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Application of fractals: create an artificial habitat with several small (SS) strategy in marine environment
e c o l o g i c a l e n g i n e e r i n g 3 2 ( 2 0 0 8 ) 44–51
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Application of fractals: create an artificial habitat with several small (SS) strategy in marine environment Chun-Hsiung Lan a , Kuo-Torng Lan b , Che-Yu Hsui a,∗ a b
Graduate Institute of Management Sciences, Nan Hua University, 32 Chung Keng Li, Dalin, Chiayi 622, Taiwan, ROC Department of Information Technology and Communication, Tungnan University, Shenkeng, Taipei 22202, Taiwan, ROC
a r t i c l e
i n f o
a b s t r a c t
Article history:
In 2006, Lan and Hsui applied perspectives on landscape ecology to propose a spatially
Received 9 November 2006
explicit model, and suggested that the cluster type deployment of artificial habitat in a
Received in revised form
marine environment might be better than other configurations in maximizing habitat com-
8 August 2007
plexity with a fractals approach. The limitation is that, however, it could only design a single
Accepted 30 August 2007
large island pattern subject to its solving algorithm. Hence, by applying more sophisticated algorithms, Evolution computational (EC) algorithm, we mimic more spatially explicit structural patterns to conduct several small (SS) clusters pattern in an artificial habitat such as
Keywords:
those found in nature landscape; additionally, the deployment in a community follows the
Artificial habitats
concept of DARCs model, which applied the cellular automata (CA) concept with Moore
Fractal geometry
neighborhood rule. The results show that with all the new knowledge that has been gained
Cellular automation
through the appropriate application of fractal geometry to natural sciences, it is clear that
Complexity
understanding how landscape ecology influences population ecology has allowed popula-
Landscape ecology
tion ecologists to gain new insights into their field.
Evolution computational algorithm
1.
Introduction
Landscape ecology, a subdiscipline of ecology and geography, has made tremendous progress in both theory and applications in the past two decades. The Landscape ecology focuses on spatial relationships and the interactions between patterns and processes. However, its research objective generally aims at the terrestrial with greater use of computer methods such as remote sensing, GIS (geographic information systems), and spatial analysis (e.g., Hulshoff, 1995; Rickers et al., 1995). Today, spatial pattern has been shown to influence many important ecological processes (Turner, 1989; Holling, 1992; Wiens et al., 1993); therefore landscape ecology not only provides understanding of the causes and consequences of habitat configuration, but also could manage the issues relative to conservation with habitat reconstruction.
∗
© 2007 Elsevier B.V. All rights reserved.
Unfortunately, owing to many limitations in the land, for instance, obtaining an available area, there have been few large-scale projects of artificial habitat. Many terrestrial landscape ecologists have proposed many theoretical models, but these are short on empirical applications in constructing an effective artificial habitat. Nevertheless, marine environment actually has the conditions for reconstructing habitat, and has been executed many years, that is artificial reefs (ARs) deployment. However, in most deploying ARs program, the configuration1 always depends upon engineers’ judgments, and before though such skillful intuition could help them find a quick, intermediary decision, it might be merely a plausible one (Lan et al., 2004; Lan and Hsui, 2006a). There only exist a few concrete criteria (about configuration) to be followed to date, such as reef volume (Rounsefell, 1972; Ogawa et al., 1977) or the distance between adjacent artificial reef
1 Corresponding author. Tel.: +886 937686586; fax: +886 5 2427186. Here, the configuration focuses on the spatial arrangement, not E-mail address: [email protected] (C.-Y. Hsui). sited (location) issue. 0925-8574/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ecoleng.2007.08.007
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communities (Bohnsack and Sutherland, 1985). Hence, if we could apply the terrestrial research experience to construct an artificial habitat in marine environment, it should be the future direction. Much regarding the role artificial reefs play in the ecosystem, past approaches may have limited our ability to fully understand the artificial reef deployments. Operating from the concept of landscape ecology, many terrestrial ecologists have gained new insight and perspective. Perhaps it is time for artificial reef researchers to adopt a similar approach. Fortunately, the first initiatives were performed by Lan et al. (2004), who utilized the perspective of habitat complexity and applied the principles of ecological engineering (Mitsch and Jørgensen, 2004) to construct an artificial reef deployment model, called the layout of artificial reef communities (LARCs); and then (2006b) they modified its solving procedure to obtain the global optimal configuration and renamed it the deployment of artificial reef communities (DARCs).2 The dominant theme, the habitat complexity, of landscape ecology was performed. Many landscape ecologists deem that the configuration of spatial mosaics influences a wide array of ecological phenomena (e.g. Turner, 1989). The physical structure of a habitat generally has a strong influence on the diversity and abundance of associated organisms (Gorham and Alevizon, 1989; Hixon and Beets, 1989; Charbonnel et al., 2002). The definition of structural complexity3 assumes that the habitat complexity increases with increasing biomass or biodiversity; where the habitat complexity refers to the physical arrangement of objects in space and is described by their type and quantity at a defined spatial scale (Bohnsack, 1990). One of the possible reasons is that habitat complexity provides refuges and barriers that fragment the area, and result in more heterogeneous assemblages (Sebens, 1991). Among the numerous indices from landscape ecology, fractal dimension was commonly applied to examine the complexity (Burrough, 1981; Morse et al., 1985; Milne, 1988; Sugihara and May, 1990), in addition the potential, fractal properties of natural landscapes and populations have been the subject of increasing interest in recent years (e.g. Morse et al., 1985; Loehle, 1990; Sugihara and May, 1990; Milne, 1991, 1992; Haslett, 1994; Loehle and Wein, 1994). However, the generated candidate cells, i.e., the simulated deploying artificial reef communities (sets) (abbreviated to ARCs or ARSs), follow the specific neighborhood rules from cellular automata concept, without respect to LARCs model or DARCs model; specifically, the eight-neighbor rule (or called Moore neighborhood rule, see Batty, 1997) was applied, which would allow organisms to move to cells on the diagonal, and its overriding objective is to achieve the maximizing spatial complexity (fractals) in habitat. But subject to its solving algo-
2 LARCs model and DARCs model are intrinsic ecological engineering. Because they integrate the ecologists’ aspects into engineering, and consider finite resources in practical programs; such as Mitsch and Jørgensen (2003) mentioned: “Ecological engineering, if properly applied, is based on ecological considerations and attempts to optimize ecosystems (including limited resources) and man-made systems for the benefit of both.” 3 Refer to the compositional diversity and configurational intricacy of a system (Wu and Marceau, 2002).
