[GRASS-SVN] r66235 - grass-addons/grass7/raster/r.biodiversity

svn_grass at osgeo.org svn_grass at osgeo.org
Tue Sep 15 08:38:42 PDT 2015


Author: pvanbosgeo
Date: 2015-09-15 08:38:42 -0700 (Tue, 15 Sep 2015)
New Revision: 66235

Modified:
   grass-addons/grass7/raster/r.biodiversity/r.biodiversity.html
Log:
small edits / corrections

Modified: grass-addons/grass7/raster/r.biodiversity/r.biodiversity.html
===================================================================
--- grass-addons/grass7/raster/r.biodiversity/r.biodiversity.html	2015-09-15 14:29:55 UTC (rev 66234)
+++ grass-addons/grass7/raster/r.biodiversity/r.biodiversity.html	2015-09-15 15:38:42 UTC (rev 66235)
@@ -1,109 +1,42 @@
 <h2>DESCRIPTION</h2>
 
-<p><em>r.biodiversity</em> computes one or more biodiversity indici 
-based on 2 or more input layers. Each layer should represents a 
-species (or other categories being used), and its raster values the 
-species count. The name of the output layers will consist of the 
-base name provided by the user.
+<p><em>r.biodiversity</em> computes one or more biodiversity indici based on 2 or more input layers. Each layer should represents a species (or other categories being used), and its raster values the species count. The name of the output layers will consist of the base name provided by the user. Currently implemented are the Renyi entropy index and three specialized cases of the Renyi enthropy, 
+viz.the species richness, the Shannon index and the Simpson index (Legendre & Legendre, 1998). 
 
-<p>Currently implemented are the Rényi entropy index and three 
-specialized cases of the Renyi enthropy, viz.the species richness, the 
-Shannon index and the Simpson index (Legendre & Legendre, 1998). 
-
 <h4>The Renyi enthropy</h4>
 
-This index uantify the diversity, uncertainty, or randomness of a 
-system. The user can define the order of diversity by setting the 
-order (<i>alpha</i>) value. The order of a diversity indicates its 
-sensitivity to common and rare species. The diversity of order zero 
-( <i>alpha</i> = 0)  is completely insensitive to species 
-frequencies and is better known as species richness. Increasing the 
-order diminishes the relative weights of rare species in the 
-resulting index (Jost 2006, Legendre & Legendre 1998). The name of 
-the output layer is composed of the basename + renyi + alpha.
+<p>This index uantify the diversity, uncertainty, or randomness of a system. The user can define the order of diversity by setting the order (<i>alpha</i>) value. The order of a diversity indicates its 
+sensitivity to common and rare species. The diversity of order zero ( <i>alpha = 0</i>)  is completely insensitive to species frequencies and is better known as species richness. Increasing the order diminishes the relative weights of rare species in the resulting index (Jost 2006, Legendre & Legendre 1998). The name of the output layer is composed of the basename + renyi + alpha.
 
 <h4>Species richness</h4>
 
-<p>The species richness is simply the count of the number of layers. 
-It is a special case of the Reny enthropy: 
-
-<div class="code"><pre>s = exp(R0)</pre></div>
-
-whereby <i>s</i> is the species richness <i>R0</i> the renyi index 
-for <i>alpha=0</i>. The name of the output layer is composed of the basename + 
+<p>The species richness is simply the count of the number of layers. It is a special case of the Reny enthropy: <i>s = exp(R0)</i>, whereby <i>s</i> is the species richness <i>R0</i> the renyi index for <i>alpha=0</i>. The name of the output layer is composed of the basename + 
 richness.
 
 <h4>Shannon index</h4>
 
-<p>The Shannon (also called the Shannon-Weaver or Shannon-Wiener) 
-index is defined as 
+<p>The Shannon (also called the Shannon-Weaver or Shannon-Wiener) index is defined as <i>H = -sum(p_i x log(p_i))</i>, where <i>p_i</i> is the proportional abundance of species <i>i</i>. The function uses the natural logarithm (one can also use other bases for the log, but that is currently not implemented, and doesn't make a real difference). Note the Shannon index is a special case of the Renyi enthropy for <i>alpha = 2</i>. The name of the output layer is composed of the basename + shannon.
 
-<div class="code"><pre>H = -sum(p_i x log(p_i))</pre></div>
-
-where <i>p_i</i> is the proportional abundance of species <i>i</i>. 
-The r.biodiversity uses the natural logarithm (one can also use 
-other bases for the log, but that is currently not implemented, and 
-doesn't make a real difference). Note the Shannon index is a special 
-case of the Renyi enthropy for <i>alpha = 2<i>. The name of the 
-output layer is composed of the basename + shannon.
-
 <h4>Simpson (concentration) index</h4>
 
-<p>The Simpson's index is defined as 
+<p>The Simpson's index is defined as <i>D = sum p_i^2</i>. This is equivalent to <i>-1 * 1 / exp(R2)</i>, with <i>R2</i> the renyi index for <i>alpha=2</i>. With this index, 0 represents infinite diversity and 1, no diversity. The name of the output layer is composed of the basename + simpson.
 
