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DIVERSITY_measures_phylogenetic.Rmd
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---
title: "DIVERSITY indices : phylogenetic"
date: "06/03/2018"
output:
html_document:
number_sections: no
toc: yes
toc_float:
collapsed: false
smooth_scroll: false
---
```{r, echo=FALSE}
library(knitr)
```
<br/>
<br/>
# 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* |
| | | |
<br/>
## 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
<br/>
## Type II metrics
1. Starting with a local phylogeny
<br/>
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)
<br/>
| Index | Description <br/> presence-absence | Description <br/> abundance-weighted | Equation |
| ------------ | -------------------------------- | -------------------------------- | ------------ |
| **Phylogenetic diversity (PD)** | *1992 : Faith* <br/> Sum of all branch lengths in the portion of a phylogenetic tree connecting the focal set of species | *2002 : Barker* <br/> 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* <br/> Mean phylogenetic distance between each pair of species in the focal set | *1995 : Warwick & Clarke (1982 : Rao)*<br/> Mean phylogenetic distance between pairs of individuals, excluding (or not) same-species pairs | | |
| **Sum of phylogenetic distances (SPD)** | *1997 : Crozier* <br/> Sum of phylogenetic distances between each pair of species <br/> MPD x number of species pairs | *2007 : Helmus* <br/> Abundance-weighted MPD x number of species pairs| | |
| **Mean nearest neighbour distance (MNND)** | *2000 : Webb* <br/> 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 | | |
| | | | | |
<br/>
# 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
<br/>
**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.
<br/>
**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.
<br/>
### 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**
<br/>
### 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.*
<br/>
### Dissimilarities
- **PD dissimilarities :** differences of evolutionary features between samples or localities
(sum of branches in one site only, divided by sum of all branches).
<br/>
### 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*
<br/>
# 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
<br/>
<br/>
# 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
<!-- <div style="text-align:center"><img src="pictures_tutorials/example_ultrametric-tree.png" width=600px/></div> -->
```{r, echo=FALSE, fig.align='center', out.width='600px', fig.retina=1}
include_graphics("pictures_tutorials/example_ultrametric-tree.png")
```
- **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.
<br/>
<br/>
# 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