Quantitative Vegetation
Analysis with Forest
Inventory Vegetation
1
Outline
Objective
Review of Data Structures
Forest inventory example dataset
Species Counts
Number of trees by species and plot
Species presence (counts/percentages)
Average number of trees per plot by species
Cumulative distribution of species occurrences
Frequency (histogram) of species occurrences
Total number of trees per plot
Number of different species
Merge plot-level tables to plt table
Merge species-level tables to one table
Species Basal Area
Basal area by species and plot
Total basal area by plot
Percent basal area by species and plot
2
Objective Of This Lesson
## Learn tools in R for quantitative analyses of forest inventory vegetation data.
These tools will help you get acquainted with your vegetation dataset and
prepare you for multivariate analyses of vegetation species and modeling
species distributions.
# Explore tree data.
# Summarize tree data to plot-level.
# Species abundance (Evenness)
- the total number of trees sampled, by species (by plot).
- the average number of trees sampled per plot.
- percent plots a species occurs on.
# Species richness (Diversity)
- the number of different species per plot.
- cumulative number of different species within sampled population.
# Graphically display tree data.
# Histograms - distributions of univariate tree data (binned into categories).
# Barplots - distributions of tree data by specified category.
3
Multivariate Statistics
## Packages and Links for R and multivariate statistics
R Package – vegan (Jari Oksanen)
Contains tools for analyzing ecological communities, including species analyses and
multivariate analyses.
• Diversity indices
• Species richness and abundance models
• Ordination
R Package – labdsv (Dave Roberts)
Includes tutorials and lab exercises for a course in quantitative analysis and multivariate
statistics in vegetation ecology
• Modeling species distributions
• Ordination techniques
• Cluster analysis
Link to package on CRAN website
http://cran.r-project.org/web/packages/vegan/index.html
This document explains diversity related methods in vegan.
http://cran.r-project.org/web/packages/vegan/vignettes/diversity-vegan.pdf
R Labs for Vegetation Ecologists - Tutorial using vegan package (Dave Roberts; Montana State University)
4
http://ecology.msu.montana.edu/labdsv/R/labs/
R Data Structures
# vector
group of single objects or elements
(all elements must be the same mode)
# factors
vector of values that are limited to a fixed set of values (categories)
# list
group of objects called components
(can be different modes and lengths)
# array
group of vectors with more than 1 dimension
(all elements must be the same mode)
format: array(data=NA, dim=c(dim1, dim2, ..)
# matrix
2-dimensional array (group of vectors with rows and columns)
(all elements must be the same mode).
format: matrix(data=NA, nrow=1, ncol=1, byrow=FALSE)
# data frame 2-dimensional list (group of vectors of the same length)
(can be different modes)
format: data.frame(row, col)
Images from: https://www.stat.auckland.ac.nz/~paul/ItDT/HTML/node64.html
5
Summarizing Data Frames
apply – applies a function to rows or columns of an array, matrix, or data frame (returns a
vector or array).
sapply – applies a function to each element of a list or vector (returns a vector or array).
lapply – similar to sapply, applies a function to each element of a list or vector (returns a list).
tapply – applies a function to a vector, separated into groups defined by a second vector or
list of vectors (returns an array).
by – similar to tapply, applies a function to vector or matrix, separated in to groups by a
second vector or list vectors (returns an array or list).
aggregate – applies a function to one or more vectors, separated into groups defined by a
second vector or list of vectors (returns a data frame).
Function
Input
Output
apply
sapply
lapply
tapply
by
aggregate
array/matrix/data frame
vector/list
vector/list
vector
data frame
data frame
vector/array
vector/array
list
array/matrix
array/list
data frame
6
Graphics in R
# Common plot parameters.
xlab/ylab
main
pch
col
xlim/ylim
cex <- 0.5
# x label / y label.
# main title of graph.
# symbol type (See below).
# color of symbol (See colors()).
# axis range in the following format – c(lowest, highest).
# Make the symbol half the size.
# Graphical parameters for device.
dev.new()
par()
par(mfrow=c(1,3))
par("mar")
# add new device (display) window.
# graphical parameters of device.
# display multiple plots to one device - c(1 row, 3 columns)
# number of lines in margin surrounding plot – c(bottom, left, top, right).
# Common plotting methods.
plot(x, y)
pairs(vars)
hist(vect)
boxplot(vect)