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rithm, the neighborhood rule could only design the habitat configuration with a single large island prototype (Fig. 1(a)). Though the model and its solving algorithm have advantages to ecological engineering with integrating multidisciplinary concepts of ecology, engineering, and cost control, and so on, it still leave out to practice. In the theory of island biogeography, the isolation of the reserve from places with similar habitats has been perceived to be important in the design of reserves (Usher, 1991); besides in the reserve objective of maximizing the number of currently occurring species,4 the majority of these studies, summarized by Ovaskainen (2002), has concluded that several small (SS) is the better strategy. Hence, to maximize the spatial complexity (fractals), the development of an effective solving algorithm to design configuration of a reserve, on the premise that the deploying ARCs (ARSs) appear as multi-clusters pattern (like several small islands, see Fig. 1(b)), is urgently needed to be processed. Consequently, we will develop the evolution computational (EC) algorithm instead of the wide-ranging search algorithm in the previously proposed DARCs model (Lan and Hsui, 2006a,b) in the following section to obtain the suggested deployment with several small islands strategy.
2. Landscape pattern modelling and quantifying In this section, we first introduced the lattices, neighborhood and transition rules to construct a grid-based landscape model, and then quantified it with fractal approach. In addition, the evolution computational (EC) algorithm to solve the problem associated with configuring artificial habitat in marine environment.
2.1. Landscape pattern modelling: the lattices, neighborhood and transition rules Because artificial reefs can be deployed in an infinite variety of spatial arrangements (Jordan et al., 2005; Lan and Hsui, 2006a), the technique of latticing habitat should be conducted to eliminate confounding candidate solutions before the fractals analysis proceeds. Additionally, we applied the cellular automata (CA) concept to define the contiguous growth process of an artificial patch (in this study, it means ARCs or ARBs). The most popular neighborhood and transition rules in CA are Von Neumann rule, Moore rule, and free rule (Batty, 1997), which the diagrams show in Fig. 2. Specifically, Fig. 2 exhibits site cells (the lattices), initial position (the black cell), candidates (the gray cell) and simulated adjacent distance (ad) between two ARCs (or ARBs) in a habitat. Besides, the mathematical formulation is as follows. Let ˛t(i,j) (the black cell) means that simulated initial position is in the coordinate (i, j) in time t, and the next candidates “site-cell set” in time t + 1
4 Simberloff and Abele (1976) mentioned that most empirical SLOSS (is an acronym of the phrase “single large or several small”) studies have compared whether a single large (SL) or a several small (SS) habitat patch network currently contains more species, not considering whether the species will survive or not.
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Fig. 1 – The diagram shows an artificial reef habitat composed of several artificial reef communities (sets); in addition, any community consists of a number of artificial reef blocks (see (c)). Furthermore, (a) indicates that owing to the limitations of solving algorithm and neighborhood rule, past design proposed by Lan and Hsui (2006a,b) suggested that the optimal landscape of the artificial habitat would present as a single large cluster (island) type. In other words, the deploying AR communities (sets) formed as an aggregated clumped pattern; however, with more sophisticated algorithms and adopting the free neighborhood rule, multi-clusters pattern could be obtained (such as (b) shown), and achieve the specific several small conservation strategy.
follows the equation: ˛t+1 = [˛(i−ad,j−ad) , ˛(i−ad+1,j−ad+1) , . . . , ˛(i,j) , . . . , ˛(i+ad,j+ad) ], (i,j) where is the neighborhood rule. Imagine an ARC growing from one site cell, the historic core of development. If there is any development in the eight cells that form the square neighborhood around the cell (i.e., the so-called Moore neighborhood), then the cell is developed (Batty, 1997).
2.2.
Quantifying: the fractals approach
Fractal dimension (FD), a measure of the degree of complexity of shape, was used as a measure of spatial pattern. Thus fractal geometry has been used to describe a variety of natural
objects and phenomena. Besides, this measure was introduced as an effective method to study and compare shapes across different scales (Mandelbrot, 1983). Fractals allow comparing the pattern across scales without the correction of scale dependent changes in pattern (Milne, 1991). In addition, Kunin (1997) further pointed out that the natural communities exhibit nearly scale-independent patterns that might well be amenable to fractal analysis. The differences of fractal dimension values likely mean differences occurring in the scale of processes to affect pattern (Krummel et al., 1987; Turner, 1989). Though the technical origins of fractals in measure theory may seem abstruse, the ideas of fractal analysis are extremely simple and intuitive, and could be operated easily (Sugihara and May, 1990).
Fig. 2 – Cellular neighborhoods (·), the center of the neighborhood-black cell is developed in this case if there is at least one unit of development-gray cell in the neighborhood.
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In this paper, we use fractals as an index of spatial complexity to simulate the configuration of an artificial habitat. The deploying scale of the proposed model at least with regard to ARCs or artificial reef blocks (ARBs), is not on individual artificial reef modules.5 Because individual modules location could be designed accurately and easily before deployment; reefs deployment, may not always proceed as planned in practice for ocean current effect. Therefore Grove and Sonu (1985) suggested that reefs should be deployed as modules in communities or blocks, to make the actual postdeployment dimensions conform to the designation.
2.3.
Table 1 – The review of the DARCs/LARCs models (Lan et al., 2004; Lan and Hsui, 2006b) Item
Description
Objective
N,d
box–counting method Constraints
The DARCs model
The model, proposed by Lan et al. (2004) and Lan and Hsui (2006a,b), applies Moore rule to deploy ARs is intrinsically a grid-based landscape model, and it is also the first initiatives that it applies the perspective of landscape ecology to construct an explicit spatial model dealing with the deploying problem of an artificial habitats in marine environment. The objective of DARCs model is to achieve maximum spatial complexity (fractals) in a habitat, and one of the decision variables in this model is distance, which is between two adjacent and isolated artificial reef communities (detailed description see Table 1). Many scholars (e.g. Jordan et al., 2005) deem that the deployment of ARs often lack regard for the reef spacing on the resulting fish assemblages. Recently, Jordan et al. (2005) indicated that their experimental results show that variable isolation distance among ARs can alter the structure (i.e., abundance and species richness) of the associate fish assemblages, with specific responses for different species, trophic groups, and size classes. Specifically, they found that the fish abundance and species richness is statistically significant different in isolation treatments varying in isolation distance (reef spacing). Both the largest and smallest spacing treatments (i.e., 25 m and 0.33 m) had statistically higher mean abundance values than the 5 m and 15 m treatments. Some reasons might include that decreased foraging time will be that increased net energetic gain (Stephens and Krebs, 1986) as well as reducing the risk of predation (Milinski, 1986). Therefore, the consumption of prey items closer to a reef by resident fishes will occur more rapidly than in the farther one, and it results that a halo of decreasing density of benthic prey items approaches the reef (Ogden, 1976). Based on this reason, the substrate surrounding a patch reef having a greater isolation distance from other reefs may provide a greater density of benthic prey items than those in closer proximity to each other. Patch reefs spaced closely could result in overlapping halos with a concomitant decrease in benthic prey density and, in turn, the density of benthic foragers; thus, the spacing of reefs might be a critical factor for understanding variations in assemblage structure for patchy environs as well as determining the effectiveness of restoration efforts and the artificial reef deployment (Jordan et al., 2005). Similarly, the simulated
5 Also, the reef block may be composed of several types of modules, each of a different material (see Fig. 1); in other words, module mix-more than one module is frequently used.
