Landscape distribution statistics

2024-09-08

Landscape distribution statistics summarise the properties of all patches belonging to the same class i or of all patches in the landscape together (McGarigal et al. 2012). This includes, for example, the mean, the coefficient of variation, or the standard deviation of a certain metric. These measures are implemented in the landscapemetrics package and are indicated by the corresponding suffixes (_mn, _cv, _sd). However, other distribution statistics also might be of interest. Even though they are not implemented in landscapemetrics, R allows to calculate them straightforwardly.

library(landscapemetrics)
library(terra)
library(dplyr)

# internal data needs to be read
landscape <- terra::rast(landscapemetrics::landscape)

Implemented distribution statistics

The already implemented distribution statistics on class- and landscape-level are indicated by the corresponding suffixes (_mn = mean, _cv = Coefficient of variation , _sd = Standard deviation) and can be calculated directly.

# calculate mean shape index on class level
mean_shape_c <- lsm_c_shape_mn(landscape)

# calculate standard deviation of shape index on landscape level
sd_shape_l <- lsm_l_shape_sd(landscape)

Area-weighted mean

First, we want to calculate the metric of interest on the patch level. Additionally, we want the patch area of each patch.

# calculate required metric for each patch (e.g. lsm_p_shape)
metric_patch <- lsm_p_shape(landscape)
metric_patch

## # A tibble: 28 × 6
##    layer level class    id metric value
##    <int> <chr> <int> <int> <chr>  <dbl>
##  1     1 patch     1     1 shape   1   
##  2     1 patch     1     2 shape   1.34
##  3     1 patch     1     3 shape   1.77
##  4     1 patch     1     4 shape   1   
##  5     1 patch     1     5 shape   1   
##  6     1 patch     1     6 shape   1.90
##  7     1 patch     1     7 shape   1.38
##  8     1 patch     1     8 shape   1.44
##  9     1 patch     1     9 shape   1.12
## 10     1 patch     2    10 shape   1.63
## # ℹ 18 more rows

# calculate area for each patch
area_patch <- lsm_p_area(landscape)
area_patch

## # A tibble: 28 × 6
##    layer level class    id metric  value
##    <int> <chr> <int> <int> <chr>   <dbl>
##  1     1 patch     1     1 area   0.0001
##  2     1 patch     1     2 area   0.0005
##  3     1 patch     1     3 area   0.0072
##  4     1 patch     1     4 area   0.0001
##  5     1 patch     1     5 area   0.0001
##  6     1 patch     1     6 area   0.008 
##  7     1 patch     1     7 area   0.0016
##  8     1 patch     1     8 area   0.0003
##  9     1 patch     1     9 area   0.0005
## 10     1 patch     2    10 area   0.0034
## # ℹ 18 more rows

Now, we should join the metric value with the area of each patch, multiply the two values, and calculate the area-weighted mean. To calculate the area-weighted mean on landscape-level, comment out the dplyr::group_by() line.

# calculate weighted mean
metric_wght_mean <- dplyr::left_join(x = metric_patch, y = area_patch, 
                                     by = c("layer", "level", "class", "id")) |>
  dplyr::mutate(value.w = value.x * value.y) |>
  dplyr::group_by(class) |>
  dplyr::summarise(value.am = sum(value.w) / sum(value.y)) 

metric_wght_mean

## # A tibble: 3 × 2
##   class value.am
##   <int>    <dbl>
## 1     1     1.74
## 2     2     1.46
## 3     3     1.97

Range

The range equals to the minimum value subtracted from the maximum value of the metric of interest for each patch (McGarigal et al. 2012). This can be calculated using the min()/max() function or the range() function.

# class level
metric_range_c <- dplyr::group_by(metric_patch, class) |> 
    dplyr::summarise(range = max(value) - min(value))
metric_range_c

## # A tibble: 3 × 2
##   class range
##   <int> <dbl>
## 1     1 0.901
## 2     2 0.633
## 3     3 1.02

# landscape level
metric_range_l <- diff(range(metric_patch$value))
metric_range_l

## [1] 1.351802

Median

The median equals to the value that divides all (ordered) values into two equal groups. There is a base R function available, median(), that can be applied to values grouped by class or all values (landscape-level).

# class level
metric_md_c <- dplyr::group_by(metric_patch, class) |> 
    dplyr::summarise(median = median(value))
metric_md_c

## # A tibble: 3 × 2
##   class median
##   <int>  <dbl>
## 1     1   1.34
## 2     2   1.06
## 3     3   1.65

# landscape level
metric_md_l <- median(metric_patch$value)
metric_md_l

## [1] 1.337487

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