Optimizing wildlife habitat mitigation with a habitat defragmentation algorithm

Forest Ecology and Management 120 (1999) 245±251

Optimizing wildlife habitat mitigation with a habitat defragmentation algorithm Craig Loehle National Council of the Paper Industry for Air and Stream Improvement, 552 S. Washington Street, Suite 224, Naperville, IL 60540, USA Received 1 October 1998; accepted 2 December 1998

Abstract Habitat fragmentation is being increasingly recognized as a serious problem for a variety of wildlife species. While it is possible to approximately determine by eye where on a map a habitat alteration could be used to decrease fragmentation, this is a slow and imprecise method that is impractical for large maps. An algorithm is presented that automates this task. The method is based on concepts of diffusion-based chemical signaling. Many organisms use chemical signals spread by diffusion to detect prey or to ®nd conspeci®cs. Based on this concept, a `scent' is arti®cially generated for each unit of wildlife habitat and allowed to diffuse randomly. This creates a gradient around all habitat patches. A grid square located between two habitat patches that are close together will have a high concentration of `scent' and will be a candidate for converting to wildlife habitat to increase connectivity or to decrease edge. The algorithm chooses for conversion those squares with the highest concentration of `scent' that are not already habitat. The algorithm is shown to produce least-cost corridors to connect two patches, to ®ll in holes in an existing patch, and to decrease edge/interior ratios. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Optimization; Habitat fragmentation; Spatial models; Edge effect; Timber management; Wildlife management

1. Introduction Habitat fragmentation is increasingly being shown to adversely affect a variety of wildlife species (Bissonette, 1997; Gardner, 1998; Ribe et al., 1998; Root, 1998). Isolated habitat islands can suffer from random extinctions, but be too far from other suitable habitat for immigration to restore the population. In some cases a patch of habitat will be too small for a minimal home range or for a viable breeding population. Habitat fragments may be too small to include all types of resources that a species needs, such as a combination of drinking water, nesting trees, and food

sources. In other cases, it is the fragmentation per se that puts a species at risk. Some species suffer excessive predation at forest edges from open habitat predators, such as hawks. Cow birds are a particular problem at forest edges adjacent to farmland. Fragmentation can also interfere with seasonal movement patterns, such as elk moving along elevational gradients or salamanders moving to ponds to breed. Considerable progress has been made in both, quantifying fragmentation patterns and modeling and measuring fragmentation effects. Loehle and Wein (1994) presented a method for quantifying biodiversity on a map, and discuss a variety of other

0378-1127/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 1 1 2 7 ( 9 8 ) 0 0 5 4 6 - 5

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measures also. Other aspects of quanti®cation are discussed in Bissonette (1997) and Gustafson (1998). A number of models have recently been developed that explicitly quantify population responses to spatial patterns of habitat (Fahrig, 1998; Pulliam, 1988; Pulliam et al., 1992; Ranta et al., 1997; see also Bissonette, 1997). These models have contributed to theory by elucidating the mechanisms involved in the impacts of fragmentation, and allowing tests of various conjectures. Empirical studies, of course, are critical in establishing the true impacts of habitat fragmentation. Published studies are becoming increasingly available, not all of which have shown the effects predicted by theory (Villard, 1998). For example, Nour et al. (1998) showed that two species of tit did not show any evidence of decreased provisioning or nesting success in forest fragments. Similarly, Sarre (1998) showed that the gecko, Gehyra variegata, does not decline or suffer stochastic extinctions in forest remnant patches, a result attributable to foraging ¯exibility as evinced by differential habitat use in the remnant stands. In this paper, the author focuses on species for which fragmentation is detrimental. For example, the spotted owl (Strix occidentalis caurina) can tolerate some edges within its home range, but not a high degree of edge. The Florida scrub jay (Aphelocoma coerulescens) is a habitat specialist with poor dispersal and low population growth rates which, consequently, is very sensitive to dispersal barriers between its isolated patches of habitat (Root, 1998). Gardner (1998) showed that willie wagtails (Rhipidura leucophrys) suffer increased nest predation at forest edges which is explained by increased abundance of avian predators at edges in their study area. Once it has been established that we can quantify fragmentation, and that fragmentation is harmful to the population according to models or ®eld data, it is not clear what should be done to mitigate a given ®eld situation. General management guidelines that incorporate fragmentation considerations (e.g. Fries et al., 1998) do not provide guidance on the actions needed in any particular case. Models have been developed to generate wildlife reserves from a given unmanaged area (Hof and Joyce, 1992; Hof and Bevers, 1998) based on home range size requirements and other factors. This approach does not, however, allow for the diagnosis and correction of an existing fragmented

