a. 5: Demo
b. 5: Slides
You can access the full slideshow used in the 5-PCA narration here.
The dataset called ‘coralreefherbivores.csv’ can be downloaded here.
The dataset called ‘fishcoms_lizardisland.csv’ can be downloaded here.
c. 5: Exercises
Start by installing and loading the vegan and the ape package into your environment, along with dplyr, ggplot and patchwork (or load the former two via the tidyverse package)
Then, read in the fishcoms_lizardisland dataset, which is available above
Part I
- Retain only species in the family Chaetodontidae (butterflyfishes) in the dataset, and summarize each species’ abundance across sites, while also retaining information on each site’s exposure level. Bring the data to wide format.
- Divide your dataset into metadata and abundance data, run a PCA on the Hellinger transformed data, and plot the data using ggplot. See how the data changes depending on whether you scale and center your data.
Part II
We now want to examine how the four regimes of wave action impact reef fish community composition across all families. With more than 200 fish species across all families, this is a tough ask for PCA so we will move to distance based ordinations.
Group the data by transect, site, exposure, and species, and sum up the number of individuals (abundance). Turn the data into wide format and split it into meta and raw data as previously.
- Create a distance matrix using the vegdist function and a Bray-Curtis dissimilarity metric. Then, run a PCoA using the pcoa function, choosing the cailliez correction for negative eigenvalues. Visualize the output using ggplot.
- run a non-metric multidimensional scaling ordination (NMDS) on the raw data using the metaMDS function, a Bray-Curtis dissimilarity metric, and two dimensions. Check the stress and plot the results using ggplot. Investigate your PCoA and NMDS side-by-side.
Part IV
We will continue using the “fishcoms_lizardisland.csv” dataset, but this time, we will explore differences in fish communities between the two years, 2011 and 2015.
- Calculate fish abundance per transect, site, and year for each species.
- Put the dataset in wide format.
- Split the metadata from the numeric data.
- Run a PCoA with Bray-Curtis dissimilarity.
- Check eigenvalues. Add a correction if needed.
- Plot the PCoA with different colors and polygons for the two years.
d. 5: Solutions
Start by installing and loading the vegan and the ape package into your environment, along with dplyr, ggplot and patchwork (or load the former two via the tidyverse package)
Then, read in the fishcoms_lizardisland dataset, which is available above
Part I
- Retain only species in the family Chaetodontidae (butterflyfishes) in the dataset, and summarize each species’ abundance across sites, while also retaining information on each site’s exposure level. Bring the data to wide format.
library(vegan)
library(tidyverse)
library(ape)
library(patchwork)
# re-familiarize with the Lizard Island fish community dataset
lfish <- read.csv(file = "data/fishcoms_lizardisland.csv")
head(lfish) Site Exposure year depth transect Family
1 Big Vickis Sheltered 2011 deep 1 Acanthuridae
2 Big Vickis Sheltered 2011 deep 1 Acanthuridae
3 Big Vickis Sheltered 2011 deep 1 Acanthuridae
4 Big Vickis Sheltered 2011 deep 1 Balistidae
5 Big Vickis Sheltered 2011 deep 1 Chaetodontidae
6 Big Vickis Sheltered 2011 deep 1 Chaetodontidae
Functional.Group species abundance
1 Grazer aca.bloc 1
2 Grazer cte.bino 1
3 Grazer cte.stri 3
4 Macroinvertivore suf.chry 2
5 Obligate corallivore cha.baro 4
6 Obligate corallivore cha.ttus 2lizard.sum <- lfish %>%
filter(Family == "Chaetodontidae") %>%
group_by(Site, Exposure, species) %>%
summarize(abundance = sum(abundance))
lizard.sum# A tibble: 181 × 4
# Groups: Site, Exposure [14]
Site Exposure species abundance
<chr> <chr> <chr> <int>
1 Big Vickis Sheltered cha.afas 18
2 Big Vickis Sheltered cha.auri 6
3 Big Vickis Sheltered cha.baro 42
4 Big Vickis Sheltered cha.citr 13
5 Big Vickis Sheltered cha.ephi 10
6 Big Vickis Sheltered cha.klei 1
7 Big Vickis Sheltered cha.mela 13
8 Big Vickis Sheltered cha.mert 1
9 Big Vickis Sheltered cha.pleb 3
10 Big Vickis Sheltered cha.raff 2
# ℹ 171 more rows# spread into wide format and get rid of NAs
lizard.wide <- lizard.sum %>%
spread(key = species, value = abundance, fill = 0)
lizard.wide# A tibble: 14 × 29
# Groups: Site, Exposure [14]
Site Exposure cha.afas cha.auri cha.baro cha.citr cha.ephi
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Big Vickis Shelter… 18 6 42 13 10
2 Blue Lagoon Lagoon 0 6 0 0 1
3 Bommie Bay Oblique 0 7 8 2 5
4 Coconut Exposed 2 4 3 6 3
5 Granite Shelter… 0 9 5 5 3
6 LTMP1 Exposed 1 19 15 0 5
7 LTMP3 Exposed 3 20 17 0 2
8 Monkey's Butt Lagoon 9 12 1 0 2
9 North Reef Shelter… 1 3 2 16 1
10 Palfrey Lago… Lagoon 8 6 0 0 0
11 Pidgin Point Exposed 2 1 1 2 0
12 Resort Shelter… 5 12 0 5 0
13 Steve's Gully Oblique 15 13 7 0 5
14 Washing Mach… Oblique 2 10 11 5 8
# ℹ 22 more variables: cha.klei <dbl>, cha.line <dbl>,
# cha.lunu <dbl>, cha.mela <dbl>, cha.mert <dbl>, cha.pelw <dbl>,
# cha.pleb <dbl>, cha.raff <dbl>, cha.rain <dbl>, cha.reti <dbl>,
# cha.spec <dbl>, cha.tlis <dbl>, cha.ttus <dbl>, cha.ulie <dbl>,
# cha.unim <dbl>, cha.vaga <dbl>, chm.rost <dbl>, crd.chry <dbl>,
# hen.acum <dbl>, hen.chry <dbl>, hen.mono <dbl>, hen.vari <dbl>- Divide your dataset into metadata and abundance data, run a PCA on the Hellinger transformed data, and plot the data using ggplot. See how the data changes depending on whether you scale and center your data.
