Richness and endemism with Biodiverse

Where are the places with the most species, and the places with species found nowhere else? Those two questions, richness and endemism, are where most conservation assessments of biodiversity start, and Biodiverse (Laffan et al., 2010) is the tool many biogeographers use to answer them from species records. Terraflux's bio operators are a port of Biodiverse that give the same numbers. In this first part of three you load Biodiverse's example records into a basedata (a table of cells and species), compute richness and two endemism indices in each cell and in moving neighbourhoods, and see how the neighbourhood and the size of the cells change the picture. At the end you will be able to map richness and endemism from any table of records, and know how to read them.

The idea#

Groups, labels and the basedata#

Biodiverse has its own vocabulary, which Terraflux keeps:

a label is what is counted: a species, a genus, or any taxon (here "Genus:sp1" to "Genus:sp31");
a group is where it is counted: usually a square cell of a grid, identified by its centre;
the basedata is the table of which labels occur in which groups, with their counts (sample counts).

Records with coordinates become groups by snapping each record to the cell that holds it: with cells of 100 km, every record falls into one 100 km square, and every square with at least one record becomes a group.

Neighbourhoods: spatial conditions#

Biodiverse computes its indices for every group from the labels of its neighbourhood, described by a spatial condition, a small expression in Biodiverse's own (Perl) syntax:

Condition	Neighbourhood
`sp_self_only()`	the cell alone
`sp_circle (radius => 200000)`	the cells whose centres are within 200 km
`sp_block (size => 500000)`	the cells in the same 500 km block
`$D <= 250000`	the cells within 250 km (`$D` is the distance)
`sp_select_all()`	every cell: the whole dataset

A moving neighbourhood smooths the map and answers a different question from the cell alone: "how many species live in this region of 200 km?" rather than "how many were recorded in this square?". It also compensates in part for uneven sampling between neighbouring cells.

Richness and endemism#

Key idea: weighted endemism

Richness is the number of labels in the neighbourhood. Weighted endemism (WE; Crisp et al., 2001) weighs each species by how much of its range falls in the neighbourhood:

\[ \mathrm{WE} = \sum_{s \in \text{neighbourhood}} \frac{r_s}{R_s} \]

where $R_s$ is the number of cells where species $s$ occurs in the whole dataset (its range) and $r_s$ the number of those cells in the neighbourhood. A species found only there counts 1; a species of 100 cells, present in 2 of them, counts 0.02.

Corrected weighted endemism (CWE) divides by richness, $\mathrm{CWE} = \mathrm{WE}/\text{richness}$: the mean endemism of the species present, which removes the effect of richness itself.

Endemism matters to conservation because species with small ranges are the most exposed to loss: a centre of endemism holds species that cannot be protected anywhere else. WE and CWE were developed to find such centres in the Australian flora (Crisp et al., 2001), and Laffan and Crisp (2003) showed how strongly they depend on the scale of analysis, which is one reason Biodiverse lets neighbourhoods vary.

When to use it#

Mapping diversity and endemism from atlas data, herbarium and museum collections, or GBIF downloads.
Finding centres of endemism for protected area planning; comparing the endemism within a reserve network with the endemism of the region (Laffan et al., 2013).
Preparing phylogenetic analyses (part 2) and regionalisations (part 3), which use the same basedata and conditions.

What it is not: richness from records counts where species were found, which depends on where people looked. To estimate where species are, model their distributions first (species distributions) and import the predicted presences as a basedata with bio.raster.

What you need#

Species records with coordinates: Biodiverse's example data, sites.csv (1,795 records, 72 KB), with columns num (a record number), genus, species, x and y (coordinates in metres). It has 31 species of an unnamed genus, which landschaft's documentation places in eastern Australia. Use it to learn; the numbers have no biological meaning beyond this example.
A coordinate system in metres with equal areas, so that cells are equal: reproject records in degrees first (to_crs of bio.occurrences), or use cells in degrees knowing that they shrink towards the poles.
A cell size: here 100 km. Choose it from the precision of the records (the cells should be larger than the records' uncertainty) and from the scale of the question.

Other sources become a basedata with other operators: bio.occurrences reads GBIF downloads and Darwin Core archives (with filters on uncertainty, basis of record and GBIF's issues), bio.points and bio.vector read points, lines and polygons (range maps: every cell a polygon touches), bio.raster reads rasters (one label per layer, for example thresholded distribution models), and bio.hex and bio.h3 count records in hexagons instead of squares.

The 1,795 records over the 127 cells of 100 km that they fall in — Biodiverse's example data: the records (dots) and the 127 cells of 100 km with at least one record (green, darker with more species). The records run in an arc, densest at its bottom.

