Ecoinformatics: PCA, RDA, and more
Erica Ta
May 13, 2020
Plant Functional Traits in Hawai’i Volcanoes National Park
Evidence suggests that some non-native species are able to establish and spread in new environments because they exhibit characteristics (functional traits) that facilitate either successful competition with native plants or filling previously unfilled niches. Data collected by Jonathan Henn & Stephanie Yelenik measures plant functional traits as proxy indicators of competitive and establishment strategies to determine if these traits vary among native and invasive species and if their prevalance is dependent on environmental conditions (Henn & Yelenik 2020).
Hypothesis: I hypothesize that functional trait characteristics of plants are influenced by environmental conditions.
PCA - Statistical Analysis
Principal component analysis (PCA) was performed to quantify trait-based multivariate plant strategies based on environmental conditions. The PCA biplots show the main trade-offs across normalized functional traits and environmental factors based on principal axes of variation.
Data preparation
A unique id was created to each observation in the dataset.
Raw data included some NA values, so imputation was used to replace missing data with substituted values.
Before performing PCA, numeric values were transformed and normalized to improve data value distributions (make it closer to a normal distribution).
havo <- read.csv("HAVO_plant_cover_trait_and_environmental_data.csv", header = T) # Loading the .csv file into R1. Tidying data
## Add unique id and impute data
library(dplyr)
havo_uid <- mutate(havo,id = dplyr::row_number(Plot))
## Move unique id column to front
havo_new <- havo_uid %>% select(id, everything())2. Imputation
View(imphavo)
## Add unique id and impute data
library(dplyr)
havo_uid <- mutate(havo,id = dplyr::row_number(Plot))
## Move unique id column to front
havo_new <- havo_uid %>% select(id, everything())
## Run imputation for missing data in 'havo_new'
library(mice)
library(VIM)
#detach(package:tidyr)
havo_imp <- mice(havo_new, m = 3, maxit = 50, method = 'cart', seed = 500)
# Create imputation data table
imphavo <- complete(havo_imp,2)
#View(imphavo)
## Rename column headers for interpretability
colnames(imphavo)
imp.rename <- imphavo %>% rename(Evapotranspiration=ET.mm.,Radiation=Rad.w.m2.,Temperature=T.C., Elevation =ele.m., Precipitation=precip.mm., AvgLeafArea = AREA.cm2., AvgSpecificLeafArea = SLA.cm2.g., CarbonNitrogen = C.N, SeedMass = seedmass.g., SpeciesHeight = height.m., AvgWoodDensity = Wdensity, AvgLeafDensity = Ldens.g.cm3., MassLeafDryMatter = LDMC.g.g., OhiaCover = METPOLcov, VegCover = Cover)
# SLA.cm2.g = Mean specific leaf area
# SLAstd = Standard deviation of specific leaf area
# AREA.cm2 = Mean leaf area
# AREAstd = standard deviation of leaf area
# X:C = Mean %C content of leaves
# C.N. = Carbon:nitrogen of leaves
# X.N = Mean %N content of leaves
# seedmass.g. = seed mass of species from literature
# height.m = height of species from literature
# Wdensity = mean wood density
# Ldensstd = standard deviation of leaf density
# Ldens.g.cm3 = Mean leaf density
# LDMCstd = Standard deviation of leaf dry-matter content
# LDMC.g.g. = Mass of leaf dry-matter content
# METPOLcov = Cover of ohia in plot
# Cover = Cover of species in the plot indicated in other columns3. Normalizing data
View(newnum)
# Let's standardize
# remove non-numeric columns and redundant data columns
nums <- dplyr::select_if(imp.rename, is.numeric)
newnum <- nums[,-c(1:4,8,10,12,14,18:19, 21)]
library(dplyr)
library(vegan)
havonorm <- decostand(newnum, "normalize")PCA Results
PCA aims to represent features that contribute to variation of data along the ordination in reduced space.
Explained variance by eigenvalues
The amount of variance retained by each principal component is measured by eigenvalues. Eigenvalues measure the amount of variation retained by each principal component.
## Compute PCA with ncp = 3
library(ggplot2)
library(FactoMineR)
library(factoextra)
res.pca <-PCA(havonorm, ncp = 3, graph = FALSE)
## Eigenvalue
eig.val <- get_eigenvalue(res.pca)
eig.val
## Compute hierarchical clustering on principal components
res.hcpc <-HCPC(res.pca, graph = FALSE)
## Scree plot: the plot of eigenvalues ordered from largest to smallest. The number of component is determined at the point, beyond which the remaining eigenvalues are all relatively small and comparable size (Jollife 2002, Peres-Neto, Jackson, and Somers (2005)).
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0,50))
Fig 2. Scree plot of eigenvalues ordered from smallest to largest. Dimension 1 and Dimension 2 corresponds to the directions with the maximum amount of variation in the dataset at a total of 56.1% of variation explained by the first two eigenvalues.
Biplots of Sites and Variables Interpretation
Two plots were produced that show objects as points and variables as arrows. PCA Scaling 1 and PCA Scaling 2 illustrate the same analysis between two versions of shrinking and stretchingvariance of individual variables. The proportion of variance accounted by the first two axes is 0.561 or 56.1%. Elevation and Precipitation show the longest arrows as well as Temperature, Radiation, and MassDryLeafMatter that stretch beyond the circle’s radius, illustrating a higher contribution than average to the variability in this data set. Carbon:nitrogen content in leaves, temperature, and mass of dry leaves are grouped together and appear to be highly correlated to ohia cover and average leaf area. Radiation, evapotranspiration, and average wood density are closely grouped and appear to have some correlation to ohia cover and average leaf area. Vegetation cover and species height display shorter arrows, indicating lesser importance for the ordination of sites.
## PCA
library(ggplot2)
source("evplot.R")
source("hcoplot.R")
havo.pca <- rda(havonorm, scale = TRUE)
havo.pca
## Show objects as points and variables as arrows
source("cleanplot.pca.R")
cleanplot.pca(havo.pca, point = TRUE)
Fig 3. Results of the Principal Component Analysis applied to plant functional traits measured in Hawai’i Volcanoes National Park. PCA of plant observations (n = 247). Sites were separated based on their functional traits shown as red arrows. PCA Scaling 1 and PCA Scaling 2 illustrate the same analysis between two versions of shrinking and stretchingvariance of individual variables.
