation from a point is dependent upon its immediate neighborhood. The greater the disturbance conditions in the immediate neighborhood, the greater the probability the cell will also be subject to the same disturbance.

The initial conditions define the points from which clearance propagation begins. From these points land clearance may iteratively propagate through the landscape according to the clearance probability and the amount of clearance in the local neighborhood of each cell.

Probability of Land Clearance

The probability of land clearance was assessed by determining the relationship between the spatial distribution of remnant vegetation and the distribution of six environmental and geographic variables (Table 1). Multivariate logistic regression was used to predict the presence of remnant vegetation (P(naturalness)) using SPSS . The probability of land clearance P(clearance) = 1 - P(naturalness) was then computed for each cell in the study area using the regression equation and the GRID Algebra functionality of ArcInfo such that 0 <= P(clearance) <= 1. The predictive power of the regression was assessed by graphing the number of cells supporting remnant vegetation against that predicted by the equation.

Cellular Automata

Cellular automata were programmed in ArcInfo's Arc Macro Language (AML) and GRID Algebra. The program interactively prompts the user to input the number of iterations required, the initial conditions and the clearance probability which both vary spatially. The neighborhood of a cell is defined as the 8 adjacent cells immediately surrounding it on the 2-dimensional plane. The Focalsum function is used to calculate for each cell how many neighboring cells are cleared at the beginning of each iteration. The state of each cell (cleared (1) or natural (0)) at the end of each iteration is calculated on an individual cell basis according to its neighborhood conditions and its probability of clearance using a nested conditional statement.

Model Calibration

The cellular automata were calibrated using trial and error. The CA was run using different values for P(clearance) with differing effects. Values were adjusted until the neighborhood interactions and clearance probability were considered to have approximately equal effect and the propagation of land clearance occurred in a plausible fashion and the end result resembled the current distribution of remnant vegetation.

Model 1

Initially, a linear relationship between the probability of clearance the neighborhood conditions was trialed. In effect, the heuristics stated that if one neighboring cell is cleared and P(clearance) > 0.9 then the cell is cleared, if two neighbors are cleared and P(clearance) > 0.8 then the cell is cleared and so on. Initial conditions were defined as every cell is initially vegetated except cells with a clearance probability of 0.99 which were cleared. In addition, a regeneration heuristic was also built in. In effect, if a cleared cell has all 8 neighbors vegetated for 2 consecutive iterations to regenerate. Propagation according to these heuristics was unrealistic.

Model 2

Successive recalibration of the heuristics seemed to result in more of a balance in the influence of the neighborhood function and clearance probability. In model 2 the non-linear interaction between the neighborhood conditions and clearance probability in the cellular automata resulted in a plausible pattern of propagation of clearance through the landscape (see below). The regeneration heuristic (see above) was also included.

1. If one of the neighboring cells is cleared and P(clearance) > 0.965 then the cell becomes cleared.

2. If two of the neighboring cells are cleared and P(clearance) > 0.92 then the cell becomes cleared.

3. If three of the neighboring cells are cleared and P(clearance) > 0.87 then the cell becomes cleared.

4. If four of the neighboring cells are cleared and P(clearance) > 0.82 then the cell becomes cleared.

5. If five of the neighboring cells are cleared and P(clearance) > 0.75 then the cell becomes cleared.

6. If six of the neighboring cells are cleared and P(clearance) > 0.65 then the cell becomes cleared.

7. If seven of the neighboring cells are cleared and P(clearance) > 0.45 then the cell becomes cleared.

8. If all eight of the neighboring cells are cleared and P(clearance) > 0 then the cell becomes cleared.

9. If a cell satisfies none of the above conditions then it remains in its natural state.

Model 3

A third model was run using the same heuristics as in the second model above and the same regeneration function. However, instead of settlement propagating from the most suitable land of the study area, random cells totaling 500 ha were selected for the sites of initial settlement. In addition, a random settlement function was also included in the third model. The random settlement function involved a heuristic which randomly selects vegetated cells. If any of the selected cells have a P(clearance) > 0.965 then the cell becomes cleared.

Model 4

With the advantage of hindsight provided by historical reality, it was considered that the calibration of the heuristics were a little too conservative and tended to halt the propagation of land clearance prematurely. A fourth cellular automaton was run which included randomized initial conditions as well as the regeneration and random settlement functions. However, the heuristics were relaxed slightly:

1. If one of the neighboring cells is cleared and P(clearance) > 0.95 then the cell becomes cleared.

2. If two of the neighboring cells are cleared and P(clearance) > 0.91 then the cell becomes cleared.

3. If three of the neighboring cells are cleared and P(clearance) > 0.86 then the cell becomes cleared.

4. If four of the neighboring cells are cleared and P(clearance) > 0.8 then the cell becomes cleared.

5. If five of the neighboring cells are cleared and P(clearance) > 0.72 then the cell becomes cleared.

6. If six of the neighboring cells are cleared and P(clearance) > 0.62 then the cell becomes cleared.

7. If seven of the neighboring cells are cleared and P(clearance) > 0.4 then the cell becomes cleared.

8. If all eight of the neighboring cells are cleared and P(clearance) > 0 then the cell becomes cleared.

9. If a cell satisfies none of the above conditions then it remains in its natural state.

Results

Clearance Probability

The results of logistic regression performed on the presence/absence of remnant vegetation using six environmental and geographic variables are presented below (Table 2). The regression equation was found to successfully predict whether a cell is vegetated (Figures 3 and 4).