-<div class="code"><pre>D = sum p_i^2</pre></div>. 
-
-This is equivalent to 
-
-<div class="code"><pre><pre>-1 * 1 / exp(R2)</pre></div>
-
-with <i>R2</i> the renyi index for <i>alpha=2</i>. With this index, 
-0 represents infinite diversity and 1, no diversity. The name of the 
-output layer is composed of the basename + simpson.
-
 <h4>Inverse Simpson index (Simpson's Reciprocal Index)</h4>
 
-<p>D obtains small values in datasets of high diversity and large 
-values in datasets of low diversity. This is counterintuitive 
-behavior for a diversity index. An alternative is the inverse 
-Simpson index, which is
+<p>D obtains small values in datasets of high diversity and large values in datasets of low diversity. This is counterintuitive behavior for a diversity index. An alternative is the inverse Simpson index, which is <i>ID = 1 / D)</i>. The index represents the probability that two individuals randomly selected from a sample will belong to different species. The value ranges between 0 and 1, but now, the greater the value, the greater the sample diversity. The name of the output layer is composed of the basename + invsimpson.
 
-<div class="code"><pre>ID = 1 / D)</pre></div>. 
-
-The index represents the probability that two individuals randomly 
-selected from a sample will belong to different species. The value 
-ranges between 0 and 1, but now, the greater the value, the greater 
-the sample diversity. The name of the output layer is composed of 
-the basename + invsimpson.
-
 <h4>Gini-Simpson index</h4>
 
-<p>An alternative way to overcome the problem of the 
-counter-intuitive nature of Simpson's Index is to use 
+<p>An alternative way to overcome the problem of the counter-intuitive nature of Simpson's Index is to use <i>1 - D)</i>. The lowest value of this index is 1 and represent a community containing only one species. The higher the value, the greater the diversity. The maximum value is the number of species in the sample. The name of the output layer is composed of the basename + ginisimpson.
 
-<div class="code"><pre>1 - D)</pre></div>. 
-
-The lowest value of this index is 1 and represent a community 
-containing only one species. The higher the value, the greater the 
-diversity. The maximum value is the number of species in the sample. 
-The name of the output layer is composed of the basename + 
-ginisimpson.
-
 <h2>NOTES</h2>
 
-<p>Note that if you are interested in the landscape diversity, you 
-should have a look at the <a href= 
-"https://grass.osgeo.org/grass70/manuals/addons/r.diversity.html"> 
-r.diversity</a> addon or the various related r.li.* addons (see 
-below). These functions requires one input layer and compute the 
-diversity using a moving window.
+<p>Note that if you are interested in the landscape diversity, you should have a look at the <a href= 
+"https://grass.osgeo.org/grass70/manuals/addons/r.diversity.html"> r.diversity</a> addon or the various related r.li.* addons (see below). These functions requires one input layer and compute the diversity using a moving window.
 
 <h2>EXAMPLES</h2>
 
-<p>Suppose we have five layers, each representing number of 
-individuals of a different species. To keep it simple, let's assume 
-individuals of all five species are homogeneous distributed, with 
-respectively 60, 10, 25, 1 and 4 individuals / raster cell densities.
+<p>Suppose we have five layers, each representing number of individuals of a different species. To keep it simple, let's assume individuals of all five species are homogeneous distributed, with respectively 60, 10, 25, 1 and 4 individuals / raster cell densities.
 
 <div class="code"><pre>
 r.mapcalc "spec1 = 60"
@@ -113,24 +46,19 @@
 r.mapcalc "spec5 = 4"
 </pre></div>
 
-Now we can calculate the renyi index for alpha is 0, 1 and 2 (this 
-will give you 1.61, 1.06 and 0.83 respectively)
+Now we can calculate the renyi index for alpha is 0, 1 and 2 (this will give you 1.61, 1.06 and 0.83 respectively)
 
 <div class="code"><pre>
 r.biodiversity in=spec1,spec2,spec3,spec4,spec5 out=renyi alpha=0,1,2
 </pre></div>
 
-You can also compute the species richness, shannon, simpson, inverse 
-simpson and gini-simpson indici
+<p>You can also compute the species richness, shannon, simpson, inverse simpson and gini-simpson indici
 
 <div class="code"><pre>
 r.biodiversity -s -h -d -p -g in=spec1,spec2,spec3,spec4,spec5 out=biodiversity
 </pre></div>
 
-The species richness you get should of course be 5. The shannon 
-index is the same as the renyi index with alpha=1 (1.06). The 
-simpson should be 0.43, and inverse simpson and gini-simpson will be 
-2.3 and 0.57 respectively.
+<p>The species richness you get should of course be 5. The shannon index is the same as the renyi index with alpha=1 (1.06). The simpson should be 0.43, and inverse simpson and gini-simpson will be 2.3 and 0.57 respectively.
 
 <h2>SEE ALSO</h2>
 
@@ -146,4 +74,4 @@
 <h2>AUTHOR</h2>
 Paulo van Breugel, paulo at ecodiv.org
 
-<p><i>Last changed: $Date$</i>
+<p><i>Last changed: $Date: 2015-09-11 19:24:14 +0200 (vr, 11 sep 2015) $</i>



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