DIVERSITY indices : phylogenetic

2010 : Vellend

Indices of species’ distinctness

Index	Description	Type of tree	Reference
Taxonomic distinctness (TD)	Reciprocal of number of nodes between species and root of tree	node-based	1991 : Vane-Wright
	To account for polytomies, count number of descendants at each node rather than number of nodes		1990 : May
Species originality (SO)	Assign each node in a tree a value of 1 if more species descend from that node than its sister node, and 0 otherwise; sum the values at the nodes between a species and the root; smaller values indicate greater distinctness	node-based	1992 : Nixon & Wheeler
Pendant edge (PE)	Length of the branch connecting a species to the rest of the regional tree	distance-based	1990 : Altschul & Lipman
Species evolutionary history (SEH)	Portion of a phylogenetic tree attributable to a species; shared branches are apportioned equally among descendant lineages	distance-based	2006 : Redding & Mooers
Originality of species within a set (OSS)	Values for each species that ‘maximize the expected dissimilarity between two species randomly drawn from the set’	distance-based	2005 : Pavoine

Type I metrics

1. Calculating a distinctness score for all species in a regional phylogeny
2. Calculating some function of these scores (typically the sum) for particular subsets of species

Type II metrics

1. Starting with a local phylogeny

Aggregation of metrics according to :

• nature of the phylogenetic tree - distance-based metrics - counting nodes metrics (special case of first)
• nature of species data - abundances - presence-absence (special case of first)

Index	Description presence-absence	Description abundance-weighted	Equation
Phylogenetic diversity (PD)	1992 : Faith Sum of all branch lengths in the portion of a phylogenetic tree connecting the focal set of species	2002 : Barker For the subset tree, the number of branches multiplied by the weighted mean branch length, with weights equal to the average abundance of species sharing that branch
Mean phylogenetic distance (MPD)	2000 : Webb Mean phylogenetic distance between each pair of species in the focal set	1995 : Warwick & Clarke (1982 : Rao) Mean phylogenetic distance between pairs of individuals, excluding (or not) same-species pairs
Sum of phylogenetic distances (SPD)	1997 : Crozier Sum of phylogenetic distances between each pair of species MPD x number of species pairs	2007 : Helmus Abundance-weighted MPD x number of species pairs
Mean nearest neighbour distance (MNND)	2000 : Webb Mean phylogenetic distance from each species to its closest relative in the focal species set	Weighted mean phylogenetic distance from each species to its closest relative, with weights equal to species’ abundance

2013 : Faith

Phylogenetic Diversity (PD) : basis for a measure of biodiversity, that would consider all possible units
(genes, features, species, ecosystems).

Required information about expected relationships among the objects provided by :

• phylogeny
• associated evolutionary models linking phylogenetic pattern to variation at the level of features/units

Link between PD and species richness (SR) ?

1. When subsets of different numbers of species are selected randomly from the tree, the average PD value for a given species number has a power curve relationship with the number of species in the subset.
2. Departures from the basic power curve depend on the nature of these departures from random sets — whether the species extinctions are clumped or well dispersed on the phylogenetic tree.

PD of a set of species from a phylogenetic tree : minimum total length of all the phylogenetic branches required to connect all those species on the tree.

Loss or gain of species

• Loss of species : loss of features exclusively represented by these species = endemism

• Loss of area : loss of SR with the loss of species that were exclusively found in this area = complementarity

Probabilities of loss

Expected PD : PD given a set of species’ extinction probabilities.
Species case of Weitzman’s general expected diversity formula.

• Delta PD q : change in expected PD if probability extinction of species (e.g. in a given area) changes from q to 1.
  The value will be large to the extent that the species shares long ancestral branches with few other species.

• PD50 : change in expected PD with a current probability of extinction of 0.5 for all species.
  The value will be large when the species has long ancestral branches with few other descendants.

Dissimilarities

• PD dissimilarities : differences of evolutionary features between samples or localities
  (sum of branches in one site only, divided by sum of all branches).