max FD, in which FD was calculated by the
Solving algorithm
Assumptions
1. The total cost of the project should be less than or equal to the project budget 2. The potentially deployed sites among the project area should be greater than or equal to the number of deployed ARCs 3. The deploying distance of adjacent ARCs should conform the allowable range, and the minimum adjacent distance should be greater or equal to the diameter of an ARC 4. The number of deployed ARCs should be an integer Heuristic algorithm, and adopts the Moore neighborhood rule (i.e., ad = 1, see Fig. 2) as their neighborhood rule 1. The project area and its size are determined, and the materials of each ARC are the same 2. The spatial configuration of an artificial habitat is focused on the plane and the design scale is on the communities (set). Besides, each ARC consists the same number of AR units (modules) with the same size 3. The total cost of the project includes the purchasing cost of ARCs, the lift/lay-down (or throw) cost of ARCs and the transportation cost
results from DARCs model reveal that phenomenon (Lan and Hsui, 2006a), namely, that the artificial habitat would exhibit different spatial complexity depending on variable distance between two adjacent artificial reef communities. In other words, spacing is species-specific dependent variable, and has a nonlinea relationship with habitat complexity. Bohnsack and Sutherland (1985) suggested the general spacing criterion, that the distance between adjacent artificial reef blocks (ARBs) range from 50 to 100 m, and the ARCs’ is 300–500 m. The DARCs model, however, is restricted to its solving algorithm (i.e., adopts the Moore neighborhood rule with ad = 1, see Fig. 2), and consequently, the configuration could only be deployed as single large island (cluster) pattern. Therefore, we developed the evolution computational algorithm to conduct the artificial habitat design with free neighborhood rule (i.e., ad = x, see Fig. 2), and constructing a multi-clusters pattern.
2.4.
Evolution computational (EC) algorithm
As argued previously, the island biogeographers regard that the isolation of the reserve from places with similar habitats has been perceived to be important in the design of reserves; thus, to provide a multi-clusters deployment, the EC algorithm will be developed as follows instead of the wide-ranging search algorithm formerly proposed DARCs model (Lan and Hsui, 2006a,b). To be specific, the design configuration of artificial habitat used cellular automata models with the free neighborhood rule to obtain several small clusters pattern.
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In this study, we used the evolutionary algorithms (Fogel, 1994; Back, 1996) to design the reef deployment. The original evolutionary algorithms are designed to deal with function optimization problems. But the problem we faced in this study are a two-dimensional discrete pattern design, and some evolution steps, such as mutation, must be modified to fit the problem. In our algorithm, we treat the pattern of an ARC deployment as an individual among the population; the mutation is to dilate or erode the pattern in some bits (A bit 1 in the pattern represents a reef and bit 0 means background during the deploying process). In the traditional EC algorithm, the mutation means adding some small disturbance (a small real number) to the individual (a real number). For our model, the mutation is modified as changing some bits 1 (edge points of the deployed pattern) to 0 (the background bits) or alter some bits 0 (neighbor points, i.e., the background points besides the deployed reef) to 1. The other steps, such as evaluation, selection, and et cetera, are the same as the traditional evolutionary algorithm. The EC fractal algorithms are depicted below: (1) Initialization: Randomly generate an initial population of individuals (i.e., chromosomes in evolution word). Each individual x i is a binary-valued vector that represents one of ARC deploy-
(2)
(3)
(4)
(5)
ments. The vector’s bit that has only a value of 1 or 0 means an ARC existed at the corresponding cell or not. Mutation: Create a single offspring x i from each parent x i , ∀i ∈ {1, 2, . . ., }, by performing the following steps: (i) Generate a random number R with a Gaussian or Cauchy distribution. And truncate the fraction of R to get a random integer. (ii) If R > 0, then dilate the individual x i R bits (dilation algorithms). (iii) If R < 0, then erode the individual x i R bits (erosion algorithms). Evaluation: Calculate all parent’s and offspring’s box-counting fractal dimension as its fitness function values, f (x i ) and f (x i ), ∀i ∈ {1, 2, . . ., }. Selection: Select individuals from the union of parent x i and offspring x i , ∀i ∈ {1, 2, . . ., }. The individuals construct the next population. In our simulated program, the ranking selection is adapted in this study. Termination: If the halting condition is satisfied, then stop the iteration, otherwise, increment the generation number, k = k + 1, and go to step 2.
Fig. 3 – The framework is combining DARBs model and EC algorithm to design an artificial habitat in marine environment. In the first stage, the design scale focuses on an artificial reef community (set), i.e., to decide the configuration (spatial arrangement) of artificial reef blocks. And in this stage, the Moore neighborhood rule is applied to obtain the clumped deployment; additionally, we design the arrangement of an artificial reefs habitat with EC algorithm in the second stage (i.e., adopts free neighborhood rule to deploy artificial reef communities (sets)), to obtain multi-isolated islands pattern for achieving a specific conservation strategy.
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Fig. 4 – Two kind of different landscapes comparisons. The red cells (i.e., patches) are the suggested deployment of artificial reef communities in a marine reserve. The left-hand side is the conventional engineering common designation, namely, the pattern presents a uniform distribution (where FD = 1.29); and the right-hand side shows the landscape structure which was obtained by EC algorithm, and its FD = 1.55.
Fig. 5 – The detailed evolutionary environment setting windows.