habitat. Sessions (1992) showed that Steiner networks could be used to generate least-cost corridors between given wildlife habitat zones, where cost can be considered in terms of stand economic values. This latter approach cannot address general fragmentation, however. It is also doubtful whether this approach is feasible for maps with many habitat patches. One approach that could potentially improve a given landscape via optimal management is a stochastic harvest scheduling approach (Bettinger et al., 1997, 1998; Van Deusen, 1996). In this approach, discrete regimes are de®ned, which can be applied to any given stand (spatially circumscribed portion of the map, even a pixel). The algorithm randomly tries the available regimes for each stand, rejecting those that are not feasible, and preferentially keeping those that improve the solution in some way. Such algorithms are able to control spatial pattern via computation of neighborhood interactions. However, because fragmentation is a global property of the map, each time a stand (pixel) regime is altered, the fragmentation index must be recomputed to see if this change contributes to defragmentation. This computation might turn out to be much too expensive to do millions of times in a run. More signi®cantly, a stochastic model is not capable of building a corridor to connect habitat patches unless they are trivially close, because stochastic additions of habitat between two cells will have a cost, but will show no bene®t until the patches are actually connected. Thomson et al. (1996) have developed a GIS-based tool, FEN_Maker, to generate restricted forest habitat regions (subject to restricted or no management). This tool is able to generate corridors between regions, but the corridors must be hand-digitized from the generated map buffer contours. From these considerations, it is clear that a technique that could directly defragment a map could be useful. Section 2 presents such an algorithm. 2. A defragmentation algorithm The basic problem is to take an existing landscape and manipulate it in terms of fragmentation to improve the habitat for certain species. This will include connecting existing patches, reducing the edge/interior ratio, and making irregularly shaped patches more

C. Loehle / Forest Ecology and Management 120 (1999) 245±251

regular. The author assumes that available management actions can alter given pieces of land to make them more suitable as habitat. Management actions could include purchase of land to prevent alteration, restoration of agricultural land, forest type conversion (e.g. pine to hardwood), etc. It is also assumed that the budget for such actions is limited, so that the least-cost solution is sought. While it is not hard to look at a map and make alterations that will reduce fragmentation, it is dif®cult to do so in a least-cost way, and manual adjustments are very slow. An intelligent algorithm is needed. An approach is suggested by noting that blind organisms (e.g. slime mold amoeba) are able to ®nd each other by following chemical signals on a gradient. If we consider each unit of wildlife habitat to be a source of `scent' which spreads out in all directions, then non-habitat that lies between two patches of habitat will have a higher concentration of scent than regions far from a patch. In fact, the region with the highest concentration will be along the shortest path between the two patches. If we add squares of new habitat to this zone, we will be able to connect two patches automatically. An algorithm was developed to implement this idea. Given a habitat map, it is assumed that all nonhabitat can be converted to suitable habitat by some management action. If not, then the algorithm can be programmed to ignore all regions that cannot be converted (e.g. water, roads). A grid-type map with discrete (0 or 1) habitat classi®cation is simulated here for convenience of computation. Scent generation is simulated for ®ve time-steps, though longer simulations could be done for larger maps. If too long a simulation of scent diffusion is done, scent will ®ll the map unless there is a decay term. In this case there would be no gradient. Five units of scent (purely for computational convenience) are generated for each grid that represents wildlife habitat at each time step. The scent then diffuses randomly in all directions. Since a grid map is used, an approximation to diffusion is achieved by sending an equal fraction (0.1) of the scent on a given grid square to the four cardinal directions and also a reduced fraction (0.04) to the four squares touching at the corners. A simple search of all grid squares locates the non-habitat grid square with the highest scent. This grid square is converted to wildlife habitat. The scent generation routine is then

