Package 'landscapemetrics'

Description

A real landscape of area near Augusta, Georgia obtained from the National Land Cover Database (NLCD)

Usage

augusta_nlcd

Format

A raster object.

Source

https://www.mrlc.gov/nlcd2011.php

References

Homer, C.G., Dewitz, J.A., Yang, L., Jin, S., Danielson, P., Xian, G., Coulston, J., Herold, N.D., Wickham, J.D., and Megown, K., 2015, Completion of the 2011 National Land Cover Database for the conterminous United States-Representing a decade of land cover change information. Photogrammetric Engineering and Remote Sensing, v. 81, no. 5, p. 345-354

Description

Calculate correlation

Usage

calculate_correlation(
  metrics,
  method = "pearson",
  diag = TRUE,
  simplify = FALSE
)

Arguments

Details

The functions calculates the correlation between all metrics. In order to calculate correlations, for the landscape level more than one landscape needs to be present. All input must be structured as returned by the landscapemetrics package.

Value

list

Examples

landscape <- terra::rast(landscapemetrics::landscape)
metrics <- calculate_lsm(landscape, what = c("patch", "class"))
calculate_correlation(metrics, method = "pearson")

Description

Calculate a selected group of metrics

Usage

calculate_lsm(
  landscape,
  level = NULL,
  metric = NULL,
  name = NULL,
  type = NULL,
  what = NULL,
  directions = 8,
  count_boundary = FALSE,
  consider_boundary = FALSE,
  edge_depth = 1,
  cell_center = FALSE,
  classes_max = NULL,
  neighbourhood = 4,
  ordered = TRUE,
  base = "log2",
  full_name = FALSE,
  verbose = TRUE,
  progress = FALSE
)

Arguments

Details

Wrapper to calculate several landscape metrics. The metrics can be specified by the arguments what, level, metric, name and/or type (combinations of different arguments are possible (e.g. ⁠level = "class", type = "aggregation metric"⁠). If an argument is not provided, automatically all possibilities are selected. Therefore, to get all available metrics, don't specify any of the above arguments.

For all metrics based on distances or areas please make sure your data is valid using check_landscape.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

list_lsm

Examples

## Not run: 
landscape <- terra::rast(landscapemetrics::landscape)
calculate_lsm(landscape, progress = TRUE)
calculate_lsm(landscape, what = c("patch", "lsm_c_te", "lsm_l_pr"))
calculate_lsm(landscape, level = c("class", "landscape"),
type = "aggregation metric")

## End(Not run)

Description

Check input landscape

Usage

check_landscape(landscape, verbose = TRUE)

Arguments

Details

This function extracts basic information about the input landscape. It includes a type of coordinate reference system (crs) - either "geographic", "projected", or NA, units of the coordinate reference system, a class of the input landscape's values and the number of classes found in the landscape.

Value

tibble

Examples

augusta_nlcd <- terra::rast(landscapemetrics::augusta_nlcd)
check_landscape(augusta_nlcd)
podlasie_ccilc <- terra::rast(landscapemetrics::podlasie_ccilc)
check_landscape(podlasie_ccilc)
landscape <- terra::rast(landscapemetrics::landscape)
check_landscape(c(landscape, landscape))

Description

Extract metrics

Usage

extract_lsm(
  landscape,
  y,
  extract_id = NULL,
  metric = NULL,
  name = NULL,
  type = NULL,
  what = NULL,
  directions = 8,
  progress = FALSE,
  verbose = TRUE,
  ...
)

Arguments

Details

This functions extracts the metrics of all patches the spatial object(s) y (e.g. spatial points) are located within. Only patch level metrics are possible to extract. Please be aware that the output is slightly different to all other lsm-function of landscapemetrics. Returns a tibble with chosen metrics and the ID of the spatial objects.

Value

tibble

See Also

calculate_lsm

Examples

landscape <- terra::rast(landscapemetrics::landscape)

points <- matrix(c(10, 5, 25, 15, 5, 25), ncol = 2, byrow = TRUE)
extract_lsm(landscape, y = points)
extract_lsm(landscape, y = points, type = "aggregation metric")

## Not run: 
# use lines


## End(Not run)

Description

Fast calculation of adjacencies between classes in a raster

Usage

get_adjacencies(landscape, neighbourhood = 4, what = "full", upper = FALSE)

Arguments

Details

A fast implementation with Rcpp to calculate the adjacency matrix for raster. The adjacency matrix is most often used in landscape metrics to describe the configuration of landscapes, is it is a cellwise count of edges between classes.

The "full" adjacency matrix is double-count method, as it contains the pairwise counts of cells between all classes. The diagonal of this matrix contains the like adjacencies, a count for how many edges a shared in each class with the same class.

The "unlike" adjacencies are counting the cellwise edges between different classes.

Value

matrix with adjacencies between classes in a raster and between cells from the same class.

Examples

landscape <- terra::rast(landscapemetrics::landscape)
# calculate full adjacency matrix
get_adjacencies(landscape, 4)

# equivalent with the terra package:
adjacencies <- terra::adjacent(landscape, 1:terra::ncell(landscape), "rook", pairs = TRUE)
table(terra::values(landscape, mat = FALSE)[adjacencies[,1]],
terra::values(landscape, mat = FALSE)[adjacencies[,2]])

# count diagonal neighbour adjacencies
diagonal_matrix <- matrix(c(1,  NA,  1,
                            NA,  0, NA,
                            1,  NA,  1), 3, 3, byrow = TRUE)
get_adjacencies(landscape, diagonal_matrix)

Description

Get boundary cells of patches

Usage

get_boundaries(
  landscape,
  consider_boundary = FALSE,
  edge_depth = 1,
  as_NA = FALSE,
  patch_id = FALSE,
  return_raster = TRUE
)

Arguments

Details

All boundary/edge cells are labeled 1, all non-boundary cells 0. NA values are not changed. Boundary cells are defined as cells that neighbour either a NA cell or a cell with a different value than itself. Non-boundary cells only neighbour cells with the same value than themself.

Value

List with SpatRaster or matrix

Examples

landscape <- terra::rast(landscapemetrics::landscape)
class_1 <- get_patches(landscape, class = 1)[[1]][[1]]

get_boundaries(class_1)
get_boundaries(class_1, return_raster = FALSE)

Description

Centroid of patches

Usage

get_centroids(
  landscape,
  directions = 8,
  cell_center = FALSE,
  return_vec = FALSE,
  verbose = TRUE
)

Arguments

Details

Get the coordinates of the centroid of each patch. The centroid is by default defined as the mean location of all cell centers. To force the centroid to be located within each patch, use the cell_center argument. In this case, the centroid is defined as the cell center that is the closest to the mean location.

Examples

# get centroid location
landscape <- terra::rast(landscapemetrics::landscape)
get_centroids(landscape)

Description

Diameter of the circumscribing circle around patches

Usage

get_circumscribingcircle(landscape, directions = 8, level = "patch")

Arguments

Details

The diameter of the smallest circumscribing circle around a patch in the landscape is based on the maximum distance between the corners of each cell. This ensures that all cells of the patch are included in the patch.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

References

Based on C++ code from Project Nayuki (https://www.nayuki.io/page/smallest-enclosing-circle).