Dissimilarities with abundance information

• Chao’s framework

• Effective rare PD : defines “Valley numbers” in which the flexible parameter provides increasing focus on low abundance.
  Effective amount of rare feature diversity

Dissimilarities (beta) & partitioning

PhyloSor :

• derived from the taxonomic-based Sorensen dissimilarity index

UniFrac :

• derived from the taxonomic-based Jaccard dissimilarity index
• total branch length unique to each community relative to the total branch length linking all species in both communities
• measures the proportion of evolutionary history unique to each community

Glossary

• Node-based tree : simplest type of phylogenetic tree which represents only the topology, with no information on the lengths of branches connecting the nodes.

• Distance-based tree : with quantitative branch lengths.

• Ultrametric tree = in which the distances from the root to every branch tip are equal
  = if the branch lengths are proportional to divergence time, all branch tips are the same distance from the tree base (first node) = a) on the graph, b) is non-ultrametric

• Balanced tree : all tips are separated from the root by the same number of nodes, which is equivalent to saying that all lineages bifurcate the same number of times.

• Imbalanced tree : one lineage descending from each node connects directly to a tip with no further bifurcations.

• Polytomie : node where the lineage splits into three or more (most commonly due to data limitations).

• Evenness : an even distribution of branches within the community has branches with about equal abundance; uneven distributions may be dominated by one or a few abundant branches.

Citations

• Faith D. P. (2013). Biodiversity and evolutionary history: useful extensions of the PD phylogenetic diversity assessment framework. Ann N Y Acad Sci. Jun; 1289:69-89. https://doi.org/10.1111/nyas.12186

• Vellend, M., Cornwell, W., Magnuson-Ford, K. & Mooers, A. (2010). Measuring phylogenetic biodiversity.

  • Altschul, S. & Lipman, D. (1990). Equal animals. Nature 348, 493–494. https://doi.org/10.1038/348493c0
  • May, R.M. (1990). Taxonomy as destiny. Nature, 347, 129-130.
  • Nixon, K. & Wheeler, Q. (1990). An Amplification of the Phylogenetic Species Concept. Cladistics. 6. 211-223. https://doi.org/10.1111/j.1096-0031.1990.tb00541.x
  • Nixon, K. & Wheeler, Q. (1991). Extinction and the origin of species. Extinction and Phylogeny.
  • Pavoine, S., Ollier, S. & Dufour, A.‐B. (2005). Is the originality of a species measurable?. Ecology Letters, 8: 579-586. https://doi.org/10.1111/j.1461-0248.2005.00752.x
  • Redding, D.W. & Mooers, A.Ø. (2006). Incorporating Evolutionary Measures into Conservation Prioritization. Conservation Biology, 20: 1670-1678. https://doi.org/10.1111/j.1523-1739.2006.00555.x
  • Vane-Wright, R.I., Humphries, C.J. & Williams, P.H. (1991). What to protect? - Systematics and the agony of choice. Biological Conservation, 55, 235-254. https://doi.org/10.1016/0006-3207(91)90030-D
  • Barker, G. (2002). Phylogenetic diversity: a quantitative framework for measurement of priority and achievement in biodiversity conservation. Biological Journal of the Linnean Society. 76. 165-194. https://doi.org/10.1046/j.1095-8312.2002.00055.x
  • Crozier, R. (1997). Preserving the Information Content of Species: Genetic Diversity, Phylogeny, and Conservation Worth. Annual Review of Ecology and Systematics, 28, 243-268. http://www.jstor.org/stable/2952493
  • Faith, D. (1992). Conservation evaluation and phylogenetic diversity. Biological Conservation. 61. 1-10. https://doi.org/10.1016/0006-3207(92)91201-3
  • Helmus, M., Bland, T., Williams, C. & Ives, A. (2007). Phylogenetic measures of biodiversity. Am Nat 169(3):E68-E83. The American naturalist. 169. https://doi.org/10.1086/511334
  • Rao, C. R. (1982). Diversity and Dissimilarity Coefficients: A Unified Approach. Theoretical population biology, 21, 24-43. Theoretical Population Biology. 21. 24-43. https://doi.org/10.1016/0040-5809(82)90004-1
  • Warwick, R. & Clarke, K. (1995). New ‘biodiversity’ measures reveal a decrease in taxonomic distinctness with increasing stress. Marine Ecology Progress Series. 129. 301-305. https://doi.org/10.3354/meps129301
  • Webb, C. (2000). Exploring the Phylogenetic Structure of Ecological Communities: An Example for Rain Forest Trees. The American naturalist. 156. 145-155. https://doi.org/10.1086/303378