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Quantitative Vegetation Analysis

with Forest Inventory Vegetation

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Outline

Objective Review of Data StructuresForest inventory example datasetSpecies Counts

Number of trees by species and plotSpecies presence (counts/percentages)Average number of trees per plot by speciesCumulative distribution of species

occurrencesFrequency (histogram) of species

occurrencesTotal number of trees per plotNumber of different speciesMerge plot-level tables to plt tableMerge species-level tables to one table

Species Basal AreaBasal area by species and plotTotal basal area by plotPercent basal area by species and plot

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## 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.

Objective Of This Lesson

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## 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 websitehttp://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)http://ecology.msu.montana.edu/labdsv/R/labs/

Multivariate Statistics

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# 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)

R Data Structures

Images from: https://www.stat.auckland.ac.nz/~paul/ItDT/HTML/node64.html

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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 Outputapply array/matrix/data frame vector/arraysapply vector/list vector/arraylapply vector/list listtapply vector array/matrixby data frame array/listaggregate data frame data frame

Summarizing Data Frames

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# Common plot parameters.xlab/ylab # x label / y label.main # main title of graph.pch # symbol type (See below).col # color of symbol (See colors()).xlim/ylim # axis range in the following format – c(lowest, highest).cex <- 0.5 # Make the symbol half the size.

# Graphical parameters for device.dev.new() # add new device (display) window.par() # graphical parameters of device.par(mfrow=c(1,3)) # display multiple plots to one device - c(1 row, 3 columns)par("mar") # number of lines in margin surrounding plot – c(bottom, left, top, right).

# Common plotting methods.plot(x, y) # Scatterplot – distribution of paired quantitative variables.pairs(vars) # Matrix of scatterplots of combinations of var.hist(vect) # histogram – distribution of binned, quantitative vector values.boxplot(vect) # boxplot – distribution of categorical variables.barplot # bar plot – distribution of quantitative data in categorical groups.

Graphics in R

pch

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## Initialize R Environment

# Create a new folder named 'Outfolder' in working directoryif(!file.exists("Outfolder")){ dir.create("Outfolder") }

# Set working directory..setwd("C:/Rworkshop")

# Set optionsoptions(scipen=6) # bias against scientific notation

# Load librarieslibrary(RODBC) # ODBC database interface

Initialize R Environment

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## Read in data filesplt <- 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) ## Total number of plotshead(plt) ## 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) ## Total number of conditionshead(cond) ## 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) ## Total number of treeshead(tree) ## Display first six tree records.

Forest Inventory Data

## 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.

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## 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.

Forest Inventory Data

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# 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") # Add regression lineabline(1,1, col=4) # Add 1-1 reference line

pairs(tree[,c("BA", "DIA", "HT")])help(pairs) # Copy/Paste Examples code to Rpairs(tree[,c("BA", "DIA", "HT")], lower.panel=panel.smooth,

diag.panel=panel.hist)

Data Exploration

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# 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)bpdatbpdat <- na.omit(aggregate(BA, list(SPNM), sum))bpdatnames(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 framesdettach(tree)

Data Exploration

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## 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 dataspcnt <- 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",] ## Select row name of matrixtree[tree$PLT_CN == 2377744010690,] ## Select column name of data frame

## Now, get percentage of tree records by species and plotspcnt.perc <- round(prop.table(spcnt, margin=1) * 100)head(spcnt)head(spcnt.perc)

Species Counts

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## 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) ## Sum of plots each species occurs insppres ## Display resultsis.vector(sppres) ## 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

sppressptrees

# 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.

Species Counts

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## 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 labelsmain <- "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)

Species Counts

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## What is the percentage of plots each species occur in?

totplots <- nrow(plt)spperc <- sppres / totplots * 100sppercspperc <- 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 orderbarplot(sort(spperc[spperc > 4], decreasing=TRUE))

## Add labelsmain <- "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 pagepar(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.

Species Counts

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## Display the average number of trees per plot by speciespar(mfrow=c(1,1))barplot(sort(spavg), cex.names=0.5)

## Add labelsmain <- "Average species per plot"xlab <- "Species"ylab <- "Average species per plot"barplot(sort(spavg[spavg > 10]), main=main, ylab=ylab, xlab=xlab, cex.names=0.75, 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))spsp <- 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

Species Counts

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## 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 labelsmain <- "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.

Species Counts

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## 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 labelsmain <- "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 breakshist(sppres, main=main, xlab=xlab, breaks=2)

Species Counts

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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 numericis.vector(totcnt)# ortotcnt2 <- tapply(tree$PLT_CN, tree$PLT_CN, length)class(totcnt2)# ortotcnt3 <- aggregate(tree$PLT_CN, list(tree$PLT_CN), length)class(totcnt3)

# Check resultshead(spcnt) # Display first 6 rows of spcnthead(totcnt) # Display first 6 elements of totcnt

## Show histogram with labelsmain <- "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]

Species Counts

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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 resultshead(spcnt) # Display first 6 rows of spcnthead(numspp) # 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")

Species Counts

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## Review of tables created using species counts.

## By plotspcnt <- 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 speciessppres <- 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

Species Counts

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## 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) # Doesn't workhead(spcnt.df)

## Use as.data.frame.matrix to convert a matrix to a data frame.spcnt.df <- as.data.frame.matrix(spcnt)head(spcnt.df)

Species Counts

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## 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 namesplt2[,spnames][is.na(plt2[,spnames])] <- 0head(plt2)

Species Counts

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## Let's merge the plot-level species data to plot table (cont..)

## totcnt - Total number of trees by plothead(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 0plt2[,"totcnt"][is.na(plt2[,"totcnt"])] <- 0head(plt2)

## numspp - Number of different species by plothead(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 0plt2[,"numspp"][is.na(plt2[,"numspp"])] <- 0head(plt2)

Species Counts

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## Now let's merge the species-level data to 1 table named sptab.sppres # Number of plots a species occurs insptrees # Number of trees by speciesspavg # Average number of trees per plot by species spperc # 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")sptabnames(sptab)[names(sptab)=="Row.names"] <- "Species"

## Convert 1-dimensional tables to data frames using 'data.frame' as well.sptrees.df <- data.frame(sptrees)sptrees.dfnames(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

Species Counts

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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 plotspba <- tapply(tree$BA, tree[,c("PLT_CN", "SPNM")], sum)dim(spba)head(spba)spba[is.na(spba)] <- 0spba <- round(spba, 3)head(spba)

# Check resultsspba["2377744010690",] ## Select row name of matrixtree[tree$PLT_CN == 2377744010690,] ## Select column name of data frame

oneplot <- tree[tree$PLT_CN == 2377744010690,] ## Set to an objectsum(oneplot$BA) ## Sum BA column

Species Basal Area

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## 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 oneplottotba[names(totba) == unique(oneplot$PLT_CN)]sum(oneplot$BA)

## Percent basal area by species and plotspbaperc <- round((spba / as.vector(totba)) * 100, 2)head(spbaperc)# orspbaperc2 <- round(prop.table(spba, margin=1) * 100, 2)head(spbaperc2)

# Check resultsspbaperc["2378381010690",]spba["2378381010690",]totba["2378381010690"]

Species Basal Area

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## 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.

Exercise 1