Examples

landscape <- terra::rast(landscapemetrics::landscape)

# get circle around each patch
get_circumscribingcircle(landscape)

# get circle around whole class
get_circumscribingcircle(landscape, level = "class")

Description

Euclidean distance to nearest neighbour

Usage

get_nearestneighbour(landscape, return_id = FALSE)

Arguments

Details

Fast and memory safe Rcpp implementation for calculating the minimum Euclidean distances to the nearest patch of the same class in a raster or matrix. All patches need an unique ID (see get_patches). Please be aware that the patch ID is not identical to the patch ID of all metric functions (lsm_). If return_ID = TRUE, for some focal patches several nearest neighbour patches might be returned.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

References

Based on RCpp code of Florian Privé [email protected]

Examples

# get patches for class 1
landscape <- terra::rast(landscapemetrics::landscape)
class_1 <- get_patches(landscape, class = 2)[[1]][[1]]

# calculate the distance between patches
get_nearestneighbour(class_1)
get_nearestneighbour(class_1, return_id = TRUE)

Description

Connected components labeling to derive patches in a landscape.

Usage

get_patches(
  landscape,
  class = "all",
  directions = 8,
  to_disk = getOption("to_disk", default = FALSE),
  return_raster = TRUE
)

Arguments

Details

Searches for connected patches (neighbouring cells of the same class i). The 8-neighbours rule ('queen's case) or 4-neighbours rule (rook's case) is used. Returns a list with raster. For each class the connected patches have the value 1 - n. All cells not belonging to the class are NA.

Landscape metrics rely on the delineation of patches. Hence, get_patches is heavily used in landscapemetrics. As raster can be quite big, the fact that get_patches creates a copy of the raster for each class in a landscape becomes a burden for computer memory. Hence, the argument to_disk allows to store the results of the connected labeling algorithm on disk. Furthermore, this option can be set globally, so that every function that internally uses get_patches can make use of that.

Value

List of SpatRaster

References

Vincent, L., Soille, P. 1991. Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence. 13 (6), 583-598

Examples

landscape <- terra::rast(landscapemetrics::landscape)

# check for patches of class 1
patched_raster <- get_patches(landscape, class = 1)

# count patches
nrow(terra::unique(patched_raster[[1]][[1]]))

# check for patches of every class
patched_raster <-  get_patches(landscape)

Description

This function returns the unique values of an object.

Usage

get_unique_values(x, simplify = FALSE, verbose = TRUE)

Arguments

Details

Fast and memory friendly Rcpp implementation to find the unique values of an object.

Examples

landscape <- terra::rast(landscapemetrics::landscape)

get_unique_values(landscape)

landscape_stack <- c(landscape, landscape, landscape)
get_unique_values(landscape_stack)

landscape_matrix <- terra::as.matrix(landscape, wide = TRUE)
get_unique_values(landscape_matrix)

x_vec <- c(1, 2, 1, 1, 2, 2)
get_unique_values(x_vec)

landscape_list <- list(landscape, landscape_matrix, x_vec)
get_unique_values(landscape_list)

Description

An example map to show landscapemetrics functionality generated with the nlm_randomcluster() algorithm.

Usage

landscape

Format

A raster object.

Source

Simulated neutral landscape model with R. https://github.com/ropensci/NLMR/

Description

Convert raster input to list

Usage

landscape_as_list(landscape)

## S3 method for class 'SpatRaster'
landscape_as_list(landscape)

## S3 method for class 'RasterLayer'
landscape_as_list(landscape)

## S3 method for class 'RasterBrick'
landscape_as_list(landscape)

## S3 method for class 'RasterStack'
landscape_as_list(landscape)

## S3 method for class 'stars'
landscape_as_list(landscape)

## S3 method for class 'list'
landscape_as_list(landscape)

## S3 method for class 'matrix'
landscape_as_list(landscape)

## S3 method for class 'numeric'
landscape_as_list(landscape)

## S3 method for class 'PackedSpatRaster'
landscape_as_list(landscape)

Arguments

Details

Mainly for internal use

Value

list

Examples

landscape <- terra::rast(landscapemetrics::landscape)
landscape_as_list(c(landscape, landscape))

Description

List landscape metrics

Usage

list_lsm(
  level = NULL,
  metric = NULL,
  name = NULL,
  type = NULL,
  what = NULL,
  simplify = FALSE,
  verbose = TRUE
)

Arguments

Details

List all available landscape metrics depending on the provided filter arguments. If an argument is not provided, automatically all possibilities are selected. Therefore, to get all available metrics, use simply list_lsm(). For all arguments with exception of the what argument, it is also possible to use a negative subset, i.e. all metrics but the selected ones. Therefore, simply use e.g. level = "-patch". Furthermore, it is possible to only get a vector with all function names instead of the full tibble.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Examples

list_lsm(level = c("patch", "landscape"), type = "aggregation metric")
list_lsm(level = "-patch", type = "area and edge metric")
list_lsm(metric = "area", simplify = TRUE)

list_lsm(metric = "area", what = "lsm_p_shape")
list_lsm(metric = "area", what = c("patch", "lsm_l_ta"))
list_lsm(what = c("lsm_c_tca", "lsm_l_ta"))

Description

A single tibble for every abbreviation of every metric that is reimplemented in landscapemetrics and its corresponding full name in the literature.

Usage

lsm_abbreviations_names

Format

A tibble object.

Details

Can be used after calculating the metric(s) with a join to have a more readable results tibble or for visualizing your results.

Examples

landscape <- terra::rast(landscapemetrics::landscape)
patch_area <- lsm_p_area(landscape)
patch_area <- merge(x = patch_area, y = lsm_abbreviations_names, by = c("level", "metric"))

Description

Aggregation index (Aggregation metric)

Usage

lsm_c_ai(landscape)

Arguments

Details

$AI = \Bigg[\frac{g_{ii}}{max-g_{ii}} \Bigg](100)$

where $g_{ii}$ is the number of like adjacencies based on the single-count method and $max-g_{ii}$ is the classwise maximum number of like adjacencies of class i.

AI is an 'Aggregation metric'. It equals the number of like adjacencies divided by the theoretical maximum possible number of like adjacencies for that class. The metric is based on he adjacency matrix and the the single-count method.

Units

Percent

Range

0 <= AI <= 100

Behaviour

Equals 0 for maximally disaggregated and 100 for maximally aggregated classes.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

He, H. S., DeZonia, B. E., & Mladenoff, D. J. 2000. An aggregation index (AI) to quantify spatial patterns of landscapes. Landscape ecology, 15(7), 591-601.

See Also

lsm_l_ai

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_ai(landscape)

Description

Coefficient of variation of patch area (Area and edge metric)

Usage

lsm_c_area_cv(landscape, directions = 8)

Arguments

Details

$AREA_{CV} = cv(AREA[patch_{ij}])$

where $AREA[patch_{ij}]$ is the area of each patch in hectares.

AREA_CV is an 'Area and Edge metric'. The metric summarises each class as the Coefficient of variation of all patch areas belonging to class i. The metric describes the differences among patches of the same class i in the landscape and is easily comparable because it is scaled to the mean.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Hectares

Range

AREA_CV >= 0

Behaviour

Equals AREA_CV = 0 if all patches are identical in size. Increases, without limit, as the variation of patch areas increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_area,
lsm_c_area_mn, lsm_c_area_sd,
lsm_l_area_mn, lsm_l_area_sd, lsm_l_area_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_area_cv(landscape)

Description

Mean of patch area (Area and edge metric)

Usage

lsm_c_area_mn(landscape, directions = 8)

Arguments

Details

$AREA_{MN} = mean(AREA[patch_{ij}])$

where $AREA[patch_{ij}]$ is the area of each patch in hectares

AREA_MN is an 'Area and Edge metric'. The metric summarises each class as the mean of all patch areas belonging to class i. The metric is a simple way to describe the composition of the landscape. Especially together with the total class area (lsm_c_ca), it can also give an an idea of patch structure (e.g. many small patches vs. few larges patches).

