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<h1 class="title toc-ignore">DIVERSITY indices : phylogenetic</h1>
<h4 class="date">06/03/2018</h4>
</div>
<p><br/> <br/></p>
<div id="vellend" class="section level1">
<h1>2010 : Vellend</h1>
<div id="indices-of-species-distinctness" class="section level2">
<h2>Indices of species’ distinctness</h2>
<table>
<colgroup>
<col width="30%" />
<col width="42%" />
<col width="13%" />
<col width="13%" />
</colgroup>
<thead>
<tr class="header">
<th>Index</th>
<th>Description</th>
<th>Type of tree</th>
<th>Reference</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><strong>Taxonomic distinctness (TD)</strong></td>
<td>Reciprocal of number of nodes between species and root of tree</td>
<td>node-based</td>
<td><em>1991 : Vane-Wright</em></td>
</tr>
<tr class="even">
<td></td>
<td>To account for polytomies, count number of descendants at each node rather than number of nodes</td>
<td></td>
<td><em>1990 : May</em></td>
</tr>
<tr class="odd">
<td><strong>Species originality (SO)</strong></td>
<td>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</td>
<td>node-based</td>
<td><em>1992 : Nixon & Wheeler</em></td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><strong>Pendant edge (PE)</strong></td>
<td>Length of the branch connecting a species to the rest of the regional tree</td>
<td>distance-based</td>
<td><em>1990 : Altschul & Lipman</em></td>
</tr>
<tr class="even">
<td><strong>Species evolutionary history (SEH)</strong></td>
<td>Portion of a phylogenetic tree attributable to a species; shared branches are apportioned equally among descendant lineages</td>
<td>distance-based</td>
<td><em>2006 : Redding & Mooers</em></td>
</tr>
<tr class="odd">
<td><strong>Originality of species within a set (OSS)</strong></td>
<td>Values for each species that ‘maximize the expected dissimilarity between two species randomly drawn from the set’</td>
<td>distance-based</td>
<td><em>2005 : Pavoine</em></td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p><br/></p>
</div>
<div id="type-i-metrics" class="section level2">
<h2>Type I metrics</h2>
<ol style="list-style-type: decimal">
<li>Calculating a distinctness score for all species in a regional phylogeny</li>
<li>Calculating some function of these scores (typically the sum) for particular subsets of species</li>
</ol>
<p><br/></p>
</div>
<div id="type-ii-metrics" class="section level2">
<h2>Type II metrics</h2>
<ol style="list-style-type: decimal">
<li>Starting with a local phylogeny</li>
</ol>
<p><br/></p>
<p>Aggregation of metrics according to :</p>
<ul>
<li>nature of the phylogenetic tree - distance-based metrics - counting nodes metrics (special case of first)</li>
<li>nature of species data - abundances - presence-absence (special case of first)</li>
</ul>
<p><br/></p>
<table>
<colgroup>
<col width="13%" />
<col width="36%" />
<col width="36%" />
<col width="13%" />
</colgroup>
<thead>
<tr class="header">
<th>Index</th>
<th>Description <br/> presence-absence</th>
<th>Description <br/> abundance-weighted</th>
<th>Equation</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><strong>Phylogenetic diversity (PD)</strong></td>
<td><em>1992 : Faith</em> <br/> Sum of all branch lengths in the portion of a phylogenetic tree connecting the focal set of species</td>
<td><em>2002 : Barker</em> <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</td>
<td></td>
</tr>
<tr class="even">
<td><strong>Mean phylogenetic distance (MPD)</strong></td>
<td><em>2000 : Webb</em> <br/> Mean phylogenetic distance between each pair of species in the focal set</td>
<td><em>1995 : Warwick & Clarke (1982 : Rao)</em><br/> Mean phylogenetic distance between pairs of individuals, excluding (or not) same-species pairs</td>
<td></td>
</tr>
<tr class="odd">
<td><strong>Sum of phylogenetic distances (SPD)</strong></td>
<td><em>1997 : Crozier</em> <br/> Sum of phylogenetic distances between each pair of species <br/> MPD x number of species pairs</td>
<td><em>2007 : Helmus</em> <br/> Abundance-weighted MPD x number of species pairs</td>
<td></td>
</tr>
<tr class="even">
<td><strong>Mean nearest neighbour distance (MNND)</strong></td>
<td><em>2000 : Webb</em> <br/> Mean phylogenetic distance from each species to its closest relative in the focal species set</td>