Variable contributions
library(corrplot)
var <- get_pca_var(res.pca)
corrplot(var$contrib, is.corr=FALSE)
Fig 4. The contributions of variables in accounting for the variability in a given principal component are expressed in percentage. Radiation, Temperature, Evapotranspiration, Mass of Dry Leaf Matter, Ohia Cover, Elevation, and Precipitation are correlated with PC1 (i.e. Dim.1) and PC2 (i.e., Dim.2) are the most important in explaining the variability in the data set.
#Contributions of variables to PCs
# The most important (or contributing) variables can be highlighted on the correlation plot as follow:
fviz_pca_var(res.pca, col.var = "contrib",
gradient.cols = c("#D55E00","#CC79A7","#0072B2"), repel = TRUE
)
Fig 5. The most contributing variables are highlighted on the correlation plot. Arrows and variables shown in blue contribute most to explaining variability like Radiation, Temperature, Pricipitation, and MassLeafDryMatter.
Cluster + Ordination Analysis
Cluster analysis was used to identify groups of similar observations in sites. The patterns and groups that emerge from cluster analysis may indicate or confirm results from the redundancy statistical analysis.
## FactoMineR
library(FactoMineR)
library(factoextra)
# Compute PCA with ncp = 3
res.pca <-PCA(havonorm, ncp = 3, graph = FALSE)
# Compute hierarchical clustering on principal components
res.hcpc <-HCPC(res.pca, graph = FALSE)
# Visualize the dendogram
fviz_dend(res.hcpc,
cex = 0.7, # Label size
palette = "jco", # Color palette see ?ggpubr::ggpar
rect = TRUE, rect_fill = TRUE, # Add rectangle around groups
rect_border = "jco", # Rectangle color
labels_track_height = 0.8 # Augment the room for labels
)
Fig 6. Final dendrogram illustrating boxes around the three selected groups.
fviz_cluster(res.hcpc,
repel = TRUE, # Avoid label overlapping
show.clust.cent = TRUE, # Show cluster centers
palette = "jco", # Color palette see ?ggpubr::ggpar
ggtheme = theme_minimal(),
main = "Factor map"
)
Fig 7. Factor map representing sites grouped within the 3 cluster solution.
spe.ch <- vegdist(havonorm, "euc")
spe.ch.ward <- hclust(spe.ch, method = "ward.D2")
dend <- as.dendrogram(spe.ch.ward)
heatmap(as.matrix(spe.ch), Rowv=dend, symm=TRUE, margin=c(3,3))
Fig 8. Dendrogram in a square matrix of colored pixels where color intensity represents similarity among sites.
# Additional code for other clustering visualizations
# env.w <- hclust(dist(scale(havonorm)), "ward.D2")
# env.w
# head(env.w)
#
# gr <- cutree(env.w, k = 4)
# gr1 <- levels(factor(gr))
#
# sit.sc1 <- scores(havo.pca, display = "wa",
# scaling =2)
#
#
# p <- plot(havo.pca, display = "wa", scaling = 2, type = "n", main = "PCA correlation with clusters")
#
# abline(v = 0, lty = "dotted")
# abline(h = 0, lty = "dotted")
#
# for (i in 1:length(gr1)) {points(sit.sc1[gr==i,], pch = (14 + i), cex = 2, col = i+1)}
#
# text(sit.sc1, row.names(1), cex = 0.7, pos = 3)
#
# ordicluster(p, env.w, col = "dark grey")
#
# spe.ch <- vegdist(havonorm, "euc")
#
# spe.ch.ward <- hclust(spe.ch, method = "ward.D2")
## Plot spe.ch.ward to see the dendrogram
# k <- 4
#
# spebc.ward.g <- cutree(spe.ch.ward, k)
#
# grw <- spebc.ward.g
#
# k <- length(levels(factor(grw)))
#
# for (i in 1:k) {points(havonorm[grw==i,1], havonorm[grw==i, 2], pch = i+20, cex = 3, col = i-1, bg = i+1)}
#
# text(havonorm, row.names(havonorm), cex = 0.8, col = "white", font =2)RDA - Statistical Analysis
A Redundancy Analysis (RDA) was performed to test the hypothesis that there is an influence between plant functional traits and environmental factors. The RDA method combines regression and principal component analysis and is a direct extension of regression analysis to model multivariate response data. RDA is a multivariate (meaning multiresponse) multiple linear regression followed by a PCA of the table of fitted values.
#RDA
library(ade4)
library(vegan)
library(ellipse)
library(FactoMineR)
#subset explanatory variables into new data frame
exp.havo <- select(filter(havonorm),c(Evapotranspiration:Precipitation))
resp.havo <- select(filter(havonorm),c(VegCover, OhiaCover, MassLeafDryMatter, AvgLeafArea, AvgLeafDensity, AvgWoodDensity, SpeciesHeight, SeedMass, CarbonNitrogen))
# Change column names for easier interpretability
colnames(exp.havo)## [1] "Evapotranspiration" "Radiation" "Temperature"
## [4] "Elevation" "Precipitation"#ET.mm = Evapotranspiration
#Rad.w.m2 = Radiation value for the plot
#T.C. = Temperature value for the plot
#ele.m. = Elevation value for the plot
#precip.mm = Precipitation value for the plot
colnames(resp.havo)## [1] "VegCover" "OhiaCover" "MassLeafDryMatter"
## [4] "AvgLeafArea" "AvgLeafDensity" "AvgWoodDensity"
## [7] "SpeciesHeight" "SeedMass" "CarbonNitrogen"# SLA.cm2.g = Mean specific leaf area
# SLAstd = Standard deviation of specific leaf area
# AREA.cm2 = Mean leaf area
# AREAstd = standard deviation of leaf area
# X:C = Mean %C content of leaves
# C.N. = Carbon:nitrogen of leaves
# X.N = Mean %N content of leaves
# seedmass.g. = seed mass of species from literature
# height.m = height of species from literature
# Wdensity = mean wood density
# Ldensstd = standard deviation of leaf density
# Ldens.g.cm3 = Mean leaf density
# LDMCstd = Standard deviation of leaf dry-matter content
# LDMC.g.g. = Mass of leaf dry-matter content
# METPOLcov = Cover of ohia in plot
# Cover = Cover of species in the plot indicated in other columns
#exp.rename <- exp.havo %>% rename(Evapotranspiration=ET.mm.,Radiation=Rad.w.m2.,Temperature=T.C., Elevation =ele.m., Precipitation=precip.mm.)