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Hectares

Range

AREA_MN > 0

Behaviour

Approaches AREA_MN = 0 if all patches are small. Increases, without limit, as the patch areas increase.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_area, mean,
lsm_c_area_cv, lsm_c_area_sd,
lsm_l_area_mn, lsm_l_area_sd, lsm_l_area_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_area_mn(landscape)

Description

Standard deviation of patch area (Area and edge metric)

Usage

lsm_c_area_sd(landscape, directions = 8)

Arguments

Details

$AREA_{SD} = sd(AREA[patch_{ij}])$

where $AREA[patch_{ij}]$ is the area of each patch in hectares.

AREA_SD is an 'Area and Edge metric'. The metric summarises each class as the standard deviation of all patch areas belonging to class i. The metric describes the differences among patches of the same class i in the landscape.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Hectares

Range

AREA_SD >= 0

Behaviour

Equals AREA_SD = 0 if all patches are identical in size. Increases, without limit, as the variation of patch areas increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_area, sd
lsm_c_area_mn, lsm_c_area_cv,
lsm_l_area_mn, lsm_l_area_sd, lsm_l_area_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_area_sd(landscape)

Description

Total (class) area (Area and edge metric)

Usage

lsm_c_ca(landscape, directions = 8)

Arguments

Details

$CA = sum(AREA[patch_{ij}])$

where $AREA[patch_{ij}]$ is the area of each patch in hectares.

CA is an 'Area and edge metric' and a measure of composition. The total (class) area sums the area of all patches belonging to class i. It shows if the landscape is e.g. dominated by one class or if all classes are equally present. CA is an absolute measure, making comparisons among landscapes with different total areas difficult.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Hectares

Range

CA > 0

Behaviour

Approaches CA > 0 as the patch areas of class i become small. Increases, without limit, as the patch areas of class i become large. CA = TA if only one class is present.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_area, sum,
lsm_l_ta

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_ca(landscape)

Description

Coefficient of variation of core area index (Core area metric)

Usage

lsm_c_cai_cv(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$CAI_{CV} = cv(CAI[patch_{ij}]$

where $CAI[patch_{ij}]$ is the core area index of each patch.

CAI_CV is a 'Core area metric'. The metric summarises each class as the Coefficient of variation of the core area index of all patches belonging to class i. The core area index is the percentage of core area in relation to patch area. A cell is defined as core area if the cell has no neighbour with a different value than itself (rook's case). The metric describes the differences among patches of the same class i in the landscape.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Percent

Range

CAI_CV >= 0

Behaviour

Equals CAI_CV = 0 if the core area index is identical for all patches. Increases, without limit, as the variation of the core area indices increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_cai,
lsm_c_cai_mn, lsm_c_cai_sd,
lsm_l_cai_mn, lsm_l_cai_sd, lsm_l_cai_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_cai_cv(landscape)

Description

Mean of core area index (Core area metric)

Usage

lsm_c_cai_mn(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$CAI_{MN} = mean(CAI[patch_{ij}]$

where $CAI[patch_{ij}]$ is the core area index of each patch.

CAI_MN is a 'Core area metric'. The metric summarises each class as the mean of the core area index of all patches belonging to class i. The core area index is the percentage of core area in relation to patch area. A cell is defined as core area if the cell has no neighbour with a different value than itself (rook's case).

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Percent

Range

0 <= CAI_MN <= 100

Behaviour

CAI_MN = 0 when all patches have no core area and approaches CAI_MN = 100 with increasing percentage of core area within patches.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_cai, mean,
lsm_c_cai_sd, lsm_c_cai_cv,
lsm_l_cai_mn, lsm_l_cai_sd, lsm_l_cai_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_cai_mn(landscape)

Description

Standard deviation of core area index (Core area metric)

Usage

lsm_c_cai_sd(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$CAI_{SD} = sd(CAI[patch_{ij}]$

where $CAI[patch_{ij}]$ is the core area index of each patch.

CAI_SD is a 'Core area metric'. The metric summarises each class as the standard deviation of the core area index of all patches belonging to class i. The core area index is the percentage of core area in relation to patch area. A cell is defined as core area if the cell has no neighbour with a different value than itself (rook's case). The metric describes the differences among patches of the same class i in the landscape.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Percent

Range

CAI_SD >= 0

Behaviour

Equals CAI_SD = 0 if the core area index is identical for all patches. Increases, without limit, as the variation of core area indices increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_cai, sd
lsm_c_cai_mn, lsm_c_cai_cv,
lsm_l_cai_mn, lsm_l_cai_sd, lsm_l_cai_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_cai_sd(landscape)

Description

Coefficient of variation of related circumscribing circle (Shape metric)

Usage

lsm_c_circle_cv(landscape, directions = 8)

Arguments

Details

$CIRCLE_{CV} = cv(CIRCLE[patch_{ij}])$

where $CIRCLE[patch_{ij}]$ is the related circumscribing circle of each patch.

CIRCLE_CV is a 'Shape metric' and summarises each class as the Coefficient of variation of the related circumscribing circle of all patches belonging to class i. CIRCLE describes the ratio between the patch area and the smallest circumscribing circle of the patch and characterises the compactness of the patch. CIRCLE_CV describes the differences among patches of the same class i in the landscape. Because it is scaled to the mean, it is easily comparable.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

CIRCLE_CV >= 0

Behaviour

Equals CIRCLE_CV if the related circumscribing circle is identical for all patches. Increases, without limit, as the variation of related circumscribing circles increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Baker, W. L., and Y. Cai. 1992. The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology 7: 291-302.

Based on C++ code from Project Nayuki (https://www.nayuki.io/page/smallest-enclosing-circle).

See Also

lsm_p_circle, mean,
lsm_c_circle_mn, lsm_c_circle_sd,
lsm_l_circle_mn, lsm_l_circle_sd, lsm_l_circle_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_circle_cv(landscape)

Description

Mean of related circumscribing circle (Shape metric)

Usage

lsm_c_circle_mn(landscape, directions = 8)

Arguments

Details

$CIRCLE_{MN} = mean(CIRCLE[patch_{ij}])$

where $CIRCLE[patch_{ij}]$ is the related circumscribing circle of each patch.

CIRCLE_MN is a 'Shape metric' and summarises each class as the mean of the related circumscribing circle of all patches belonging to class i. CIRCLE describes the ratio between the patch area and the smallest circumscribing circle of the patch and characterises the compactness of the patch.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

CIRCLE_MN > 0

Behaviour

Approaches CIRCLE_MN = 0 if the related circumscribing circle of all patches is small. Increases, without limit, as the related circumscribing circles increase.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Baker, W. L., and Y. Cai. 1992. The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology 7: 291-302.

Based on C++ code from Project Nayuki (https://www.nayuki.io/page/smallest-enclosing-circle).

See Also

lsm_p_circle, mean,
lsm_c_circle_sd, lsm_c_circle_cv,
lsm_l_circle_mn, lsm_l_circle_sd, lsm_l_circle_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_circle_mn(landscape)

Description

Standard deviation of related circumscribing circle (Shape metric)

Usage

lsm_c_circle_sd(landscape, directions = 8)

Arguments

Details

$CIRCLE_{SD} = sd(CIRCLE[patch_{ij}])$

where $CIRCLE[patch_{ij}]$ is the related circumscribing circle of each patch.

CIRCLE_SD is a 'Shape metric' and summarises each class as the standard deviation of the related circumscribing circle of all patches belonging to class i. CIRCLE describes the ratio between the patch area and the smallest circumscribing circle of the patch and characterises the compactness of the patch. The metric describes the differences among patches of the same class i in the landscape.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

CIRCLE_SD >= 0

Behaviour

Equals CIRCLE_SD if the related circumscribing circle is identical for all patches. Increases, without limit, as the variation of related circumscribing circles increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Baker, W. L., and Y. Cai. 1992. The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology 7: 291-302.