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And the dilation/eroding algorithms used in the mutation step is described clearly as follows: Dilation algorithms: (1) For a randomly chosen edge point, select a neighbor point and change the bit form 0 to 1. (2) Repeat the step 1 R times. (3) Finally, erode the individual R bits to keep the number of reefs unchanged. Erosion algorithms: (1) For a randomly chosen edge point, change the bit from 1 to 0. (2) Repeat the step 1 R times. (3) Finally, dilate the individual R bits to maintain the total bits unchanged. For our simulation program, the Builder C++ 6.0 package is adapted to implement the EC algorithm. We run the program 10 epochs in different initialization and get the best pattern for deployment of reef. For every epoch, the evolution is terminated after 500 generations. To compare the searching capability of Gaussian or Cauchy distribution, our program is designed to use Gaussian or Cauchy distribution for mutation. The simulation results reveal that the Cauchy mutation is better than the Gaussian and match Rudolph’s conclusion (Rudolph, 1997).
3. Applications: the framework of designing AR ecosystem In this section, we proposed a two-staged framework to design the spatial arrangement of an artificial habitat in marine environment. The deploying scale mainly focuses on artificial reef communities as former model. But we perform EC algorithm, where neighborhood and transition rule adopts the free neighborhood rule (i.e., ad = x), to construct a multi-clusters pattern with achieving specific conservation strategy. On the other hand, the configuration design of an ARC adopts the Moore neighborhood rule with ad = 1 to deploy artificial reef blocks (i.e., so-called DARBs model), which could clump ARBs into patches of the same attribute class (such as shown in Fig. 1(c)). To be more specific, Fig. 3 shows the framework that combining DARBs model and EC algorithm to achieve a maximizing habitat complexity design with several isolated clusters (such as Fig. 1(b) shown).
4.
Results and discussion
To provide a numerical example, suppose we visit a project that needs to construct a marine artificial habitat as a conservation reserve. Except for the premise of our objective function, maximize the habitat complexity (fractals), the commonly adopted deploying ARs strategy is clumped6 con-
figuration in past engineering concept. We will compare the conventional deployment with EC algorithm suggestions as follows. Our simulations were performed on a hypothetical 25-ha conservation reserve consisting of a 10 × 10 array of 100 0.25ha square cells (Fig. 4). Each cell means the allowable deploying site of ARCs; furthermore, the project budget could only deploy ARCs to the number of 13. The program developed in language C++ and the evolution parameters adapted in the simulation are Population size (number of chromosome) Evolution generation (number of generation) Mutation style Selection type Initialization For the stochastic characteristics of
12 1200 Cauchy Ranking Uniform distribution the EC algorithm, every
simulation is performed 10 epochs and gets the best one as our simulation result. According to such conditions, the conventional configuration shown in the left-hand side of Fig. 4, the pattern is as a single large island and has fractal dimension (FD) with 1.29; in contrast with common deployment, the right-hand side of Fig. 4 is the suggested configuration that applies EC algorithm, and exhibits as two small islands; besides its FD = 1.55 is greater than the single island pattern. The detailed evolutionary environment setting is shown in Fig. 5. The insights gained from such results shows, that the conventional design with single island pattern is not necessarily better than multi-clusters pattern on the complexity perspective, and it might be attributed to its highly nonlinear property in fractals simulation process. However, with our intuition, single island pattern sometimes has larger complexity than dispersal patterns. In addition, on the conservation aspects, if we regard several small (SS) islands as the better strategy, then the EC algorithm could effectively help us deploying an multi-clusters pattern reserve, to improve the defect proposed by Lan and Hsui (2006a,b), whose algorithm could only design a single island configuration.
5.
Conclusion remarks
In this paper, computer simulations of landscapes provide useful models for gaining new insights on the configuration of an artificial habitat, especially in module groupings and spacing intervals. The simulated landscapes could not only allow ecologists to explore some of the consequences of the geometrical configuration of environmental variability for species coexistence and richness, but point the way toward future research. Many additional questions arise from this work, for example: understanding the importance of spatial scales; the relationship between landscape structure and habitat spatial complexity; an increased understanding of landscape structures; and the ability to more accurately model landscapes and ecosystems.
6
Although Yoshimuda (1982) argued that attractiveness generally increased with the number of artificial reefs deployed, it seems that the uniform arrangement of artificial reefs on the whole seabed would be better; however, the reef resources are some-
times constrained by finite budgets, thus this kind of deployment is infeasible in practice.
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One of the most valuable aspects of fractal geometry, however, is the way that it bridges the gap between ecologists of differing fields. By providing a common language, fractal geometry allows ecologists to communicate and share ideas and concepts. Furthermore, such fractals-based model, if they prove to hold more generally to species distributions, may make it possible to increase greatly our understanding of local and regional patterns of biological diversity.
Acknowledgement The authors would like to thank the anonymous referees who kindly provided the comments to improve this work.
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Lan, C.H., Hsui, C.Y., 2006a. Insight from complexity: a new approach to designing the deployment of artificial reef communities. Bull. Mar. Sci. 78, 21–28. Lan, C.H., Hsui, C.Y., 2006b. The deployment of artificial reef ecosystem: modelling, simulation and application. Simulat. Model. Pract. Theory 14, 663–675. Loehle, C., 1990. Home range: a fractal approach. Landsc. Ecol. 5, 39–52. Loehle, C., Wein, G., 1994. Landscape habitat diversity—a multiscale information theory approach. Ecol. Model. 73, 311–329. Mandelbrot, B.B., 1983. The Fractal Geometry of Nature. Freeman, San Francisco. Milne, B.T., 1988. Measuring the fractal geometry of landscapes. Appl. Math. Comput. 27, 67–79. Milne, B.T., 1991. Heterogeneity as a multiscale characteristic of landscapes. In: Kolasa, J., Pickett, S.T.A. (Eds.), Ecological Heterogeneity, vol. 86: Ecological Studies. Springer, New York, pp. 69–84. Milne, B.T., 1992. Spatial aggregation and neutral models in fractal landscapes. Am. Nut. 139, 32–57. Milinski, M., 1986. Constraints placed by predators on feeding behaviour. In: Pitcher, T.J. (Ed.), The Behavior of Teleost Fishes. Johns Hopkins University Press, pp. 236–252. Mitsch, W.J., Jørgensen, S.E., 2003. Ecological engineering: a field whose time has come. Ecol. Eng. 20, 363–377. Mitsch, W.J., Jørgensen, S.E., 2004. Ecological Engineering and Ecosystem Restoration. Wiley, New York. Morse, D.R., Lawton, J.H., Dodson, M.M., Williamson, M.H., 1985. Fractal dimensions of vegetation and the distribution of arthropod body lengths. Nature 314, 731–733. Ogawa, S., Takeuchi, R., Hattori, H., 1977. An estimate for the optimum size of artificial reefs. Bull. Jap. Soc. Fish. Oceanogr. 