Build the model#

1. The basedata#

bio.table (library subject Biodiversity analysis) reads a delimited text file as Biodiverse's import does. Its settings:

path: the file, sites.csv;
group_columns = ["x", "y"]: the columns that place a record;
cell_sizes = [100000, 100000]: the size of the cells along each group column (in metres here). 0 keeps the coordinates as they are; a negative size treats a column as text (groups by name, such as a region);
label_columns = ["genus", "species"]: the columns that name a label, joined with : ("Genus:sp1");
count_columns: columns of counts, summed (default 1 per record). binarise = true makes every count 1.

Its output, basedata, is the groups × labels table that every bio operator reads.

2. The spatial analysis#

bio.spatial runs Biodiverse's calculations over the neighbourhood of every group. Connect sites.basedata to its basedata, and set:

conditions = ["sp_circle (radius => 200000)"]: one condition (or two, for the indices that compare two neighbourhoods);
calculations = ["richness", "endemism_whole"]: Biodiverse's calculations by name (with or without calc_). richness gives RICHNESS_ALL (and RICHNESS_SET1); endemism_whole gives ENDW_WE (weighted endemism), ENDW_CWE (corrected), ENDW_RICHNESS and ENDW_SINGLE, with ranges measured over the whole dataset (endemism_central measures them differently when two neighbourhoods are used).

Its outputs: table, a row per group with its coordinates and every index; maps, a stack with an index per layer when the groups are cells of two axes (as here); lists, the list indices.

Records into cells of 100 km, then richness and endemism in each cell alone and within 200 km of it, the maps written to GeoTIFFs.

Model file (TOML)

format = "terraflux/1"

[[nodes]]
id = "sites"
op = "bio.table"
params = { path = "sites.csv", group_columns = ["x", "y"], label_columns = ["genus", "species"], cell_sizes = [100000, 100000] }
note = "The records snapped to cells of 100 km."

[[nodes]]
id = "cells"
op = "bio.spatial"
inputs = { basedata = "sites.basedata" }
params = { conditions = ["sp_self_only()"], calculations = ["richness", "endemism_whole"] }
note = "Each cell alone."

[[nodes]]
id = "neighbourhood"
op = "bio.spatial"
inputs = { basedata = "sites.basedata" }
params = { conditions = ["sp_circle (radius => 200000)"], calculations = ["richness", "endemism_whole"] }
note = "The cells within 200 km."

[[nodes]]
id = "save"
op = "raster.write"
inputs = { value = "neighbourhood.maps" }
params = { path = "indices_200km.tif" }
note = "A band per index, named after it."

The run takes a fraction of a second. raster.write writes the maps stack as a GeoTIFF with one band per index, each named after it (RICHNESS_ALL, ENDW_WE...), ready for a GIS.

ApplicationCommand line

Select neighbourhood and press Ctrl+Enter: its result shows in the Viewer, a map at a time; a double-click keeps it there as a layer, and Plots › Save as a new plot keeps that view with the model.

terraflux run endemism.toml

writes indices_200km.tif next to the model; add [outputs.indices] from = "neighbourhood.table" to the model to get the table as a CSV with --out.

Read the results#

Ranges: the raw material of endemism#

The range sizes of the 31 species, in cells of 100 km. Four occur in one or two cells; one in 49. Endemism indices give the narrow-ranged species most of their weight.

Most species are found in a few cells: 13 of the 31 in five cells or fewer, one in 49. This skew is typical of real data, and it is why weighted endemism differs from richness: a cell with three narrow-ranged species can outweigh one with ten widespread ones.

Richness and weighted endemism#

Move the slider over the neighbourhood: the cell alone, then circles of 100, 200 and 300 km. The maps are weighted endemism on one scale for all frames; the numbers are richness and endemism.

Neighbourhood Cell alone — Weighted endemism of every cell, for its own records and for the cells within 100, 200 and 300 km of it, on the same scale. Larger neighbourhoods smooth the map and raise the values; the two concentrations, at the bottom of the arc and on its right arm, stand out from 200 km.

Neighbourhood 100 km — Weighted endemism of every cell, for its own records and for the cells within 100, 200 and 300 km of it, on the same scale. Larger neighbourhoods smooth the map and raise the values; the two concentrations, at the bottom of the arc and on its right arm, stand out from 200 km.

