Project Description

The data for the 5x5 matrix was created by selecting 10 arbitrary polymorphic loci from the chimp alignment. The sequences of 5 different chimp populations were used: Mahale (ME), Bodongo, Gombe, Tai, and Mali (MW). The pairwise similarities were calculated from the 10 loci to create a similarlity and dissimilarity matrix. The data from the similarity matrix was used in this project to generate distance- based trees.

Preliminaries

# install.packages(ape)
# install.packages(phangorn)

library(ape)
library(phangorn)

Example 1: 3 Sequences

Similarity matrix

This matrix is based on the proportion of bases that are identical between sequence. This is often referred to as PID for Proportion Identical or Percentage Identical.

BLAST reports PID in its main output. PID is a very simple metric of similarity; more sophisticated measures are used in pratice.

Make a similarity matrix with the matrix() command. Note that I have to declare the number of rows

# Bad matrix 1
matrix(c(1.0, 0.5, 0.3,
         0.5, 1.0, 0.4,
         0.3, 0.4, 1.0))
##       [,1]
##  [1,]  1.0
##  [2,]  0.5
##  [3,]  0.3
##  [4,]  0.5
##  [5,]  1.0
##  [6,]  0.4
##  [7,]  0.3
##  [8,]  0.4
##  [9,]  1.0
# Good matrix, need to declare number of rows in order to product a matrix
matrix(c(1.0, 0.5, 0.3,
         0.5, 1.0, 0.4,
         0.3, 0.4, 1.0),
       nrow = 3)
##      [,1] [,2] [,3]
## [1,]  1.0  0.5  0.3
## [2,]  0.5  1.0  0.4
## [3,]  0.3  0.4  1.0

Store the matrix

my_sim_mat <- matrix(c(1.0, 0.5, 0.3,
                       0.5, 1.0, 0.4,
                       0.3, 0.4, 1.0),
                 nrow = 3,
                 byrow = T)
#byrow

Label the matrix with row.names() and colnames()

row.names(my_sim_mat) <- c("G","T","M")
colnames(my_sim_mat) <- c("G","T","M")

Disimilarity matrix

Similarity, disimilarity, and distance are all related. Most methods use distance, not similarity.

We can do vectorized math to recalculate the matrix

my_dist_mat <- 1-my_sim_mat

Convert to R’s distance format

as.dist() = convert to a distance matrix - - get rid of duplicate info, go from 3x3 to 2x2 -

my_dist_mat2 <- as.dist(my_dist_mat)

Build a neighbor-joining (nj) tree

Neighbor Joining is one of the most common ways to build a tree using molecular data that’s been converted to sequences; its one of the options within BLAST.

Build the tree with nj()

my_nj <- ape::nj(my_dist_mat2)

Plot the tree as an “unrooted” tree - clustering algorithms- put similar things together, related to classification

plot(my_nj, "unrooted")

Plot the tree as an “rooted” tree

plot(my_nj)

UPGMA/WPGMA are other algorithms that work with distance matrices. They are not commonly used now but are useful for teaching becaues they can easily be done by hand on small datasets.

my_upgma <- phangorn::upgma(my_dist_mat2)

Plot the UPGMA tree

plot(my_upgma)

#horizontal axis represents distance, no info given in vertical axis

Compare the rooted NJ and the UPGMA

par(mfrow = c(1,2))
plot(my_nj)
plot(my_upgma)

WPGMA tree

plot(wpgma(my_dist_mat2))

Minimum evolution tree

plot(fastme.ols(my_dist_mat2))

Example 2: 5 Sequences (hw)

Build the matrix.

Be sure to add the nrow = … statemetn.

five_sim_mat <- matrix(c(1.0,     0.0,  0.0,  0.0,  0.0,        
                         0.7,   1.0,    0.0,  0.0,  0.0,                
                         0.7,   0.6,    1.0,    0.0,  0.0,      
                         0.5,     0.4,  0.4,    1.0,    0.0,        
                         0.5,   0.4,    0.4,    0.8,    1.0), 
                       nrow = 5, 
                       byrow = T)

Name things

row.names(five_sim_mat) <- c("ME","B", "G", "T", "MW") ######
colnames(five_sim_mat)  <- c("ME","B", "G", "T", "MW") ######

Turn into a distnace matrix. This is 2 steps and requires the as.dist() command

five_dist_mat <- 1- five_sim_mat  ######
five_dist_mat2 <- as.dist(five_dist_mat) ######

Neighbor-Joining tree with nj()

five_nj <- nj(five_dist_mat2)

Plot unrooted NJ tree

plot(five_nj, "unrooted")

#not rooted,  MW, T form a clade

Plot rooted NJ tree

plot(five_nj)

Build UPGMA tree

five_upgma <- phangorn::upgma(five_dist_mat2)

Plot UPGMA tree

plot(five_upgma)

Compare rooted NJ and UPGMA plots

par(mfrow = c(1,2))
plot(five_nj)
plot(five_upgma)

Build WPGMA tree

plot(wpgma(five_dist_mat2))

Compare rooted WPGMA and UPGMA plots

par(mfrow = c(1,2))
plot(wpgma(five_dist_mat2))
plot(five_upgma)

Build Minimum evolution tree

plot(fastme.ols(five_dist_mat2))