2. Why Quantify Landscape Pattern? Comparison (space & time) –Study areas –Landscapes Inference –Agents of pattern formation –Link to ecological processes

3. Programs for Quantifying Landscape Pattern FRAGSTATS –http://www.umass.edu/lan deco/research/fragstats/do cuments/Metrics/Metrics %20TOC.htm Patch Analyst –http://flash.lakeheadu.ca/~ rrempel/patch/

4. Quantifying Landscape Pattern Just because one can measure it, doesn’t mean one should –Does the metric make sense?...biologically relevant? –Avoid correlated metrics –Cover the bases (comp., config., conn.)

5. Landscape Metrics - Considerations Selecting Metrics…… –Subset of metrics needed that: i) explain (capture) variability in pattern ii) minimize redundancy (i.e., correlation among metrics = multicollinearity) –O’Neill et al. (1988) Indices of landscape pattern. Landscape Ecology 1:153-162 i) eastern U.S. landscapes differentiated using –dominance –contagion –fractal dimension

6. Landscape Metrics - Considerations Selecting Metrics…… –Use species-based metrics –Use Principal Components Analysis (PCA)? –Use Ecologically Scaled Landscape Indices (ESLI; landscape indices, scale of species, and relationship to process)

7. Quantifying Pattern: Corridors Internal: –Width –Contrast –Env. Gradient External: –Length –Curvilinearity –Alignment –Env. Gradient –Connectivity (gaps)

8. Quantifying Pattern: Patches Levels: –Patch-level Metrics for indiv. patches –Class-level Metrics for all patches of given type or class –Zonal or Regional Metrics pooled over 1 or more classes within subregion of landscape –Landscape-level Metrics pooled over all patch classes over entire extent

9. Quantifying Pattern: Patches Composition: –Variety & abundance of elements Configuration: –Spatial characteristics & dist’n of elements

10. Quantifying Pattern: Patches Composition: –Mean (or mode, median, min, max) –Internal heterogeneity (var, range) Spatial Characters: –Area (incl. core areas) –Perimeter –Shape

11. Quantifying Pattern: Landscapes (patch based) Composition: –Number of patch type Patch richness –Proportion of each type Proportion of landscape –Diversity Shannon’s Diversity Index Simpson’s Divesity Index –Evenness Shannon’s Evenness Index Simpson’s Index

12. Quantifying Pattern: Patches Configuration : –Patch Size & Density Mean patch size Patch density Patch size variation Largest patch index

13. Patch-Centric vs. Landscape-Centric Mean – avg patch attribute; for randomly selected patch Area-weighted mean- avg patch attribute; for a cell selected at random

14. Patch-Centric vs. Landscape-Centric Consider relevant perspective…landscape more relevant?...use area- weighted Look at patch dist’ns…right- skewed = large differences

15. Quantifying Pattern: Patches Configuration : –Shape Complexity Shape Index Fractal Dimension Fractals = measure of shape complexity (also amount of edge) Fractal dimension (d) ranges from 1.0 (simple shapes) to 2.0 (more complex shapes) ln(A)/ln(P), where A = area, P = perimeter

16. Quantifying Pattern: Patches Configuration : –Core Area (interior habitat) # core areas Core area density Core area variation Mean core area Core area index

18. Quantifying Pattern: Patches, Zonal Configuration : –Isolation / Proximity Proximity index Mean nearest neighbor distance

20. Proximity where, within a user-specified search distance: s k = area of patch k within the search buffer n k = nearest-neighbor distance between the focal patch cell and the nearest cell of patch k

21. Proximity Index (PXi) = measure of relative isolation of patches; high (absolute) values indicate relative connectedness of patches

22. Quantifying Pattern Overlay hexagon grid onto landcover map Compare bobcat habitat attributes to population of hexagon core areas

23. Quantifying Pattern Landscape metrics include: Composition (e.g., proportion cover type) Configuration (e.g., patch isolation, shape, adjacency) Connectivity (e.g., landscape permeability)

24. Quantifying Pattern & Modeling Calculate and use Penrose distance to measure similarity between more bobcat & non-bobcat hexagons Where: population i represent core areas of radio-collared bobcats population j represents NLP hexagons p is the number of landscape variables evaluated μ is the landscape variable value k is each observation V is variance for each landscape variable after Manly (2005)

25. Penrose Model for Michigan Bobcats VariableMean Vector bobcat hexagons NLP hexagons % ag-openland15.832.4 % low forest51.410.4 % up forest17.643.7 % non-for wetland8.62.3 % stream3.40.9 % transportation3.05.2 Low for core27.63.6 Mean A per disjunct core 0.72.6 Dist ag50.044.9 Dist up for55.043.6 CV nonfor wet A208.3120.1

26. Quantifying Pattern & Modeling Each hexagon in NLP then receives a Penrose Distance (PD) value Remap NLP using these hexagons Determine mean PD for bobcat-occupied hexagons Preuss 2005