# isolate metadata
lizard.meta <- lizard.wide[1:2]
lizard.meta# A tibble: 14 × 2
# Groups: Site, Exposure [14]
Site Exposure
<chr> <chr>
1 Big Vickis Sheltered
2 Blue Lagoon Lagoon
3 Bommie Bay Oblique
4 Coconut Exposed
5 Granite Sheltered
6 LTMP1 Exposed
7 LTMP3 Exposed
8 Monkey's Butt Lagoon
9 North Reef Sheltered
10 Palfrey Lagoon Lagoon
11 Pidgin Point Exposed
12 Resort Sheltered
13 Steve's Gully Oblique
14 Washing Machine Oblique # A tibble: 14 × 27
cha.afas cha.auri cha.baro cha.citr cha.ephi cha.klei cha.line
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 18 6 42 13 10 1 0
2 0 6 0 0 1 0 0
3 0 7 8 2 5 12 0
4 2 4 3 6 3 9 0
5 0 9 5 5 3 3 1
6 1 19 15 0 5 7 1
7 3 20 17 0 2 3 4
8 9 12 1 0 2 0 1
9 1 3 2 16 1 2 0
10 8 6 0 0 0 0 0
11 2 1 1 2 0 2 0
12 5 12 0 5 0 10 0
13 15 13 7 0 5 2 1
14 2 10 11 5 8 13 0
# ℹ 20 more variables: cha.lunu <dbl>, cha.mela <dbl>,
# cha.mert <dbl>, cha.pelw <dbl>, cha.pleb <dbl>, cha.raff <dbl>,
# cha.rain <dbl>, cha.reti <dbl>, cha.spec <dbl>, cha.tlis <dbl>,
# cha.ttus <dbl>, cha.ulie <dbl>, cha.unim <dbl>, cha.vaga <dbl>,
# chm.rost <dbl>, crd.chry <dbl>, hen.acum <dbl>, hen.chry <dbl>,
# hen.mono <dbl>, hen.vari <dbl># the decostand() function in vegan allows for transformations like Hellinger
lizard.hell <- decostand(lizard.raw, method = "hellinger")
head(lizard.hell) cha.afas cha.auri cha.baro cha.citr cha.ephi cha.klei
1 0.33859959 0.1954906 0.5172194 0.2877543 0.2523772 0.07980869
2 0.00000000 0.4399413 0.0000000 0.0000000 0.1796053 0.00000000
3 0.00000000 0.2773501 0.2964997 0.1482499 0.2344036 0.36313652
4 0.15911146 0.2250176 0.1948709 0.2755891 0.1948709 0.33752637
5 0.00000000 0.3841106 0.2862992 0.2862992 0.2217664 0.22176638
6 0.09853293 0.4294951 0.3816164 0.0000000 0.2203263 0.26069362
cha.line cha.lunu cha.mela cha.mert cha.pelw cha.pleb
1 0.00000000 0.0000000 0.2877543 0.07980869 0.00000000 0.1382327
2 0.00000000 0.0000000 0.1796053 0.00000000 0.00000000 0.3110855
3 0.00000000 0.1482499 0.2096570 0.00000000 0.00000000 0.0000000
4 0.00000000 0.1948709 0.2250176 0.11250879 0.00000000 0.1125088
5 0.12803688 0.0000000 0.2560738 0.00000000 0.00000000 0.0000000
6 0.09853293 0.0000000 0.1970659 0.00000000 0.09853293 0.0000000
cha.raff cha.rain cha.reti cha.spec cha.tlis cha.ttus
1 0.1128665 0.1128665 0 0.1128665 0.00000000 0.3743359
2 0.0000000 0.1796053 0 0.0000000 0.00000000 0.5679618
3 0.0000000 0.2344036 0 0.0000000 0.00000000 0.5929995
4 0.0000000 0.1591115 0 0.0000000 0.15911146 0.5511783
5 0.0000000 0.1280369 0 0.0000000 0.00000000 0.3387537
6 0.0000000 0.2413554 0 0.0000000 0.09853293 0.5119921
cha.ulie cha.unim cha.vaga chm.rost crd.chry hen.acum
1 0.1382327 0.0000000 0.2986168 0.1382327 0.1128665 0.00000000
2 0.2540003 0.0000000 0.1796053 0.3110855 0.0000000 0.25400025
3 0.0000000 0.0000000 0.3476767 0.0000000 0.0000000 0.00000000
4 0.0000000 0.2515773 0.2976703 0.0000000 0.0000000 0.00000000
5 0.1280369 0.0000000 0.5580998 0.2217664 0.0000000 0.00000000
6 0.1706640 0.1393466 0.2203263 0.0000000 0.0000000 0.09853293
hen.chry hen.mono hen.vari
1 0.0000000 0.0000000 0.0000000
2 0.0000000 0.1796053 0.0000000
3 0.0000000 0.0000000 0.1815683
4 0.1591115 0.1125088 0.0000000
5 0.0000000 0.0000000 0.0000000
6 0.1393466 0.1706640 0.0000000# run a PCA and retain percent variation explained by PC1 and PC2
lizard.pca <- summary(rda(lizard.hell, scale = T))
lizard.pca
Call:
rda(X = lizard.hell, scale = T)
Partitioning of correlations:
Inertia Proportion
Total 27 1
Unconstrained 27 1
Eigenvalues, and their contribution to the correlations
Importance of components:
PC1 PC2 PC3 PC4 PC5 PC6
Eigenvalue 5.2730 3.8918 3.7217 3.3114 2.58968 1.9738
Proportion Explained 0.1953 0.1441 0.1378 0.1226 0.09591 0.0731
Cumulative Proportion 0.1953 0.3394 0.4773 0.5999 0.69583 0.7689
PC7 PC8 PC9 PC10 PC11 PC12
Eigenvalue 1.81768 1.47629 1.0449 0.75706 0.44481 0.3725
Proportion Explained 0.06732 0.05468 0.0387 0.02804 0.01647 0.0138
Cumulative Proportion 0.83626 0.89093 0.9296 0.95768 0.97415 0.9879
PC13
Eigenvalue 0.32549
Proportion Explained 0.01206
Cumulative Proportion 1.00000# extract the site scores and merge with metadata
lizard.scores <- as.data.frame(lizard.pca$sites) %>%
bind_cols(lizard.meta)
# create convex hulls grouped by site exposure based on site scores
lizard.hulls <- lizard.scores %>%
group_by(Exposure) %>%
slice(chull(PC1, PC2))
# extract the loadings from species scores
lizard.loadings <- as.data.frame(lizard.pca$species) %>%
mutate(species = rownames(.))