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restarted to generate a new condition for the next choice. Wildlife habitat grid squares are added until the available limit of land conversion, as determined by cost or feasibility, is reached. The complete code for the algorithm is given in the Appendix A. The speci®c algorithm is as follows. The algorithm is a discrete approximation to a continuous diffusion process. Scent generation, S, for grid square (i,j) is given by Si;j ˆ s; Si;j ˆ 0;

Hi;j ˆ 1 Hi;j ˆ 0

where H is the binary variable for wildlife habitat (1 for current habitat), and s an arbitrary scent amount (ˆ5 here). To be more general, H could be a measure of habitat quality with s ˆ f(H). For each grid square, scent moves outward in all directions as Fi;j;k ˆ b;

k ˆ …l; r; up; dn†

Fi;j;k ˆ c;

k ˆ …diag†

where L is the level of scent and F the ¯ow. Values b ˆ 0.1 and c ˆ 0.04 were used. Much larger values of b can produce negative scent levels, and c < b must logically hold. At each time step t in the scent generation process, each pixel is updated as X X Fi;j;k Li;j;t ‡ Fn Lnt Li;j;t‡1 ˆ Li;j;t ‡ Si;j;t ÿ k

n

where k is summed over the neighbors of the focal cell and n the set of all (i,j) pairs for the neighbors of this same cell. This process is repeated for a period of time long enough to obtain a gradient (®ve time steps in the examples used) but not so long that the map ®lls with scent. The length of time to generate a scent will depend on the map scale and distance (in cells) between habitat patches. The highest scent grid square that is not already wildlife habitat is found by a simple search of the map. This is the square that will be converted. Ties are broken by merely taking the ®rst one found. 3. Defragmentation demonstration Several distinct cases were tested, including joining patches, ®lling gaps, and reducing edge/interior ratios. The algorithm successfully performed all three functions in a least-cost way.

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Fig. 1. Time progress of algorithm joining two patches. Fig. 2. Time progress of algorithm filling in gaps in a patch.

The ®rst case tested the joining of two patches. At each iteration, a single square was added to the map. As can be seen in Fig. 1, the algorithm successfully joined the patches by approximately the shortest route. Note that because a rectangular grid is used here, a slight deviation from the shortest route is generated. This is characteristic of a diffusion gradient approach, because the shortest route will have the highest concentration of `scent'. This means that the process ®nds the least-cost corridor to connect the patches, in the sense that `cost' is related to area that must be purchased. This would not be true if habitat units varied in their current purchase price or value, as in the Sessions (1992) analysis. In the second case (Fig. 2), the algorithm was tested for ®lling in gaps. A tuning fork-type shape was created that is all `edge' due to the gap down the middle. The defragmentation algorithm proceeded to ®ll the gap in a stepwise manner, as shown in the ®gure. The third case tested the ability of the algorithm to reduce the edge/interior ratio by creating more com-

pact ®gures. The test case was a long rectangle. We know that the maximal interior to edge ratio is produced by a circle. The defragmentation algorithm proceeded in a stepwise fashion by rounding out the rectangle and making various approximations of a circle. However, given the crude rectangular approximation to continuous diffusion used here, and the coarse scale of gridding, it could not produce a good circle with the addition of only a few units (Fig. 3).

Fig. 3. Time progress of reducing edge/perimeter ratio for a long patch. (a) initial, (b) after 10 time steps.