Based on C++ code from Project Nayuki (https://www.nayuki.io/page/smallest-enclosing-circle).

See Also

lsm_p_circle, mean,
lsm_c_circle_mn, lsm_c_circle_cv,
lsm_l_circle_mn, lsm_l_circle_sd, lsm_l_circle_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_circle_sd(landscape)

Description

Clumpiness index (Aggregation metric)

Usage

lsm_c_clumpy(landscape)

Arguments

Details

$Given G_{i} = \Bigg(\frac{g_{ii}}{ (\sum\limits_{k=1}^m g_{ik}) - min e_{i}} \Bigg)$

$CLUMPY = \Bigg[ \frac{G_{i} - P_{i}}{P_{i}} for G_{i} < P_{i} \& P_{i} < .5; else \\ \frac{G_{i} - P_{i}}{1 -P_{i}} \Bigg]$

where $g_{ii}$ is the number of like adjacencies, $g_{ik}$ is the classwise number of all adjacencies including the focal class, $min e_{i}$ is the minimum perimeter of the total class in terms of cell surfaces assuming total clumping and $P_{i}$ is the proportion of landscape occupied by each class.

CLUMPY is an 'Aggregation metric'. It equals the proportional deviation of the proportion of like adjacencies involving the corresponding class from that expected under a spatially random distribution. The metric is based on he adjacency matrix and the the double-count method.

Units

None

Range

-1 <= CLUMPY <= 1

Behaviour

Equals -1 for maximally disaggregated, 0 for randomly distributed and 1 for maximally aggregated classes.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_clumpy(landscape)

Description

Patch Cohesion Index (Aggregation metric)

Usage

lsm_c_cohesion(landscape, directions = 8)

Arguments

Details

$COHESION = 1 - (\frac{\sum \limits_{j = 1}^{n} p_{ij}} {\sum \limits_{j = 1}^{n} p_{ij} \sqrt{a_{ij}}}) * (1 - \frac{1} {\sqrt{Z}}) ^ {-1} * 100$

where $p_{ij}$ is the perimeter in meters, $a_{ij}$ is the area in square meters and $Z$ is the number of cells.

COHESION is an 'Aggregation metric'. It characterises the connectedness of patches belonging to class i. It can be used to asses if patches of the same class are located aggregated or rather isolated and thereby COHESION gives information about the configuration of the landscape.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Percent

Ranges

0 < COHESION < 100

Behaviour

Approaches COHESION = 0 if patches of class i become more isolated. Increases if patches of class i become more aggregated.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Schumaker, N. H. 1996. Using landscape indices to predict habitat connectivity. Ecology, 77(4), 1210-1225.

See Also

lsm_p_perim, lsm_p_area,
lsm_l_cohesion

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_cohesion(landscape)

Description

Coefficient of variation of Contiguity index (Shape metric)

Usage

lsm_c_contig_cv(landscape, directions = 8)

Arguments

Details

$CONTIG_{CV} = cv(CONTIG[patch_{ij}])$

where $CONTIG[patch_{ij}]$ is the contiguity of each patch.

CONTIG_CV is a 'Shape metric'. It summarises each class as the mean of each patch belonging to class i. CONTIG_CV asses the spatial connectedness (contiguity) of cells in patches. The metric coerces patch values to a value of 1 and the background to NA. A nine cell focal filter matrix:

filter_matrix <- matrix(c(1, 2, 1,
                          2, 1, 2,
                          1, 2, 1), 3, 3, byrow = T)

... is then used to weight orthogonally contiguous pixels more heavily than diagonally contiguous pixels. Therefore, larger and more connections between patch cells in the rookie case result in larger contiguity index values.

Units

None

Range

CONTIG_CV >= 0

Behaviour

CONTIG_CV = 0 if the contiguity index is identical for all patches. Increases, without limit, as the variation of CONTIG increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

LaGro, J. 1991. Assessing patch shape in landscape mosaics. Photogrammetric Engineering and Remote Sensing, 57(3), 285-293

See Also

lsm_p_contig, lsm_c_contig_mn, lsm_c_contig_cv,
lsm_l_contig_mn, lsm_l_contig_sd, lsm_l_contig_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_contig_cv(landscape)

Description

Mean of Contiguity index (Shape metric)

Usage

lsm_c_contig_mn(landscape, directions = 8)

Arguments

Details

$CONTIG_{MN} = mean(CONTIG[patch_{ij}])$

where $CONTIG[patch_{ij}]$ is the contiguity of each patch.

CONTIG_MN is a 'Shape metric'. It summarises each class as the mean of each patch belonging to class i. CONTIG_MN asses the spatial connectedness (contiguity) of cells in patches. The metric coerces patch values to a value of 1 and the background to NA. A nine cell focal filter matrix:

filter_matrix <- matrix(c(1, 2, 1,
                          2, 1, 2,
                          1, 2, 1), 3, 3, byrow = T)

... is then used to weight orthogonally contiguous pixels more heavily than diagonally contiguous pixels. Therefore, larger and more connections between patch cells in the rookie case result in larger contiguity index values.

Units

None

Range

0 >= CONTIG_MN <= 1

Behaviour

CONTIG equals the mean of the contiguity index on class level for all patches.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

LaGro, J. 1991. Assessing patch shape in landscape mosaics. Photogrammetric Engineering and Remote Sensing, 57(3), 285-293

See Also

lsm_p_contig, lsm_c_contig_sd, lsm_c_contig_cv,
lsm_l_contig_mn, lsm_l_contig_sd, lsm_l_contig_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_contig_mn(landscape)

Description

Standard deviation of Contiguity index (Shape metric)

Usage

lsm_c_contig_sd(landscape, directions = 8)

Arguments

Details

$CONTIG_{SD} = sd(CONTIG[patch_{ij}])$

where $CONTIG[patch_{ij}]$ is the contiguity of each patch.

CONTIG_SD is a 'Shape metric'. It summarises each class as the mean of each patch belonging to class i. CONTIG_SD asses the spatial connectedness (contiguity) of cells in patches. The metric coerces patch values to a value of 1 and the background to NA. A nine cell focal filter matrix:

filter_matrix <- matrix(c(1, 2, 1,
                          2, 1, 2,
                          1, 2, 1), 3, 3, byrow = T)

... is then used to weight orthogonally contiguous pixels more heavily than diagonally contiguous pixels. Therefore, larger and more connections between patch cells in the rookie case result in larger contiguity index values.

Units

None

Range

CONTIG_CV >= 0

Behaviour

CONTIG_SD = 0 if the contiguity index is identical for all patches. Increases, without limit, as the variation of CONTIG increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

LaGro, J. 1991. Assessing patch shape in landscape mosaics. Photogrammetric Engineering and Remote Sensing, 57(3), 285-293

See Also

lsm_p_contig, lsm_c_contig_mn, lsm_c_contig_cv,
lsm_l_contig_mn, lsm_l_contig_sd, lsm_l_contig_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_contig_sd(landscape)

Description

Coefficient of variation of core area (Core area metric)

Usage

lsm_c_core_cv(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$CORE_{CV} = cv(CORE[patch_{ij}])$

where $CORE[patch_{ij}]$ is the core area in square meters of each patch.

