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I am trying to cluster a biological population on the basis of morphological characters using UPGMA clustering method, but I am not sure which distance should I use- Mahalanobis or Euclidean. What are the benefits of using the two distances and when to use them in reference to biological population clustering using morphological traits.

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  • $\begingroup$ UPGMA aka between-group average linkage method does not require any specific sort of distance (albeit if a distance is metric one, there may arise issues of interpretation in somebody's eyes). So, the load of the decision what or which distance to prefer is entirely on you. You should consider standardizing first if your morphological traits are of different units. Mahalanobis distance is quite seldom used in clustering: you see, it would have been good if knew covariances in each cluster, - but you can't know them before clustering is done! $\endgroup$
    – ttnphns
    Sep 22 '14 at 18:39
  • $\begingroup$ thanks for the answer and I would also like to know whether bootstrapping is important in such clustering analysis of species using morphological traits. $\endgroup$ Sep 23 '14 at 6:36
  • $\begingroup$ lapse correction in my comment above. is metric one -> isn't metric one. $\endgroup$
    – ttnphns
    Sep 23 '14 at 9:36
  • $\begingroup$ The distance should be chosen so that it reflects what is a substantially meaningful concept of distance in your application. Sec 3.2 of arxiv.org/abs/1503.02059 may be helpful. $\endgroup$ Nov 29 '19 at 18:33
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The Mahalanobis distance takes into account the distribution of the existing points. This distribution affects whether or not a point is considered "close" in a particular dimension. If your points extend along a particular direction, say the x-axis for simplicity, then a reduced x-distance is used to determine if new points belong to the cluster.

As pointed out by ttnphns, you would need to compute the covariance matrix of the clusters as you construct the groups. With UPGMA this would be possible and may lead to interesting insights.

Can you not compare and contrast the results with both Mahalanobis and Euclidean metrics?

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  • $\begingroup$ Any chance you mean Manhattan instead of Mahalanobis? Mahalanobis distance is essentially the same as Euclidean, after a data transformation. Instead of using Mahalanobis distance, it may be beneficial to transform your data. $\endgroup$ Sep 23 '14 at 11:41

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