# plot the PCA results with color and convex hulls as exposure and species as loadings
lizard.plot2 <- ggplot() +
geom_point(data = lizard.scores, aes(x = PC1, y = PC2, color = Exposure), size = 2) +
geom_polygon(data = lizard.hulls, aes(x = PC1, PC2, fill = Exposure), alpha = 0.5) +
geom_segment(data = lizard.loadings, aes(x = 0, xend = PC1*3,
y = 0, yend = PC2*3), lwd = 0.1) +
geom_text(data = lizard.loadings, aes(x = PC1*3, y = PC2*3, label = species), size = 3) +
scale_fill_viridis_d() +
scale_color_viridis_d() +
theme_bw() +
xlab("PC1 (21.8%)") +
ylab("PC2 (17.8%)") +
ggtitle("Hellinger transformed PCA, scale = T")
lizard.plot2
# run the same PCA, but with scale = F
# retain percent variation explained by PC1 and PC2
lizard.pca <- summary(rda(lizard.hell, scale = F))
# extract the site scores and merge with metadata
lizard.scores <- as.data.frame(lizard.pca$sites) %>%
bind_cols(lizard.meta)
# create convex hulls grouped by site exposure based on site scores
lizard.hulls <- lizard.scores %>%
group_by(Exposure) %>%
slice(chull(PC1, PC2))
# extract the loadings from species scores
lizard.loadings <- as.data.frame(lizard.pca$species) %>%
mutate(species = rownames(.))
# plot the PCA results with color and convex hulls as exposure and species as loadings
lizard.plot3 <- ggplot() +
geom_point(data = lizard.scores, aes(x = PC1, y = PC2, color = Exposure), size = 2) +
geom_polygon(data = lizard.hulls, aes(x = PC1, PC2, fill = Exposure), alpha = 0.5) +
geom_segment(data = lizard.loadings, aes(x = 0, xend = PC1*2,
y = 0, yend = PC2*2), lwd = 0.1) +
geom_text(data = lizard.loadings, aes(x = PC1*2, y = PC2*2, label = species), size = 3) + # you can spread out loadings by multiplying values
scale_fill_viridis_d() +
scale_color_viridis_d() +
theme_bw() +
xlab("PC1 (30.3%)") +
ylab("PC2 (20.5%)") +
ggtitle("Hellinger transformed PCA, scale = F")
lizard.plot3
Part II
We now want to examine how the four regimes of wave action impact reef fish community composition across all families. With more than 200 fish species across all families, this is a tough ask for PCA so we will move to distance based ordinations.
Group the data by transect, site, exposure, and species, and sum up the number of individuals (abundance). Turn the data into wide format and split it into meta and raw data as previously.
# call the entire dataset
# group by transect, site, exposure, and species
# summarize the species abundances
lizard.sum <- lfish %>%
group_by(transect, Site, Exposure, species) %>%
summarize(abundance = sum(abundance))
# convert data to wide format
lizard.wide <- lizard.sum %>%
spread(key = species, value = abundance, fill = 0)
# isolate metadata
lizard.meta <- lizard.wide[1:3]
# isolate numeric data
lizard.raw <- lizard.wide %>%
ungroup() %>%
select(-c(1:3))- Create a distance matrix using the vegdist function and a Bray-Curtis dissimilarity metric. Then, run a PCoA using the pcoa function, choosing the cailliez correction for negative eigenvalues. Visualize the output using ggplot.
# create a distance matrix with vegdist() from the vegan package
# use the Bray-Curtis dissimilarity metric, which is a dissimilarity measure designed to handle abundance data
lizard.dist <- vegdist(lizard.raw, method = "bray")
# run the PCoA using the cmdscale() function
lizard.pcoa <- pcoa(lizard.dist, correction = "cailliez")
lizard.pcoa$correction
[1] "cailliez" "3"
$note
[1] "Cailliez correction applied to negative eigenvalues: D' = -0.5*(D + 0.104329701745338 )^2, except diagonal elements"
$values
Eigenvalues Corr_eig Rel_corr_eig Broken_stick Cum_corr_eig
1 1.7237838249 2.047441399 0.1879345664 0.106963576 0.1879346
2 1.1452242740 1.381051412 0.1267666554 0.081963576 0.3147012
3 0.6463909538 0.799445512 0.0733810725 0.069463576 0.3880823
4 0.5537202216 0.691401691 0.0634637343 0.061130243 0.4515460
5 0.4762933230 0.599868974 0.0550619498 0.054880243 0.5066080
6 0.3911930529 0.499924068 0.0458880108 0.049880243 0.5524960
7 0.3342038932 0.432179235 0.0396697152 0.045713576 0.5921657
8 0.3073084585 0.401637311 0.0368662732 0.042142147 0.6290320
9 0.2848822844 0.375651340 0.0344810219 0.039017147 0.6635130
10 0.2359893126 0.312830802 0.0287147272 0.036239370 0.6922277
11 0.2240308465 0.303378349 0.0278470868 0.033739370 0.7200748
12 0.1880727102 0.258826312 0.0237576571 0.031466642 0.7438325
13 0.1847468591 0.256072043 0.0235048428 0.029383309 0.7673373
14 0.1440149003 0.206747423 0.0189773379 0.027460232 0.7863147
15 0.1391043155 0.202020965 0.0185434965 0.025674518 0.8048581
16 0.1303949702 0.188639231 0.0173151877 0.024007851 0.8221733
17 0.1281279671 0.187273350 0.0171898135 0.022445351 0.8393631
18 0.1209120374 0.178769672 0.0164092613 0.020974763 0.8557724
19 0.1039267405 0.158533473 0.0145517813 0.019585874 0.8703242
20 0.0953221167 0.146572789 0.0134539106 0.018270085 0.8837781
21 0.0827185050 0.131936709 0.0121104654 0.017020085 0.8958886
22 0.0761160962 0.123728268 0.0113570129 0.015829608 0.9072456
23 0.0664507120 0.112464123 0.0103230775 0.014693245 0.9175687
24 0.0618909965 0.105977306 0.0097276528 0.013606288 0.9272963
25 0.0539588474 0.097940583 0.0089899623 0.012564622 0.9362863
26 0.0507426737 0.092264447 0.0084689500 0.011564622 0.9447552
27 0.0454963831 0.086465149 0.0079366326 0.010603083 0.9526919
28 0.0388430427 0.077826274 0.0071436706 0.009677157 0.9598355
