Spatial Data Analysis

1. Spatial Data Analysis The accurate description of data related to a process operating in space, the exploration of patterns and relationships in such data, and the search for explanation of such patterns and relationships Spatial Analysis vs. Spatial Data Analysis Spatial Analysis = what is here, and where are all the X’s ??? Spatial Data Analysis = observation data for a process operating in space and methods are used to describe or explain the behavior, and/or relationship with other phenomena.

2. Types of Metics • Area Metrics • Patch Density, Size and Variability • Edge Metrics • Shape Metrics • Core Area Metrics • Nearest-Neighbor Metrics • Diversity Metrics • Contagion and Interspersion Metrics

3. Landscape Ecology • Structure = the spatial relationships among the distinctive ecosystems or “elements” • Function = the interactions among the spatial elements • Change = the alteration in the structure and function of the ecological mosaic over time

4. Fragstats: McGarigal, K. and Marks, B.J. 1995, Fragstats: Spatial Pattern Analysis Program for Quantifying Landscape Structure. General Technical Report, PNW-GTR-351. Portland, OR, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, 122p.

5. Terms • Landscape = a “mosaic” of patches. • Patch = the basic “element” or “unit” of the landscape defined relative to the phenomenon, that are dynamic and occur at multiple ecological scales with unique and meaningful boundaries • Matrix = the most extensive and most connected element dominating the function of the landscape • Class = a category or type of patch • Ecological Scale = both the “Extent” (area within the landscape boundary) and “Grain” (the size of the units of observation) defining the dynamics of the phenomenon.

6. Landscape Structure Physiognomy / Pattern • Composition = The presence and amount of each element type without spatially explicit measures. • Proportion, richness, evenness, diversity • Configuration = The physical distribution in space and spatial character of elements. • Isolation, placement, adjacency • ** some metrics do both **

7. Area Metrics • Absolute Metrics • Total Area (TA) • Class Area (CA) • Relative Metrics • Percent • (%extent), or %land = percent of total occupied by each class • (LSIM) = Landscape similarity Index: • For each element LSIM = %extent • Largest (LPI), Smallest (SPI)

8. Density, Size and Variability • Number of element (NE) or Patches (NP) • Density of Element - patch density (PD) = number of elements on a per unit basis • Mean Element or Patch size (MPS) • for the landscape • for the class • Patch size coefficient of variation (PSCV) = a measure of relative variation, the difference in patch size among patches, (I.e. variability as a percentage of the mean).

9. Edge Metrics • Total Edge (TE) and Edge Density (ED), for all classes and by class • Perimeter (PERIM) by patch • Edge Contrast Index (EDGECON) = difference across a boundary • total edge contrast • mean edge contrast • area-weighted mean edge contrast • contrast-weighted edge density

10. Shape Metricsperimeter-area relationships • Shape Index (SHAPE) -- complexity of patch compared to standard shape • vector uses circular; raster uses square • Mean Shape Index (MSI) = perimeter-to-area ratio • Area-Weighted Mean Shape Index (AWMSI) • Landscape Shape Index (LSI) • Fractal Dimension (D), or (FRACT) • log P = 1/2D*log A; P = perimeter, A = area • P = sq.rt. A raised to D, and D = 1 (a line) • as polygons move to complexity P = A, and D -> 2 • A few fractal metrics • Double log fractal dimension (DLFD) • Mean patch fractal (MPFD) • Area-weighted mean patch fractal dimension (AWMPFD)

11. Core Area Metrics • The area within a patch beyond a buffer or “edge” distance • Corresponding metrics with those dealing with • Density • Size • Variability

12. Nearest-Neighbor Metrics • The distance from a patch to the nearest neighboring patch of the SAME type • Nearest-neighbor distance (near) = just distance • Proximity index (PROXIM), using a search radius – distinguishes sparse distribution from complex clusters

13. Diversity Metrics • Influenced by the compositional and structural components of diversity: • Richness = the number present • Evenness = the distribution of area among different types • Shannon’s Diversity Index (SHDI): magnitude not meaningful, a relative index • Simpson’s diversity Index (SIDI): the probability that any types selected would be different – (also a modified version)

14. More on Diversity • Patch Richness (PR) and Patch Richness Density (PRD) • Evenness – or, the distribution of area among types • The compliment is Dominance • Evenness = 1- dominance • Shannon’s evenness index (SHEI) • Simpson’s Evenness Index (SIEI)

15. Contagion, Interspersion and Juxtaposition • When first proposed (O’Neill 1988) proved incorrect, Li & Reynolds (1993) alternative • Based upon the product of two (2) probabilities • Randomly chosen cell belongs to patch “i” • Conditional probability of given type “i” neighboring cells belongs to “j” • Interspersion (the intermixing of units of different patch types) and Juxtaposition (the mix of different types being adjacent) index (IJI)