How to read them:

Richness of the cell alone is mostly sampling. A cell has 2.9 species on average and 11 at most; its neighbours often have far fewer, because fewer records were made there. Within 200 km, richness rises to 8.6 on average and the map becomes a gradient.
Weighted endemism follows richness, but not entirely. Their rank correlation is 0.80 for the cells alone and 0.88 within 200 km: species-rich places tend to have more narrow-ranged species simply because they have more species. The cell with the highest WE on its own (2.34, with 7 species) is at the bottom of the arc; within 200 km the maximum (5.37, with 16 species) is also at the bottom of the arc, a little to the right.
Corrected weighted endemism removes richness. CWE correlates only weakly with richness (0.27 alone, 0.32 within 200 km), and its highest values within 200 km are on the upper right arm (0.49, with 7 species): fewer species, but more of them narrow-ranged.

Corrected weighted endemism (CWE) — Weighted endemism (WE)

In the literature

Report the data source and its filters, the coordinate system, the cell size, the spatial condition, and the index names as Biodiverse gives them (ENDW_WE, ENDW_CWE). Crisp et al. (2001) and Laffan and Crisp (2003) are the classic examples of mapping weighted endemism; González-Orozco et al. (2011) of richness and endemism of a genus across a continent.

Settings that change the answer#

The cell size#

Cell size 50 km — Richness of each cell alone with cells of 50, 100 and 200 km (each map on its own scale). Larger cells hold more records and more species, and fewer cells are empty between records.

Cell size 100 km — Richness of each cell alone with cells of 50, 100 and 200 km (each map on its own scale). Larger cells hold more records and more species, and fewer cells are empty between records.

The cell size changes every number: mean richness doubles from 50 to 200 km, and the ranges, measured in cells, change with it, so weighted endemism is not comparable between cell sizes. Laffan and Crisp (2003) recommend analysing several scales. A neighbourhood larger than the cell (as in the first slider) is another way to vary the scale while keeping the cells' precision.

The others#

The spatial condition: its size, and its shape (circles, blocks, annuli for "what is around but not here").
endemism_whole or endemism_central: ranges over the whole dataset or relative to the neighbourhoods.
Counts or presence: with binarise, a cell with 50 records of a species counts the same as one with 1. The indices of this part use presence; abundance-based indices (abc_counts...) use the counts.
The data's extent: ranges are measured within the dataset. A species that is narrow-ranged in your study area may be widespread beyond it; restrict "endemism" to what the data can show.

Common pitfalls#

Sampling effort. Richness of records rises with the number of records. Look at the number of records per cell before interpreting richness, and compare with a randomisation (part 2).
Coordinates in degrees with a cell size meant in metres (or the reverse): every record snaps to one cell, or each to its own.
Duplicates and errors: records of the same species at the same place inflate counts (but not presence); misidentified or misplaced records create false narrow-range "endemics". bio.occurrences drops duplicates and records with GBIF's issues; check the remaining outliers by hand.
Edge effects: neighbourhoods at the edge of the data are smaller and have lower values.
CWE in species-poor cells: one narrow-ranged species alone makes CWE high. Within 200 km, a cell with a single species has a CWE of 0.43, among the highest. Read CWE beside richness.

Going further#

Part 2: phylogenetic diversity, endemism and CANAPE: the tree of life in the same cells, and tests against chance.
Part 3: regions from species composition: cluster analysis of the cells.
Species distributions: cleaning GBIF records.
The operators: bio.table, bio.occurrences, bio.points, bio.vector, bio.raster, bio.hex, bio.h3, bio.properties, bio.spatial.

References#

Crisp, M. D., Laffan, S., Linder, H. P., & Monro, A. (2001). Endemism in the Australian flora. Journal of Biogeography, 28(2), 183–198. https://doi.org/10.1046/j.1365-2699.2001.00524.x
González-Orozco, C. E., Laffan, S. W., & Miller, J. T. (2011). Spatial distribution of species richness and endemism of the genus Acacia in Australia. Australian Journal of Botany, 59(7), 601–609. https://doi.org/10.1071/BT11112
Laffan, S. W., & Crisp, M. D. (2003). Assessing endemism at multiple spatial scales, with an example from the Australian vascular flora. Journal of Biogeography, 30(4), 511–520. https://doi.org/10.1046/j.1365-2699.2003.00875.x
Laffan, S. W., Lubarsky, E., & Rosauer, D. F. (2010). Biodiverse, a tool for the spatial analysis of biological and related diversity. Ecography, 33(4), 643–647. https://doi.org/10.1111/j.1600-0587.2010.06237.x
Laffan, S. W., Ramp, D., & Roger, E. (2013). Using endemism to assess representation of protected areas – the family Myrtaceae in the Greater Blue Mountains World Heritage Area. Journal of Biogeography, 40(3), 570–578. https://doi.org/10.1111/jbi.12001