#resp.rename <- resp.havo %>% rename(AvgLeafArea = AREA.cm2., MeanLeafArea = SLA.cm2.g., CarbonNitrogen = C.N)
#Add unique ID
#havo_uid <- mutate(havonorm,id = dplyr::row_number(Plot))
## Move unique id column to front
havo_new <- havo_uid %>% select(id, everything())
# raw = explatory variables
# pred = response variables
# gwd_rda <- rda(pred_norm ~ ., raw_norm)
havo.rda <- rda(resp.havo ~ ., exp.havo)
summary(havo.rda)##
## Call:
## rda(formula = resp.havo ~ Evapotranspiration + Radiation + Temperature + Elevation + Precipitation, data = exp.havo)
##
## Partitioning of variance:
## Inertia Proportion
## Total 9.388e-05 1.0000
## Constrained 2.984e-05 0.3178
## Unconstrained 6.402e-05 0.6820
##
## Eigenvalues, and their contribution to the variance
##
## Importance of components:
## RDA1 RDA2 RDA3 PC1 PC2
## Eigenvalue 2.923e-05 5.146e-07 9.159e-08 4.326e-05 1.717e-05
## Proportion Explained 3.114e-01 5.482e-03 9.758e-04 4.609e-01 1.830e-01
## Cumulative Proportion 3.114e-01 3.169e-01 3.179e-01 7.789e-01 9.618e-01
## PC3 PC4
## Eigenvalue 3.120e-06 4.633e-07
## Proportion Explained 3.324e-02 4.936e-03
## Cumulative Proportion 9.951e-01 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## RDA1 RDA2 RDA3
## Eigenvalue 2.923e-05 5.146e-07 9.159e-08
## Proportion Explained 9.797e-01 1.725e-02 3.070e-03
## Cumulative Proportion 9.797e-01 9.969e-01 1.000e+00
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores: 0.3898278
##
##
## Species scores
##
## RDA1 RDA2 RDA3 PC1 PC2
## VegCover 0.000298 -1.289e-04 -4.778e-05 2.057e-05 -0.0003022
## OhiaCover 0.002423 7.985e-05 -6.475e-05 -1.757e-04 0.0004700
## MassLeafDryMatter -0.001857 -1.609e-04 8.135e-06 6.318e-04 -0.0003970
## AvgLeafArea 0.108018 3.434e-03 1.030e-02 -3.872e-02 0.1644995
## AvgLeafDensity -0.002792 -6.353e-05 -4.258e-04 5.579e-04 -0.0009430
## AvgWoodDensity -0.002754 4.877e-04 1.117e-04 -4.033e-04 -0.0006402
## SpeciesHeight 0.002828 -2.854e-02 1.702e-03 1.272e-02 0.0131924
## SeedMass 0.004464 1.976e-03 1.869e-03 -5.305e-03 0.0006064
## CarbonNitrogen -0.188679 1.581e-03 5.969e-03 2.614e-01 0.0237373
## PC3
## VegCover 4.186e-04
## OhiaCover 2.497e-04
## MassLeafDryMatter 2.288e-04
## AvgLeafArea -5.076e-03
## AvgLeafDensity -6.285e-04
## AvgWoodDensity -1.127e-03
## SpeciesHeight 7.075e-02
## SeedMass -4.376e-05
## CarbonNitrogen -4.197e-03
##
##
## Site scores (weighted sums of species scores)
##
## RDA1 RDA2 RDA3 PC1 PC2 PC3
## row1 -1.113e-02 5.769e-02 -0.217284 -1.027e-02 -0.0141971 -6.837e-03
## row2 -1.071e-02 5.981e-02 -0.204739 -1.361e-03 -0.0140300 -1.872e-02
## row3 8.853e-03 5.136e-02 -0.384130 -2.013e-02 -0.0206353 -1.388e-03
## row4 9.750e-04 5.460e-02 -0.343819 4.844e-04 -0.0250753 -2.607e-02
## row5 -6.472e-03 5.885e-02 -0.254298 7.059e-03 -0.0216954 -2.421e-02
## row6 -2.668e-03 5.693e-02 -0.264045 -7.481e-03 -0.0198376 -8.204e-03
## row7 -3.146e-02 6.897e-02 -0.001389 1.350e-02 -0.0064825 -1.309e-02
## row8 -3.223e-02 7.025e-02 0.034263 1.198e-02 -0.0017617 -1.688e-02
## row9 -4.353e-02 7.486e-02 0.121136 2.471e-02 -0.0046703 -2.030e-02
## row10 -1.142e-02 5.929e-02 -0.193602 -9.989e-03 -0.0039130 -4.887e-03
## row11 -5.482e-02 7.889e-02 0.236143 1.990e-02 0.0036688 -1.620e-03
## row12 -4.699e-02 7.627e-02 0.177256 1.727e-02 0.0004243 -1.322e-02
## row13 -3.831e-02 7.220e-02 0.088371 7.454e-03 0.0012393 -8.217e-03
## row14 -3.142e-02 6.851e-02 0.005647 5.085e-03 -0.0052428 -1.485e-02
## row15 -6.231e-02 8.698e-02 0.213732 3.266e-02 -0.0060417 -3.293e-02
## row16 -2.625e-02 7.042e-02 -0.147569 9.106e-03 -0.0153151 -3.291e-02
## row17 -4.066e-02 7.729e-02 0.001017 1.662e-02 -0.0073417 -3.154e-02
## row18 -5.648e-02 8.477e-02 0.163097 3.079e-02 -0.0025742 -3.129e-02
## row19 -4.211e-02 7.710e-02 -0.001039 1.874e-02 -0.0098036 -3.236e-02
## row20 -4.469e-02 7.897e-02 0.039636 1.567e-02 -0.0005541 -2.764e-02
## row21 -7.451e-02 9.308e-02 0.344174 3.433e-02 0.0040212 -1.742e-02
## row22 -8.945e-03 6.175e-02 -0.320672 -2.240e-02 -0.0134260 -1.552e-02
## row23 -6.321e-02 8.899e-02 0.252075 2.741e-02 0.0024810 -2.313e-02
## row24 -4.190e-02 7.747e-02 0.010310 1.178e-02 -0.0083554 -2.488e-02
## row25 3.194e-02 -7.707e-02 -0.304019 -1.602e-02 -0.0146276 2.128e-02
## row26 3.253e-02 -6.545e-02 -0.442095 -8.796e-03 -0.0289116 2.897e-02
## row27 3.469e-02 -6.301e-02 -0.463284 -7.835e-03 -0.0316760 3.192e-02
## row28 3.578e-02 -5.387e-02 -0.437438 -2.117e-03 -0.0336981 3.386e-02
## row29 2.997e-02 -6.201e-02 -0.512480 6.170e-04 -0.0411970 3.826e-02
## row30 3.906e-02 -6.436e-02 -0.275346 -1.128e-02 -0.0161428 1.253e-02
## row31 4.859e-02 -7.864e-02 -0.315405 -2.943e-02 -0.0072730 2.606e-02
## row32 2.512e-02 -6.222e-02 -0.290462 -4.728e-04 -0.0244138 7.146e-03
## row33 2.798e-02 -7.267e-02 -0.359240 -6.737e-03 -0.0258705 1.622e-02
## row34 3.036e-02 -6.668e-02 -0.405749 -1.026e-02 -0.0271088 7.927e-03
## row35 4.525e-02 -9.149e-02 -0.358796 -2.784e-02 -0.0111797 4.649e-02
## row36 3.330e-02 -5.915e-02 -0.172694 -5.110e-03 -0.0118526 1.067e-02
## row37 4.129e-02 -8.371e-02 -0.397039 -2.422e-02 -0.0172350 3.065e-02
## row38 3.210e-02 -3.926e-02 -0.185982 -1.452e-02 -0.0099855 1.180e-02
## row39 3.199e-02 -3.015e-02 -0.169344 -4.767e-03 -0.0153581 2.284e-03
## row40 5.285e-02 -3.654e-02 -0.139125 -2.913e-02 0.0026634 1.900e-02
## row41 2.714e-02 -3.207e-02 -0.257613 -1.382e-03 -0.0247217 1.420e-03
## row42 1.634e-02 -2.426e-02 0.275712 1.943e-03 0.0165197 1.675e-02
## row43 4.848e-02 -3.871e-02 -0.430309 -2.543e-02 -0.0228224 3.978e-04
## row44 2.475e-02 7.031e-02 -0.086061 -6.549e-03 -0.0019488 -3.639e-02
## row45 3.819e-02 7.683e-02 -0.019730 -5.544e-03 0.0039527 -2.390e-02
## row46 3.126e-02 8.907e-02 0.203442 5.948e-03 0.0140720 -2.609e-02
## row47 8.185e-03 9.021e-02 0.292422 4.063e-03 0.0245702 -3.677e-02
## row48 2.809e-02 8.445e-02 0.145546 4.304e-03 0.0088619 -4.557e-02
## row49 3.771e-02 6.088e-02 -0.269931 -2.043e-02 -0.0080596 -3.108e-02
## row50 3.791e-02 9.579e-02 0.324343 7.794e-04 0.0251420 -4.959e-02
## row51 3.334e-02 8.450e-02 0.129756 -3.434e-03 0.0125997 -4.944e-02
## row52 -5.831e-03 -4.666e-02 -0.211492 -1.175e-02 -0.0080090 2.994e-03
## row53 -1.045e-02 -4.727e-02 -0.163449 -6.293e-03 -0.0104176 2.320e-02
## row54 -2.590e-02 -3.822e-02 0.017115 -9.676e-04 -0.0013364 1.085e-02
## row55 -1.263e-02 -2.876e-02 -0.048025 -1.439e-03 -0.0014807 2.477e-03
## row56 7.766e-03 -4.267e-02 -0.300383 -2.415e-02 -0.0113187 1.460e-02
## row57 3.393e-02 -3.545e-02 -0.480506 -2.767e-02 -0.0184550 9.110e-03
## row58 3.332e-02 -3.129e-02 -0.390149 -2.703e-02 -0.0111703 9.019e-03
## row59 2.492e-02 -2.627e-02 -0.343338 -1.533e-02 -0.0148484 8.096e-03
## row60 4.072e-03 -4.256e-02 -0.274752 -1.914e-02 -0.0132333 9.769e-03
## row61 -6.795e-03 -3.367e-02 -0.089568 -1.176e-02 0.0024839 1.210e-02
## row62 -7.917e-03 -3.652e-02 -0.035937 -1.214e-02 0.0078669 1.196e-02
## row63 1.709e-02 -5.410e-02 -0.381977 -3.664e-02 -0.0071002 1.457e-02
## row64 -1.406e-02 -4.489e-02 -0.126578 -5.219e-03 -0.0087254 1.310e-02
## row65 -3.159e-02 -3.479e-02 0.044566 1.008e-02 -0.0038271 9.569e-03
## row66 -9.991e-03 -3.051e-02 -0.040708 -7.743e-03 0.0029097 9.064e-03
## row67 5.236e-03 -4.152e-02 -0.137663 -2.721e-02 0.0115151 1.804e-02
## row68 1.673e-03 -5.211e-02 -0.284026 -2.585e-02 -0.0069451 1.407e-02
## row69 -1.096e-02 -4.568e-02 -0.131607 -1.488e-02 -0.0016797 1.240e-02
## row70 -4.558e-04 -5.033e-02 -0.207527 -2.582e-02 -0.0005494 1.400e-02
## row71 -1.179e-02 -4.347e-02 -0.117892 -1.134e-02 -0.0002250 3.182e-03
## row72 -7.580e-03 -4.347e-02 -0.151726 -1.009e-02 -0.0036880 8.743e-04
## row73 -1.767e-02 -4.488e-02 -0.064459 -1.825e-02 0.0037261 3.281e-02
## row74 -1.084e-02 -4.620e-02 -0.099179 -2.037e-02 0.0021325 1.841e-02
## row75 -3.367e-02 -3.480e-02 0.120261 -5.976e-05 0.0084572 1.937e-02
## row76 -1.304e-02 -4.356e-02 -0.119181 -1.439e-02 -0.0030479 1.887e-02
## row77 5.781e-02 7.387e-02 0.113600 -2.591e-02 0.0250502 -2.350e-02
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## row106 -6.355e-02 1.643e-02 0.232263 3.254e-02 -0.0022110 -1.643e-02