barplot
# Scatterplot – distribution of paired quantitative variables.
# Matrix of scatterplots of combinations of var.
# histogram – distribution of binned, quantitative vector values.
# boxplot – distribution of categorical variables.
# bar plot – distribution of quantitative data in categorical groups.
pch
7
Initialize R Environment
## Initialize R Environment
# Create a new folder named 'Outfolder' in working directory
if(!file.exists("Outfolder")){
dir.create("Outfolder") }
# Set working directory..
setwd("C:/Rworkshop")
# Set options
options(scipen=6)
# bias against scientific notation
# Load libraries
library(RODBC)
# ODBC database interface
8
Forest Inventory Data
## Read in data files
plt <- read.csv("PlotData/plt.csv", stringsAsFactors=FALSE)
cond <- read.csv("PlotData/cond.csv", stringsAsFactors=FALSE)
tree <- read.csv("PlotData/tree.csv", stringsAsFactors=FALSE)
ref <- read.csv("PlotData/ref_SPCD.csv", stringsAsFactors=FALSE)
## The plt table contains plot-level data, where there is 1 record (row) for each plot.
dim(plt)
head(plt)
## Total number of plots
## Display first six plot records.
## The cond table contains condition-level data, where there is 1 record (row) for each
## condition on a plot.
dim(cond)
head(cond)
## Total number of conditions
## Display first six cond records.
## The tree table contains tree-level data, where there is 1 record (row) for each tree on a plot.
dim(tree)
head(tree)
## Total number of trees
## Display first six tree records.
## Unique Identifiers
# CN:
Sequence number to identify unique plots (in plt table).
# PLT_CN: Sequence number to identify unique plots (in cond/tree table).
# CONDID: Identifies unique conditions within a plot.
# SUBP:
Identifies subplot number within a plot.
# TREE:
Identifies tree number within a plot.
9
Forest Inventory Data
## Tree variables of interest.
# STATUSCD
Status of tree - 1: Live; 2: Dead; 3: Removed; 0: Not in sample (remeasured)
# SPCD
Species code
# DIA
Diameter of tree (in inches).
# HT
Height of tree (in feet).
# BA
Basal area of tree (in sq. feet)
## Look at unique codes in STATUSCD and SPCD.
unique(tree$STATUSCD)
unique(tree$SPCD)
# Let's add the species names to the table.
# Merge species names to table using a reference table of species codes
# First, look at ref table.
ref
# Now, merge this table with the tree table using variable SPCD.
tree <- merge(tree, ref, by="SPCD")
head(tree)
unique(tree$SPNM)
## Unique species names in table.
unique(tree$SPCD, tree$SPNM) ## Unique species codes/names in table.
table(tree$SPNM)
## Number of records by species in table.
10
Data Exploration
# Attaching data frames (Make sure to detach).
attach(tree)
# Summary statistics.
summary(BA)
sapply(tree[,c("BA", "DIA", "HT")], summary)
# Boxplots.
boxplot(DIA~SPCD)
boxplot(BA~SPCD, xlab="Species", ylab="Basal area(sqft)",
main="Basal Area by Species")
# Scatterplots.
plot(DIA, BA)
abline(lm(BA~DIA))
# Add a regression line - (intercept, slope).
plot(DIA, HT, pch=20)
abline(lm(HT~DIA), col="red")
abline(1,1, col=4)
# Add regression line
# Add 1-1 reference line
pairs(tree[,c("BA", "DIA", "HT")])
help(pairs)
# Copy/Paste Examples code to R
pairs(tree[,c("BA", "DIA", "HT")], lower.panel=panel.smooth,
diag.panel=panel.hist)
11
Data Exploration
# Histograms.
par(mfrow=c(2,1))
hist(DIA, main="Frequency Histogram")
hist(DIA, prob=TRUE, main="Probability Histogram", ylim=c(0, 0.2))
lines(density(DIA, na.rm=TRUE))
par(mfrow=c(1,1))
# Barplots.
bpdat <- aggregate(BA, list(SPNM), sum)
bpdat
bpdat <- na.omit(aggregate(BA, list(SPNM), sum))
bpdat
names(bpdat) <- c("SPNM", "BA")
bpdat
barplot(bpdat$BA, names.arg=bpdat$SPNM, xlab="Species", ylab="Basal Area (sqft)",
main="Basal Area by Species", col="orange" )
# Dettach data frames
dettach(tree)