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4. Discussion A simulated growth process has been shown here to successfully accomplish a variety of tasks that tend to defragment a map of wildlife habitat. The algorithm is based on a gradient of a signal indicative of distance from multiple objects. Since chemical gradients in natural systems have been shown to produce a variety of spatial patterns, including the avoidance of neighbors in the case of plants and ontogeny in animal development, it may be possible to devise spatial transformation algorithms that produce even more complex changes than those presented here. For application of the algorithm to large maps, some improvements may be necessary. If an entire map is done at once, there may be a preference in the algorithm for adding to the sides of a large patch vs. connecting two small patches together. This can be ®xed by applying the algorithm to sections of the map separately. Another re®nement is that there may be a limit to how far apart two patches can be and still end up being connected by this algorithm. The algorithm could be made more general by taking habitat quality into account. If we merely let the amount of `scent' given off by a cell be proportional to the quality of the habitat (as measured by some index), then the algorithm will preferentially connect high quality patches and will connect them at a greater distance than in case of low quality patches. When we compare this method to other approaches, we can see some clear advantages. The simplicity of the algorithm should make it easy to incorporate into a Tabu search or Metropolis algorithm framework (e.g. Bettinger et al., 1997, 1998; Van Deusen, 1996). Compared to a Steiner network solution method (Sessions, 1992), the algorithm is more generally useful for defragmentation and is probably much faster. However, the Steiner network approach can create corridors in a least-cost sense when patches (stands) differ in their management conversion (e.g. purchase) price. Compared to FEN_Maker, the method is more generally useful for defragmentation and does not require manual intervention for corridor creation. It will not, however, create long corridors. 5. Conclusion This study has demonstrated that it is feasible to automate the design process for certain spatial pro-

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blems in forest management. The algorithm used was able to ®ll gaps in a habitat patch, connect patches, and reduce edge/interior ratios, all using the same algorithm. The algorithm determines a least-cost solution without using an explicit optimization process. It is also shown that the approach demonstrated is compatible with GIS technologies. Overall, the approach presented could be a useful tool for land management activities. Acknowledgements Work supported by the National Council for Air and Stream Improvement. Helpful review provided by an anonymous reviewer. Appendix A C code for defragmentation algorithm #include #include #include #include #include #include

hmath.hi hsignal.hi hstdio.hi hstdlib.hi hctype.hi hstring.hi

int grid[10][10],antigrid[10][10]; float scent[10][10],scent_flow[10][10][8]; FILE *fileptr; void main (void); void main (void) { register i,j,k,t,p; int xmaxˆ10,ymaxˆ10,maxi,maxj,addloops; float max; char output_filename[30]; strcpy(output_filename,``patch.out''); fileptrˆfopen(output_filename,``w''); //set up initial patches for(iˆ0;i
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}

if((i>1)&&(j>1)&&(i<4)&&(j<4))grid[i][j]ˆ1; if((i>3)&&(j>5)&&(i<6)&&(j<8))grid[i][j]ˆ1; if((i>1)&&(j>1)&&(i<4)&&(j<4))antigrid[i][j] ˆ0; if((i>3)&&(j>5)&&(i<6)&&(j<8))antigrid[i][j] ˆ0; }

addloopsˆ16; for(pˆ0;p
{ scent[i][j] ˆ scent[i][j]-scent_flow[i][j][0]scent_flow[i][j][1] -scent_flow[i][j][2]-scent_flow[i][j][3] -scent_flow[i][j][4] -scent_flow[i][j][5] -scent_flow[i][j][6] -scent_flow[i][j][7] ‡ (float)grid[i][j]*5.0 ‡scent_flow[i-1][j][1] ‡scent_flow[i][j-1][2] ‡scent_flow[i‡1][j][3] ‡scent_flow[i][j‡1][0] ‡scent_flow[i-1][j-1][4] ‡scent_flow[i-1][j‡1][5] ‡scent_flow[i‡1][j‡1][6] ‡scent_flow[i‡1][j-1][7]; } } } //print grid map for(jˆ0;jmax) { maxiˆi; maxjˆj; maxˆscent[i][j]; } } } } fprintf(fileptr,``max scent %f loc. %d %d \n'',max,maxi,maxj);

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if(p
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