CORE_CV is a 'Core area metric'. It equals the Coefficient of variation of the core area of each patch belonging to class i. The core area is defined as all cells that have no neighbour with a different value than themselves (rook's case). The metric describes the differences among patches of the same class i in the landscape and is easily comparable because it is scaled to the mean.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Hectares

Range

CORE_CV >= 0

Behaviour

Equals CORE_CV = 0 if all patches have the same core area. Increases, without limit, as the variation of patch core areas increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_core,
lsm_c_core_mn, lsm_c_core_sd,
lsm_l_core_mn, lsm_l_core_sd, lsm_l_core_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_core_cv(landscape)

Description

Mean of core area (Core area metric)

Usage

lsm_c_core_mn(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$CORE_{MN} = mean(CORE[patch_{ij}])$

where $CORE[patch_{ij}]$ is the core area in square meters of each patch.

CORE_MN is a 'Core area metric' and equals the mean of core areas of all patches belonging to class i. The core area is defined as all cells that have no neighbour with a different value than themselves (rook's case).

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Hectares

Range

CORE_MN >= 0

Behaviour

Equals CORE_MN = 0 if CORE = 0 for all patches. Increases, without limit, as the core area indices increase.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_core, mean,
lsm_c_core_sd, lsm_c_core_cv,
lsm_l_core_mn, lsm_l_core_sd, lsm_l_core_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_core_mn(landscape)

Description

Standard deviation patch core area (class level)

Usage

lsm_c_core_sd(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$CORE_{SD} = sd(CORE[patch_{ij}])$

where $CORE[patch_{ij}]$ is the core area in square meters of each patch.

CORE_SD is a 'Core area metric'. It equals the standard deviation of the core area of each patch belonging to class i. The core area is defined as all cells that have no neighbour with a different value than themselves (rook's case). The metric describes the differences among patches of the same class i in the landscape.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Hectares

Range

CORE_SD >= 0

Behaviour

Equals CORE_SD = 0 if all patches have the same core area. Increases, without limit, as the variation of patch core areas increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_core, sd
lsm_c_core_mn, lsm_c_core_cv,
lsm_l_core_mn, lsm_l_core_sd, lsm_l_core_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_core_sd(landscape)

Description

Core area percentage of landscape (Core area metric)

Usage

lsm_c_cpland(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$CPLAND = (\frac{\sum \limits_{j = 1}^{n} a_{ij}^{core}} {A}) * 100$

where $a_{ij}^{core}$ is the core area in square meters and $A$ is the total landscape area in square meters.

CPLAND is a 'Core area metric'. It is the percentage of core area of class i in relation to the total landscape area. A cell is defined as core area if the cell has no neighbour with a different value than itself (rook's case). Because CPLAND is a relative measure, it is comparable among landscapes with different total areas.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Percentage

Range

0 <= CPLAND < 100

Behaviour

Approaches CPLAND = 0 if CORE = 0 for all patches. Increases as the amount of core area increases, i.e. patches become larger while being rather simple in shape.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_core and lsm_l_ta

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_cpland(landscape)

Description

Disjunct core area density (core area metric)

Usage

lsm_c_dcad(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$DCAD = (\frac{\sum \limits_{j = 1}^{n} n_{ij}^{core}} {A}) * 10000 * 100$

where $n_{ij}^{core}$ is the number of disjunct core areas and $A$ is the total landscape area in square meters.

DCAD is a 'Core area metric'. It equals the number of disjunct core areas per 100 ha relative to the total area. A disjunct core area is a 'patch within the patch' containing only core cells. A cell is defined as core area if the cell has no neighbour with a different value than itself (rook's case). The metric is relative and therefore comparable among landscapes with different total areas.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Number per 100 hectares

Range

DCAD >= 0

Behaviour

Equals DCAD = 0 when DCORE = 0, i.e. no patch of class i contains a disjunct core area. Increases, without limit, as disjunct core areas become more present, i.e. patches becoming larger and less complex.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_c_ndca, lsm_l_ta,
lsm_l_dcad

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_dcad(landscape)

Description

Coefficient of variation number of disjunct core areas (Core area metric)

Usage

lsm_c_dcore_cv(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$DCORE_{CV} = cv(NCORE[patch_{ij}])$

where $NCORE[patch_{ij}]$ is the number of core areas.

DCORE_CV is an 'Core area metric'. It summarises each class as the Coefficient of variation of all patch areas belonging to class i. A cell is defined as core if the cell has no neighbour with a different value than itself (rook's case). NCORE counts the disjunct core areas, whereby a core area is a 'patch within the patch' containing only core cells. The metric describes the differences among patches of the same class i in the landscape and is easily comparable because it is scaled to the mean.

Units

None

Range

DCORE_CV >= 0

Behaviour

Equals DCORE_CV = 0 if all patches have the same number of disjunct core areas. Increases, without limit, as the variation of number of disjunct core areas increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_ncore,
lsm_c_dcore_mn, lsm_c_dcore_sd,
lsm_l_dcore_mn, lsm_l_dcore_sd, lsm_l_dcore_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_dcore_cv(landscape)

Description

Mean number of disjunct core areas (Core area metric)

Usage

lsm_c_dcore_mn(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$DCORE_{MN} = mean(NCORE[patch_{ij}])$

where $NCORE[patch_{ij}]$ is the number of core areas.

DCORE_MN is an 'Core area metric'. It summarises each class as the mean of all patch areas belonging to class i. A cell is defined as core if the cell has no neighbour with a different value than itself (rook's case). NCORE counts the disjunct core areas, whereby a core area is a 'patch within the patch' containing only core cells.

Units

None

Range

DCORE_MN > 0

Behaviour

Equals DCORE_MN = 0 if NCORE = 0 for all patches. Increases, without limit, as the number of disjunct core areas increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_ncore, mean,
lsm_c_dcore_sd, lsm_c_dcore_cv,
lsm_l_dcore_mn, lsm_l_dcore_sd, lsm_l_dcore_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_dcore_mn(landscape)

Description

Standard deviation number of disjunct core areas (Core area metric)

Usage

lsm_c_dcore_sd(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$DCORE_{SD} = sd(NCORE[patch_{ij}])$

where $NCORE[patch_{ij}]$ is the number of core areas.

DCORE_SD is an 'Core area metric'. It summarises each class as the standard deviation of all patch areas belonging to class i. A cell is defined as core if the cell has no neighbour with a different value than itself (rook's case). NCORE counts the disjunct core areas, whereby a core area is a 'patch within the patch' containing only core cells. The metric describes the differences among patches of the same class i in the landscape.

Units

None

Range

DCORE_SD >= 0

Behaviour

Equals DCORE_SD = 0 if all patches have the same number of disjunct core areas. Increases, without limit, as the variation of number of disjunct core areas increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_ncore, sd
lsm_c_dcore_mn, lsm_c_dcore_cv,
lsm_l_dcore_mn, lsm_l_dcore_sd, lsm_l_dcore_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_dcore_sd(landscape)

Description

Landscape division index (Aggregation metric)

Usage

lsm_c_division(landscape, directions = 8)

Arguments

Details

$DIVISON = (1 - \sum \limits_{j = 1}^{n} (\frac{a_{ij}} {A}) ^ 2)$

where $a_{ij}$ is the area in square meters and $A$ is the total landscape area in square meters.

DIVISION is an 'Aggregation metric. It can be in as the probability that two randomly selected cells are not located in the same patch of class i. The landscape division index is negatively correlated with the effective mesh size (lsm_c_mesh).

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Proportion

Ranges

0 <= Division < 1

Behaviour

Equals DIVISION = 0 if only one patch is present. Approaches DIVISION = 1 if all patches of class i are single cells.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Jaeger, J. A. 2000. Landscape division, splitting index, and effective mesh size: new measures of landscape fragmentation. Landscape ecology, 15(2), 115-130.

