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Calculate Evenness Over Time or Space

Source: R/indicator_wrappers.R
pielou_evenness_map.Rd

Calculate evenness over a gridded map or as a time series (see 'Details' for more information).

Usage

pielou_evenness_map(data, ...)

pielou_evenness_ts(data, ...)

williams_evenness_map(data, ...)

williams_evenness_ts(data, ...)

Arguments

data

A data cube object (class 'processed_cube').

...

Arguments passed on to compute_indicator_workflow

cell_size

(Optional) Length of grid cell sides, in km or degrees. Only used for maps and for time series that require a grid.

  • "grid" (default): use the native resolution of the cube. If this would produce more than about 1 million grid cells over the study area (for degree-based cubes: if the resolution is finer than 1 degree for 'world' or 'continent', or finer than 0.1 degrees otherwise), you are asked to confirm in an interactive session, and the function stops with an error in a non-interactive session.

  • "auto": determined automatically. For km-based grids it depends on the area of the study region: 100 km for areas of at least 1 million sq km, 10 km for at least 10,000 sq km, 1 km for at least 100 sq km, and 0.1 km for smaller areas. For degree-based grids it is 1 degree for 'world' or 'continent' and 0.1 degrees otherwise. The automatic size is never smaller than the cube's resolution.

  • A number (in the units of the cube's resolution, i.e. km or degrees), or for km-based grids a string such as "10km" or "500m".

A manually selected cell size must be a whole number multiple of the cube's resolution.

level

(Optional) Spatial level: 'cube', 'continent', 'country', 'world', 'sovereignty', or 'geounit'. (Default: 'cube')

region

(Optional) The region of interest (e.g., "Denmark"). Ignored if level is 'cube' or 'world'. (Default: "Europe")

ne_type

(Optional) The type of Natural Earth data to download: 'countries', 'map_units', 'sovereignty', or 'tiny_countries'. This parameter is ignored if level is set to 'cube' or 'world'. (Default: "countries")

ne_scale

(Optional) The scale of Natural Earth data to download: 'small' - 110m, 'medium' - 50m, or 'large' - 10m. (Default: "medium")

output_crs

(Optional) The CRS you want for your calculated indicator. (Leave blank to let the function choose a default based on grid reference system.)

first_year

(Optional) Exclude data before this year. (Uses all data in the cube by default.)

last_year

(Optional) Exclude data after this year. (Uses all data in the cube by default.)

spherical_geometry

(Optional) If set to FALSE, will temporarily disable spherical geometry while the function runs. Should only be used to solve specific issues. (Default is TRUE).

make_valid

(Optional) Calls st_make_valid() from the sf package after creating the grid. Increases processing time but may help if you are getting polygon errors. (Default is FALSE).

shapefile_path

(optional) Path of an external shapefile to merge into the workflow. For example, if you want to calculate your indicator for particular features such as protected areas or wetlands.

shapefile_crs

(Optional) CRS of a .wkt shapefile. If your shapefile is .wkt and you do NOT use this parameter, the CRS will be assumed to be EPSG:4326 and the coordinates will be read in as lat/long. If your shape is NOT a .wkt the CRS will be determined automatically.

invert

(optional) Calculate an indicator over the inverse of the shapefile (e.g. if you have a protected areas shapefile this would calculate an indicator over all non protected areas within your cube). Default is FALSE.

include_land

(Optional) Include occurrences which fall within the land area. Default is TRUE. Note that this is purely a geographic filter, and does not filter based on whether the occurrence is actually terrestrial. Grid cells which fall partially on land and partially on ocean will be included even if include_land is FALSE. To exclude terrestrial and/or freshwater taxa, you must manually filter your data cube before calculating your indicator.

