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Metric Definitions (fromMcGarigal and Marks, 1994 and McGarigal and Marks,1995)Class Area (CA)Sum ofareas of all patches belonging to a given class.
Example: Conifer Class Area (CA) =359047.844+......+65819.984
CA = 69.6626 hectares
If the map units are not specified(i.e., Data Frame properties; see Set map units) and \"State areas in Hectares\" has not beenselected in the \"Advanced Options\" of the \"Spatial Statistics\"dialog box, then the resulting statistics will be reported innative map units (vector layers (themes) only).
In the example; CA = 696626.012 (mapunits). This is the case for most statistics.
Landscape Area (TLA)Sum of areas of all patches in thelandscape.
Example: Landscape Area (TLA) =46872.719 + 359047.844 +... + 62423.574
TLA = 184.11 hectares
Percentage of Landscape(ZLAND)
When analyzing by class,ZLAND is the percentage of the total landscape made up of thecorresponding class (patch type).
Number of Patches (NumP)Total number of patches in thelandscape if \"Analyze by Landscape\" is selected, or Number ofPatches for each individual class, if \"Analyze by Class\" isselected.
Example: Class Level: Number of Patches(NumP)
Mixedwood = 5, Conifer = 4, Deciduous =5
Landscape Level: Number of Patches(NumP) = 14
Patch Richness(PR)
PR isthe number of different patch types within the landcape\'sboundary.
PatchRichness Density (PRD)
PRDis equal to PR divided by the total area of the landscape (metressquared) multiplied by 10,000 and then 100 (to convert to hundredsof hectares).
Largest Patch Index(LPI)
The LPI is equal to thepercent of the total landscape that is made up by the largestpatch.
When the entire landscapeis made up of a single patch, the LPI will equal 100. As the sizeof the largest patch decreases, the LPI approaches0.
Mean Patch Size (MPS)Average patch size.
Example: Mean Patch Size of ConiferPatches (Class Level)
MPS = (359047.844 + 139531.484 ...+65819.984)/4
MPS = 17.42 hectares
Example: Mean Patch Size of Patches(Landscape Level)
MPS = (46872.719 + 359047.844 + ... +62432.574)/14
MPS = 13.15 hectares
Median Patch Size (MedPS)The middle patch size, or 50thpercentile.
Example: Median Patch size of ConiferPatches (Class Level)
MedPS = 13.22 hectares
Example: Median Patch size of allpatches (Landscape Level)
MedPS = 7.59 hectares
Patch Size Standard Deviation (PSSD)Standard Deviation of patch areas.
Example: Patch Size Standard Deviationof Conifer Patches (Class Level)
PSSD = 11.05 hectares
Example: Patch Size Standard Deviationof all patches (Landscape Level)
PSSD = 9.51 hectares
Patch Size Coefficient of Variance (PSCoV)Coefficient of variation ofpatches.
Example: Coefficient of Variation ofConifer patches (Class Level)
PSCoV = PSSD/MPS = (11.05 hectares /17.42 hectares) *100 = 63
Example: Coefficient of Variation ofall patches (Landscape Level)
PSCoV = (9.51 hectares / 13.15hectares)*100 =72
Total Edge (TE)Perimeter of patches.
Example: Total Edge Conifer (ClassLevel)
TE = Sum of perimeter of all coniferpatches.
TE = 10858.88 metres
Units are expressed in native mapsunits.
Example: Total Edge all patches(Landscape Level)
TE = Sum of perimeter of allpatches
TE = 28607.27 metres
Important
In thecase of vector layers (themes), edge calculations include all theedge on the landscape including boundary edge. The contrastedweighted edge feature allows edge weight at the boundaries to beset to zero. In the case of raster (grid) layers (themes), edgecalculations do not include the edges that surround the landscapeboundary edge or any interior edges that include pixels classifiedas No Data.
Edge Density (ED)Amount of edge relative to thelandscape area.
Example: Edge Density Conifer (ClassLevel)
ED = TE / TLA
ED = 10858.88 metres/184.11 hectares =58.98 metres/hectare
Example: Edge Density of all Patches(Landscape Level)
ED = 28607.27 metres/184.11 hectares =155.38 metres/hectare
Mean Patch Edge (MPE)Average amount of edge per patch.