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## row121 8.337e-03 5.476e-02 -0.286377 -2.746e-02 -0.0026319 -2.860e-02
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## row160 -2.838e-02 -1.068e-01 0.445885 4.058e-02 0.0094187 4.644e-02
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## row163 2.977e-02 -4.803e-02 -0.459538 -4.133e-02 -0.0090915 9.427e-03
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## row171 4.649e-02 -3.536e-02 -0.435044 -3.011e-02 -0.0159959 6.917e-03
## row172 2.520e-02 -3.905e-02 -0.247711 -3.435e-02 -0.0014549 1.192e-02
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## row175 2.442e-02 -5.022e-02 -0.446842 -4.127e-02 -0.0083211 1.613e-02
## row176 2.196e-02 -5.545e-02 -0.357712 -4.450e-02 -0.0009386 1.548e-02
## row177 1.468e-02 -5.307e-02 -0.279910 -3.899e-02 0.0020324 1.463e-02
## row178 2.531e-02 -5.279e-02 -0.369583 -3.960e-02 -0.0023542 3.595e-03
## row179 2.579e-02 -3.850e-02 -0.335380 -1.429e-02 -0.0173329 1.776e-02
## row180 1.256e-02 -5.986e-02 -0.379108 -4.326e-02 -0.0057477 2.322e-02
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## row182 4.807e-02 5.693e-02 0.943191 2.873e-03 0.0750569 -1.043e-02
## row183 3.470e-02 5.603e-02 0.909102 1.505e-02 0.0641494 -8.981e-03
## row184 3.847e-02 4.680e-02 0.649104 1.406e-02 0.0434461 -5.142e-04
## row185 6.006e-02 8.053e-02 1.251880 7.850e-03 0.0959383 -4.873e-03
## row186 5.448e-02 9.177e-02 1.655917 1.059e-02 0.1250584 -3.411e-02
## row187 4.673e-02 3.916e-02 0.886628 -7.220e-03 0.0753306 -1.271e-02
## row188 2.878e-02 3.904e-02 0.693402 9.265e-03 0.0489733 -2.921e-02
## row189 1.246e-02 7.968e-02 0.129266 -2.004e-02 0.0214125 -3.034e-02
## row190 4.389e-02 8.836e-02 0.170652 -3.062e-03 0.0170825 -2.075e-02
## row191 2.166e-02 6.636e-02 -0.154763 -1.137e-02 -0.0019999 -2.607e-02
## row192 3.554e-02 8.302e-02 0.120385 -1.959e-02 0.0258112 -3.214e-02
## row193 1.145e-02 7.702e-02 0.046259 1.997e-03 0.0061268 -3.082e-02
## row194 3.423e-03 9.717e-02 0.456196 -5.545e-03 0.0375990 -3.974e-02
## row195 -7.498e-03 3.438e-02 -0.078171 -1.674e-02 0.0017848 -1.786e-02
## row196 -3.051e-02 4.557e-02 0.100333 9.469e-03 0.0049264 -2.106e-02
## row197 -2.275e-02 3.911e-02 0.009330 -3.114e-04 0.0047036 -2.041e-02
## row198 8.259e-03 3.028e-02 -0.193466 -3.098e-02 0.0102093 -1.280e-02
## row199 -1.448e-02 3.565e-02 -0.032716 -1.764e-02 0.0081523 -9.585e-03
## row200 4.695e-02 4.339e-02 -0.712809 -1.233e-02 -0.0485652 2.106e-02
## row201 3.600e-02 4.772e-02 -0.601074 -2.386e-02 -0.0304225 1.256e-03
## row202 4.655e-02 4.412e-02 -0.681424 -3.278e-02 -0.0308828 1.062e-02
## row203 3.183e-02 6.032e-02 -0.391793 1.298e-03 -0.0312930 -1.335e-02
## row204 -4.756e-03 6.256e-02 -0.328259 1.105e-02 -0.0324476 -2.699e-02
## row205 1.552e-02 5.589e-02 -0.479777 -7.714e-03 -0.0327969 -1.699e-02
## row206 4.589e-02 1.735e-02 -0.167630 -1.196e-02 -0.0047770 2.456e-04
## row207 1.983e-02 5.802e-03 -0.154078 -1.152e-02 -0.0023228 -7.226e-03
## row208 -7.373e-03 1.955e-02 0.145921 1.288e-02 0.0066630 -1.244e-02
## row209 -1.560e-03 1.726e-02 0.053569 1.145e-02 0.0001590 -9.804e-03
## row210 3.724e-02 1.448e-02 -0.241623 -8.158e-04 -0.0180134 8.048e-03
## row211 1.480e-03 1.594e-02 -0.010563 2.167e-02 -0.0152588 -2.211e-02
## row212 4.803e-02 7.935e-03 -0.114542 -2.611e-02 0.0073934 -9.375e-03
## row213 -2.778e-02 3.030e-02 0.492978 3.977e-02 0.0147721 -1.280e-02
## row214 3.668e-02 2.013e-02 0.207228 -1.446e-02 