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How to Create a Dendrogram Using the UPGMA Algorithm for Free

A dendrogram is a diagram that shows the hierarchical clustering of data points based on their similarity or distance. It can be useful for visualizing the relationships between different groups or variables. One of the methods to construct a dendrogram is the UPGMA (Unweighted Pair Group Method with Arithmetic Mean) algorithm, which is a simple and widely used technique.

In this article, we will explain what the UPGMA algorithm is, how it works, and how you can use a free online tool called DendroUPGMA to create a dendrogram from your own data.

What is the UPGMA algorithm

The UPGMA algorithm is a type of agglomerative hierarchical clustering method, which means that it starts with each data point as a separate cluster and then merges them into larger clusters based on their similarity or distance. The algorithm follows these steps:

Calculate a similarity or distance matrix for all the data points. This matrix shows how similar or dissimilar each pair of data points is.

Find the pair of data points (or clusters) that have the highest similarity or lowest distance and merge them into a new cluster. The height of the branch that connects them in the dendrogram is proportional to their similarity or distance.

Update the similarity or distance matrix by replacing the rows and columns of the merged data points (or clusters) with a new row and column that represent the new cluster. The similarity or distance between the new cluster and any other data point (or cluster) is calculated as the arithmetic mean of the similarities or distances between the new cluster's constituents and the other data point (or cluster).

Repeat steps 2 and 3 until all the data points (or clusters) are merged into one single cluster.

The UPGMA algorithm assumes that the data points (or clusters) are equally weighted and that the distances are additive, meaning that the distance between two clusters is equal to the sum of the distances between their constituents. These assumptions may not hold true for some types of data, so it is important to check whether the UPGMA algorithm is appropriate for your data before using it.

How to use DendroUPGMA to create a dendrogram

DendroUPGMA is a web server that allows you to create a dendrogram using the UPGMA algorithm for free. You can access it at http://genomes.urv.cat/UPGMA/. To use it, you need to provide your data in one of these formats:

A set of variables (raw data) for each data point. For example, if you want to compare the codon usage between genes, you can provide the frequency of each codon for each gene. You can use either a fasta-like format or a one-line format for this option.

A similarity matrix that shows how similar each pair of data points is. For example, if you want to compare the genetic diversity between populations, you can provide a matrix of genetic distances or Fst values for each pair of populations.

A distance matrix that shows how dissimilar each pair of data points is. For example, if you want to compare the geographic distance between cities, you can provide a matrix of kilometers or miles for each pair of cities.

After uploading your data, you need to choose some options for your analysis, such as:

The similarity index or distance coefficient used to compare between the set of variables (if you chose option a). You can choose from Pearson correlation coefficient, Jaccard index, Dice coefficient, Euclidean distance, Manhattan distance, Mean square deviation, or Root mean square deviation.

The transformation of r to generate distance values (if you chose Pearson correlation coefficient as your similarity index).

The clustering method: UPGMA or WPGMA.

Whether you want to normalize (standardize) your input data (only available for distance coefficients).

Whether you want to generate bootstrap replicates to assess the confidence of your clustering.

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