Example: Mean Patch Edge Conifer (ClassLevel)
MPE = TE / NumP
MPE = 10858.88 metres/4 patches =2714.72 metres/patch
Example: Mean Patch Edge all Patches(Landscape Level)
MPE = TE / NumP
MPE = 28607.27 metres/14 patches =2043.38 metres/patch
Contrasted Weighted EdgeDensity (CWED)
CWED is a measure ofdensity of edge in a landscape (metres per hectare) with auser-specified contrast weight.
CWED is equal to 0 when there is noedge in the landscape, in other words the whole landscape and it\'sborder are made up of a single patch. It\'s value increases as theamount of edge in the landscape increases and/or as the userincreases the contrast weight.
Landscape Shape Index(LSI)
LSI is the totallandscape boundary and all edge within the boundary divided by thesquare root of the total landscape area (square metres) andadjusted by a constant (circular standard for vector layers, squarestandard for rasters). The LSI will increase with increasinglandscape shape irregularity or increasing amounts of edge withinthe landscape.
Double Log Fractal Dimension(DLFD)
DLFD is a measure ofpatch perimeter complexity. It nears 1 when patch shapes are\'simple\', such as circles or squares and it approaches 2 as patchshape perimeter complexity increases.
Mean Perimeter-Area Ratio (MPAR)Shape Complexity.
Example: Mean perimeter-area ratioConifer (Class Level)
MPAR = Sum of each patchesperimeter/area ratio divided by number of patches.
MPAR = (132 m/ha + 112 m/ha + 201 m/ha+ 84 m/ha)/4 patches
MPAR = 182 metres/hectare
Example: Mean perimeter-area ratio allpatches (Landscape Level)
MPAR = (200 m/ha + 132 m/ha + ... + 175m/ha)/14 patches
MPAR = 185 metres/hectare
Mean Shape Index (MSI)Shape Complexity.
MSI is equal to 1when all patches are circular (for polygons) or square (for rasters(grids)) and it increases with increasing patch shapeirregularity.
MSI = sum of each patch\'s perimeterdivided by the square root of patch area (in hectares) for eachclass (when analyzing by class) or all patches (when analyzing bylandscape), and adjusted for circular standard ( for polygons), orsquare standard (for rasters (grids)), divided by the number ofpatches.
Area Weighted Mean ShapeIndex (AWMSI)
AWMSI is equal to 1 whenall patches are circular (for polygons) or square (for rasters(grids)) and it increases with increasing patch shapeirregularity.
AWMSI equals the sum ofeach patch\'s perimeter, divided by the square root of patch area(in hectares) for each class (when analyzing by class) or for allpatches (when analyzing by landscape), and adjustedfor circular standard ( for polygons), or square standard (forrasters (grids)), divided by the number of patches. It differs from the MSIin that it\'s weighted by patch area so larger patches will weighmore than smaller ones.
Mean Patch Fractal Dimension (MPFD)Shape Complexity.
Mean patch fractal dimension (MPFD) isanother measure of shape complexity. Mean fractal dimensionapproaches one for shapes with simple perimeters and approaches twowhen shapes are more complex.
Area Weighted Mean Patch Fractal Dimension (AWMPFD)Shape Complexity adjusted for shapesize.
Area weighted mean patch fractaldimension is the same as mean patch fractal dimension with theaddition of individual patch area weighting applied to each patch.Because larger patches tend to be more complex than smallerpatches, this has the effect of determining patch complexityindependent of its size. The unit of measure is the same as meanpatch fractal dimension.
Mean Nearest Neighbor (MNN)Measure of patch isolation.
The nearest neighbor distance of anindividual patch is the shortest distance to a similar patch (edgeto edge). The mean nearest neighbor distance is the average ofthese distances (metres) for individual classes at the class leveland the mean of the class nearest neighbor distances at thelandscape level.
Interspersion Juxtaposition Index (IJI)Measure of patch adacency.
Approaches zero when the distributionof unique patch adjacencies becomes uneven and 100 when all patchtypes are equally adjacent.
Interspersion requires that thelandscape be made up of a minimum of three classes. At the classlevel interspersion is a measure of relative interspersion of eachclass. At the landscape level it is a measure of the interspersionof the each patch in the landscape.
Mean Proximity Index (MPI)Measure of the degree of isolation andfragmentation.
Mean proximity index is a measure ofthe degree of isolation and fragmentation of a patch. MPI uses thenearest neighbor statistic. The distance threshold default is1,000,000. If MPI is required at specific distances, select Set MPIThreshold from the main Patch pull-down menu and enter a thresholddistance.