0.0258852 -3.338e-03
## row215 1.023e-02 -2.836e-03 -0.334698 7.177e-03 -0.0321177 -1.344e-02
## row216 -4.007e-05 1.110e-02 -0.148355 1.949e-02 -0.0249792 -1.659e-02
## row217 5.478e-02 -1.595e-02 0.401371 -1.181e-02 0.0405853 1.489e-02
## row218 6.444e-02 7.812e-03 0.745208 -1.039e-02 0.0667752 1.211e-02
## row219 6.401e-02 4.583e-03 0.553238 -6.951e-03 0.0487256 1.847e-02
## row220 7.894e-02 3.408e-02 1.111970 -8.873e-03 0.0949576 1.482e-02
## row221 -4.545e-03 5.135e-02 -0.214528 -1.081e-02 -0.0086589 -2.872e-02
## row222 -2.863e-02 6.094e-02 0.003372 1.304e-02 -0.0091734 -1.099e-02
## row223 -1.172e-03 4.733e-02 -0.283304 -2.346e-02 -0.0108890 -1.745e-02
## row224 -1.394e-02 5.413e-02 -0.179531 -6.840e-05 -0.0127994 -2.201e-02
## row225 1.981e-03 4.828e-02 -0.299173 -2.046e-02 -0.0086030 -1.530e-02
## row226 -2.562e-02 5.770e-02 -0.069144 2.689e-03 -0.0040201 -2.042e-02
## row227 3.354e-04 4.988e-02 -0.241544 -1.657e-02 -0.0104974 -1.824e-02
## row228 -2.323e-02 6.023e-02 -0.025675 3.641e-03 -0.0050878 -2.373e-02
## row229 -1.768e-02 5.525e-02 -0.145725 -2.471e-03 -0.0086283 -2.190e-02
## row230 -7.557e-03 4.956e-02 -0.240890 -1.780e-02 -0.0025183 -1.473e-02
## row231 -6.726e-02 7.531e-02 0.327696 3.592e-02 0.0033783 -3.239e-02
## row232 -1.037e-02 5.196e-02 -0.188725 -1.105e-02 -0.0059362 -2.587e-02
## row233 -2.038e-02 5.428e-02 -0.135978 1.316e-03 -0.0094241 -3.393e-02
## row234 -1.976e-02 5.365e-02 -0.131799 -1.700e-02 -0.0021748 -3.863e-03
## row235 -1.640e-02 5.460e-02 -0.119499 -1.451e-02 -0.0030063 -1.526e-02
## row236 -2.545e-02 5.825e-02 -0.044393 -6.807e-03 -0.0002749 -9.704e-03
## row237 5.323e-02 -1.345e-01 -0.061328 -5.832e-02 0.0297751 5.607e-02
## row238 4.322e-02 -1.475e-01 -0.204724 -4.862e-02 0.0098732 6.695e-02
## row239 5.272e-02 -1.399e-01 -0.083512 -6.123e-02 0.0290001 5.807e-02
## row240 -7.939e-03 5.210e-02 -0.137594 1.795e-02 -0.0218323 -3.057e-02
## row241 6.405e-03 4.455e-02 -0.324872 1.359e-02 -0.0349388 -3.160e-02
## row242 2.765e-02 3.205e-02 -0.595267 -4.182e-03 -0.0457384 -2.038e-02
## row243 3.995e-03 3.704e-02 -0.388104 9.090e-04 -0.0306663 -1.708e-02
## row244 9.444e-03 4.150e-02 -0.377112 9.624e-03 -0.0368117 -2.255e-02
## row245 1.733e-02 4.483e-02 -0.355259 1.214e-03 -0.0293972 -3.539e-02
## row246 -2.023e-02 4.765e-02 -0.160542 2.550e-02 -0.0277718 -2.291e-02
## row247 -1.139e-03 4.014e-02 -0.322354 7.105e-03 -0.0291601 -1.399e-02
##
##
## Site constraints (linear combinations of constraining variables)
##
## RDA1 RDA2 RDA3 PC1 PC2 PC3
## row1 -0.018675 0.0432154 4.169e-02 -1.027e-02 -0.0141971 -6.837e-03
## row2 -0.008122 0.0168415 -1.643e-02 -1.361e-03 -0.0140300 -1.872e-02
## row3 -0.008077 0.0513084 3.427e-02 -2.013e-02 -0.0206353 -1.388e-03
## row4 0.008845 -0.0030934 -2.904e-02 4.844e-04 -0.0250753 -2.607e-02
## row5 0.007858 0.0054859 -3.480e-02 7.059e-03 -0.0216954 -2.421e-02
## row6 -0.005457 0.0411797 4.524e-02 -7.481e-03 -0.0198376 -8.204e-03
## row7 -0.014254 0.0392710 -2.802e-02 1.350e-02 -0.0064825 -1.309e-02
## row8 -0.018038 0.0296239 -3.922e-02 1.198e-02 -0.0017617 -1.688e-02
## row9 -0.014084 0.0280362 -1.586e-02 2.471e-02 -0.0046703 -2.030e-02
## row10 -0.021573 0.0465400 -6.793e-02 -9.989e-03 -0.0039130 -4.887e-03
## row11 -0.033341 0.0752927 2.834e-02 1.990e-02 0.0036688 -1.620e-03
## row12 -0.027464 0.0447620 3.408e-02 1.727e-02 0.0004243 -1.322e-02
## row13 -0.030159 0.0516863 1.146e-02 7.454e-03 0.0012393 -8.217e-03
## row14 -0.024051 0.0331949 3.056e-02 5.085e-03 -0.0052428 -1.485e-02
## row15 -0.023376 0.0114845 4.059e-02 3.266e-02 -0.0060417 -3.293e-02
## row16 -0.011333 -0.0050299 -1.730e-02 9.106e-03 -0.0153151 -3.291e-02
## row17 -0.019504 0.0037231 -2.948e-02 1.662e-02 -0.0073417 -3.154e-02
## row18 -0.020642 0.0120118 -3.996e-02 3.079e-02 -0.0025742 -3.129e-02
## row19 -0.017857 0.0024526 -1.688e-02 1.874e-02 -0.0098036 -3.236e-02
## row20 -0.026550 0.0130206 -6.944e-02 1.567e-02 -0.0005541 -2.764e-02
## row21 -0.036661 0.0531533 2.754e-02 3.433e-02 0.0040212 -1.742e-02
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## row223 -0.024458 0.0041795 4.034e-02 -2.346e-02 -0.0108890 -1.745e-02