29 0.0329721021 0.071845038 0.0065946533 0.008784300 0.9664302
30 0.0246977736 0.061895057 0.0056813449 0.007922231 0.9721115
31 0.0195081685 0.054447557 0.0049977391 0.007088898 0.9771093
32 0.0126607325 0.048501185 0.0044519219 0.006282446 0.9815612
33 0.0103924229 0.044826215 0.0041145965 0.005501196 0.9856758
34 0.0079417893 0.042796658 0.0039283036 0.004743620 0.9896041
35 0.0004461808 0.034572345 0.0031733942 0.004008326 0.9927775
36 0.0000000000 0.024678559 0.0022652440 0.003294040 0.9950427
37 -0.0071451768 0.020459275 0.0018779561 0.002599596 0.9969207
38 -0.0092778157 0.017090137 0.0015687030 0.001923920 0.9984894
39 -0.0136295336 0.012806918 0.0011755465 0.001266026 0.9996649
40 -0.0198114162 0.003650404 0.0003350705 0.000625000 1.0000000
41 -0.0259698794 0.000000000 0.0000000000 0.000000000 1.0000000
42 -0.0281545469 0.000000000 0.0000000000 0.000000000 1.0000000
Cum_br_stick
1 0.1069636
2 0.1889272
3 0.2583907
4 0.3195210
5 0.3744012
6 0.4242815
7 0.4699950
8 0.5121372
9 0.5511543
10 0.5873937
11 0.6211331
12 0.6525997
13 0.6819830
14 0.7094432
15 0.7351178
16 0.7591256
17 0.7815710
18 0.8025457
19 0.8221316
20 0.8404017
21 0.8574218
22 0.8732514
23 0.8879446
24 0.9015509
25 0.9141155
26 0.9256802
27 0.9362832
28 0.9459604
29 0.9547447
30 0.9626669
31 0.9697558
32 0.9760383
33 0.9815395
34 0.9862831
35 0.9902914
36 0.9935855
37 0.9961851
38 0.9981090
39 0.9993750
40 1.0000000
41 1.0000000
42 1.0000000
$vectors
Axis.1 Axis.2 Axis.3 Axis.4 Axis.5
1 -0.169343902 0.111362282 0.044303106 0.104292114 -0.046394081
2 -0.451281604 0.114325972 -0.094927345 0.023648248 0.088962412
3 0.159803853 0.049922107 -0.044296366 0.127301353 0.042865962
4 0.110401192 -0.143316894 -0.169753553 0.016459880 -0.010569206
5 0.262134305 0.270832648 0.045551841 -0.032484782 0.012568717
6 0.013867453 -0.322687479 0.017001603 -0.035814885 -0.059302934
7 0.015234736 -0.264395699 -0.049010994 -0.090509674 -0.064912874
8 -0.211178112 -0.138801631 0.227704230 -0.098001556 0.172054733
9 0.168286115 -0.043361153 0.020701078 0.013116016 -0.017867373
10 -0.364013023 0.043814726 -0.105910018 -0.083957935 -0.214425424
11 0.050287582 -0.224119652 -0.231347906 0.084867915 0.164266117
12 0.168140226 0.128265348 -0.147813518 -0.283977803 -0.168372000
13 0.007677336 -0.145804213 0.074787355 -0.066385812 -0.153178770
14 0.055376418 -0.013336868 -0.001015276 0.035801613 -0.088934689
15 -0.210262137 0.075344861 0.093621305 0.068057230 0.013102024
16 -0.427170514 0.040946293 -0.176232807 -0.058110707 0.080936479
17 0.090801781 0.017532823 0.027054205 0.188692377 0.014687192
18 0.074555675 -0.222151821 -0.143056189 -0.030046549 -0.037711083
19 0.230138156 0.264666597 0.051949465 -0.024954209 0.014063083
20 0.025580231 -0.291084943 -0.016635631 -0.057735860 -0.184002881
21 0.020392030 -0.254786126 -0.073064253 -0.018848897 -0.155671847
22 -0.213405343 -0.080691422 0.269909352 -0.018949505 0.175080200
23 0.253941794 -0.028540411 0.098353719 0.024501475 0.038052762
24 -0.357736333 0.074330479 -0.020006864 0.047842684 -0.166770593
25 0.141707196 -0.125316972 -0.148210361 0.082823970 0.186726753
26 0.211729977 0.324698546 -0.060413632 -0.232992305 0.009572404
27 -0.025387340 -0.043907012 0.177208266 0.126345576 -0.018674142
28 0.139600069 -0.008031405 0.026226317 0.157300197 0.023778084
29 -0.140565449 0.193857385 -0.005355031 0.044217942 -0.074366481
30 -0.390984455 0.176500523 -0.122493624 -0.015717838 0.128308890
31 0.114021352 -0.101267519 0.094098672 0.025854130 0.113874909
32 0.150646805 -0.042847986 -0.112235206 0.027401681 -0.003487300
33 0.163748562 0.163380808 0.140587730 0.004175263 -0.026327636
34 0.045020697 -0.185569191 0.158446329 0.075310714 -0.002698490
35 -0.041610168 -0.203567529 0.149895658 -0.400188339 0.205562610
36 -0.167252931 0.104032274 0.109530486 0.113595079 -0.080454973
37 0.145421117 0.082719968 0.138710236 0.048767279 -0.090152914
38 -0.330250941 0.135962648 -0.027030723 0.004406455 0.021900806
39 0.178077348 0.033848600 -0.295398175 0.104706269 0.173673454
40 0.234611185 0.287383041 0.008954106 -0.192099973 0.052453703
41 0.073013160 0.049278691 0.134537671 0.101341932 -0.073463211
42 0.196225903 0.140579304 -0.064925258 0.089949235 0.005247608
Axis.6 Axis.7 Axis.8 Axis.9 Axis.10
1 -0.0197532965 -0.027801241 -0.022747705 0.130367974 -0.069444201
2 -0.1420812357 -0.059254567 -0.013855686 -0.072623605 -0.038896642
3 0.1084983418 0.089256411 -0.058085002 0.088744744 -0.047806840
4 0.0529796830 -0.122924768 -0.057258032 0.036792618 -0.004896148
5 -0.0039671325 -0.174265742 -0.042392237 -0.003977175 0.019263302
6 -0.0120032006 0.062623675 0.009396645 0.074232426 -0.124925766
7 -0.0222768723 0.056185656 -0.098059221 -0.054340079 0.076737629
8 0.0282679021 0.123384976 -0.014063703 0.036459577 0.132576064
9 -0.1295334112 0.002427031 0.016808797 -0.159069959 0.073559007
10 0.1382806049 0.014405731 0.098963730 -0.099753163 0.025568627
11 0.0032641572 -0.065819496 0.134514830 0.087446409 0.065133851
12 -0.0734932382 0.119211062 -0.032481554 0.065263023 0.023341599
13 -0.0657359024 0.024321124 -0.045635135 -0.016271714 0.153301527
14 0.0466522732 0.084171820 -0.171145509 -0.084800143 0.036712489
15 -0.1583418094 -0.026211307 -0.169353958 0.073553534 -0.027610742
16 -0.1549797229 -0.045309572 -0.034371827 -0.025286791 0.008482984
17 0.0308634381 0.039201877 -0.004909861 -0.025232121 0.001473440