<td>Weighted mean phylogenetic distance from each species to its closest relative, with weights equal to species’ abundance</td>
<td></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p><br/></p>
</div>
</div>
<div id="faith" class="section level1">
<h1>2013 : Faith</h1>
<p><strong>Phylogenetic Diversity (PD) :</strong> basis for a measure of biodiversity, that would consider all possible units<br />
(genes, features, species, ecosystems).</p>
<p>Required information about expected relationships among the objects provided by :</p>
<ul>
<li>phylogeny</li>
<li>associated evolutionary models linking phylogenetic pattern to variation at the level of features/units</li>
</ul>
<p><br/></p>
<p><strong>Link between PD and species richness (SR) ?</strong></p>
<ol style="list-style-type: decimal">
<li>When subsets of different numbers of species are selected randomly from the tree, the average PD value for a given species number has a <em>power curve relationship</em> with the number of species in the subset.</li>
<li>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.</li>
</ol>
<p><br/></p>
<p><strong>PD of a set of species from a phylogenetic tree :</strong> minimum total length of all the phylogenetic branches required to connect all those species on the tree.</p>
<p><br/></p>
<div id="loss-or-gain-of-species" class="section level3">
<h3>Loss or gain of species</h3>
<ul>
<li><p><strong>Loss of species :</strong> loss of features exclusively represented by these species = <strong>endemism</strong></p></li>
<li><p><strong>Loss of area :</strong> loss of SR with the loss of species that were exclusively found in this area = <strong>complementarity</strong></p></li>
</ul>
<p><br/></p>
</div>
<div id="probabilities-of-loss" class="section level3">
<h3>Probabilities of loss</h3>
<p><strong>Expected PD :</strong> PD given a set of species’ extinction probabilities.<br />
<em>Species case of Weitzman’s general expected diversity formula.</em></p>
<ul>
<li><p><strong>Delta PD q :</strong> change in expected PD if probability extinction of species (e.g. in a given area) changes from <code>q</code> to 1.<br />
<em>The value will be large to the extent that the species shares long ancestral branches with few other species.</em></p></li>
<li><p><strong>PD50 :</strong> change in expected PD with a current probability of extinction of 0.5 for all species.<br />
<em>The value will be large when the species has long ancestral branches with few other descendants.</em></p></li>
</ul>
<p><br/></p>
</div>
<div id="dissimilarities" class="section level3">
<h3>Dissimilarities</h3>
<ul>
<li><strong>PD dissimilarities :</strong> differences of evolutionary features between samples or localities<br />
(sum of branches in one site only, divided by sum of all branches).</li>
</ul>
<p><br/></p>
</div>
<div id="dissimilarities-with-abundance-information" class="section level3">
<h3>Dissimilarities with abundance information</h3>
<ul>
<li><p><strong>Chao’s framework</strong></p></li>
<li><p><strong>Effective rare PD :</strong> defines “Valley numbers” in which the flexible parameter provides increasing focus on low abundance.<br />
<em>Effective amount of rare feature diversity</em></p></li>
</ul>
<p><br/></p>
</div>
</div>
<div id="dissimilarities-beta-partitioning" class="section level1">
<h1>Dissimilarities (beta) & partitioning</h1>
<p><strong>PhyloSor :</strong></p>
<ul>
<li>derived from the taxonomic-based <em>Sorensen</em> dissimilarity index</li>
</ul>
<p><strong>UniFrac :</strong></p>
<ul>
<li>derived from the taxonomic-based <em>Jaccard</em> dissimilarity index</li>
<li>total branch length unique to each community relative to the total branch length linking all species in both communities</li>
<li>measures the proportion of evolutionary history unique to each community</li>
</ul>
<p><br/> <br/></p>
</div>
<div id="glossary" class="section level1">
<h1>Glossary</h1>
<ul>
<li><p><strong>Node-based tree :</strong> simplest type of phylogenetic tree which represents only the topology, with no information on the lengths of branches connecting the nodes.</p></li>
<li><p><strong>Distance-based tree :</strong> with quantitative branch lengths.</p></li>
<li><p><strong>Ultrametric tree</strong> = in which the distances from the root to every branch tip are equal<br />