30, 39–45. Ogden, J.C., 1976. Some aspects of herbivore–plant relationships on Caribbean reefs and seagrass beds. Aquat. Bot. 2,103–116. Ovaskainen, O., 2002. Long-term persistence of species and the SLOSS problem. J. Theor. Biol. 218, 419–433. Rickers, J.R., Queen, L.P., Arthaud, G.J., 1995. A proximity-based approach to assessing habitat. Landsc. Ecol. 10, 309–321. Rounsefell, G.A., 1972. Ecological effects of offshore construction. J. Mar. Sci. 2, A1–A119. Rudolph, G., 1997. Local convergence rates of simple evolutionary algorithms with Cauchy mutations. IEEE Trans. Evol. Compt. 1, 249–256. Sebens, K.P., 1991. Habitat structure and community dynamics in marine benthic systems. In: Bell, S.S., McCoy, E.D., Mushinsky, H.R. (Eds.), Habitat Structure: The Physical Arrangement of Objects in Space. Chapman & Hall, New York, pp. 211–234. Simberloff, D., Abele, L.G., 1976. Island biogeography theory and conservation practice. Science 191, 285–286. Stephens, D.W., Krebs, J.R., 1986. Foraging Theory. Princeton University Press. Sugihara, G., May, R.M., 1990. Applications of fractals in ecology. Trends Ecol. Evol. 5, 79–86. Turner, M.G., 1989. Landscape ecology: the effect of pattern on process. Annu. Rev. Ecol. Syst. 20, 171–197. Usher, M.B., 1991. Habitat structure and the design of nature reserves. In: Bell, S.S., McCoy, E.D., Mushinsky, H.R. (Eds.), Habitat Structure: The Physical Arrangement of Objects in Space. Chapman & Hall, New York, pp. 373–391. Wiens, J.A., Stenseth, N.C., van Horne, B., Ims, R.A., 1993. Ecological mechanisms and landscape ecology. Oikos 66, 369–380. Wu, J., Marceau, D., 2002. Modeling complex ecological systems: an introduction. Ecol. Model. 153, 1–6. Yoshimuda, N.C., 1982. Discussion of installation planning. In: Vik, S.F. (Ed.), Japanese Artificial Reef Technology, vol. 604. Aquabio Inc., pp. 137–165 (F.L. Tech. Rep.).
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecoleng
Application of fractals: create an artificial habitat with several small (SS) strategy in marine environment Chun-Hsiung Lan a , Kuo-Torng Lan b , Che-Yu Hsui a,∗ a b
Graduate Institute of Management Sciences, Nan Hua University, 32 Chung Keng Li, Dalin, Chiayi 622, Taiwan, ROC Department of Information Technology and Communication, Tungnan University, Shenkeng, Taipei 22202, Taiwan, ROC
a r t i c l e
i n f o
a b s t r a c t
Article history:
In 2006, Lan and Hsui applied perspectives on landscape ecology to propose a spatially
Received 9 November 2006
explicit model, and suggested that the cluster type deployment of artificial habitat in a
Received in revised form
marine environment might be better than other configurations in maximizing habitat com-
8 August 2007
plexity with a fractals approach. The limitation is that, however, it could only design a single
Accepted 30 August 2007
large island pattern subject to its solving algorithm. Hence, by applying more sophisticated algorithms, Evolution computational (EC) algorithm, we mimic more spatially explicit structural patterns to conduct several small (SS) clusters pattern in an artificial habitat such as
Keywords:
those found in nature landscape; additionally, the deployment in a community follows the
Artificial habitats
concept of DARCs model, which applied the cellular automata (CA) concept with Moore
Fractal geometry
neighborhood rule. The results show that with all the new knowledge that has been gained
Cellular automation
through the appropriate application of fractal geometry to natural sciences, it is clear that
Complexity
understanding how landscape ecology influences population ecology has allowed popula-
Landscape ecology
tion ecologists to gain new insights into their field.
Evolution computational algorithm
1.
Introduction
Landscape ecology, a subdiscipline of ecology and geography, has made tremendous progress in both theory and applications in the past two decades. The Landscape ecology focuses on spatial relationships and the interactions between patterns and processes. However, its research objective generally aims at the terrestrial with greater use of computer methods such as remote sensing, GIS (geographic information systems), and spatial analysis (e.g., Hulshoff, 1995; Rickers et al., 1995). Today, spatial pattern has been shown to influence many important ecological processes (Turner, 1989; Holling, 1992; Wiens et al., 1993); therefore landscape ecology not only provides understanding of the causes and consequences of habitat configuration, but also could manage the issues relative to conservation with habitat reconstruction.
∗
© 2007 Elsevier B.V. All rights reserved.
Unfortunately, owing to many limitations in the land, for instance, obtaining an available area, there have been few large-scale projects of artificial habitat. Many terrestrial landscape ecologists have proposed many theoretical models, but these are short on empirical applications in constructing an effective artificial habitat. Nevertheless, marine environment actually has the conditions for reconstructing habitat, and has been executed many years, that is artificial reefs (ARs) deployment. However, in most deploying ARs program, the configuration1 always depends upon engineers’ judgments, and before though such skillful intuition could help them find a quick, intermediary decision, it might be merely a plausible one (Lan et al., 2004; Lan and Hsui, 2006a). There only exist a few concrete criteria (about configuration) to be followed to date, such as reef volume (Rounsefell, 1972; Ogawa et al., 1977) or the distance between adjacent artificial reef
1 Corresponding author. Tel.: +886 937686586; fax: +886 5 2427186. Here, the configuration focuses on the spatial arrangement, not E-mail address: [email protected] (C.-Y. Hsui). sited (location) issue. 0925-8574/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ecoleng.2007.08.007
e c o l o g i c a l e n g i n e e r i n g 3 2 ( 2 0 0 8 ) 44–51
communities (Bohnsack and Sutherland, 1985). Hence, if we could apply the terrestrial research experience to construct an artificial habitat in marine environment, it should be the future direction. Much regarding the role artificial reefs play in the ecosystem, past approaches may have limited our ability to fully understand the artificial reef deployments. Operating from the concept of landscape ecology, many terrestrial ecologists have gained new insight and perspective. Perhaps it is time for artificial reef researchers to adopt a similar approach. Fortunately, the first initiatives were performed by Lan et al. (2004), who utilized the perspective of habitat complexity and applied the principles of ecological engineering (Mitsch and Jørgensen, 2004) to construct an artificial reef deployment model, called the layout of artificial reef communities (LARCs); and then (2006b) they modified its solving procedure to obtain the global optimal configuration and renamed it the deployment of artificial reef communities (DARCs).2 The dominant theme, the habitat complexity, of landscape ecology was performed. Many landscape ecologists deem that the configuration of spatial mosaics influences a wide array of ecological phenomena (e.g. Turner, 1989). The physical structure of a habitat generally