Phylogenetic diversity, endemism and CANAPE

Two places with ten species each are not equally diverse if the first holds ten species of one genus and the second ten species from ten families: the second holds more of the tree of life. In this part you bring the phylogeny into the analysis of part 1: you map phylogenetic diversity (PD), the length of the tree's branches present in each neighbourhood, and phylogenetic endemism (PE), those branches weighted by how restricted they are. Then you ask whether the patterns are more than what richness alone would give, with Biodiverse's randomisations, and classify the significant places with CANAPE into centres of recent and of ancient endemism. At the end you will have the maps and the tests that spatial phylogenetics studies report.

The idea#

Phylogenetic diversity#

Faith (1992) proposed to measure the diversity of a set of species by the total length of the branches of the phylogeny that connect them (to the root). Branch length stands for evolutionary history, or for the features (genes, traits) accumulated along a lineage: a set of distantly related species spans more of the tree, and so more features, than a set of close relatives. PD has become a standard measure in conservation, from setting priorities between areas to valuing the evolutionarily distinct species.

Phylogenetic endemism#

Rosauer et al. (2009) combined PD with weighted endemism (part 1). Each branch of the tree has a range, the cells where any of the species descending from it occurs. Phylogenetic endemism weighs every branch by the share of its range inside the neighbourhood:

Key idea: PD and PE

For the set of branches \(B\) connecting the species of a neighbourhood to the root, with lengths \(L_b\),

\[ \mathrm{PD} = \sum_{b \in B} L_b \qquad\qquad \mathrm{PE} = \sum_{b \in B} L_b \, \frac{r_b}{R_b} \]

where \(R_b\) is the range of branch \(b\) (the cells of all its descendant species) and \(r_b\) the part of it inside the neighbourhood. A long branch found only here adds its whole length to PE; a short branch, or a widespread one, adds little. PE is high where long, range-restricted lineages occur.

Is it more than chance? Randomisations#

PD and PE grow with richness: more species bring more branches. To ask whether a place has more (or less) phylogenetic diversity or endemism than its richness explains, Biodiverse randomises the data many times and compares. Its default, rand_structured, reshuffles which species occur in which cells while keeping the richness of every cell and the range size of every species (Laffan & Crisp, 2003). Each index is then given a p-rank: the share of randomisations in which the observed value was higher. A p-rank of 0.99 means the observed value beat 99% of the random ones.

CANAPE#

Mishler et al. (2014) added a test that tells why a place is a centre of endemism. Relative PE (RPE) is PE on the real tree divided by PE on a comparison tree with the same topology but equal branch lengths. If the range-restricted branches of a place are longer than average (old lineages that survive in a small area), RPE is high; if they are shorter (young lineages, recent speciation), RPE is low. The categorical analysis of neo- and palaeo-endemism (CANAPE) then classifies each cell:

PE on the real or on the comparison tree is significantly high (p-rank ≥ 0.95), else not significant;
if so, RPE significantly high: palaeo-endemism (old lineages); significantly low: neo-endemism (recent radiations); neither: mixed endemism;
if both PEs are highly significant (p-rank ≥ 0.99): super-endemism.

Mishler et al. developed it on the Australian Acacia, and it has since been used for floras and faunas across the world (for example the native flora of California; Thornhill et al., 2017).

When to use it#

Prioritising places for the evolutionary history they hold, beyond species counts.
Understanding the history of a flora or fauna: refugia of old lineages (palaeo-endemism) against cradles of recent speciation (neo-endemism).
Testing whether a pattern is real: any Biodiverse index can be randomised in the same way.

What you need#

The records of part 1: sites.csv.
A phylogeny of the labels, in Newick or Nexus, with branch lengths, its tips named as the labels ("Genus:sp1"). Here Biodiverse's example tree, tree.nex. It is not a real phylogeny: its file says it was made by a Sorenson clustering of the example data. It serves to learn the method; with real data, use a dated or molecular phylogeny of your taxa.
Time: 999 randomisations of the example took a few seconds; for thousands of cells and species, plan for minutes to hours.

The example tree of the 31 species — Biodiverse's example tree: 31 species, branch lengths from the root to the tips of about 1 (an ultrametric tree), 21.2 in all. Made by clustering the species, it stands in for a real phylogeny here.

Build the model#

1. The tree#

bio.tree reads a tree as Biodiverse does: path (the file, or the Newick text itself), format (nexus or newick, guessed from the text), and index (which tree of a file with several). Nexus Translate tables are applied; nodes without names get Biodiverse's names (0___, 1___...).

2. PD, PE and RPE#

The bio.spatial of part 1 takes the tree in its tree input. Add the phylogenetic calculations to its list: pd (PD, and PD_P, its share of the whole tree), pe (PE_WE and PE_WE_P) and phylo_rpe2 (PHYLO_RPE2, the relative PE, with PHYLO_RPE_NULL2 and PHYLO_RPE_DIFF2).

3. Randomisations and CANAPE#

bio.randomise runs the same analysis on randomised data. It takes the basedata and the tree, the same conditions, and the calculations to test; function = "rand_structured" (the default), iterations = 999 and a rand_seed (the same seed gives the same randomisations, and the same as Biodiverse's). Its outputs: table (the observed indices), p_rank, z_scores, comparison (Biodiverse's counters), and, when pe and phylo_rpe2 are among the calculations, canape (a code per cell: 0 not significant, 1 neo, 2 palaeo, 3 mixed, 4 super); maps has the p-ranks and CANAPE as layers.

Records in cells of 100 km and the example tree; PD, PE and relative PE within 200 km; and the same tested against 999 randomisations, with CANAPE.

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] }

[[nodes]]
id = "tree"
op = "bio.tree"
params = { path = "tree.nex" }
note = "Tips named as the labels, Genus:sp1..."