18 -0.0070651204 -0.001315762 0.024706360 0.192584529 -0.005995451
19 0.0557488085 -0.266279074 0.018169965 0.016813790 0.079040030
20 -0.1369440704 0.001464967 0.056907202 -0.040062761 -0.062633828
21 0.0435329186 -0.068951552 -0.055398457 0.009636068 -0.057217569
22 0.0442913803 0.082675386 0.106365735 0.069227313 -0.040375080
23 -0.1704205673 -0.013322929 0.162020444 -0.208122904 -0.078611175
24 0.2205051880 -0.094980301 0.231943705 -0.034722452 -0.036297939
25 -0.0552026763 0.038840338 0.042771053 -0.016694810 0.123418475
26 -0.0466543513 0.101803817 0.127181656 0.025733937 0.025041435
27 -0.0774016090 -0.039249988 0.036959135 0.084788227 0.069716340
28 0.0865361797 0.084866862 -0.109912191 0.007354105 0.002787894
29 0.0573023721 0.008055381 -0.044767167 0.102479274 -0.010848163
30 -0.1263420007 0.001597870 -0.104390940 -0.063988416 -0.150593588
31 0.0599410714 0.040044421 0.074779925 -0.015881409 -0.093377121
32 0.0007983876 -0.114458547 -0.007820878 0.078901942 -0.071055384
33 -0.0907703330 -0.121337128 -0.003026797 0.045907220 0.034495963
34 -0.0810181862 -0.069446753 0.093697935 0.016161322 -0.040931244
35 0.2275841363 -0.154759027 -0.128359765 -0.084850639 -0.044167531
36 0.1322799807 0.104060943 -0.036775307 -0.065163055 -0.046844846
37 -0.0081487465 0.027614051 -0.020462804 -0.131206871 -0.019714702
38 0.0342984409 0.043777982 0.059138140 0.041292188 0.225054249
39 0.1246584588 0.093829691 0.019952927 -0.140076192 -0.005820761
40 -0.0255936717 0.169177219 0.083052065 0.104201114 -0.114289904
41 0.0109532832 0.043092248 -0.017047360 -0.009346092 0.017858912
42 0.1004901480 0.009597217 -0.105009152 -0.036470984 -0.001209192
Axis.11 Axis.12 Axis.13 Axis.14 Axis.15
1 -0.144086282 0.033341494 -0.0627504758 -0.0281932481 0.135447899
2 0.035246546 0.047517146 0.0037963278 -0.0281616142 -0.040930700
3 -0.044081252 0.074691437 -0.0454597073 0.0550804260 -0.104956623
4 0.096982269 -0.002764116 0.0290087331 -0.0257089328 0.071356616
5 0.026047575 -0.049100737 -0.1590288023 0.0118565702 -0.028566293
6 -0.013233288 0.046776831 -0.1298410645 0.0260617868 0.043570996
7 0.004533183 -0.148257174 -0.0610074545 0.0144388163 -0.063396730
8 0.108467046 -0.076806018 -0.0362494844 0.0364591361 0.045400141
9 -0.046891608 0.086293496 0.0425193023 0.0564527625 0.110280353
10 0.007019900 0.028025629 -0.0008451588 0.0267719421 0.009290673
11 0.039998249 -0.048063499 0.0199608941 -0.2014924280 -0.054860078
12 0.063467032 0.047310117 0.0057218311 -0.0238902302 -0.002672240
13 -0.063992446 0.012320960 0.0069391669 0.0240467073 -0.074845617
14 0.097333462 0.063864886 0.0208177651 -0.0939068979 0.089223685
15 -0.124206535 -0.132911118 0.0993709168 0.0171258876 -0.047958249
16 0.042691412 0.046694817 -0.0448818359 -0.0437769953 -0.040951306
17 -0.007448865 0.059173799 0.1082723796 0.0156884219 -0.094297063
18 0.009460354 -0.007107786 0.0478789190 0.1204947951 -0.009758791
19 0.093648818 0.025178201 -0.1001357645 0.0629265529 -0.078050123
20 -0.023270496 0.080535990 -0.0260135941 0.0002636819 -0.082197344
21 0.039535987 -0.050433840 -0.0598075816 -0.0189905258 0.016621016
22 0.081021274 0.066321516 -0.0722679178 -0.0029814893 0.025346368
23 -0.004261601 -0.011853102 0.0136645041 0.0282158614 0.023795579
24 -0.029642700 -0.013846215 0.0690905603 -0.0278830212 -0.005044924
25 -0.081050960 -0.037386718 -0.0215425563 -0.0270596432 0.084276530
26 0.050426140 -0.066234024 0.0254390275 -0.0057889304 0.038579465
27 -0.006861895 0.045029331 -0.0190199628 -0.0706745218 0.017694376
28 0.106273083 0.118591719 0.1053943906 -0.0369346141 -0.059980802
29 -0.067105170 -0.015330367 -0.0839008727 -0.0155601791 0.073020584
30 0.074475546 0.004436735 -0.0015732173 0.0613072853 -0.006123657
31 0.122114879 -0.048932336 0.0217287462 0.0909340943 -0.026859843
32 0.010955657 -0.115351574 0.1671528483 0.0860594623 0.077273221
33 0.001616547 0.012738337 0.0616263612 -0.0483075409 0.003289582
34 -0.017680341 0.023981626 0.0113198144 0.0285743474 0.010585915
35 -0.150993905 0.056367412 0.0795200080 -0.0420876969 -0.006702287
36 0.067317842 -0.174885907 -0.0082339519 -0.0331160124 -0.017112711
37 -0.007697602 -0.091681327 0.0167559442 -0.0776077746 0.018502127
38 -0.048823489 0.039994504 0.0624967259 0.1068509816 0.004420572
39 -0.152882480 -0.027542412 -0.1027151115 0.0444013026 -0.018597518
40 -0.080035282 0.011985611 0.0504738628 -0.0736083146 -0.047216001
41 -0.114011953 -0.005254134 -0.0433786159 -0.0197248745 -0.064097817
42 0.049625347 0.092570811 0.0097041004 0.0314446634 0.077201021
Axis.16 Axis.17 Axis.18 Axis.19
1 0.0192632332 -0.125762344 -0.0213001078 0.0599528120
2 -0.0517199194 0.028211313 0.0393555810 -0.0115324188
3 -0.0602362245 -0.028226820 -0.0001916871 -0.0812641550
4 0.0268926969 0.033724681 -0.0354882824 -0.0810995591
5 -0.0158896761 0.019932586 0.0378531043 0.0120845244
6 -0.0603284286 -0.029532961 -0.0457869886 0.0443106654
7 0.0142647279 -0.016619965 0.0241941048 -0.0007296062
8 0.0014025525 -0.019325673 -0.0583409199 -0.0106466286
9 -0.1101529216 -0.007516075 0.0540730201 -0.1161948385
10 -0.1145128123 0.035558926 0.0258727214 0.0562724453
11 -0.0127841324 -0.050289431 0.0015709414 -0.0136197115
12 0.0742787226 -0.077603214 0.0867844568 0.0316301707
13 0.0667261564 -0.025848259 0.0176895893 -0.0270557943
14 -0.0064372093 0.011507279 -0.0196968444 0.0714082656