has a strong influence on the diversity and abundance of associated organisms (Gorham and Alevizon, 1989; Hixon and Beets, 1989; Charbonnel et al., 2002). The definition of structural complexity3 assumes that the habitat complexity increases with increasing biomass or biodiversity; where the habitat complexity refers to the physical arrangement of objects in space and is described by their type and quantity at a defined spatial scale (Bohnsack, 1990). One of the possible reasons is that habitat complexity provides refuges and barriers that fragment the area, and result in more heterogeneous assemblages (Sebens, 1991). Among the numerous indices from landscape ecology, fractal dimension was commonly applied to examine the complexity (Burrough, 1981; Morse et al., 1985; Milne, 1988; Sugihara and May, 1990), in addition the potential, fractal properties of natural landscapes and populations have been the subject of increasing interest in recent years (e.g. Morse et al., 1985; Loehle, 1990; Sugihara and May, 1990; Milne, 1991, 1992; Haslett, 1994; Loehle and Wein, 1994). However, the generated candidate cells, i.e., the simulated deploying artificial reef communities (sets) (abbreviated to ARCs or ARSs), follow the specific neighborhood rules from cellular automata concept, without respect to LARCs model or DARCs model; specifically, the eight-neighbor rule (or called Moore neighborhood rule, see Batty, 1997) was applied, which would allow organisms to move to cells on the diagonal, and its overriding objective is to achieve the maximizing spatial complexity (fractals) in habitat. But subject to its solving algo-
2 LARCs model and DARCs model are intrinsic ecological engineering. Because they integrate the ecologists’ aspects into engineering, and consider finite resources in practical programs; such as Mitsch and Jørgensen (2003) mentioned: “Ecological engineering, if properly applied, is based on ecological considerations and attempts to optimize ecosystems (including limited resources) and man-made systems for the benefit of both.” 3 Refer to the compositional diversity and configurational intricacy of a system (Wu and Marceau, 2002).
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rithm, the neighborhood rule could only design the habitat configuration with a single large island prototype (Fig. 1(a)). Though the model and its solving algorithm have advantages to ecological engineering with integrating multidisciplinary concepts of ecology, engineering, and cost control, and so on, it still leave out to practice. In the theory of island biogeography, the isolation of the reserve from places with similar habitats has been perceived to be important in the design of reserves (Usher, 1991); besides in the reserve objective of maximizing the number of currently occurring species,4 the majority of these studies, summarized by Ovaskainen (2002), has concluded that several small (SS) is the better strategy. Hence, to maximize the spatial complexity (fractals), the development of an effective solving algorithm to design configuration of a reserve, on the premise that the deploying ARCs (ARSs) appear as multi-clusters pattern (like several small islands, see Fig. 1(b)), is urgently needed to be processed. Consequently, we will develop the evolution computational (EC) algorithm instead of the wide-ranging search algorithm in the previously proposed DARCs model (Lan and Hsui, 2006a,b) in the following section to obtain the suggested deployment with several small islands strategy.
2. Landscape pattern modelling and quantifying In this section, we first introduced the lattices, neighborhood and transition rules to construct a grid-based landscape model, and then quantified it with fractal approach. In addition, the evolution computational (EC) algorithm to solve the problem associated with configuring artificial habitat in marine environment.
2.1. Landscape pattern modelling: the lattices, neighborhood and transition rules Because artificial reefs can be deployed in an infinite variety of spatial arrangements (Jordan et al., 2005; Lan and Hsui, 2006a), the technique of latticing habitat should be conducted to eliminate confounding candidate solutions before the fractals analysis proceeds. Additionally, we applied the cellular automata (CA) concept to define the contiguous growth process of an artificial patch (in this study, it means ARCs or ARBs). The most popular neighborhood and transition rules in CA are Von Neumann rule, Moore rule, and free rule (Batty, 1997), which the diagrams show in Fig. 2. Specifically, Fig. 2 exhibits site cells (the lattices), initial position (the black cell), candidates (the gray cell) and simulated adjacent distance (ad) between two ARCs (or ARBs) in a habitat. Besides, the mathematical formulation is as follows. Let ˛t(i,j) (the black cell) means that simulated initial position is in the coordinate (i, j) in time t, and the next candidates “site-cell set” in time t + 1
4 Simberloff and Abele (1976) mentioned that most empirical SLOSS (is an acronym of the phrase “single large or several small”) studies have compared whether a single large (SL) or a several small (SS) habitat patch network currently contains more species, not considering whether the species will survive or not.
46
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Fig. 1 – The diagram shows an artificial reef habitat composed of several artificial reef communities (sets); in addition, any community consists of a number of artificial reef blocks (see (c)). Furthermore, (a) indicates that owing to the limitations of solving algorithm and neighborhood rule, past design proposed by Lan and Hsui (2006a,b) suggested that the optimal landscape of the artificial habitat would present as a single large cluster (island) type. In other words, the deploying AR communities (sets) formed as an aggregated clumped pattern; however, with more sophisticated algorithms and adopting the free neighborhood rule, multi-clusters pattern could be obtained (such as (b) shown), and achieve the specific several small conservation strategy.
follows the equation: ˛t+1 = [˛(i−ad,j−ad) , ˛(i−ad+1,j−ad+1) , . . . , ˛(i,j) , . . . , ˛(i+ad,j+ad) ], (i,j) where is the neighborhood rule. Imagine an ARC growing from one site cell, the historic core of development. If there is any development in the eight cells that form the square neighborhood around the cell (i.e., the so-called Moore neighborhood), then the cell is developed (Batty, 1997).
2.2.
Quantifying: the fractals approach
Fractal dimension (FD), a measure of the degree of complexity of shape, was used as a measure of spatial pattern. Thus fractal geometry has been used to describe a variety of natural
objects and phenomena. Besides, this measure was introduced as an effective method to study and compare shapes across different scales (Mandelbrot, 1983). Fractals allow comparing the pattern across scales without the correction of scale dependent changes in pattern (Milne, 1991). In addition, Kunin (1997) further pointed out that the natural communities exhibit nearly scale-independent patterns that might well be amenable to fractal analysis. The differences of fractal dimension values likely mean differences occurring in the scale of processes to affect pattern (Krummel et al., 1987; Turner, 1989). Though the technical origins of fractals in measure theory may seem abstruse, the ideas of fractal analysis are extremely simple and intuitive, and could be operated easily (Sugihara and May, 1990).