Clearance Propagation

Neighborhood interactions seemed to dominate model 1 and clearance propagation was not realistic. Initial colonization sites within areas with a high probability of clearance quickly coalesced and became large disturbance patches. These concentrations of clearance expanded along geometrically simple paths such that disturbance proceeded as a front or wave. Patches also tended to be geometrically simple rather than the fractal shapes commonly found in the landscape. Hence, this first model illustrates the sensitivity of the CA to the heuristics and the need for precise calibration, and it is not considered further.

Recalibration of the heuristics in Model 2 resulted in a more fractal propagation of clearance through the landscape and a balance between the influence of neighborhood and clearance probability. The propagation of land clearance was much more realistic and quickly spread throughout the Adelaide Plains, McClaren Vale, coastal Fleurieu Peninsula and eastern Mt. Lofty Ranges areas. 

The third model using the same heuristics as the second with a random grid of initial conditions and including randomized settlement and regeneration heuristics, demonstrated the limited effect of initial conditions on fragmentation. Contrary to expectations land clearance propagation from random initial conditions was very similar to that propagating from the highest probability cells as in the second model.

In model 4 heuristics were significantly altered to facilitate more extreme fragmentation of the remnant habitat of the study area. As a result land clearance tended to cease much later in the process at a more advanced stage of fragmentation (Figure 5). Although there is little quantitative information documenting the spread of clearance in the Mt. Lofty Ranges, anecdotal reports and historical aerial photography seem to support this model . The final landscape structure produced by model 4 was very similar to that extant today (compare Figure 5 and Figure 2). 

Discussion

The Evolution of Landscape Structure

Linear heuristics in model 1 defining the interaction of neighborhood and clearance probability did not yield an intuitively plausible model of clearance propagation through the landscape. A non-linear relationship yielded much more plausible fractal expansion of land clearance. Decreasing the P(clearance) requirements for the various neighborhood conditions in the heuristics increased the speed of land clearance and caused fragmentation to cease at a more advanced stage.

Non-linear systems are often very sensitive to small variations in initial conditions. Surprisingly however, initial conditions had little effect on the propagation of clearance through the landscape. The very first few iterations exhibited significantly different initial clearance loci but within a few iterations, behavior of the systems converged. Typically, initial cleared loci within the large expanses of high P(clearance) coalesced rapidly. Even the implementation of a random land clearance element did not significantly alter the propagation of clearance through the landscape.

Implications for Ecology and Conservation

Landscape structural metrics can be calculated which provide indicators of the ecological viability of patches of remnant natural habitat. However, regression does not reveal how the landscape structure came to be. The propagation of land clearance as indicated by the cellular automata suggests several possible ecological effects of the fragmentation process.

Significant disparities occurred in the time since isolation of patches in different parts of the study area. Land clearance and fragmentation occurred early and proceeded quickly through the northern and eastern parts of the study area in addition to the McClaren Vale area. Many small, isolated patches of remnant habitat in these areas are residual to this rapid expansion and have been isolated for a relatively long time. Ecologically, it is suspected that these patches may be more degraded than remnants experiencing a shorter time since isolation due to the process of species relaxation (Begon and others 1996). Species relaxation causes the gradual decline of species populations and gradual extinction through various processes related to the change in spatial habitat structure including inbreeding depression, unrequited immigration, and demographic stochasticities. Time since fragmentation and isolation is extremely important ecologically and may affect the nature and effectiveness of regional conservation measures.

Land clearance separated major habitat concentrations such as the Fleurieu Peninsula from the central ranges fairly early on. Thus, it is possible that, because of the long time since separation, species populations may exhibit significantly different genetic material. As fragmentation progressed, the large expanse of natural habitat in the center and north of the study area became heavily incised, significantly reduced in area, yet it remained connected until late in the fragmentation process. Incursions from both the east and west finally resulted in the fragmentation of this last remaining contiguous expanse.

Thus, patches of remnant habitat along the spine of the Ranges were of significant size and remained connected until much later in the process of fragmentation. Hence, species relaxation not have proceeded nearly as far as it has in patches isolated for longer periods. Therefore, at present these nodes have suffered less degradation in terms of species relaxation and may offer greater ecological infrastructure on which to base conservation and restoration efforts. However, relaxation is continuing to occur and this advantage may be lost if significant measures in the form of region biodiversity planning are not taken to mitigate further relaxation.

Conclusions

Theories of complex systems and self-organization suggest that the evolution of complex structure in nature may be the result of the operation of non-linear processes. Cellular automata provide a tool by which the non-linear spatial propagation of land clearance could be modeled. It is not the intention here to oversimplify the complex system of the evolution of landscape structure under modern landuse. However, the aim of creating a clearance propagation model by which land clearance could possibly have occurred was achieved. The global operation of spatial propagation of the cellular automata, influenced by clearance probability, provides a possible mechanism of clearance propagation in the Mt. Lofty Ranges study area. It is not the end result of the model that is of interest in this study but rather the propagation of land clearance. The cellular automata reveal significant ecological implications of the fragmentation process that are not considered by standard landscape structural metrics. This propagation has significant implications for biodiversity conservation and restoration because it suggests areas that may have been subject to isolation for longer periods of time and where species relaxation may have progressed to an advanced degree. Conservation measures might be most effective targeting areas isolated later in the fragmentation process and restoration effort concentrated on the habitat patches more severely degraded by species relaxation.

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Author

Brett A. Bryan

Education Coordinator

National Key Centre for Social Applications of GIS

Doctoral Candidate

Department of Geographical and Environmental Studies

Department of Applied and Molecular Ecology

University of Adelaide, North Terrace Adelaide, South Australia 5005.
Email:bbryan@gisca.adelaide.edu.au, Tel: +61-8-8303-3973, Fax: +61-8-8303-3498.