15 -0.0685889618 -0.064836988 -0.0224000666 0.0660841497
16 -0.0260148395 -0.019137679 -0.0218548872 -0.0679069624
17 0.0197672783 -0.095381095 0.0949098725 -0.0201259138
18 -0.1140924088 0.021138973 -0.0168065834 0.0346114665
19 -0.0188571231 -0.007242483 -0.0383981914 0.0536985820
20 0.1336834906 0.031294727 -0.0369318961 0.0263507892
21 -0.0479065613 -0.010299802 -0.0434717574 -0.0841943441
22 0.0285097852 -0.020532902 -0.0153100269 -0.0454360667
23 0.0007648133 -0.104136346 -0.0908626447 0.0064880015
24 0.0185753284 -0.042536412 0.0142966029 0.0218919297
25 0.0092234144 0.039263887 0.1114621416 0.0886480417
26 -0.0452052783 0.016102154 -0.0283812230 0.0524445478
27 -0.0282527497 0.090138698 0.0495335629 0.0236728951
28 -0.0283292682 0.032024035 -0.0958233151 0.0916193566
29 0.0650608040 0.012376062 0.0608609010 -0.0630238953
30 0.0586662326 0.060633467 0.0177935947 0.0335610887
31 -0.0067560329 -0.066155689 0.1510495924 0.0193093880
32 0.0575144436 0.055879405 -0.0194204690 -0.0351541495
33 0.0520988977 -0.070090528 -0.0520278864 -0.0195679133
34 0.0772074130 0.156017946 0.0235649954 0.0382576225
35 0.0007674031 0.000344795 0.0224096015 0.0131448925
36 0.0593035458 0.014750037 0.0008702876 -0.0304677423
37 -0.0705437238 0.037990250 -0.0331420796 -0.0228783172
38 0.0524014407 0.014355577 -0.0887963930 -0.0331509956
39 0.0613687238 0.009308687 -0.0857747173 0.0273246381
40 -0.0177951438 0.085916501 -0.0244053701 -0.0699375238
41 -0.0426657643 0.087349651 0.0313640585 -0.0145966170
42 0.0493280756 -0.012744970 0.0291036072 -0.0241831202
Axis.20 Axis.21 Axis.22 Axis.23 Axis.24
1 -0.002131362 0.012259861 -0.0196992525 -0.060740824 -2.032434e-02
2 -0.043135474 0.025827937 0.0323542314 -0.022190521 3.845920e-03
3 -0.042312052 0.105522675 -0.0119684752 -0.029553413 4.530723e-02
4 0.041420110 -0.050122380 0.0555951877 -0.049026588 -1.271760e-02
5 0.005827331 -0.020936413 -0.0175043137 -0.059041951 -7.106306e-02
6 -0.070190421 -0.016020215 -0.0575944394 -0.001890542 4.632957e-02
7 0.070378024 0.001204899 -0.0111340111 -0.024708033 9.971439e-02
8 0.038081384 0.012279850 0.0077589702 0.035269235 -4.674713e-02
9 0.074868350 -0.044851474 -0.0333763171 -0.038411689 -1.541185e-02
10 -0.052812984 -0.012898641 -0.0216698401 -0.014940243 4.704319e-05
11 0.001698562 0.027116784 -0.0402622075 0.014676657 -3.350764e-02
12 0.045233894 -0.056221354 -0.0048906327 0.042305210 -8.337892e-03
13 -0.069713339 0.036379167 -0.0511967918 0.016838467 -4.976119e-04
14 -0.004865128 -0.002282313 0.0185900559 -0.047334546 2.563458e-02
15 0.097325013 0.007182292 0.0263023696 0.001845498 2.790714e-03
16 0.017437267 0.043286520 0.0019735657 0.011931928 2.262578e-02
17 -0.060689939 -0.071609920 0.0633100457 0.005512213 1.344218e-02
18 0.015541723 -0.037171112 0.0428597297 0.060055341 -1.605930e-02
19 0.035282179 -0.017900159 -0.0465549052 0.008832986 5.323375e-02
20 0.035043341 0.048511510 -0.0055053025 -0.053325177 -7.517459e-02
21 -0.052526865 -0.028199027 0.0662566017 0.029320510 -2.250469e-02
22 0.015819424 -0.067078342 -0.0158477302 0.014179577 2.460059e-02
23 -0.000202563 0.032668706 -0.0082344112 0.053308205 -1.365690e-02
24 0.097921389 -0.005894142 -0.0113346201 0.029440700 2.928396e-02
25 -0.051574292 -0.027907656 -0.0412835354 0.001899211 3.543709e-02
26 -0.068436899 0.089643793 0.0927797707 0.001345774 -1.508036e-02
27 0.011149491 0.040052391 -0.0099943177 0.022285398 -1.554967e-02
28 0.036853965 -0.009118436 -0.0199261731 -0.021368480 -3.952900e-02
29 0.026583805 0.040851435 0.0623951432 0.019980568 -2.008480e-02
30 -0.030393913 -0.052949311 -0.0424549125 0.045648049 -9.493119e-03
31 0.014095156 0.037542690 0.0253192514 -0.080095758 -4.298341e-02
32 -0.051000318 0.028399050 -0.1060848908 -0.005870775 -1.389234e-02
33 -0.103430230 -0.074139351 0.0448125834 0.008569644 4.951377e-02
34 0.021859498 0.020915910 0.0945652978 -0.005499474 8.139949e-02
35 -0.026429457 0.022411079 0.0109730354 0.006686024 -1.621954e-02
36 -0.052311010 -0.018579819 -0.0375102136 -0.010195062 -5.137855e-03
37 -0.002633535 0.027430097 0.0002985697 -0.002614678 2.555169e-02
38 -0.027746488 -0.002451079 -0.0008081089 -0.062281465 -1.088238e-02
39 0.026815745 -0.046126407 0.0580031658 0.003699657 -1.062487e-02
40 0.052564158 -0.044721886 -0.0537234326 -0.042939952 3.968057e-02
41 -0.015372756 -0.055219119 -0.0105275295 0.085446282 -8.896190e-02
42 0.046109216 0.102911909 -0.0250612105 0.112952035 2.600353e-02
Axis.25 Axis.26 Axis.27 Axis.28 Axis.29
1 0.0162516839 -0.013735161 -0.051507585 -0.041300585 -0.0118290240
2 -0.0516174532 -0.011956403 -0.017266634 -0.072251116 0.0023073632
3 -0.0174863154 -0.006613766 0.043830046 0.046871309 -0.0207699640
4 0.0699408736 -0.046033848 -0.001028177 0.033900342 0.0374609284
5 0.0222283956 -0.056189550 0.075188820 -0.003152217 -0.0296360272
6 0.0127059271 -0.052524301 -0.015813999 0.047996063 0.0056020819
7 -0.0161962584 -0.034024199 -0.011230514 -0.038691338 0.0357258158
8 -0.0572386766 -0.009325826 -0.010820281 0.042302409 -0.0453953330
9 -0.0087471888 0.008769239 -0.009639198 0.025408854 -0.0184373244
10 -0.0200330252 0.038385412 -0.006152028 0.002891094 -0.0086424145
11 0.0156532808 0.016053878 -0.046086190 0.009395093 -0.0423278384
12 -0.0362725172 -0.015493214 0.004759824 -0.005610562 -0.0076148443
13 0.0653724665 0.012324231 -0.034009086 0.002120227 0.0316181538