Fig. 2 – Cellular neighborhoods (·), the center of the neighborhood-black cell is developed in this case if there is at least one unit of development-gray cell in the neighborhood.
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In this paper, we use fractals as an index of spatial complexity to simulate the configuration of an artificial habitat. The deploying scale of the proposed model at least with regard to ARCs or artificial reef blocks (ARBs), is not on individual artificial reef modules.5 Because individual modules location could be designed accurately and easily before deployment; reefs deployment, may not always proceed as planned in practice for ocean current effect. Therefore Grove and Sonu (1985) suggested that reefs should be deployed as modules in communities or blocks, to make the actual postdeployment dimensions conform to the designation.
2.3.
Table 1 – The review of the DARCs/LARCs models (Lan et al., 2004; Lan and Hsui, 2006b) Item
Description
Objective
N,d
box–counting method Constraints
The DARCs model
The model, proposed by Lan et al. (2004) and Lan and Hsui (2006a,b), applies Moore rule to deploy ARs is intrinsically a grid-based landscape model, and it is also the first initiatives that it applies the perspective of landscape ecology to construct an explicit spatial model dealing with the deploying problem of an artificial habitats in marine environment. The objective of DARCs model is to achieve maximum spatial complexity (fractals) in a habitat, and one of the decision variables in this model is distance, which is between two adjacent and isolated artificial reef communities (detailed description see Table 1). Many scholars (e.g. Jordan et al., 2005) deem that the deployment of ARs often lack regard for the reef spacing on the resulting fish assemblages. Recently, Jordan et al. (2005) indicated that their experimental results show that variable isolation distance among ARs can alter the structure (i.e., abundance and species richness) of the associate fish assemblages, with specific responses for different species, trophic groups, and size classes. Specifically, they found that the fish abundance and species richness is statistically significant different in isolation treatments varying in isolation distance (reef spacing). Both the largest and smallest spacing treatments (i.e., 25 m and 0.33 m) had statistically higher mean abundance values than the 5 m and 15 m treatments. Some reasons might include that decreased foraging time will be that increased net energetic gain (Stephens and Krebs, 1986) as well as reducing the risk of predation (Milinski, 1986). Therefore, the consumption of prey items closer to a reef by resident fishes will occur more rapidly than in the farther one, and it results that a halo of decreasing density of benthic prey items approaches the reef (Ogden, 1976). Based on this reason, the substrate surrounding a patch reef having a greater isolation distance from other reefs may provide a greater density of benthic prey items than those in closer proximity to each other. Patch reefs spaced closely could result in overlapping halos with a concomitant decrease in benthic prey density and, in turn, the density of benthic foragers; thus, the spacing of reefs might be a critical factor for understanding variations in assemblage structure for patchy environs as well as determining the effectiveness of restoration efforts and the artificial reef deployment (Jordan et al., 2005). Similarly, the simulated
5 Also, the reef block may be composed of several types of modules, each of a different material (see Fig. 1); in other words, module mix-more than one module is frequently used.
max FD, in which FD was calculated by the
Solving algorithm
Assumptions
1. The total cost of the project should be less than or equal to the project budget 2. The potentially deployed sites among the project area should be greater than or equal to the number of deployed ARCs 3. The deploying distance of adjacent ARCs should conform the allowable range, and the minimum adjacent distance should be greater or equal to the diameter of an ARC 4. The number of deployed ARCs should be an integer Heuristic algorithm, and adopts the Moore neighborhood rule (i.e., ad = 1, see Fig. 2) as their neighborhood rule 1. The project area and its size are determined, and the materials of each ARC are the same 2. The spatial configuration of an artificial habitat is focused on the plane and the design scale is on the communities (set). Besides, each ARC consists the same number of AR units (modules) with the same size 3. The total cost of the project includes the purchasing cost of ARCs, the lift/lay-down (or throw) cost of ARCs and the transportation cost
results from DARCs model reveal that phenomenon (Lan and Hsui, 2006a), namely, that the artificial habitat would exhibit different spatial complexity depending on variable distance between two adjacent artificial reef communities. In other words, spacing is species-specific dependent variable, and has a nonlinea relationship with habitat complexity. Bohnsack and Sutherland (1985) suggested the general spacing criterion, that the distance between adjacent artificial reef blocks (ARBs) range from 50 to 100 m, and the ARCs’ is 300–500 m. The DARCs model, however, is restricted to its solving algorithm (i.e., adopts the Moore neighborhood rule with ad = 1, see Fig. 2), and consequently, the configuration could only be deployed as single large island (cluster) pattern. Therefore, we developed the evolution computational algorithm to conduct the artificial habitat design with free neighborhood rule (i.e., ad = x, see Fig. 2), and constructing a multi-clusters pattern.
2.4.
Evolution computational (EC) algorithm
As argued previously, the island biogeographers regard that the isolation of the reserve from places with similar habitats has been perceived to be important in the design of reserves; thus, to provide a multi-clusters deployment, the EC algorithm will be developed as follows instead of the wide-ranging search algorithm formerly proposed DARCs model (Lan and Hsui, 2006a,b). To be specific, the design configuration of artificial habitat used cellular automata models with the free neighborhood rule to obtain several small clusters pattern.
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In this study, we used the evolutionary algorithms (Fogel, 1994; Back, 1996) to design the reef deployment. The original evolutionary algorithms are designed to deal with function optimization problems. But the problem we faced in this study are a two-dimensional discrete pattern design, and some evolution steps, such as mutation, must be modified to fit the problem. In our algorithm, we treat the pattern of an ARC deployment as an individual among the population; the mutation is to dilate or erode the pattern in some bits (A bit 1 in the pattern represents a reef and bit 0 means background during the deploying process). In the traditional EC algorithm, the mutation means adding some small disturbance (a small real number) to the individual (a real number). For our model, the mutation is modified as changing some bits 1 (edge points of the deployed pattern) to 0 (the background bits) or alter some bits 0 (neighbor points, i.e., the background points besides the deployed reef) to 1. The other steps, such as evaluation, selection, and et cetera, are the same as the traditional evolutionary algorithm. The EC fractal algorithms are depicted below: (1) Initialization: Randomly generate an initial population of individuals (i.e., chromosomes in evolution word). Each individual x i is a binary-valued vector that represents one of ARC deploy-
(2)
(3)
(4)
(5)
ments. The vector’s bit that has only a value of 1 or 0 means an ARC existed at the corresponding cell or not. Mutation: Create a single offspring x i from each parent x i , ∀i ∈ {1, 2, . . ., }, by performing the following steps: (i) Generate a random number R with a Gaussian or Cauchy distribution. And truncate the fraction of R to get a random integer. (ii) If R > 0, then dilate the individual x i R bits (dilation algorithms). (iii) If R < 0, then erode the individual x i R bits (erosion algorithms). Evaluation: Calculate all parent’s and offspring’s box-counting fractal dimension as its fitness function values, f (x i ) and f (x i ), ∀i ∈ {1, 2, . . ., }. Selection: Select individuals from the union of parent x i and offspring x i , ∀i ∈ {1, 2, . . ., }. The individuals construct the next population. In our simulated program, the ranking selection is adapted in this study. Termination: If the halting condition is satisfied, then stop the iteration, otherwise, increment the generation number, k = k + 1, and go to step 2.
