LAB EXERCISE #3 Neutral Landscape Analysis Summary of Key Results and Conclusions

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1 LAB EXERCISE #3 Neutral Landscape Analysis Summary of Key Results and Conclusions Below is a brief summary of the key results and conclusions of this exercise. Note, this is not an exhaustive summary, as there are many subtle details of the exercise that could be discussed. Question 1: Test the following null hypothesis: H1: The configuration of habitat in each real landscape is not different from a randomly structured landscape containing the same percentage of habitat. In other words, how likely is it that the configuration of habitat in each real landscape could have been produced in the absence of any ecological pattern-generating processes. And answer the following questions: Do you reject the null hypothesis and, if so, on the basis of what empirical evidence? Be sure to interpret your result in terms of the landscape metrics; i.e., what the metrics tell you about landscape pattern? Also, is your evidence against the null hypothesis equally strong among the three real landscapes or does it differ with changes in the proportion of the landscape that is forest, and if it differs, why? Summary of Results: 1. In all three real landscapes, all of the metrics are outside the range of variation expected under a random neutral model (see table below). 2. Largest cluster size, edge, fractal, and radius are all greater in the real landscape than random landscapes when habitat is rare (21%), due to contagious habitat in real landscape, but all less in the real landscape than random landscapes when habitat is abundant (65-79%), due to the percolation (hence large percolating cluster) of the random landscapes. Total number of clusters follows the inverse relationship for the same reasons. 3. Total number of edges is less in the real landscapes regardless of habitat amount due to the greater contagion in real landscapes than random landscapes. 4. Area-weighted average cluster size and correlation length follow the same relationship as the largest cluster size for the same reasons and because these metrics are dominated by the largest cluster. Note that when habitat is abundant (65-79%), the area-weighted average cluster size is very similar to the largest cluster size statistics because the landscape is dominated by a single large percolating cluster. 5. The deviation between the real landscape and the random landscape lessens as habitat area increases for most metrics (e.g., see Correlation length). Reg21% Variable Units Real Random(min) Random(max) Deviation L.C.size ha L.C.edge m L.C.fract

2 L.C._rms m TTL clstr N TTL edgs m Sav size ha Cor_len m Reg66% Variable Units Real Random(min) Random(max) Deviation L.C.size ha L.C.edge m L.C.fract L.C._rms m TTL clstr N TTL edgs m Sav size ha Cor_len m Reg78% Variable Units Real Random(min) Random(max) Deviation L.C.size ha L.C.edge m L.C.fract L.C._rms m TTL clstr N TTL edgs m Sav size ha Cor_len m Conclusion/Implications: The results warrant rejecting the null hypothesis for all 3 real landscapes; all three landscapes exhibit significantly different patterns than would expected by chance alone. However, when habitat is abundant (i.e., large p), certain components of landscape structure can be adequately explained by a random distribution of habitat (i.e., simple random neutral landscape). In particular, above the percolation threshold, the largest cluster size and total number of clusters in random landscapes converge on the corresponding statistics for the real landscapes. However, when habitat is rare, the neutral model increasingly fails to explain the real landscape structure, indicating that nonrandom processes increasingly control landscape structure as habitat area is reduced. 2

3 Question 2. How do you interpret the lacunarity plot? Based on the lacunarity of the real landscapes in comparison to the random and fractal landscapes, what does the lacunarity analysis reveal about the nature of the pattern-forming agents? Summary of Results: 1. Lacunarity decreases as habitat area increases (see Figure 1). Why? Because the range of variation in box mass (or, alternatively, gap sizes) increases as p decreases. 2. Lacunarity decreases as box size increases. Why? Because the range of variation in box mass (or, alternatively, gap sizes) decreases as box size increases, because as box size increases, each box is more likely (on average) to include the average density of habitat cells (p). 3. When box size equals the map grain size (block size in hierarchical maps and cluster size in fractal maps), under constant p, lacunarity values for real, random, and fractal landscapes are equivalent. Hence, lacunarity for random landscape approaches zero immediately as box size increases (grain = single cell), but is delayed in fractal landscapes increasingly as contagion increases (i.e., as grain increases). Why? Because once the box size is larger than the grain size of patches (clusters), then most boxes will contain a similar amount of habitat and the variation in box mass will plummet. 4. Presence of a threshold effect in lacunarity (as box size increases) decreases as habitat area increases. Why? Because at low p, small boxes will have high variation in box mass (some will be full, some will be empty), and as box size increases there will be a point at which the box is large enough so that all boxes have some habitat (perhaps even the same amount) and lacunarity will plummet. However, at high p, small and large boxes alike will have little variation in box mass (all will be mostly full), thus lacunarity will be universally lower and will not likely exhibit a threshold effect as box size increases. 5. Threshold in lacunarity at a particular box size indicates scale at which the box size approximates the scale of the habitat clusters; that is, where among box variance begins to diminish and subsequent variance is mostly associated with within-box variation. 6. A linear shape of the lacunarity curve (i.e., straight diagonal line) may reflect self-similar patterns in the landscape. 7. Lacunarity of all three real landscapes approximates the distribution of the corresponding low contagion fractal landscapes across the full range of scales. 8. The variation depicted among the replicate landscapes provides reasonably convincing evidence that the real landscapes are most similar to the low contagion landscapes and are different from the more contagious landscapes and the random landscape. 9. Another way to interpret the lacunarity plots is by plotting the deviation in lacunarity between the real and neutral landscape in relation to scale (box size)(figure 3). This provides a direct measure of the magnitude of difference between curves and can help to portray the magnitude and nature of the differences between real and neutral landscapes. For example, based on inspection of the deviation plots in figure 3, it is clear that Reg1 landscape containing the least amount of forest cover is the most nonrandom across almost the full range of scales (Fig. 3a) and the most unlike the high contagion neutral landscape (Fig. 3d). Similarly, all three real landscapes are most like the low contagion neutral landscapes and show a consistent pattern of greater contagion than the corresponding low fractal landscapes at fine 3

