Numerical Ecology Chapter 9.Rpres

Numerical Ecology Chapter 9
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author: Joey Bernhardt
date: January 31 2016

Plan for today
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- PCA
- PCoA
- NMDS
- Correspondence analysis


Goals of ordination
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- represent the data along a reduced number of orthogonal axes, constructed in such a way that they represent, in decreasing order, the main trends of the data


Ordination
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- Imagine an n × p data set containing n objects and p variables

PCA
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- The first principal axis (or principal-component axis) of a PCA of this data set is the line that goes through the greatest dimension of the concentration ellipsoid describing this multinormal distribution

- objects are represented as points and variables are displayed as arrows

Prepare the data
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```{r}
# Load the required packages
# (vegan must be loaded after ade4 to avoid some conflicts)
library(ade4)
library(vegan)
library(gclus)
library(ape)

# Load additional functions
# (files must be in the working directory)
source("evplot.R")
source("cleanplot.pca.R")
source("PCA.R")
source("CA.R")
```
PCA on the environmental dataset
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```{r}
# Import the data from CSV files
# (files must be in the working directory)
spe <- read.csv("DoubsSpe.csv", row.names=1)
env <- read.csv("DoubsEnv.csv", row.names=1)
spa <- read.csv("DoubsSpa.csv", row.names=1)
# Remove empty site 8
spe <- spe[-8,]
env <- env[-8,]
spa <- spa[-8,]



# PCA based on a correlation matrix
# Argument scale=TRUE calls for a standardization of the variables
env.pca <- rda(env, scale=TRUE)
env.pca
summary(env.pca) # Default scaling 2
summary(env.pca, scaling=1)
```

Slide With Plot
========================================================

```{r, echo=FALSE}
plot(cars)
```