Landscape Ecology. Lab 2: Indices of Landscape Pattern

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1 Introduction In this lab exercise we explore some metrics commonly used to summarize landscape pattern. You will begin with a presettlement landscape entirely covered in forest. You will then develop this landscape, mimicking the clearing of forest for agricultural land uses, and track this change as reflected in landscape pattern metrics. This lab is inspired by Cadiz Township, in south central Wisconsin. At settlement, most of the area was oak forest, intergrading to oak savanna and then to prairie to the west. Except for a hilly northern fringe and the equally hilly area west of the Pecatonica River, the township is relatively homogeneous (figure 1). Figure 1. History of forest fragmentation in Cadiz Township, southern Wisconsin. patches.lab 1 9/9/99

2 The question arises, How unusual is this trajectory of fragmentation? Is it different from a random fragmentation sequence? To answer these questions, we need to develop a framework of reference within which to interpret these patterns. Objectives The goal of the exercise is to understand the procedures for characterizing landscape pattern, and to examine how pattern metrics change with increasing fragmentation of intact habitats as development proceeds. Specifically, you will Define patches as clusters of contiguous like-valued cells in a raster map; Describe individual patches in terms of patch area and shape complexity; Summarize landscapes in terms of average patch metrics, edge density, and patch dispersion, in relation to the proportion of area occupied by forest; Illustrate how these metrics vary as a landscape undergoes a conversion from intact natural habitat to increasingly fragmented habitat patches interspersed among human land uses; Speculate on how these trends might vary under alternative development scenarios. Note that this is not about Cadiz Township, but is a more general illustration. Materials The data consist of landscapes provided as raster maps. The study area is a 30x30 grid of 1-ha cells (100x100 m). We will be concerned only with forest cover, and so the maps are collapsed into two values, forest versus nonforest. Each map is summarized and labelled in terms of the proportion of forest cover remaining (e.g., the 60% cover map). In addition to the maps, you will need a pencil, some paper, and a hand calculator (or a spreadsheet, if you prefer). Procedure The lab exercise consists of 3 basic steps, which will be repeated for a variety of maps. The first step is the identification of discrete patches of each cover type. The second step is to compute metrics for each patch. The third step entails integrating these patch-level metrics to the landscape level. To save time, you will analyze only a single map, and the class will pool its results for the final synthesis. We will arrange this data-pooling in class. Landscape Fragmentation To fragment the landscape from intact forest into agriculture, raster maps were generated with a specified proportion, p, of forest cover remaining. For each cell, a uniform random number x was drawn on the interval [0,1]; if x< p, the cell was given a value of 1 (forest), otherwise it was scored 0 (nonforest). Maps were generated ranging from ~10 to 90% forest cover. Because each map is a realization of a stochastic process, at least 3 replicate maps were generated at patches.lab 2 9/9/99

3 each level. Thus, we will have slightly different maps at each cover level p; we will average the analyses from the replicate maps at each level p. The initial (unfragmented 100% forest) and final (0% forest) maps needn t be analyzed, because these will produce either trivial or undefined landscape metrics. Patch Definition A patch of a given cover type is defined as a cluster of cells of the same cover type, which are contiguous using a 4-neighbor rule (i.e., touching in any of the 4 cardinal directions, but not counting the diagonals). You might try to envision the logical algorithm whereby this is done by computer; but for our purposes you can use your eyes and a pencil, drawing a line around each discrete cluster (patch). As you delineate patches, number them sequentially and label them somewhere in the patch. You will tally patch metrics using these labels, so be careful to match these properly. Different maps need not retain the same patch numbering scheme. You need only be concerned with the forest (shaded) type; ignore the nonforest cover type. Patch Metrics For each patch of forest, tally these metrics: The number of cells in the cluster, N_Cells. The amount of edge, as the number of edge cells, N_Edge. Edge cells are those that have at least one side facing nonforest (do not count cells that touch nonforest only on the diagonal). For cells on the perimeter of the map, count the outside edge as if it really is edge (this isn t necessarily true, but is consistent with the area tally). Tally inner as well as outer edges. Also tally the length of edge L_Edge, as the number of sides that are edges, as many as 4 edges per cell. The distance to the nearest other patch of forest. Calculate the nearestneighbor distance, NND, using the Pythagorean theorem and the row and column positions of cell i and j, slightly adjusted: NND = ( x i x j ) 2 + ( y i y j ) 2 1. (1) Here, subtracting 1 adjusts the estimate for center-to-edge distance (this is not strictly correct but is computationally expedient). In maps with high p values, you may have a single patch of the dominant cover type; in these cases, the nearest-neighbor distance is undefined (set this to 0). As you proceed, construct a table in which you tally these raw metrics: Patch N_Cells N_Edge L_Edge NND A S (see below) patches.lab 3 9/9/99