4 scales (i.e., small box sizes) and less contagion at coarse scales (i.e., large box sizes)(fig. 3b). Conclusion/Implications: Not surprisingly, all real landscapes are more lacunar (i.e., greater contagion) than the random landscape. The forest contagion is due to the patterns of anthropogenic land use primarily agricultural practices that preserved a few large woodlots rather than many scattered small groups of trees and land ownership patterns in which entire parcels are preserved as forest tracts. All three real landscapes in fact exhibit a low degree of contagion relative to the fractal neutral landscapes (i.e., the lacunarity curves for the real landscapes are not significantly different from the low contagion fractal landscapes [H=0.1] across most box sizes). Thus, all real landscapes exhibit a relatively high degree of forest fragmentation (i.e., low contagion) for the reasons mentioned previously. This suggests that low contagion fractal landscapes would provide a suitable model for testing hypotheses about pattern-generation in these real landscapes. Lastly, the apparent self-similarity of the three real landscapes above a certain box size implies that the pattern of heterogeneity in these landscapes is relatively constant across relatively coarse scales. Thus, organisms that scale the environment differently may perceive the same degree of heterogeneity at least above some intermediate scale. Question 3: Using the correlation length and frequency of map percolation, determine how the gap-crossing ability (using nearest neighbor rules as a surrogate) of a species influences the connectivity of the landscape and whether this relationship varies in relation to the spatial contagion of habitat (i.e., random versus fractal landscape patterns). Discuss the implications of these findings for understanding the consequences of forest fragmentation on organisms. Summary of Results: 1. Correlation length increases dramatically as nearest-neighbor rule increases for random landscape, but only mildly so for fractal landscape (Fig. 4b). 2. Percolation occurs in contagious landscape using the 4-neighbor rule, but not in random landscape (Fig. 4a). Why? At relatively low p s (below Pcrit), contagious distributions will be more likely to percolate than random due to clumping. At higher p s (above Pcrit), however, random landscapes will almost certainly percolate, yet fractal landscapes will often not, depending on the actual habitat distribution. Conclusion/Implications: Gap crossing ability is most important in poorly connected landscapes (need to cross gaps to achieve connectivity) and is of particular interest when the habitat is rare (below Pcrit). Under these conditions, habitat contagion is vital for species with low gap-crossing ability in order to achieve connectivity. When habitat is rare (i.e., below Pcrit), contagion enhances the connectivity for species with limited gap-crossing ability, because individuals will not have to cross gaps to find habitat and may (by chance) be able to move all the way across the landscape (percolate) without having to cross any gaps. On the other hand, for gap-crossing (highly vagile) species, a noncontagious landscape may provide greater connectivity than a 4

5 contagious one with the same habitat area, at least when p is less than Pcrit, because individuals can easily cross over gaps to find habitat and in this manner may used highly dispersed habitat as stepping stone to move across the landscape. Ultimately, the relationship between habitat configuration and connectivity depends on the life history characteristics of the organism. 5

6 Figure 1a. Lacunarity plots for the landscapes corresponding to the real landscape with 21% habitat. Figure 1b. Lacunarity plots for the landscape corresponding to the real landscape with 66% habitat. 6

7 Figure 1c. Lacunarity plots for the landscapes corresponding to the real landscape with 78% habitat. 7

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