[[nodes]]
id = "indices"
op = "bio.spatial"
inputs = { basedata = "sites.basedata", tree = "tree.tree" }
params = { conditions = ["sp_circle (radius => 200000)"], calculations = ["richness", "endemism_whole", "pd", "pe", "phylo_rpe2"] }
note = "PD, PE and RPE within 200 km."

[[nodes]]
id = "random"
op = "bio.randomise"
inputs = { basedata = "sites.basedata", tree = "tree.tree" }
params = { conditions = ["sp_circle (radius => 200000)"], calculations = ["richness", "pd", "pe", "phylo_rpe2"], function = "rand_structured", iterations = 999, rand_seed = 2024 }
note = "999 randomisations keeping richness and ranges; p-ranks and CANAPE."

[[nodes]]
id = "save"
op = "raster.write"
inputs = { value = "random.maps" }
params = { path = "canape.tif" }

Read the results#

PD and PE#

Phylogenetic endemism (PE) — Phylogenetic diversity (PD)

PD against richness for the 127 cells (within 200 km): rank correlation 0.99. With this tree, PD adds almost nothing to richness; it is the endemism and the randomisations that bring new information.

PD is nearly a function of richness here (rank correlation 0.99), largest (11.9) where richness is largest (17 species). This is common, and the reason PD alone is rarely enough. PE follows weighted endemism closely (0.96) but not exactly: it rises highest (3.77) in a cell of the upper right arm, where long branches have small ranges.

Against chance#

The p-rank of PE against 999 randomisations — The p-rank of PE: red where PE is higher than in 95% (or 99%) of the randomisations, blue where it is lower. The upper right arm and the left tip have more phylogenetic endemism than their richness explains; the lower tail has less.

The randomisations change the picture. The bottom of the arc, high in PE, is not significant: its PE is what its many species would give anyway. The upper right arm is significantly high (15 cells at p ≥ 0.95, 2 at p ≥ 0.99), and so are a few cells at the left tip. The lower tail of the arc is significantly low (19 cells at p ≤ 0.01): its species are widespread ones, and so are their branches.

CANAPE#

CANAPE class	Cells
Not significant	92
Neo-endemism	0
Palaeo-endemism	5
Mixed endemism	28
Super-endemism	2

Read with care, given the artificial tree, the story is one of two centres: a large mixed centre on the upper right arm, with two cells of super-endemism at its heart, where short and long range-restricted branches occur together; and a small palaeo-endemic centre on the left, where the restricted branches are long, the pattern of old lineages persisting in a small area. CANAPE has more cells (35) than the p-rank map of PE alone (17 above 0.95), because its first test accepts significance on either tree. These counts are those landschaft's documentation reports for the same data and seed, which Biodiverse also gives.

In the literature

Report the phylogeny (source, dating, how tips were matched to the records), the spatial condition, the randomisation (its function, iterations and seed) and the significance thresholds, the PD and PE maps, the CANAPE map with its counts, and how many tips of the tree had no record. Mishler et al. (2014) and Thornhill et al. (2017) are good models.

Settings that change the answer#

The phylogeny. Branch lengths are what PD and PE measure: a dated tree, a molecular one, or one with equal lengths give different maps. Missing species bias PD downwards where they occur.
The randomisation. rand_structured keeps richness and ranges; the spatially structured forms (rand_spatially_structured, rand_diffusion, rand_random_walk) also keep ranges contiguous, a stricter null model that usually makes fewer cells significant; rand_independent_swaps and rand_curveball are swap algorithms.
Iterations: 999 is the minimum for a p-rank of 0.99 to mean something; more make the edges of significance stable.
The neighbourhood and the cell size, as in part 1: CANAPE at 100 km cells within 200 km is one scale of many.

Common pitfalls#

Tips that do not match labels. A label absent from the tree is ignored by phylogenetic indices, silently lowering PD and PE. Check that every label is a tip (same spelling, same separator).
Reading PD as more than richness. With many trees PD correlates strongly with richness. Look at the randomisations (or at PD's standardised effect) before claiming high phylogenetic diversity.
Too few iterations, or comparing p-ranks of runs with different seeds and conditions.
Multiple testing: with 127 cells and a threshold of 0.05, about six cells are expected significant by chance alone in each tail. Prefer clusters of significant cells to single ones.

Going further#

Part 1: richness and endemism.
Part 3: regions from species composition, including phylogenetic dissimilarity (PHYLO_SORENSON).
Spatial prioritization: taking PE surfaces into a conservation plan.
The operators: bio.tree, bio.spatial, bio.randomise, bio.matrix, bio.properties.

References#

Faith, D. P. (1992). Conservation evaluation and phylogenetic diversity. Biological Conservation, 61(1), 1–10. https://doi.org/10.1016/0006-3207(92)91201-3
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
Mishler, B. D., Knerr, N., González-Orozco, C. E., Thornhill, A. H., Laffan, S. W., & Miller, J. T. (2014). Phylogenetic measures of biodiversity and neo- and paleo-endemism in Australian Acacia. Nature Communications, 5, 4473. https://doi.org/10.1038/ncomms5473
Rosauer, D., Laffan, S. W., Crisp, M. D., Donnellan, S. C., & Cook, L. G. (2009). Phylogenetic endemism: a new approach for identifying geographical concentrations of evolutionary history. Molecular Ecology, 18(19), 4061–4072. https://doi.org/10.1111/j.1365-294X.2009.04311.x
Thornhill, A. H., Baldwin, B. G., Freyman, W. A., et al. (2017). Spatial phylogenetics of the native California flora. BMC Biology, 15(1). https://doi.org/10.1186/s12915-017-0435-x