## row224 -0.010201 0.0026773 -1.699e-02 -6.840e-05 -0.0127994 -2.201e-02
## row225 -0.018573 0.0100299 -2.922e-02 -2.046e-02 -0.0086030 -1.530e-02
## row226 -0.021252 0.0078921 -4.014e-02 2.689e-03 -0.0040201 -2.042e-02
## row227 -0.015261 0.0056683 2.403e-02 -1.657e-02 -0.0104974 -1.824e-02
## row228 -0.017448 0.0030688 1.222e-02 3.641e-03 -0.0050878 -2.373e-02
## row229 -0.017833 0.0026182 -1.687e-02 -2.471e-03 -0.0086283 -2.190e-02
## row230 -0.026829 0.0111421 -6.953e-02 -1.780e-02 -0.0025183 -1.473e-02
## row231 -0.027290 -0.0024592 2.903e-03 3.592e-02 0.0033783 -3.239e-02
## row232 -0.020945 -0.0120214 -2.403e-02 -1.105e-02 -0.0059362 -2.587e-02
## row233 -0.015909 -0.0272833 -2.388e-02 1.316e-03 -0.0094241 -3.393e-02
## row234 -0.038313 0.0421391 2.714e-02 -1.700e-02 -0.0021748 -3.863e-03
## row235 -0.031821 0.0155239 3.305e-02 -1.451e-02 -0.0030063 -1.526e-02
## row236 -0.032974 0.0328406 1.076e-02 -6.807e-03 -0.0002749 -9.704e-03
## row237 -0.021625 -0.0140166 -2.937e-03 -5.832e-02 0.0297751 5.607e-02
## row238 -0.015159 0.0063646 2.406e-02 -4.862e-02 0.0098732 6.695e-02
## row239 -0.025222 -0.0145869 6.712e-03 -6.123e-02 0.0290001 5.807e-02
## row240 0.018791 -0.0143630 6.467e-03 1.795e-02 -0.0218323 -3.057e-02
## row241 0.031917 -0.0212251 1.894e-02 1.359e-02 -0.0349388 -3.160e-02
## row242 0.036009 -0.0049024 2.298e-02 -4.182e-03 -0.0457384 -2.038e-02
## row243 0.013824 0.0046113 -3.997e-05 9.090e-04 -0.0306663 -1.708e-02
## row244 0.030912 -0.0018057 2.004e-02 9.624e-03 -0.0368117 -2.255e-02
## row245 0.027328 -0.0332024 1.773e-02 1.214e-03 -0.0293972 -3.539e-02
## row246 0.016644 0.0026650 -3.000e-03 2.550e-02 -0.0277718 -2.291e-02
## row247 0.015243 0.0156239 -2.859e-03 7.105e-03 -0.0291601 -1.399e-02
##
##
## Biplot scores for constraining variables
##
## RDA1 RDA2 RDA3 PC1 PC2 PC3
## Evapotranspiration -0.86705 0.03230 0.09834 0 0 0
## Radiation -0.93307 -0.01847 0.19877 0 0 0
## Temperature -0.98375 0.11172 -0.06449 0 0 0
## Elevation 0.08915 -0.38505 0.48954 0 0 0
## Precipitation 0.29443 0.23064 -0.44333 0 0 0R2adj <- RsquareAdj(havo.rda)$adj.r.squared
print(R2adj)## [1] 0.3036926#rda.ev <- havo.rda$CA$eigRDA Interpretation
The numerical output shows that the first two canonical axes explain together 31.6% of the total variance of the data. The triplot shows that Temperature, Evapotranspiration, and Radiation highly contribute to the dispersion of the sites along the first axis. Carbon to nitrogen leaf content is shown to be highly correlated with Temperature, Evapotranspiration, and Radiation. Although exhibiting shorter arrows, Species Height is shown to be correlated with Elevation as well as Average Leaf Area is correlated with Precipitation.
# Plot RDA triplot
gwd.sc <- scores(havo.rda, choices = 1:2, scaling = 3, display = "sp")
bg <- c("#ff7f00","#1f78b4","#ffff33","#a6cee3") # 4 nice colors for groups
plot(havo.rda, type="n", main = "Triplot of RDA - Scaling 3", scaling=3)
text(havo.rda, display="species", pch=20, cex=1.4, col="gray32", scaling=3)
#points(havo.rda, display="sites", pch=21, cex=1.3, col="gray32", scaling=3, bg=bg[group])
#text(havo.rda, display="sites", pch=21, cex=0.5, col="gray32", scaling=3, bg=bg[group])
text(havo.rda, scaling=3, display="bp", col="#0868ac", cex=1.4)
arrows(0, 0, gwd.sc[,1], gwd.sc[,2], length = 0, lty = 1, col = "#e31a1c")
Fig 9. RDA triplot of the normalized HAVO plant functional trait data, scaling 3. The response variables are represented in red and the explanatory variables are represented in blue.
