Soil Profile Distances

D.E. Beaudette

2020-06-17

Introduction

Interpreting Dendrograms

Dendrograms are a convenient way of depicting pair-wise dissimilarity between objects, commonly associated with the topic of cluster analysis. This is a complex subject that is best left to experts and textbooks, so I won’t even attempt to cover it here. Unfortunately the interpretation of dendrograms is not very intuitive, especially when the source data are complex. In addition, pair-wise dissimilarity computed between soil profiles and visualized via dendrogram should not be confused with the use of dendrograms in the field of cladistics– where relation to a common ancestor is depicted.

An example is presented below that illustrates the relationship between dendrogram and dissimilarity as evaluated between objects with 2 variables. Essentially, the level at which branches merge (relative to the “root” of the tree) is related to their similarity. In the example below it is clear that (in terms of clay and rock fragment content) soils 4 and 5 are more similar to each other than to soil 2. In addition, soils 1 and 3 are more similar to each other than soils 4 and 5 are to soil 2. Recall that in this case pair-wise dissimilarity is based on the Euclidean distance between soils in terms of their clay content and rock fragment content. Therefore proximity in the scatter plot of frock frags vs. clay is directly related to our simple evaluation of “dissimilarity”. Inline-comments in the code below elaborate further.

## Dissimilarities :
##           1         2         3         4
## 2 13.038405                              
## 3 12.727922 20.099751                    
## 4 19.723083 10.049876 20.615528          
## 5 26.419690 16.124515 26.076810  6.708204
## 
## Metric :  euclidean 
## Number of objects : 5

A Soils Example

##          auburn dunstone sobrante
## auburn     0.00     0.67     1.00
## dunstone   0.67     0.00     0.94
## sobrante   1.00     0.94     0.00


##             auburn  dunstone  sobrante
## auburn   0.0000000 0.8461538 0.5205128
## dunstone 0.8461538 0.0000000 0.6333333
## sobrante 0.5205128 0.6333333 0.0000000


This document is based on aqp version 1.20.