See Also

lsm_p_area, lsm_l_ta,
lsm_l_division

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_division(landscape)

Description

Edge Density (Area and Edge metric)

Usage

lsm_c_ed(landscape, count_boundary = FALSE, directions = 8)

Arguments

Details

$ED = \frac{\sum \limits_{k = 1}^{m} e_{ik}} {A} * 10000$

where $e_{ik}$ is the total edge length in meters and $A$ is the total landscape area in square meters.

ED is an 'Area and Edge metric'. The edge density equals the sum of all edges of class i in relation to the landscape area. The boundary of the landscape is only included in the corresponding total class edge length if count_boundary = TRUE. The metric describes the configuration of the landscape, e.g. because an aggregation of the same class will result in a low edge density. The metric is standardized to the total landscape area, and therefore comparisons among landscapes with different total areas are possible.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Meters per hectare

Range

ED >= 0

Behaviour

Equals ED = 0 if only one patch is present (and the landscape boundary is not included) and increases, without limit, as the landscapes becomes more patchy

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_c_te, lsm_l_ta,
lsm_l_ed

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_ed(landscape)

Description

Coefficient of variation of euclidean nearest-neighbor distance (Aggregation metric)

Usage

lsm_c_enn_cv(landscape, directions = 8, verbose = TRUE)

Arguments

Details

$ENN_{CV} = cv(ENN[patch_{ij}])$

where $ENN[patch_{ij}]$ is the euclidean nearest-neighbor distance of each patch.

ENN_CV is an 'Aggregation metric'. It summarises each class as the Coefficient of variation of each patch belonging to class i. ENN measures the distance to the nearest neighbouring patch of the same class i. The distance is measured from edge-to-edge. The range is limited by the cell resolution on the lower limit and the landscape extent on the upper limit. The metric is a simple way to describe patch isolation. Because it is scaled to the mean, it is easily comparable among different landscapes.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Meters

Range

ENN_CV >= 0

Behaviour

Equals ENN_CV = 0 if the euclidean nearest-neighbor distance is identical for all patches. Increases, without limit, as the variation of ENN increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

McGarigal, K., and McComb, W. C. (1995). Relationships between landscape structure and breeding birds in the Oregon Coast Range. Ecological monographs, 65(3), 235-260.

See Also

lsm_p_enn,
lsm_c_enn_mn, lsm_c_enn_sd,
lsm_l_enn_mn, lsm_l_enn_sd, lsm_l_enn_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_enn_cv(landscape)

Description

Mean of euclidean nearest-neighbor distance (Aggregation metric)

Usage

lsm_c_enn_mn(landscape, directions = 8, verbose = TRUE)

Arguments

Details

$ENN_{MN} = mean(ENN[patch_{ij}])$

where $ENN[patch_{ij}]$ is the euclidean nearest-neighbor distance of each patch.

ENN_MN is an 'Aggregation metric'. It summarises each class as the mean of each patch belonging to class i. ENN measures the distance to the nearest neighbouring patch of the same class i. The distance is measured from edge-to-edge. The range is limited by the cell resolution on the lower limit and the landscape extent on the upper limit.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Meters

Range

ENN_MN > 0

Behaviour

Approaches ENN_MN = 0 as the distance to the nearest neighbour decreases, i.e. patches of the same class i are more aggregated. Increases, without limit, as the distance between neighbouring patches of the same class i increases, i.e. patches are more isolated.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

McGarigal, K., and McComb, W. C. (1995). Relationships between landscape structure and breeding birds in the Oregon Coast Range. Ecological monographs, 65(3), 235-260.

See Also

lsm_p_enn, mean,
lsm_c_enn_sd, lsm_c_enn_cv,
lsm_l_enn_mn, lsm_l_enn_sd, lsm_l_enn_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_enn_mn(landscape)

Description

Standard deviation of euclidean nearest-neighbor distance (Aggregation metric)

Usage

lsm_c_enn_sd(landscape, directions = 8, verbose = TRUE)

Arguments

Details

$ENN_{SD} = sd(ENN[patch_{ij}])$

where $ENN[patch_{ij}]$ is the euclidean nearest-neighbor distance of each patch.

ENN_CV is an 'Aggregation metric'. It summarises each class as the standard deviation of each patch belonging to class i. ENN measures the distance to the nearest neighbouring patch of the same class i. The distance is measured from edge-to-edge. The range is limited by the cell resolution on the lower limit and the landscape extent on the upper limit. The metric is a simple way to describe patch isolation. Because it is scaled to the mean, it is easily comparable among different landscapes.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Meters

Range

ENN_SD >= 0

Behaviour

Equals ENN_SD = 0 if the euclidean nearest-neighbor distance is identical for all patches. Increases, without limit, as the variation of ENN increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

McGarigal, K., and McComb, W. C. (1995). Relationships between landscape structure and breeding birds in the Oregon Coast Range. Ecological monographs, 65(3), 235-260.

See Also

lsm_p_enn, sd
lsm_c_enn_mn, lsm_c_enn_cv,
lsm_l_enn_mn, lsm_l_enn_sd, lsm_l_enn_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_enn_sd(landscape)

Description

Coefficient of variation fractal dimension index (Shape metric)

Usage

lsm_c_frac_cv(landscape, directions = 8)

Arguments

Details

$FRAC_{CV} = cv(FRAC[patch_{ij}])$

where $FRAC[patch_{ij}]$ equals the fractal dimension index of each patch.

FRAC_CV is a 'Shape metric'. The metric summarises each class as the Coefficient of variation of the fractal dimension index of all patches belonging to class i. The fractal dimension index is based on the patch perimeter and the patch area and describes the patch complexity. The Coefficient of variation is scaled to the mean and comparable among different landscapes.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

FRAC_CV >= 0

Behaviour

Equals FRAC_CV = 0 if the fractal dimension index is identical for all patches. Increases, without limit, as the variation of the fractal dimension indices increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Mandelbrot, B. B. 1977. Fractals: Form, Chance, and Dimension. San Francisco. W. H. Freeman and Company.

See Also

lsm_p_frac,
lsm_c_frac_mn, lsm_c_frac_sd,
lsm_l_frac_mn, lsm_l_frac_sd, lsm_l_frac_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_frac_cv(landscape)

Description

Mean fractal dimension index (Shape metric)

Usage

lsm_c_frac_mn(landscape, directions = 8)

Arguments

Details

$FRAC_{MN} = mean(FRAC[patch_{ij}])$

where $FRAC[patch_{ij}]$ equals the fractal dimension index of each patch.

FRAC_MN is a 'Shape metric'. The metric summarises each class as the mean of the fractal dimension index of all patches belonging to class i. The fractal dimension index is based on the patch perimeter and the patch area and describes the patch complexity. The Coefficient of variation is scaled to the mean and comparable among different landscapes.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

FRAC_MN > 0

Behaviour

Approaches FRAC_MN = 1 if all patches are squared and FRAC_MN = 2 if all patches are irregular.

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Mandelbrot, B. B. 1977. Fractals: Form, Chance, and Dimension. San Francisco. W. H. Freeman and Company.

See Also

lsm_p_frac, mean,
lsm_c_frac_sd, lsm_c_frac_cv,
lsm_l_frac_mn, lsm_l_frac_sd, lsm_l_frac_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_frac_mn(landscape)

Description

Standard deviation fractal dimension index (Shape metric)

Usage

lsm_c_frac_sd(landscape, directions = 8)

Arguments

Details

$FRAC_{SD} = sd(FRAC[patch_{ij}])$

where $FRAC[patch_{ij}]$ equals the fractal dimension index of each patch.