Fig. 3 – The framework is combining DARBs model and EC algorithm to design an artificial habitat in marine environment. In the first stage, the design scale focuses on an artificial reef community (set), i.e., to decide the configuration (spatial arrangement) of artificial reef blocks. And in this stage, the Moore neighborhood rule is applied to obtain the clumped deployment; additionally, we design the arrangement of an artificial reefs habitat with EC algorithm in the second stage (i.e., adopts free neighborhood rule to deploy artificial reef communities (sets)), to obtain multi-isolated islands pattern for achieving a specific conservation strategy.
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Fig. 4 – Two kind of different landscapes comparisons. The red cells (i.e., patches) are the suggested deployment of artificial reef communities in a marine reserve. The left-hand side is the conventional engineering common designation, namely, the pattern presents a uniform distribution (where FD = 1.29); and the right-hand side shows the landscape structure which was obtained by EC algorithm, and its FD = 1.55.
Fig. 5 – The detailed evolutionary environment setting windows.
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And the dilation/eroding algorithms used in the mutation step is described clearly as follows: Dilation algorithms: (1) For a randomly chosen edge point, select a neighbor point and change the bit form 0 to 1. (2) Repeat the step 1 R times. (3) Finally, erode the individual R bits to keep the number of reefs unchanged. Erosion algorithms: (1) For a randomly chosen edge point, change the bit from 1 to 0. (2) Repeat the step 1 R times. (3) Finally, dilate the individual R bits to maintain the total bits unchanged. For our simulation program, the Builder C++ 6.0 package is adapted to implement the EC algorithm. We run the program 10 epochs in different initialization and get the best pattern for deployment of reef. For every epoch, the evolution is terminated after 500 generations. To compare the searching capability of Gaussian or Cauchy distribution, our program is designed to use Gaussian or Cauchy distribution for mutation. The simulation results reveal that the Cauchy mutation is better than the Gaussian and match Rudolph’s conclusion (Rudolph, 1997).
3. Applications: the framework of designing AR ecosystem In this section, we proposed a two-staged framework to design the spatial arrangement of an artificial habitat in marine environment. The deploying scale mainly focuses on artificial reef communities as former model. But we perform EC algorithm, where neighborhood and transition rule adopts the free neighborhood rule (i.e., ad = x), to construct a multi-clusters pattern with achieving specific conservation strategy. On the other hand, the configuration design of an ARC adopts the Moore neighborhood rule with ad = 1 to deploy artificial reef blocks (i.e., so-called DARBs model), which could clump ARBs into patches of the same attribute class (such as shown in Fig. 1(c)). To be more specific, Fig. 3 shows the framework that combining DARBs model and EC algorithm to achieve a maximizing habitat complexity design with several isolated clusters (such as Fig. 1(b) shown).
4.
Results and discussion
To provide a numerical example, suppose we visit a project that needs to construct a marine artificial habitat as a conservation reserve. Except for the premise of our objective function, maximize the habitat complexity (fractals), the commonly adopted deploying ARs strategy is clumped6 con-
figuration in past engineering concept. We will compare the conventional deployment with EC algorithm suggestions as follows. Our simulations were performed on a hypothetical 25-ha conservation reserve consisting of a 10 × 10 array of 100 0.25ha square cells (Fig. 4). Each cell means the allowable deploying site of ARCs; furthermore, the project budget could only deploy ARCs to the number of 13. The program developed in language C++ and the evolution parameters adapted in the simulation are Population size (number of chromosome) Evolution generation (number of generation) Mutation style Selection type Initialization For the stochastic characteristics of
12 1200 Cauchy Ranking Uniform distribution the EC algorithm, every
simulation is performed 10 epochs and gets the best one as our simulation result. According to such conditions, the conventional configuration shown in the left-hand side of Fig. 4, the pattern is as a single large island and has fractal dimension (FD) with 1.29; in contrast with common deployment, the right-hand side of Fig. 4 is the suggested configuration that applies EC algorithm, and exhibits as two small islands; besides its FD = 1.55 is greater than the single island pattern. The detailed evolutionary environment setting is shown in Fig. 5. The insights gained from such results shows, that the conventional design with single island pattern is not necessarily better than multi-clusters pattern on the complexity perspective, and it might be attributed to its highly nonlinear property in fractals simulation process. However, with our intuition, single island pattern sometimes has larger complexity than dispersal patterns. In addition, on the conservation aspects, if we regard several small (SS) islands as the better strategy, then the EC algorithm could effectively help us deploying an multi-clusters pattern reserve, to improve the defect proposed by Lan and Hsui (2006a,b), whose algorithm could only design a single island configuration.
5.
Conclusion remarks
In this paper, computer simulations of landscapes provide useful models for gaining new insights on the configuration of an artificial habitat, especially in module groupings and spacing intervals. The simulated landscapes could not only allow ecologists to explore some of the consequences of the geometrical configuration of environmental variability for species coexistence and richness, but point the way toward future research. Many additional questions arise from this work, for example: understanding the importance of spatial scales; the relationship between landscape structure and habitat spatial complexity; an increased understanding of landscape structures; and the ability to more accurately model landscapes and ecosystems.
6
Although Yoshimuda (1982) argued that attractiveness generally increased with the number of artificial reefs deployed, it seems that the uniform arrangement of artificial reefs on the whole seabed would be better; however, the reef resources are some-
times constrained by finite budgets, thus this kind of deployment is infeasible in practice.
e c o l o g i c a l e n g i n e e r i n g 3 2 ( 2 0 0 8 ) 44–51
One of the most valuable aspects of fractal geometry, however, is the way that it bridges the gap between ecologists of differing fields. By providing a common language, fractal geometry allows ecologists to communicate and share ideas and concepts. Furthermore, such fractals-based model, if they prove to hold more generally to species distributions, may make it possible to increase greatly our understanding of local and regional patterns of biological diversity.
Acknowledgement The authors would like to thank the anonymous referees who kindly provided the comments to improve this work.
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