14 -0.0140572879 0.052947468 0.012345322 0.018940793 -0.0504524498
15 0.0380363330 0.050645942 0.017111205 0.035038574 -0.0070061935
16 -0.0195544263 -0.037835087 0.019437554 0.021023550 0.0107629308
17 -0.0076589878 0.018433234 0.014860655 0.031821343 -0.0106928435
18 -0.0147953007 -0.031536652 0.036667511 -0.060723017 -0.0296148798
19 -0.0164201249 0.076028698 -0.048534747 0.011999601 0.0053712164
20 -0.0322848955 0.022883982 0.022364045 0.010386463 -0.0237805564
21 0.0432075788 0.093368198 0.003933634 -0.031666866 0.0098029980
22 0.0010640037 0.044792303 0.018269352 -0.016146319 0.0339053018
23 0.0161072488 0.011116515 0.053054408 -0.019276853 0.0232236346
24 0.0113360287 -0.044712165 0.030207017 0.036088221 0.0061343375
25 0.0162705943 0.011045971 0.057608146 0.012881215 0.0283865808
26 0.0378442211 0.001019108 -0.008681707 0.038609754 0.0261413957
27 -0.0082027779 0.021586587 0.050112415 -0.034624477 0.0291472880
28 -0.0105730671 -0.030513408 0.004647620 -0.010960948 0.0745876855
29 -0.0650959992 0.033015120 0.005541323 0.027507494 0.0618185110
30 0.0553720766 0.001049106 -0.021053703 0.037943614 -0.0020776145
31 0.0139545317 -0.003420580 -0.063790081 -0.026132430 0.0159207468
32 -0.0866333488 0.022201607 -0.005803529 0.012558798 0.0119865678
33 -0.0517193218 -0.049742648 -0.004259032 -0.010090623 -0.0129392953
34 0.0178538474 -0.011647544 -0.027034780 0.014113247 -0.0473298826
35 0.0001080057 -0.007700937 0.016976601 -0.008708187 0.0009780183
36 0.0235478842 -0.004793761 0.053721557 -0.031727837 -0.0347467187
37 -0.0318403253 -0.049855378 -0.049080020 -0.006318845 0.0099112781
38 0.0497960066 -0.014013122 -0.003696216 -0.028890174 -0.0090589845
39 -0.0441447047 0.016554635 -0.021612715 -0.014612061 -0.0016616146
40 0.0290830125 0.033582709 -0.004437590 -0.029607907 -0.0132165258
41 0.0025693941 -0.038141414 -0.064621754 0.020594426 0.0019381132
42 0.0522686075 -0.015994977 -0.014477491 -0.049900121 -0.0355006184
Axis.30 Axis.31 Axis.32 Axis.33
1 0.023273788 0.007059238 -0.0007670678 0.0195806506
2 0.023514308 0.008440087 -0.0195077968 0.0110975392
3 0.007375624 0.025390309 -0.0390045934 -0.0097693699
4 -0.016680805 0.014459311 -0.0280898481 0.0322033656
5 0.031192837 -0.001720378 0.0149296218 -0.0260083261
6 0.002665144 -0.014296165 0.0156883844 0.0104191851
7 0.003520665 0.045509962 0.0031206605 -0.0005696576
8 0.020377376 -0.001119220 0.0103908389 0.0164699962
9 0.003159080 -0.010225433 -0.0131623474 0.0021752624
10 0.003586673 0.018143397 -0.0074652988 -0.0047852612
11 0.017964324 0.001426710 -0.0117823493 -0.0133338783
12 0.045901358 0.001736214 -0.0274019560 -0.0019639413
13 -0.001011061 -0.022414931 -0.0033340383 0.0019938052
14 -0.035873204 0.030231437 0.0159758623 -0.0090562313
15 -0.011840620 -0.003567843 -0.0131455924 -0.0125259663
16 -0.024800932 -0.008369656 0.0515838968 0.0073353911
17 0.030098046 -0.021843007 0.0274835839 0.0300012999
18 -0.028947747 -0.028184923 -0.0004814388 0.0041950076
19 -0.008276518 -0.015480804 -0.0003693324 0.0263415402
20 -0.043421184 -0.024885361 -0.0066925564 0.0001134196
21 0.028744420 -0.002497579 0.0185513489 -0.0232132933
22 -0.013523917 -0.004583220 -0.0280938395 -0.0273975523
23 0.023750875 0.036922000 0.0055920084 0.0068566916
24 -0.010733006 0.001053063 0.0049789985 -0.0101555841
25 -0.012398229 -0.017703405 0.0074725893 -0.0106192254
26 -0.010197356 0.003378759 -0.0079557267 0.0099955114
27 -0.020450093 0.009692024 -0.0164942748 0.0318266100
28 0.039536246 -0.005274599 0.0118099877 -0.0116848775
29 0.006151913 -0.012842398 0.0152052807 -0.0091278179
30 -0.002516420 -0.004844648 -0.0182194172 -0.0101578416
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Axis.25 Axis.26 Axis.27 Axis.28
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41 1.315165e-02 0.0144239113 -0.0962105666 -0.0170586359
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Axis.33 Axis.34 Axis.35 Axis.36
1 0.044365766 0.0028402155 0.0711507445 0.0009201103
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Axis.37 Axis.38 Axis.39 Axis.40
1 -0.0165418634 -0.0011633264 -0.0079495912 -1.508493e-03
2 0.0747427526 -0.0284400411 0.0016503723 -3.123105e-03
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42 0.0138739479 -0.0266000974 -0.0164685097 1.537980e-02
$trace.cor
[1] 10.89444
attr(,"class")
[1] "pcoa"# extract the site scores and merge with metadata
lizard.scores <- as.data.frame(lizard.pcoa$vectors) %>%
bind_cols(lizard.meta)
# create convex hulls grouped by site exposure based on site scores
lizard.hulls <- lizard.scores %>%
group_by(Exposure) %>%
slice(chull(Axis.1, Axis.2))
# plot PCoA with color and convex hulls as exposure
# you cannot add loadings to a PCoA because it only works as a distance matrix
lizard.plot.pcoa <- ggplot() +
geom_point(data = lizard.scores, aes(x = Axis.1, y = Axis.2, color = Exposure), size = 2) +
geom_polygon(data = lizard.hulls, aes(x = Axis.1, Axis.2, fill = Exposure), alpha = 0.5) +
scale_fill_viridis_d() +
scale_color_viridis_d() +
theme_bw() +
xlab("PCo1") +
ylab("PCo2") +
ggtitle("PCoA")
lizard.plot.pcoa
- run a non-metric multidimensional scaling ordination (NMDS) on the raw data using the metaMDS function, a Bray-Curtis dissimilarity metric, and two dimensions. Check the stress and plot the results using ggplot. Investigate your PCoA and NMDS side-by-side.