FRAC_SD is a 'Shape metric'. The metric summarises each class as the standard deviation of the fractal dimension index of all patches belonging to class i. The fractal dimension index is based on the patch perimeter and the patch area and describes the patch complexity.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

FRAC_SD>= 0

Behaviour

Equals FRAC_SD = 0 if the fractal dimension index is identical for all patches. Increases, without limit, as the variation of the fractal dimension indices increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Mandelbrot, B. B. 1977. Fractals: Form, Chance, and Dimension. San Francisco. W. H. Freeman and Company.

See Also

lsm_p_frac, sd
lsm_c_frac_mn, lsm_c_frac_cv,
lsm_l_frac_mn, lsm_l_frac_sd, lsm_l_frac_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_frac_sd(landscape)

Description

Coefficient of variation radius of gyration (Area and edge metric)

Usage

lsm_c_gyrate_cv(landscape, directions = 8, cell_center = FALSE)

Arguments

Details

$GYRATE_{CV} = cv(GYRATE[patch_{ij}])$

where $GYRATE[patch_{ij}]$ equals the radius of gyration of each patch.

GYRATE_CV is an 'Area and edge metric'. The metric summarises each class as the Coefficient of variation of the radius of gyration of all patches belonging to class i. GYRATE measures the distance from each cell to the patch centroid and is based on cell center-to-cell center distances. The metrics characterises both the patch area and compactness. The Coefficient of variation is scaled to the mean and comparable among different landscapes.

If cell_center = TRUE some patches might have several possible cell-center centroids. In this case, the gyrate index is based on the mean distance of all cells to all possible cell-center centroids.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Meters

Range

GYRATE_CV >= 0

Behaviour

Equals GYRATE_CV = 0 if the radius of gyration is identical for all patches. Increases, without limit, as the variation of the radius of gyration increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Keitt, T. H., Urban, D. L., & Milne, B. T. 1997. Detecting critical scales in fragmented landscapes. Conservation ecology, 1(1).

See Also

lsm_p_gyrate,
lsm_c_gyrate_mn, lsm_c_gyrate_sd,
lsm_l_gyrate_mn, lsm_l_gyrate_sd, lsm_l_gyrate_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_gyrate_cv(landscape)

Description

Mean radius of gyration (Area and edge metric)

Usage

lsm_c_gyrate_mn(landscape, directions = 8, cell_center = FALSE)

Arguments

Details

$GYRATE_{MN} = mean(GYRATE[patch_{ij}])$

where $GYRATE[patch_{ij}]$ equals the radius of gyration of each patch.

GYRATE_MN is an 'Area and edge metric'. The metric summarises each class as the mean of the radius of gyration of all patches belonging to class i. GYRATE measures the distance from each cell to the patch centroid and is based on cell center-to-cell center distances. The metrics characterises both the patch area and compactness.

If cell_center = TRUE some patches might have several possible cell-center centroids. In this case, the gyrate index is based on the mean distance of all cells to all possible cell-center centroids.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Meters

Range

GYRATE_MN >= 0

Behaviour

Approaches GYRATE_MN = 0 if every patch is a single cell. Increases, without limit, when only one patch is present.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Keitt, T. H., Urban, D. L., & Milne, B. T. 1997. Detecting critical scales in fragmented landscapes. Conservation ecology, 1(1).

See Also

lsm_p_gyrate, mean,
lsm_c_gyrate_sd, lsm_c_gyrate_cv,
lsm_l_gyrate_mn, lsm_l_gyrate_sd, lsm_l_gyrate_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_gyrate_mn(landscape)

Description

Standard deviation radius of gyration (Area and edge metric)

Usage

lsm_c_gyrate_sd(landscape, directions = 8, cell_center = FALSE)

Arguments

Details

$GYRATE_{SD} = sd(GYRATE[patch_{ij}])$

where $GYRATE[patch_{ij}]$ equals the radius of gyration of each patch.

GYRATE_SD is an 'Area and edge metric'. The metric summarises each class as the standard deviation of the radius of gyration of all patches belonging to class i. GYRATE measures the distance from each cell to the patch centroid and is based on cell center-to-cell center distances. The metrics characterises both the patch area and compactness.

If cell_center = TRUE some patches might have several possible cell-center centroids. In this case, the gyrate index is based on the mean distance of all cells to all possible cell-center centroids.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Meters

Range

GYRATE_SD >= 0

Behaviour

Equals GYRATE_SD = 0 if the radius of gyration is identical for all patches. Increases, without limit, as the variation of the radius of gyration increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Keitt, T. H., Urban, D. L., & Milne, B. T. 1997. Detecting critical scales in fragmented landscapes. Conservation ecology, 1(1).

See Also

lsm_p_gyrate,
lsm_c_gyrate_mn, lsm_c_gyrate_cv,
lsm_l_gyrate_mn, lsm_l_gyrate_sd, lsm_l_gyrate_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_gyrate_sd(landscape)

Description

Interspersion and Juxtaposition index (Aggregation metric)

Usage

lsm_c_iji(landscape, verbose = TRUE)

Arguments

Details

$IJI = \frac{- \sum \limits_{k = 1}^{m} \Bigg[ \Bigg( \frac{e_{ik}}{\sum \limits_{k = 1}^{m} e_{ik}} \Bigg) ln \Bigg( \frac{e_{ik}}{\sum \limits_{k = 1}^{m} e_{ik}} \Bigg) \Bigg]}{ln(m - 1)} * 100$

where $e_{ik}$ are the unique adjacencies of all classes (lower/upper triangle of the adjacency table - without the diagonal) and $m$ is the number of classes.

IJI is an 'Aggregation metric'. It is a so called "salt and pepper" metric and describes the intermixing of classes (i.e. without considering like adjacencies - the diagonal of the adjacency table). The number of classes to calculate IJI must be >= than 3.

Units

Percent

Range

0 < IJI <= 100

Behaviour

Approaches 0 if a class is only adjacent to a single other class and equals 100 when a class is equally adjacent to all other classes.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

McGarigal, K., & Marks, B. J. 1995. FRAGSTATS: spatial pattern analysis program for quantifying landscape structure. Gen. Tech. Rep. PNW-GTR-351. Portland, OR: US Department of Agriculture, Forest Service, Pacific Northwest Research Station. 122 p, 351.

See Also

lsm_l_iji

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_iji(landscape)

Description

Largest patch index (Area and Edge metric)

Usage

lsm_c_lpi(landscape, directions = 8)

Arguments

Details

$LPI = \frac{\max \limits_{j = 1}^{n} (a_{ij})} {A} * 100$

where $max(a_{ij})$ is the area of the patch in square meters and $A$ is the total landscape area in square meters.

The largest patch index is an 'Area and edge metric'. It is the percentage of the landscape covered by the corresponding largest patch of each class i. It is a simple measure of dominance.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Percentage

Range

0 < LPI <= 100

Behaviour

Approaches LPI = 0 when the largest patch is becoming small and equals LPI = 100 when only one patch is present

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_area, lsm_l_ta,
lsm_l_lpi

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_lpi(landscape)

Description

Landscape shape index (Aggregation metric)

Usage

lsm_c_lsi(landscape)

Arguments

Details

$LSI = \frac{e_{i}} {\min e_{i}}$

where $e_{i}$ is the total edge length in cell surfaces and $\min e_{i}$ is the minimum total edge length in cell surfaces.

LSI is an 'Aggregation metric'. It is the ratio between the actual edge length of class i and the hypothetical minimum edge length of class i. The minimum edge length equals the edge length if class i would be maximally aggregated.

Units

None

Ranges

LSI >= 1

Behaviour

Equals LSI = 1 when only one squared patch is present or all patches are maximally aggregated. Increases, without limit, as the length of the actual edges increases, i.e. the patches become less compact.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Patton, D. R. 1975. A diversity index for quantifying habitat "edge". Wildl. Soc.Bull. 3:171-173.