4 Finally, fill in the table by computing the last two metrics: Patch Area (A), as a proportion of the landscape. Simply divide the number of cells in the patch (column 2, above), by the total number of cells in the map (30x30=900). Enter this value into its column in the table. Edge/Area Shape Index (S), defined as 0.25E/SQRT(N) where E is edge length (L_Edge) and N is the number of cells in the patch (N_Cells). This index takes on a value of 1.0 for a square, and increases in value for more irregular shapes. You will find that the number of patches per map ranges from 1 to >100, depending on the proportion of forest cover. Landscape Metrics From the tabled values above, compute these summary indices for the entire set of patches: Total Area (A tot ) in this cover type (the sum of the column of A s for all patches, above, which should be approximately equal to the proportion of the map in forest cover, p (allowing for some variability from the random numbers). Total Number of Patches (NP) (the number of rows in the table above). Largest Patch Size (LP) and Average Patch Size (xp), as well as a Frequency Distribution of Patch Sizes for the map. The largest is simply that; the average is either the average of all values of A, or A tot /NP (which are equivalent). Total Edge (E tot ), the sum of all values N_Edge, divided by total forest area N_Cells and converted to a percentage. Mean Shape Index (xs), computed as the average value of S for all patches. Mean Nearest-Neighbor Distance (xnnd), the average value of NND for all patches. Tally these values for the map that you analyze, using the following format: Map A tot NP LP xp E tot xs xnnd p30a Also tally the number of patches in each of the size classes tabled below: Map >256 p30a Benchmark: You will augment these two tables with landscape-level metrics computed by others in the class. You should turn in the table with the map-level summary statistics and the frequency distribution of patch sizes for your landscape. These will be collated for all landscapes and redistributed to the class so you can finish this analysis with the pooled data. patches.lab 4 9/9/99

5 Your Lab Report For general information on lab write-ups, see the webpage Some specifics for this lab follow. Introduction Introduce the general topic of landscape pattern and why we are interested in it. Specifically, what is the purpose and rationale for analyzing random landscapes? Include a statement of your objectives. Close the introduction by anticipating your main results somewhat--in effect enticing the reader to finish the paper! Background In cases where there is already a lot known (a lot of work published) it is appropriate to include a Background section in which you summarize what we know about the topic, and identify uncertainties to prioritize further work. Presumably, this discussion should echo, in a more in-depth way, the points you raise in your Introduction. In this case, your background discussion should review the main components of landscape pattern and how they vary across landscapes. The papers by O Neill et al. (1988), Gardner et al. (1987, 1992), and Gustafson (1998) should be central to your background discussion. Methods Data It will be appropriate in this lab to describe the data and analyses separately. Present your data by explaining what the data are, where they came from, and so on. In this lab, it will be sufficient to describe how they were generated (e.g., Maps were generated in which varying proportions p of each map was occupied by habitat with p ranging from 0.1 to 0.9. ). Analyses Describe the analyses thoroughly but without extraneous detail. This means that if you use a nonstandard or novel method, you need to present it fully. For standard methods, simply cite an appropriate source (e.g., I computed Moran s I (Legendre and Fortin 1989) ). For quite familiar methods, simply state the method (e.g., I computed linear regressions ). You should not include details that are irrelevant in the sense that the particular tool doesn t matter (e.g., nobody needs to know whether you did your calculations in Excel, and nobody cares what graphics package you like). Here, you might include the equations for the metrics but cite O Neill et al. (1988) as the source for more detailed explanations. Results Your Results section should simply present your results as clearly and concisely as possible. In general, figures or tables will provide the most effective summary. These should be called from a narrative that highlights the main points. patches.lab 5 9/9/99

6 To illustrate your results, generate graphs in which you plot the landscapelevel metrics NP, LP, xp, E tot, xs, and xnnd versus the proportion of the landscape covered by forest (A tot ). This may require several graphs, because the metrics are in different units. Finally, generate histograms of the frequency distributions of patch sizes, averaged for three sets of replicate maps with cover densities in the range p < 30, 30-70, and >70%. This section should not include your personal interpretation or views on the results, although it is permissible to explain particularly complicated results if necessary. Discussion Interpret your results in a narrative discussion, in which you: Highlight key trends in your results: How does each of these metrics vary as the landscape is increasingly fragmented? Is the trend simple and linear, or nonlinear? If nonlinear, does there seem to be a threshold value where the metric changes dramatically? Relate the trends in total forest area, mean patch size, and nearest-neighbor distance to each other. Why would you expect these metrics to covary? How does the size distribution of patches vary with p? How does this relate to the trends in the other metrics? Finally, consider the random-fragmentation sequence and the possibility that real landscapes might not be developed according to strictly random decisions. In your discussion, speculate as to what differences in landscape pattern you might expect under some alternative scenarios of landscape fragmentation: What if forests were cleared in discrete parcels of a given size, for example, as 40-acre (16 ha) agricultural fields? How would this affect patch size, shape, and dispersion if the same total forest area was removed at each iteration? What if there were considerable spatial constraints on fragmentation, for example, if flat sites or certain soils types were cleared preferentially, with less favorable sites cleared later? What if clearing a given area increased the likelihood that nearby areas would be cleared in the near future (e.g., because of the proximity of roads)? How might these scenarios affect landscape pattern? What purpose does the analysis of randomly patterned landscapes serve in helping us to understand real landscapes? How might you alter this exercise to construct expected values under the alternative scenarios outlined above? Since your discussion might range far from your specific results, it might be appropriate to collect the main points and conclusions into a closing section or paragraph that finishes your report, bringing it back if possible to the objectives you itemized at the end of your Introduction. That is, we hope that once you ve finished the paper you can answer the questions that motivated the exercise in the first place. References Please note that my on-line lecture notes are not citable. patches.lab 6 9/9/99