12
Species Counts
## How many trees does each plot have by species (plot-level)?
## Get the number of tree records by species and plot
# Create a pivot table of species by plotid, using table function.
spcnt <- table(tree$PLT_CN, tree$SPNM)
dim(spcnt)
head(spcnt)
# ..or using tapply
# Note: there are usually several different ways to manipulate the data
spcnt <- tapply(tree$PLT_CN, tree[,c("PLT_CN", "SPNM")], length)
head(spcnt)
spcnt[is.na(spcnt)] <- 0
# Change NA values to 0 values
head(spcnt)
is.data.frame(spcnt)
is.matrix(spcnt)
# Check results (for one plot)
spcnt["2377744010690",]
tree[tree$PLT_CN == 2377744010690,]
## Select row name of matrix
## Select column name of data frame
## Now, get percentage of tree records by species and plot
spcnt.perc <- round(prop.table(spcnt, margin=1) * 100)
head(spcnt)
head(spcnt.perc)
13
Species Counts
## How many plots does each species occur in (species-level)?
# Sum the columns of spcnt that are not equal to 0.
sppres <- apply(spcnt > 0, 2, sum)
sppres
is.vector(sppres)
## Sum of plots each species occurs in
## Display results
## Is this object a vector?
# Compare to the table of count of tree records by species.
table(tree$SPNM)
# Set the table count of tree records to an object and divide by sppres, rounding to a whole number.
# This gives you the average number of trees per plot by species.
sptrees <- table(tree$SPNM)
spavg <- round(sptrees / sppres)
spavg
sppres
sptrees
# Note: The average number of mahogany species per plot is 59.
#
Look at sppres, mahogany only occurs on one plot.
#
Look at spavg, there is 59 records of mahogany species.
# So, 59 trees occurred on one plot. You can see how summarizing in different ways gives you more
# information about the big picture.
14
Species Counts
## Let's look at this graphically.
## Display a barplot of species presence
# This shows the distribution of species for the plots sampled.. or the number of plots each species
occurs on.
barplot(sppres)
## Make axis names 50% smaller.
barplot(sppres, cex.names=0.5)
## Now, sort the counts.
barplot(sort(sppres), cex.names=0.5)
## Show only species with counts greater than 10.
barplot(sort(sppres[sppres > 10]))
## Change plot to show species counts in descending order.
help(sort)
barplot(sort(sppres[sppres > 10], decreasing=TRUE))
## Add labels
main <- "Distribution of Species Presence"
xlab <- "Species"
ylab <- "Number of plots"
barplot(sort(sppres[sppres > 10]), main=main, ylab=ylab, xlab=xlab, cex.names=0.7)
15
Species Counts
## What is the percentage of plots each species occur in?
totplots <- nrow(plt)
spperc <- sppres / totplots * 100
spperc
spperc <- round(spperc, 2)
sort(spperc)
barplot(sort(spperc), cex.names=0.5)
## Make axis names 50% smaller
## Show only species with counts greater than 10 and in descending order
barplot(sort(spperc[spperc > 4], decreasing=TRUE))
## Add labels
main <- "Percent species occurrence"
xlab <- "Species"
ylab <- "Percent plots"
barplot(sort(spperc[spperc > 4]), main=main, ylab=ylab, xlab=xlab, ylim=c(0,50))
## Let's look at species presence and percent species occurrence on same page
par(mfrow=c(2,1))
barplot(sort(sppres), main="Species Presence", ylab="Number of plots",
xlab=xlab, cex.names=0.5, cex.axis=0.75)
barplot(sort(spperc), main="Percent species occurrence", ylab="Percent plots",
xlab=xlab, cex.names=0.5, cex.axis=0.75)
# Note: Notice the scale is different.
16
Species Counts
## Display the average number of trees per plot by species
par(mfrow=c(1,1))
barplot(sort(spavg), cex.names=0.5)
## Add labels
main <- "Average species
xlab <- "Species"
ylab <- "Average species
barplot(sort(spavg[spavg
cex.names=0.75,
per plot"
per plot"
> 10]), main=main, ylab=ylab, xlab=xlab,
ylim=c(0,60))
# Note: Remember, mahogany was only sampled on one plot, and there were 59 trees on the plot.
# Add the number of plots as text to the bar plot.
# First, combine the spplot and sppres tables so the species labels match the species bars.
sp <- data.frame(cbind(spavg, sppres))
sp
sp <- sp[order(sp$spavg, decreasing=TRUE),]
sp
ylim <- c(0, 1.1* max(sp$spavg))
bp <- barplot(sp$spavg, main=main, ylab=ylab, xlab=xlab, cex.names=0.6,
ylim=ylim, names.arg=row.names(sp))
text(bp, y=sp$spavg, label=sp$sppres, pos=3, cex=0.8)
help(barplot)
## Look at barplot help file
17
Species Counts
## More ways to look at species distributions.
# Display the cumulative distribution of species occurrences..
# This shows you the rate species richness changes with the number of plots sampled.
plot(sort(sppres))
# Add labels
main <- "Cumulative Distribution of Species Occurrences"
xlab <- "Cumulative count of species"
ylab <- "Number of plots"
plot(sort(sppres), main=main, xlab=xlab, ylab=ylab)
# Note: 10 different species were found after sampling less than 20 plots.. but it took over 120
#
plots to sample 15 different species.