include_ocean

(Optional) Include occurrences which fall outside the land area. Default is TRUE. Set as "buffered_coast" to include a set buffer size around the land area rather than the entire ocean area. Note that this is purely a geographic filter, and does not filter based on whether the occurrence is actually marine. Grid cells which fall partially on land and partially on ocean will be included even if include_ocean is FALSE. To exclude marine taxa, you must manually filter your data cube before calculating your indicator.

buffer_dist_km

(Optional) The distance to buffer around the land if include_ocean is set to "buffered_coast". Default is 50 km.

force_grid

(Optional) Forces the calculation of a grid even if this would not normally be part of the pipeline, i.e. for time series. A grid is needed for time series of area-based rarity, Hill diversity and relative occupancy (and for completeness with gridded_average = TRUE). This is switched on automatically for these indicators: the wrappers area_rarity_ts(), hill0_ts(), hill1_ts() and hill2_ts() already set force_grid = TRUE, so do not pass it to them. (Default: FALSE)

Value

An S3 object with the classes 'indicator_map' or 'indicator_ts' and 'pielou_evenness' or 'williams_evenness' containing the calculated indicator values and metadata.

Details

Evenness

Species evenness is a commonly used indicator that measures how uniformly individuals are distributed across species in a region or over time. It provides a complement to richness by taking relative abundance into account. Although GBIF provides information about abundances as individual counts, the majority of entries lack this information. Hence, evenness can only be calculated using the proportions of observations rather than proportions of individuals. Strictly speaking, the evenness measures therefore indicate how uniformly species are represented in the respective data set rather than the true evenness of the ecological community.

Pielou's evenness

Pielou's evenness (1966) is a well-known and commonly used evenness measure. It is calculated as:

$$ E = \frac{-\sum_{i=1}^{S} p_i \ln(p_i)}{\ln(S)} $$ where S is the number of species observed in the grid cell (maps) or year (time series) and pi is the proportion of occurrences represented by species i. Species absent from a cell or year do not count towards S, and evenness is NA when fewer than two species are present.

Williams' evenness

An analysis of evenness properties by Kvålseth (2015) showed that an evenness index introduced by Williams in 1977 in an unpublished manuscript has two important properties which Pielou's does not. The properties in question are complex mathematical properties known as the Schur-Concavity and value validity, but we attempt to describe them here more simply. If a measure of evenness is Schur-concave, it means that when the distribution of individuals becomes more evenly spread across species, the measure of evenness will stay the same or increase, but never decrease. Value validity means that an evenness index should provide sensible and meaningful values across its range for any given distribution of species abundances. Kvålseth referred to this evenness measure as E9 but we refer to it as Williams' evenness.

Williams' evenness is calculated as:

$$ 1 - \sqrt{\frac{S\sum_{i=1}^{S} p_i^2 - 1}{S - 1}} $$

where S is the number of species observed in the grid cell (maps) or year (time series) and pi is the proportion of occurrences represented by species i. Species absent from a cell or year do not count towards S, and evenness is NA when fewer than two species are present.

Functions

  • pielou_evenness_map():

  • pielou_evenness_ts():

  • williams_evenness_map():

  • williams_evenness_ts():

References

Pielou, E. C. (1966). The measurement of diversity in different types of biological collections. Journal of theoretical biology, 13, 131-144.

Kvålseth, T. O. (2015). Evenness indices once again: critical analysis of properties. SpringerPlus, 4, 1-12.

See also

compute_indicator_workflow(), add_ci()

Examples

# \donttest{
pe_map <- pielou_evenness_map(example_cube_1,
  level = "country",
  region = "Denmark"
)
plot(pe_map)

# }
# \donttest{
pe_ts <- pielou_evenness_ts(example_cube_1, first_year = 1985)
plot(pe_ts)

# }
# \donttest{
we_map <- williams_evenness_map(example_cube_1,
  level = "country",
  region = "Denmark"
)
plot(we_map)

# }
# \donttest{
we_ts <- williams_evenness_ts(example_cube_1, first_year = 1985)
plot(we_ts)

# }