# use metaMDS() to run the nMDS
# specify the data, the dimensions, the number of tries to give the nMDS to find a solution, and the distance metric
lizard.mds <- metaMDS(comm = lizard.raw, k = 2, trymax = 1000, distance = "bray")Square root transformation
Wisconsin double standardization
Run 0 stress 0.1771763
Run 1 stress 0.1810028
Run 2 stress 0.2203687
Run 3 stress 0.1766167
... New best solution
... Procrustes: rmse 0.007816616 max resid 0.03922981
Run 4 stress 0.1781625
Run 5 stress 0.2001068
Run 6 stress 0.2280744
Run 7 stress 0.2564566
Run 8 stress 0.1763359
... New best solution
... Procrustes: rmse 0.03777374 max resid 0.2145651
Run 9 stress 0.1766939
... Procrustes: rmse 0.03832485 max resid 0.2164338
Run 10 stress 0.399861
Run 11 stress 0.2779887
Run 12 stress 0.2001068
Run 13 stress 0.1764021
... Procrustes: rmse 0.008460118 max resid 0.04426154
Run 14 stress 0.2251037
Run 15 stress 0.1766939
... Procrustes: rmse 0.03832441 max resid 0.2164351
Run 16 stress 0.1764591
... Procrustes: rmse 0.008742445 max resid 0.04361434
Run 17 stress 0.1764021
... Procrustes: rmse 0.008459815 max resid 0.04426455
Run 18 stress 0.2623902
Run 19 stress 0.178213
Run 20 stress 0.1763359
... Procrustes: rmse 5.324252e-06 max resid 1.763463e-05
... Similar to previous best
*** Best solution repeated 1 times# view results of nMDS
lizard.mds
Call:
metaMDS(comm = lizard.raw, distance = "bray", k = 2, trymax = 1000)
global Multidimensional Scaling using monoMDS
Data: wisconsin(sqrt(lizard.raw))
Distance: bray
Dimensions: 2
Stress: 0.1763359
Stress type 1, weak ties
Best solution was repeated 1 time in 20 tries
The best solution was from try 8 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: expanded scores based on 'wisconsin(sqrt(lizard.raw))' # view stressplot
stressplot(lizard.mds)
# extract the site scores and merge with metadata
lizard.scores <- as.data.frame(lizard.mds$points) %>%
bind_cols(lizard.meta)
# create convex hulls grouped by site exposure based on site scores
lizard.hulls <- lizard.scores %>%
group_by(Exposure) %>%
slice(chull(MDS1, MDS2))
# plot nMDS with color and convex hulls as exposure
lizard.plot.mds <- ggplot() +
geom_point(data = lizard.scores, aes(x = MDS1, y = MDS2, color = Exposure), size = 2) +
geom_polygon(data = lizard.hulls, aes(x = MDS1, MDS2, fill = Exposure), alpha = 0.5) +
scale_fill_viridis_d() +
scale_color_viridis_d() +
theme_bw() +
xlab("MDS1") +
ylab("MDS2") +
ggtitle("nMDS")
lizard.plot.mds
# view PcOA and nMDS together for comparison
# despite using the same distance metric (Bray-Curtis), the nMDS produces a cleaner, better separation among the transects than the PCoA.
pcoamds <- lizard.plot.pcoa / lizard.plot.mds
pcoamds
Part IV
We will continue using the “fishcoms_lizardisland.csv” dataset, but this time, we will explore differences in fish communities between the two years, 2011 and 2015.
- Calculate fish abundance per transect, site, and year for each species.
- Put the dataset in wide format.
- Split the metadata from the numeric data.
- Run a PCoA with Bray-Curtis dissimilarity.
- Check eigenvalues. Add a correction if needed.
- Plot the PCoA with different colors and polygons for the two years.
library(fishualize)
lizard.d.bray <- vegdist(lizard.raw, method = "bray")
lizard.pcoa.bray <- pcoa(lizard.d.bray)
lizard.pcoa.bray <- pcoa(lizard.d.bray, correction = "cailliez")
lizard.scores.b <- as.data.frame(lizard.pcoa.bray$vectors) %>%
bind_cols(lizard.meta)
lizard.hulls.b <- lizard.scores.b %>%
group_by(year) %>%
slice(chull(Axis.1, Axis.2))
lizard.plot.b <- ggplot() +
geom_point(data = lizard.scores.b, aes(x = Axis.1, y = Axis.2, color = as.factor(year)), size = 2) +
geom_polygon(data = lizard.hulls.b, aes(x = Axis.1, Axis.2, fill = as.factor(year)), alpha = 0.5) +
scale_fill_fish_d(option = "Stegastes_nigricans", end = 0.8) +
scale_color_fish_d(option = "Stegastes_nigricans", end = 0.8) +
theme_bw() +
xlab("PCo1 (12.5%)") +
ylab("PCo2 (8.4%)") +
ggtitle("PCoA") +
guides(color = guide_legend(title = "Year"), fill = "none")
lizard.plot.b