18
Species Counts
## More ways to look at species distributions.
# Display a histogram of species occurrences.
# This shows you the distribution of species presence for the plots sampled.
hist(sppres)
## Add labels
main <- "Distribution of species presence"
xlab <- "Species presence"
hist(sppres, main=main, xlab=xlab)
# Note: 10 species occurred in less than 20 plots, while 3 species occurred in over 100 plots.
# Display histogram with only 2 breaks
hist(sppres, main=main, xlab=xlab, breaks=2)
19
Species Counts
Total counts
# Display a histogram of the total number of trees per plot.
# This shows you the distribution of all trees for the plots sampled.
# Sum the rows of spcnt to get the total number of trees by plot.
totcnt <- apply(spcnt, 1, sum)
## All columns must be numeric
is.vector(totcnt)
# or
totcnt2 <- tapply(tree$PLT_CN, tree$PLT_CN, length)
class(totcnt2)
# or
totcnt3 <- aggregate(tree$PLT_CN, list(tree$PLT_CN), length)
class(totcnt3)
# Check results
head(spcnt)
head(totcnt)
# Display first 6 rows of spcnt
# Display first 6 elements of totcnt
## Show histogram with labels
main <- "Distribution of the total number of trees per plot"
xlab <- "Number of trees per plot"
hist(totcnt, main=main, xlab=xlab)
## Let's look at exactly how many plots had over 100 trees.
totcnt[totcnt > 100]
20
Species Counts
Number of different species (diversity).
# Display a histogram of the number of different species (diversity) per plot.
# This shows you the distribution of species diversity for the plots sampled.
# Sum the rows of spcnt that are greater than 0 to get the number of different species by plot.
numspp <- apply(spcnt > 0, 1, sum)
# Check results
head(spcnt)
head(numspp)
# Display first 6 rows of spcnt
# Display first 6 elements of numspp
## Display histogram with labels.
main <- "Distribution of Number of Different Species"
xlab <- "Number of different species per plot"
hist(numspp, main=main, xlab=xlab)
# Note: Over 60% of the plots have less than 3 different species on a plot
# I want to distinguish between 1, 2 and 3.. so, plot the count for each value (In new window).
dev.new()
barplot(table(numspp), main=main, xlab=xlab, ylab="Number of plots")
21
Species Counts
## Review of tables created using species counts.
## By plot
spcnt <- table(tree$PLT_CN, tree$SPNM)
head(spcnt)
# Number of trees by species and plot
totcnt <- tapply(tree$PLT_CN, tree$PLT_CN, length)
head(totcnt)
# Total number of trees by plot
numspp <- apply(spcnt > 0, 1, sum)
head(numspp)
# Number of different species by plot
## By species
sppres <- apply(spcnt > 0, 2, sum)
sppres
# Number of plots a species occurs in
sptrees <- table(tree$SPNM)
sptrees
# Number of trees by species
spavg <- round(sptrees / sppres)
spavg
# Average number of trees per plot by species
spperc <- round(sppres / totplots * 100, 2)
spperc
# Percent plots a species occurs on
22
Species Counts
## Let's merge the plot-level species data to plot table.
help(merge)
# Note: must be 2 data frames
## spcnt - Number of trees by species and plot.
head(spcnt)
dim(spcnt)
dim(plt)
## Merge spcnt matrix with plt table.
is.data.frame(plt)
is.data.frame(spcnt)
class(spcnt)
is.matrix(spcnt)
## Convert spcnt to a data frame.
spcnt.df <- data.frame(spcnt)
head(spcnt.df)
# Doesn't work
## Use as.data.frame.matrix to convert a matrix to a data frame.
spcnt.df <- as.data.frame.matrix(spcnt)
head(spcnt.df)
23
Species Counts
## Let's merge the plot-level species data to plot table (cont..)
## Merge spcnt to plt table.
plt2 <- merge(plt, spcnt.df, by.x="CN", by.y='row.names', all.x=TRUE)
head(plt2)
dim(plt2)
## Note: Using all.x=TRUE makes sure all plot records are retained.
## The default for merge is all.x=FALSE, where only plots with tree records would merge.
test <- merge(plt, spcnt.df, by.x="CN", by.y='row.names')
head(test)
dim(test)
dim(plt)
## Change NA values to 0 (No trees on plot).
spnames <- colnames(spcnt)
# Get species column names
plt2[,spnames][is.na(plt2[,spnames])] <- 0
head(plt2)
