title: R metaMDS ordination distances
body: <p>I have been doing some ordinations on a data set that I have of abundances of species at different sampling points.  I am using <code>metaMDS()</code> in vegan to do this.  With this function you can either:</p>
  <ol>
  <li>enter directly the community data  (sites in rows and species in columns) and specify what type of distance you want it to use (i.e. jaccard, brays curtis, euclidean, etc.) and the function calls <code>vegdist()</code> to do this.</li>
  </ol>
  <p>On the other hand you can</p>
  <ol start="2">
  <li>give the <code>metaMDS</code> a distance matrix you have already created, potentially using <code>vegdist()</code> (separate from the <code>metaMDS()</code> function).</li>
  </ol>
  <p>Where I am confused is that if I do the first strategy I get one answer, and when I do the second (and then putting that distance matrix into the <code>metaMDS()</code> function) I get a totally different answer (very different stress values, different ordination coordinates).  And when I call for the distance matrix created in the first strategy the distances are drastically different then what I get from just <code>vegdist()</code> function.  I read in passing, researching something else, that when <code>metaMDS()</code> calls the <code>vegdist()</code> function it is finding the distances in multi-dimensional space, while just using <code>vegdist()</code> is in a single dimension.</p>
  <p>Essentially I am asking is how does <code>metaMDS()</code> call and compute the distances with <code>vegdist()</code> (is it doing it in multi-dimensional space?) and how is that different than simply using <code>vegdist()</code> itself? Hopefully in understanding these differences I can discern which is the best and most appropriate method for my dataset.</p>
  <pre><code>    mrja&lt;-read.table(&quot;example.txt&quot;)
      jac&lt;-vegdist(mrja,method=&quot;jaccard&quot;)
      head(jac)
  [1] 0.7910448 0.8721461 0.7157360 0.9075908 0.9335038 0.9104478 ###first six distances
      
      ordjac1&lt;-metaMDS(jac,k=2)
      ordjac1$stress
  [1] 0.169781
      ordjac1
  
  Call:
  metaMDS(comm = jac, k = 2) 
  
  global Multidimensional Scaling using monoMDS
  
  Data:     jac 
  Distance: jaccard 
  
  Dimensions: 2 
  Stress:     0.169781 
  Stress type 1, weak ties
  No convergent solutions - best solution after 20 tries
  Scaling: centring, PC rotation 
  Species: scores missing
  
      ordjac2&lt;-metaMDS(mrja,k=2,distance=&quot;jaccard&quot;)
      ordjac2$stress
  [1] 0.2367037
      
      head(ordjac2$dist)
  [1] 5.259303e-06 2.812693e-05 1.879357e-02 1.216611e-01 3.913638e-02
  [6] 7.444730e-02   ###first six distances
  
      ordjac2
  
  Call:
  metaMDS(comm = mrja, distance = &quot;jaccard&quot;, k = 2) 
  
  global Multidimensional Scaling using monoMDS
  
  Data:     wisconsin(sqrt(mrja)) 
  Distance: jaccard 
  
  Dimensions: 2 
  Stress:     0.2367037 
  Stress type 1, weak ties
  No convergent solutions - best solution after 20 tries
  Scaling: centring, PC rotation, halfchange scaling 
  Species: expanded scores based on ‘wisconsin(sqrt(mrja))’
  </code></pre>