Both MNN and MPI use the nearestneighbor statistic of similar polygons in their algorithm.Occasionally a blank or zero will be reported in MNN and MPIfields. This happens when one polygon vertex touches anotherpolygons border but the two similar polygons do not share a commonborder. When this happens a manual edit (move) of the touchingvertex will correct the problem in the layer (theme). This problemwill not happen when analyzing raster (grid) layers (themes).
Shannon\'s Diversity Index (SDI)Measure of relative patchdiversity.
Shannon\'s diversity index is onlyavailable at the landscape level and is a relative measure of patchdiversity. The index will equal zero when there is only one patchin the landscape and increases as the number of patch types orproportional distribution of patch types increases.
Simpson\'sDiversity Index (SIDI)
Measure of relative patchdiversity.
Simpson\'s diversity index is onlyavailable at the landscape level and is a relative measure of patchdiversity. The index will equal zero when there is only one patchin the landscape and increases as the number of patch types orproportional distribution of patch types increases.
Shannon\'s Evenness Index (SEI)Measure of patch distribution andabundance.
Shannon\'s evenness index is equal tozero when the observed patch distribution is low and approaches onewhen the distribution of patch types becomes more even. Shannon\'sevenness index is only available at the landscape level.
Simpson\'s Evenness Index(SIEI)
SIEI is a measure of the distributionof area among patch types. It equals 1 when the distribution ofarea among patches is exactly even. SIEI approaches 0 as thedistribution of area among the patches become more and moredominated by one patch type.
Modified Simpson\'s Diversity Index(MSIDI)
MSIDI is a measure ofpatch diversity. It equals zero when there is only one patch in thelandscape and increases as the number of different patch types (PR)increases and the area among patch types becomes moreequal.
Modified Simpson\'s EvennessIndex (MSIEI)
MSIEI is ameasure of the distribution of area among patchtypes. It equals 1 when the distribution of area among patches isexactly even. SIEI approaches 0 as the distribution of area amongthe patches become more and more dominated by one patch type. Itdiffers from SIEI in that it is derived from the Modified Simpson\'sDiversity Index (MSIDI) rather than the Simpson\'s Diversity Index(SIDI).
Important
Direct analyses of Core Area through thespatial statistics dialogue are only available for raster (grid)layers (themes). If core area statistics are required for vectorlayers (themes), first Create Core Areas (create a new core area theme) from thePatch pull-down menu and then calculate statistics for thenew layer (theme) as you would for a normal vector layer (theme).The results will be core area statistics.
Total Core Area (CA)The total size of disjunct corepatches.
The total size of disjunct core areapatches (hectares).
Mean Core Area (MCA)The average size of disjunct corepatches.
The mean size of disjunct core areapatches (hectares).
Number of Core Areas(NCA)
The total number ofdisjunct core areas within each patch of a corresponding patch type(or class).
Mean Core Area Index(MCAI)
MCAI is the average percentageof a landscape patch that is core area. It will be equal to 0 whenthere is no core area present in any patch in the landscape and itincreases (towards 100%) when patches contain mostly corearea.
Core Area Standard Deviation (CASD)Measure of variability in core areasize.
The standard deviation of disjunct coreareas (hectares).
Core Area Density (CAD)The relative number of disjunct corepatches relative to the landscape area.
The total number of all disjunctpatches divided by the landscape area (number of disjunct corepatches/hectare).
Total Core Area Index (TCAI)Measure of amount of core area in thelandscape.
Total core area index is a measure ofthe amount of core area in the landscape. Total core area index isa proportion of core area in the entire landscape and is equal tozero when no patches in the landscape contain core and approachesone as the relative proportion of core area in the landscapeincreases.
Core Area Percentage of Land(C_LAND)
C_LAND is the percentageof the total landscape which is made up of corearea.
Mean Core Area per Patch(MCA1)
MCA1 is the average corearea per patch (as opposed to all distunct coreareas).
It equals the sum of thecore areas of each patch or corresponding patch type, divided bythe number of total patches of the same type, divided by 10, 000(to convert to hectares).
Core Area Coefficient ofVariance (CACOV)
CACOV represents the variability insize of disjunct core areas in relation to the mean core area.
Patch Core Area StandardDeviation (CASD1)
Measure of variability inpatch core area size.
The standard deviation ofpatch core areas (hectares).
Patch Core Area Coefficientof Variation (CACV1)
The standard deviation incore areas (CASD) divided by the mean core area per patch (MCA) andmultplied by 100 (%).
The variablility in corearea among patches relative to the mean corearea.
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