24
Species Counts
## Let's merge the plot-level species data to plot table (cont..)
## totcnt - Total number of trees by plot
head(totcnt)
is.vector(totcnt)
totcnt.df <- data.frame(totcnt)
plt2 <- merge(plt2, totcnt.df, by.x="CN", by.y="row.names", all.x=TRUE)
head(plt2)
dim(plt2)
# Change NA values to 0
plt2[,"totcnt"][is.na(plt2[,"totcnt"])] <- 0
head(plt2)
## numspp - Number of different species by plot
head(numspp)
is.vector(numspp)
numspp.df <- data.frame(numspp)
plt2 <- merge(plt2, numspp.df, by.x="CN", by.y="row.names", all.x=TRUE)
head(numspp)
# Change NA values to 0
plt2[,"numspp"][is.na(plt2[,"numspp"])] <- 0
head(plt2)
25
Species Counts
## Now let's merge the species-level data to 1 table named sptab.
sppres
sptrees
spavg
spperc
#
#
#
#
Number of plots a species occurs in
Number of trees by species
Average number of trees per plot by species
Percent plots a species occurs on
## Check if all objects are vectors.
lapply(list(sppres, sptrees, spavg, spperc), is.vector)
lapply(list(sppres, sptrees, spavg, spperc), class)
## Convert vectors to data frames using 'data.frame'.
sppres.df <- data.frame(sppres)
spperc.df <- data.frame(spperc)
sptab <- merge(sppres.df, spperc.df, by="row.names")
sptab
names(sptab)[names(sptab)=="Row.names"] <- "Species"
## Convert 1-dimensional tables to data frames using 'data.frame' as well.
sptrees.df <- data.frame(sptrees)
sptrees.df
names(sptrees.df) <- c("Species", "sptrees")
sptab <- merge(sptab, sptrees.df, by="Species")
spavg.df <- data.frame(spavg)
names(spavg.df) <- c("Species", "spavg")
sptab <- merge(sptab, spavg.df, by="Species")
sptab
26
Species Basal Area
To understand more about the distribution of species across your population, let's
conduct a similar analysis using basal area instead of counts. This will give us a better
idea of the size rather than quantity of the species.
## Basal area by species and plot
spba <- tapply(tree$BA, tree[,c("PLT_CN", "SPNM")], sum)
dim(spba)
head(spba)
spba[is.na(spba)] <- 0
spba <- round(spba, 3)
head(spba)
# Check results
spba["2377744010690",]
tree[tree$PLT_CN == 2377744010690,]
## Select row name of matrix
## Select column name of data frame
oneplot <- tree[tree$PLT_CN == 2377744010690,]
sum(oneplot$BA)
## Set to an object
## Sum BA column
27
Species Basal Area
## Total basal area by plot.
totba <- tapply(tree$BA, tree[,"PLT_CN"], sum)
totba
## Let's round the totba values to 2 decimal points.
totba <- round(totba, 2)
## Check the total basal area for oneplot
totba[names(totba) == unique(oneplot$PLT_CN)]
sum(oneplot$BA)
## Percent basal area by species and plot
spbaperc <- round((spba / as.vector(totba)) * 100, 2)
head(spbaperc)
# or
spbaperc2 <- round(prop.table(spba, margin=1) * 100, 2)
head(spbaperc2)
# Check results
spbaperc["2378381010690",]
spba["2378381010690",]
totba["2378381010690"]
28
Exercise 1
## 1.1 Calculate the total basal area by species, and set to object named spbatot. Show a bar
plot of the sorted values.
## 1.2 Calculate the average basal area per plot by species and set to object named spbaavg.
Hint: use the table created from 1.1 and the sppres table. Show a bar plot of the sorted
values with labels.
## 1.3 Compare the barplot of avg basal area per plot with the barplot of avg number of trees
per plot. Do not sort tables. Show on the same page and label plots. Hint: use
par(mfrow).
## 1.4 Which species has the highest basal area per plot?
## 1.5 Which species has the highest number of trees per plot?
## 1.6 Append the spba matrix to the plt data frame, naming the new object plt3. Change any
NA values in new columns to 0 values. Make sure all records of plt are included.
## 1.7 Append the totba vector to the plt3 data frame, keeping plt3 as the name. Change any
NA values in new column to 0 values. Make sure all records of plt3 are included.
## 1.8 Merge the species-level tables created in 1.1 and 1.2 (spbatot, spbaavg) to the sptab
table.
29