See Also

lsm_p_shape,
lsm_l_lsi

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_lsi(landscape)

Description

Effective Mesh Size (Aggregation metric)

Usage

lsm_c_mesh(landscape, directions = 8)

Arguments

Details

$MESH = \frac{\sum \limits_{j = 1}^{n} a_{ij} ^ 2} {A} * \frac{1} {10000}$

where $a_{ij}$ is the patch area in square meters and $A$ is the total landscape area in square meters.

The effective mesh size is an 'Aggregation metric'. Because each patch is squared before the sums for each group i are calculated and the sum is standardized by the total landscape area, MESH is a relative measure of patch structure. MESH is perfectly, negatively correlated to lsm_c_division.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

Hectares

Range

cell size / total area <= MESH <= total area

Behaviour

Equals cellsize/total area if class covers only one cell and equals total area if only one patch is present.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Jaeger, J. A. 2000. Landscape division, splitting index, and effective mesh size: new measures of landscape fragmentation. Landscape ecology, 15(2), 115-130.

See Also

lsm_p_area, lsm_l_ta,
lsm_l_mesh

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_mesh(landscape)

Description

Number of disjunct core areas (Core area metric)

Usage

lsm_c_ndca(
  landscape,
  directions = 8,
  consider_boundary = FALSE,
  edge_depth = 1
)

Arguments

Details

$NDCA = \sum \limits_{j = 1}^{n} n_{ij}^{core}$

where $n_{ij}^{core}$ is the number of disjunct core areas.

NDCA is a 'Core area metric'. The metric summarises class i as the sum of all patches belonging to class i. A cell is defined as core if the cell has no neighbour with a different value than itself (rook's case). NDCA counts the disjunct core areas, whereby a core area is a 'patch within the patch' containing only core cells. It describes patch area and shape simultaneously (more core area when the patch is large, however, the shape must allow disjunct core areas). Thereby, a compact shape (e.g. a square) will contain less disjunct core areas than a more irregular patch.

Units

None

Range

NDCA >= 0

Behaviour

NDCA = 0 when TCA = 0, i.e. every cell in patches of class i is an edge. NDCA increases, with out limit, as core area increases and patch shapes allow disjunct core areas (i.e. patch shapes become rather complex).

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_c_tca,
lsm_p_ncore, lsm_l_ndca

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_ndca(landscape)

Description

Normalized landscape shape index (Aggregation metric)

Usage

lsm_c_nlsi(landscape)

Arguments

Details

$nLSI = \frac{e_{i} - \min e_{i}} {\max e_{i} - \min e_{i}}$

where $e_{i}$ is the total edge length in cell surfaces and $\min e_{i}$ $\max e_{i}$ are the minimum and maximum total edge length in cell surfaces, respectively.

nLSI is an 'Aggregation metric'. It is closely related to the lsm_c_lsi and describes the ratio of the actual edge length of class i in relation to the hypothetical range of possible edge lengths of class i (min/max).

Currently, nLSI ignores all background cells when calculating the minimum and maximum total edge length. Also, a correct calculation of the minimum and maximum total edge length is currently only possible for rectangular landscapes.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Ranges

0 <= nlsi <= 1

Behaviour

Equals nLSI = 0 when only one squared patch is present. nLSI increases the more disaggregated patches are and equals nLSI = 1 for a maximal disaggregated (i.e. a "checkerboard pattern").

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Patton, D. R. 1975. A diversity index for quantifying habitat "edge". Wildl. Soc.Bull. 3:171-173.

See Also

lsm_c_lsi lsm_l_lsi

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_nlsi(landscape)

Description

Number of patches (Aggregation metric)

Usage

lsm_c_np(landscape, directions = 8)

Arguments

Details

$NP = n_{i}$

where $n_{i}$ is the number of patches.

NP is an 'Aggregation metric'. It describes the fragmentation of a class, however, does not necessarily contain information about the configuration or composition of the class.

Units

None

Ranges

NP >= 1

Behaviour

Equals NP = 1 when only one patch is present and increases, without limit, as the number of patches increases

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_l_np

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_np(landscape)

Description

Perimeter-Area Fractal Dimension (Shape metric)

Usage

lsm_c_pafrac(landscape, directions = 8, verbose = TRUE)

Arguments

Details

$PAFRAC = \frac{2}{\beta}$

where $\beta$ is the slope of the regression of the area against the perimeter (logarithm) $n_{i}\sum \limits_{j = 1}^{n} \ln a_{ij} = a + \beta n_{i}\sum \limits_{j = 1}^{n} \ln p_{ij}$

PAFRAC is a 'Shape metric'. It describes the patch complexity of class i while being scale independent. This means that increasing the patch size while not changing the patch form will not change the metric. However, it is only meaningful if the relationship between the area and perimeter is linear on a logarithmic scale. Furthermore, if there are less than 10 patches in class i, the metric returns NA because of the small-sample issue.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

1 <= PAFRAC <= 2

Behaviour

Approaches PAFRAC = 1 for patches with simple shapes and approaches PAFRAC = 2 for irregular shapes

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Burrough, P. A. 1986. Principles of Geographical Information Systems for Land Resources Assessment. Monographs on Soil and Resources Survey No. 12. Clarendon Press, Oxford

See Also

lsm_p_area, lsm_p_perim,
lsm_l_pafrac

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_pafrac(landscape)

Description

Coefficient of variation perimeter-area ratio (Shape metric)

Usage

lsm_c_para_cv(landscape, directions = 8)

Arguments

Details

$PARA_{CV} = cv(PARA[patch_{ij}]$

where $PARA[patch_{ij}]$ is the perimeter area ratio of each patch.

PARA_CV is a 'Shape metric'. It summarises each class as the Coefficient of variation of each patch belonging to class i. The perimeter-area ratio describes the patch complexity in a straightforward way. However, because it is not standarised to a certain shape (e.g. a square), it is not scale independent, meaning that increasing the patch size while not changing the patch form will change the ratio.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

PARA_CV >= 0

Behaviour

Equals PARA_CV = 0 if the perimeter-area ratio is identical for all patches. Increases, without limit, as the variation of the perimeter-area ratio increases.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_para,
lsm_c_para_mn, lsm_c_para_sd,
lsm_l_para_mn, lsm_l_para_sd, lsm_l_para_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_para_cv(landscape)

Description

Mean perimeter-area ratio (Shape metric)

Usage

lsm_c_para_mn(landscape, directions = 8)

Arguments

Details

$PARA_{MN} = mean(PARA[patch_{ij}]$

where $PARA[patch_{ij}]$ is the perimeter area ratio of each patch.

PARA_MN is a 'Shape metric'. It summarises each class as the mean of each patch belonging to class i. The perimeter-area ratio describes the patch complexity in a straightforward way. However, because it is not standarised to a certain shape (e.g. a square), it is not scale independent, meaning that increasing the patch size while not changing the patch form will change the ratio.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

PARA_MN > 0

Behaviour

Approaches PARA_MN > 0 if PARA for each patch approaches PARA > 0, i.e. the form approaches a rather small square. Increases, without limit, as PARA increases, i.e. patches become more complex.

Value

tibble

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

See Also

lsm_p_para, mean,
lsm_c_para_sd, lsm_c_para_cv,
lsm_l_para_mn, lsm_l_para_sd, lsm_l_para_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_para_mn(landscape)

Description

Standard deviation perimeter-area ratio (Shape metric)

Usage

lsm_c_para_sd(landscape, directions = 8)

Arguments

Details

$PARA_{SD} = sd(PARA[patch_{ij}]$