## Other code for variations of RDA plot
#################################################################
# plot(havo.rda, scaling = 2, main = "Triplot RDA of havo.rda ~ exp.havo - scaling 2")
# plot(havo.rda, scaling = 1, main = "Triplot RDA of havo.rda ~ exp.havo - scaling 1")
#################################################################
# test.rda <- rda(resp.havo ~ ., exp.havo, scale = T)
# plot(test.rda, scaling = 2)
# spe2.sc <- scores(havo.rda, choices = 1:2, display = "sites")
#################################################################
# plot(havo.rda, main = "Triplot RDA resp.havo ~ exp.havo - scaling 2 - wa scores")
# spe2.sc <- scores(havo.rda, choices = 1:2, display = "sites")
# arrows(0,0, spe2.sc[,1],spe2.sc[,2], length = 0, lty = 1, col = "red")
#################################################################
# gwd.sc <- scores(havo.rda, choices = 1:2, scaling = 3, display = "species")
# bg <- c("#ff7f00","#1f78b4","#ffff33","#a6cee3") # 4 nice colors for groups
# plot(havo.rda, type="n", scaling=3 scale = T)
# text(havo.rda, display="species", pch=20, cex=0.7, col="gray32", scaling=3)
# points(havo.rda, display="species", pch=21, cex=1.3, col="gray32", scaling=3, bg=bg[group])
# text(havo.rda, display="species", pch=21, cex=0.5, col="gray32", scaling=3, bg=bg[group])
# text(havo.rda, scaling=3, display="bp", col="#0868ac", cex=.8)
# arrows(0, 0, gwd.sc[,1], gwd.sc[,2], length = 0, lty = 1, col = "#e31a1c")
#################################################################
# gwd.sc <- scores(havo.rda, choices = 1:2, scaling = 3, display = "sp")
# plot(havo.rda, type="n", scaling=3)
# text(havo.rda, display="species", pch=20, cex=0.6, col="darkblue", scaling=3)
# points(havo.rda, display="sites", pch=20, cex=1.0, col="darkorange", scaling=3)
# text(havo.rda, display="sites", pch=21, cex=0.6, col="black", scaling=3)
# text(havo.rda, scaling=3, display="bp", col="red", cex=.8)
# arrows(0, 0, gwd.sc[,1], gwd.sc[,2], length = 0, lty = 1, col = "blue")
#################################################################Permutation Test of RDA Results
A permutation test was generated to compare the true value of the statistic to a reference distribution to further confirm whether a linear relationship exists between plant functional traits and environmental condition variables. Permutation results are statistically significant (p < 0.01), therefore a linear relationship exists between plant functional traits and environmental condition variables.
## Permutation test of the RDA results
#With this in mind, we can now test our RDA results. Let us run a global test first, followed by a test of the canonical axes. The test function is called anova(). This name is unfortunate, since it leads to confusion with the classical ANOVA test, which it is not.
#Global test of the RDA results:
print(anova.cca(havo.rda, step = 1000))## Permutation test for rda under reduced model
## Permutation: free
## Number of permutations: 999
##
## Model: rda(formula = resp.havo ~ Evapotranspiration + Radiation + Temperature + Elevation + Precipitation, data = exp.havo)
## Df Variance F Pr(>F)
## Model 5 2.9838e-05 22.465 0.001 ***
## Residual 241 6.4021e-05
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Tests of all canonical axes:
print(anova.cca(havo.rda, by = "axis", step = 1000)) ## Permutation test for rda under reduced model
## Forward tests for axes
## Permutation: free
## Number of permutations: 999
##
## Model: rda(formula = resp.havo ~ Evapotranspiration + Radiation + Temperature + Elevation + Precipitation, data = exp.havo)
## Df Variance F Pr(>F)
## RDA1 1 2.9232e-05 110.9541 0.001 ***
## RDA2 1 5.1500e-07 1.9531 0.685
## RDA3 1 9.2000e-08 0.3476 0.998
## Residual 243 6.4021e-05
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Univariate Analysis
Based on RDA results, I hypothesize that there is a relationship between carbon to nitrogen content and Radiation, Temperature, and Evapotranspiration.
## Multiple Regression Analysis
model = lm(CarbonNitrogen ~ Radiation + Temperature + Evapotranspiration, data = imp.rename)
summary(model)##
## Call:
## lm(formula = CarbonNitrogen ~ Radiation + Temperature + Evapotranspiration,
## data = imp.rename)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.563 -12.074 -2.554 12.461 45.947
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -118.18770 56.02158 -2.110 0.0359 *
## Radiation 0.38213 0.15816 2.416 0.0164 *
## Temperature 3.90416 0.94554 4.129 5.01e-05 ***
## Evapotranspiration 0.02113 0.02501 0.845 0.3990
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.82 on 243 degrees of freedom
## Multiple R-squared: 0.1067, Adjusted R-squared: 0.09563
## F-statistic: 9.671 on 3 and 243 DF, p-value: 4.708e-06library(ggplot2)
ggplot(imp.rename, aes(y = CarbonNitrogen, x = Temperature, color = status))+ggtitle("Relationship between Temperature and Leaf Carbon:Nitrogen Content between Endemic, Indigenous, and Non-native Plants") +geom_point() + geom_smooth(method = "lm")
Fig 10. Linear model of the relationship between Temperature to Carbon:Nitrogen content among endemic, indigenous, and non-native plants.
There is a relationship between Carbon:Nitrogen content and Temperature (p < 0.05), but no significant influence between Carbon:Nitrogen and Radiation or Evapotranspiration.
Visualizations
Correlation Plot
str(havo)
#install.packages("psych")
library(psych)
library(corrr)
newnum %>% correlate() %>% network_plot()
Fig 11. Visualizing correlations between variables. The closer each variable is to each other the higher the relationship. The color of the line represents the direction of the correlation while the line shade and thickness represent the strength of the relationship. Precipitation and Radiation as well as Temperature and Elevation are highly correlated.
# It can also be called using the traditional method
# network_plot(correlate(mydata), min_cor=0.5)Violin Plot
library(ggplot2)
theme_set(theme_bw())
# plot
g <- ggplot(imp.rename, aes(Species, CarbonNitrogen, color = status)) + theme(panel.border = element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black"))
g + geom_violin() +
labs(title="Violin plot",
subtitle="Carbon:nitrogen content vs Species",
x="Plant Species",
y="Carbon:nitrogen content")
Fig 10. Violin plot illustrating Carbon:Nitrogen leaf content between different Endemic, Indigenous, and Non-native species encountered within the HAVO functional plant trait data set.
Tableau
Click [here] for a data dashboard (https://public.tableau.com/profile/erica.ta#!/vizhome/Final_15894382345730/PlantFunctionalTraitsinHawaiiVolcanoesNationalPark?publish=yes).
References
Henn, J.J. and Yelenik, S.G. 2020, Hawaii Volcanoes National Park Plant Trait, Percent Cover, and Environmental Data 2014: U.S. Geological Survey data release, https://doi.org/10.5066/P9WCNWEJ.