= 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</p></li>
</ul>
<!-- <div style="text-align:center"><img src="pictures_tutorials/example_ultrametric-tree.png" width=600px/></div> -->
<p><img src="pictures_tutorials/example_ultrametric-tree.png" width="600px" style="display: block; margin: auto;" /></p>
<ul>
<li><p><strong>Balanced tree :</strong> 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.</p></li>
<li><p><strong>Imbalanced tree :</strong> one lineage descending from each node connects directly to a tip with no further bifurcations.</p></li>
<li><p><strong>Polytomie :</strong> node where the lineage splits into three or more (most commonly due to data limitations).</p></li>
<li><p><strong>Evenness :</strong> 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.</p></li>
</ul>
<p><br/> <br/></p>
</div>
<div id="citations" class="section level1">
<h1>Citations</h1>
<ul>
<li><p>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. <a href="https://doi.org/10.1111/nyas.12186" class="uri">https://doi.org/10.1111/nyas.12186</a></p></li>
<li><p>Vellend, M., Cornwell, W., Magnuson-Ford, K. & Mooers, A. (2010). Measuring phylogenetic biodiversity.</p>
<ul>
<li>Altschul, S. & Lipman, D. (1990). Equal animals. Nature 348, 493–494. <a href="https://doi.org/10.1038/348493c0" class="uri">https://doi.org/10.1038/348493c0</a></li>
<li>May, R.M. (1990). Taxonomy as destiny. Nature, 347, 129-130.</li>
<li>Nixon, K. & Wheeler, Q. (1990). An Amplification of the Phylogenetic Species Concept. Cladistics. 6. 211-223. <a href="https://doi.org/10.1111/j.1096-0031.1990.tb00541.x" class="uri">https://doi.org/10.1111/j.1096-0031.1990.tb00541.x</a></li>
<li>Nixon, K. & Wheeler, Q. (1991). Extinction and the origin of species. Extinction and Phylogeny.</li>
<li>Pavoine, S., Ollier, S. & Dufour, A.‐B. (2005). Is the originality of a species measurable?. Ecology Letters, 8: 579-586. <a href="https://doi.org/10.1111/j.1461-0248.2005.00752.x" class="uri">https://doi.org/10.1111/j.1461-0248.2005.00752.x</a></li>
<li>Redding, D.W. & Mooers, A.Ø. (2006). Incorporating Evolutionary Measures into Conservation Prioritization. Conservation Biology, 20: 1670-1678. <a href="https://doi.org/10.1111/j.1523-1739.2006.00555.x" class="uri">https://doi.org/10.1111/j.1523-1739.2006.00555.x</a></li>
<li>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. <a href="https://doi.org/10.1016/0006-3207(91)90030-D" class="uri">https://doi.org/10.1016/0006-3207(91)90030-D</a></li>
<li></li>
<li>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. <a href="https://doi.org/10.1046/j.1095-8312.2002.00055.x" class="uri">https://doi.org/10.1046/j.1095-8312.2002.00055.x</a></li>
<li>Crozier, R. (1997). Preserving the Information Content of Species: Genetic Diversity, Phylogeny, and Conservation Worth. Annual Review of Ecology and Systematics, 28, 243-268. <a href="http://www.jstor.org/stable/2952493" class="uri">http://www.jstor.org/stable/2952493</a></li>
<li>Faith, D. (1992). Conservation evaluation and phylogenetic diversity. Biological Conservation. 61. 1-10. <a href="https://doi.org/10.1016/0006-3207(92)91201-3" class="uri">https://doi.org/10.1016/0006-3207(92)91201-3</a></li>
<li>Helmus, M., Bland, T., Williams, C. & Ives, A. (2007). Phylogenetic measures of biodiversity. Am Nat 169(3):E68-E83. The American naturalist. 169. <a href="https://doi.org/10.1086/511334" class="uri">https://doi.org/10.1086/511334</a></li>
<li>Rao, C. R. (1982). Diversity and Dissimilarity Coefficients: A Unified Approach. Theoretical population biology, 21, 24-43. Theoretical Population Biology. 21. 24-43. <a href="https://doi.org/10.1016/0040-5809(82)90004-1" class="uri">https://doi.org/10.1016/0040-5809(82)90004-1</a></li>
<li>Warwick, R. & Clarke, K. (1995). New ‘biodiversity’ measures reveal a decrease in taxonomic distinctness with increasing stress. Marine Ecology Progress Series. 129. 301-305. <a href="https://doi.org/10.3354/meps129301" class="uri">https://doi.org/10.3354/meps129301</a></li>
<li>Webb, C. (2000). Exploring the Phylogenetic Structure of Ecological Communities: An Example for Rain Forest Trees. The American naturalist. 156. 145-155. <a href="https://doi.org/10.1086/303378" class="uri">https://doi.org/10.1086/303378</a></li>
</ul></li>
</ul>
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