How to Calculate Bray-Curtis Dissimilarity in R

The Bray-Curtis dissimilarity is a measure of dissimilarity between two samples, used primarily in ecology and environmental sciences. It's especially useful for comparing community compositions, such as species abundances in different ecosystems.

The Bray-Curtis dissimilarity between two samples 𝐴 and 𝐵 is calculated as:

[Tex]D_{BC} = \frac{\sum |a_i - b_i|}{\sum (a_i + b_i)} [/Tex]

Where:

• 𝑎_𝑖 is the abundance of species or entity 𝑖 in sample 𝐴,
• 𝑏_𝑖 is the abundance of species or entity 𝑖 in sample 𝐵,
• The summation is performed over all species or entities present in either sample.

This dissimilarity measure ranges between 0 and 1, where 0 indicates complete similarity (i.e., the two samples have exactly the same species composition), and 1 indicates complete dissimilarity (i.e., the two samples share no species in common).

Calculate Bray-Curtis Dissimilarity in R

Calculating Bray-Curtis dissimilarity in R Programming Language can be done using various packages, such as vegan, ecodist, or even base R functions. Below, I'll demonstrate how to calculate Bray-Curtis dissimilarity using the vegan package, which is commonly used for ecological data analysis.

Step 1: Install and load the vegan package

R

install.packages("vegan")
library(vegan)

Step 2: Assuming that two data matrices mat1 and mat2, each representing a community composition (e.g., species abundances), then calculate Bray-Curtis dissimilarity between them using the vegdist function:

R

# Example data matrices (replace with your actual data)
mat1 <- matrix(c(5, 3, 0, 0, 2, 1), nrow = 2, byrow = TRUE)
mat2 <- matrix(c(4, 2, 1, 2, 3, 0), nrow = 2, byrow = TRUE)

# Calculate Bray-Curtis dissimilarity
bray_curtis_dist <- vegdist(rbind(mat1, mat2), method = "bray")

# Display the calculated dissimilarity matrix
print(bray_curtis_dist)

Output:

          1         2         3
2 0.6363636                    
3 0.2000000 0.4000000          
4 0.2307692 0.5000000 0.3333333

install.packages("vegan") installs the vegan package, which is used for ecological analysis. This step is required only if the package isn't already installed in your R environment.

• value 0.6363636 indicates the dissimilarity between the first and second set.
• set 1 and set 3, the dissimilarity is 0.2000000, suggesting they are more similar.
• Between set 2 and set 3, it's 0.4000000, showing they're somewhat dissimilar.
• Between set 1 and set 4, it's 0.2307692, indicating relatively low dissimilarity.
• Between set 2 and set 4, it's 0.5000000, suggesting moderate dissimilarity.
• Between set 3 and set 4, it's 0.3333333, indicating they're more similar compared to others.

R

# Load the vegan package
library(vegan)

# Create a data frame representing species abundances in different samples
data <- data.frame(
  sample = c("Sample1", "Sample2", "Sample3", "Sample4"),
  species1 = c(10, 5, 7, 8),
  species2 = c(0, 3, 6, 2),
  species3 = c(4, 1, 8, 6),
  species4 = c(2, 3, 2, 1)
)

# Remove the 'sample' column to get only the abundance data
abundance_data <- data[, -1]

# Calculate Bray-Curtis dissimilarity
bray_curtis_dist <- vegdist(abundance_data, method = "bray")

# Display the calculated dissimilarity matrix
print(bray_curtis_dist)

Output:

          1         2         3
2 0.4285714                    
3 0.3333333 0.3714286          
4 0.2121212 0.3793103 0.2000000

data.frame() creates a data frame with the specified column names and values. Here, each row represents a sample, and each column represents the abundance of a species in that sample.

• data[, -1] extracts all columns except the first (the 'sample' column), leaving only the abundance data for each species.
• vegdist(abundance_data, method = "bray") calculates the Bray-Curtis dissimilarity between the rows in the abundance data, treating each row as a different sample.

print(bray_curtis_dist) outputs the dissimilarity matrix, which shows the Bray-Curtis dissimilarity between each pair of samples.

Advantages of Bray-Curtis Dissimilarity

1. Sensitive to Compositional Differences: Bray-Curtis dissimilarity is effective in capturing differences in the relative abundance of species or other entities between samples. It considers not just the presence or absence of species, but also their proportions, which is useful when comparing ecological communities.
2. Robust to Differences in Sample Size: Unlike some other measures, Bray-Curtis dissimilarity is less affected by differences in sample size. It focuses on relative abundances, which makes it suitable for comparing samples of varying sizes.
3. Range from 0 to 1: The dissimilarity value ranges from 0 to 1, providing an intuitive interpretation: 0 means the samples are identical in composition, while 1 indicates they share no common elements.

Uses of Bray-Curtis Dissimilarity

1. Ecological Studies: To compare species composition among different ecosystems or habitats.
2. Environmental Monitoring: To track changes in ecosystem composition over time.
3. Clustering and Ordination: To group similar samples and visualize relationships among them.
4. Conservation Planning: To identify areas with unique or similar species compositions.
5. Paleoecology: To understand species changes in fossil records.
6. Bioinformatics: To compare microbial communities, such as gut or soil microbiomes.

Conclusion

Bray-Curtis dissimilarity helps measure how different two samples are by looking at their composition, like comparing the types and amounts of species in different communities. It's a useful tool in ecology and related fields because it's sensitive to relative abundances, robust to sample size differences, and less prone to outliers.

In summary, Bray-Curtis dissimilarity is a key measure for evaluating and comparing the composition of different samples, helping researchers make sense of complex data.