QK Box 16.1

title: “Q & K Box 16.1” output: html_notebook —

Worked example of PCoA: invertebrates in artificial ponds This example continues with the pond invertebrate example used in Boxes 15.2 and 15.3 and uses the data file lemminvert.csv.

Preliminaries

Load core set of packages and vegan, ape

devtools::source_url("https://raw.githubusercontent.com/mjkeough/mjkeough.github.io/refs/heads/main/R/libraries.R")   #This loads a set of packages used often

library(vegan)
library(ape)

Read data

lemminvert <- read.csv("../data/lemminvert.csv")

Do PCoA on lemmens invert data

Use B-C matrix on raw abundances

# Remove pond classification variables
lemminvert.bc <- vegdist(lemminvert[,4:32],method="bray")
# do PCoA
lemminvert.pco <- pcoa(lemminvert.bc)
print(lemminvert.pco)

$correction
[1] "none" "1"   

$note
[1] "No correction was applied to the negative eigenvalues"

$values
       Eigenvalues    Relative_eig   Rel_corr_eig   Broken_stick Cum_corr_eig
1   1.425605593977  0.263894086652 0.216855943873 0.173588509751 0.2168559439
2   1.266281010728  0.234401486766 0.193714195654 0.125969462132 0.4105701395
3   0.686166627796  0.127016417653 0.109453118588 0.102159938322 0.5200232581
4   0.454073168665  0.084053559150 0.075741758515 0.086286922449 0.5957650166
5   0.358117768704  0.066291239236 0.061804325503 0.074382160544 0.6575693421
6   0.297913465130  0.055146810670 0.053059706144 0.064858351020 0.7106290483
7   0.249986262908  0.046274998362 0.046098324391 0.056921843084 0.7567273727
8   0.200085412339  0.037037843682 0.038850272043 0.050119121996 0.7955776447
9   0.157519751844  0.029158507246 0.032667649262 0.044166741043 0.8282452940
10  0.127511876510  0.023603744494 0.028309033150 0.038875735752 0.8565543271
11  0.102437725035  0.018962264178 0.024667035862 0.034113830990 0.8812213630
12  0.086648234474  0.016039468976 0.022373626975 0.029784826661 0.9035949900
13  0.052157452222  0.009654874584 0.017363872784 0.025816572693 0.9209588627
14  0.043769562909  0.008102191010 0.016145539626 0.022153569030 0.9371044024
15  0.033994869408  0.006292795883 0.014725774444 0.018752208486 0.9518301768
16  0.024405460446  0.004517698809 0.013332921670 0.015577605311 0.9651630985
17  0.018274390907  0.003382775515 0.012442389496 0.012601414835 0.9776054880
18  0.000000000000  0.000000000000 0.008610318709 0.009800294387 0.9862158067
19 -0.008108364421 -0.001500940675 0.006387395720 0.007154791741 0.9926032024
20 -0.023412578925 -0.004333906347 0.005202865160 0.004648526077 0.9978060676
21 -0.031567746639 -0.005843510787 0.002193932429 0.002267573696 1.0000000000
22 -0.052283422430 -0.009678192950 0.000000000000 0.000000000000 1.0000000000
23 -0.067388044891 -0.012474212105 0.000000000000 0.000000000000 1.0000000000
   Cumul_br_stick
1    0.1735885098
2    0.2995579719
3    0.4017179102
4    0.4880048327
5    0.5623869932
6    0.6272453442
7    0.6841671873
8    0.7342863093
9    0.7784530503
10   0.8173287861
11   0.8514426171
12   0.8812274437
13   0.9070440164
14   0.9291975855
15   0.9479497940
16   0.9635273993
17   0.9761288141
18   0.9859291085
19   0.9930839002
20   0.9977324263
21   1.0000000000
22   1.0000000000
23   1.0000000000

$vectors
           Axis.1         Axis.2          Axis.3           Axis.4          Axis.5
1  -0.27508949873 -0.05212328360  0.014015261009  0.1089673486792  0.035340804174
2  -0.09225316967 -0.27722834929  0.061415789541  0.0473687348225 -0.014826832565
3   0.04497220159 -0.31710565088 -0.084121681319 -0.0774249988121  0.001257019948
4  -0.07478040177  0.24794033551  0.319389075209 -0.1006848698509  0.031128948998
5   0.31007361349  0.08830565568  0.021372311118 -0.0003292858567 -0.129666829527
6  -0.32990486973 -0.06914779567 -0.199921267176 -0.1273830032493 -0.232877701405
7  -0.44598071727  0.29070151329 -0.274800125698  0.0895717959311  0.192311510708
8  -0.43179013888  0.42182479954 -0.039661088651 -0.0239355519179  0.054820950193
9  -0.28813448977 -0.13905574476 -0.003969375199  0.1489252052391  0.056658377557
10 -0.10720543595  0.17517697996  0.125995564097 -0.2939766412196  0.171589947791
11 -0.15999745080  0.18903652281  0.094658999259 -0.2286412221754 -0.331423881925
12  0.31619846568  0.34300840034 -0.379288368019  0.2345505531504 -0.205494740240
13  0.16302805891 -0.12061021666  0.157297592675  0.0801902280596 -0.036058548523
14  0.02245818427 -0.25678113517 -0.013446781631  0.0039316964956  0.024786725307
15  0.05266626691  0.19087431823  0.340790209886  0.2939955826411 -0.001252034785
16  0.36841006387  0.21297423012 -0.001289891340 -0.0120565163727  0.094633825400
17  0.41642243507  0.11965964413 -0.140501002168 -0.0672173936658  0.173650106425
18 -0.08282681422 -0.17334241330  0.150216458267  0.2376349553081 -0.023016186857
19  0.03112215703 -0.23821347506  0.098020719035  0.0044359546117  0.017430630881
20  0.38304152033  0.17693621408 -0.037443612040 -0.0955406276020  0.064253824025
21 -0.05236358691 -0.37639442872 -0.230788679681 -0.0266194377851  0.041032275117
22  0.12617652088 -0.30377158448 -0.128618034598 -0.1041302858626  0.085723592360
23  0.10575708569 -0.13266453607  0.150677927422 -0.0916322205682 -0.070001783055
           Axis.6          Axis.7          Axis.8          Axis.9         Axis.10
1   0.04824095155 -0.014069004387  0.292721869963  0.093090742756 -0.016760875159
2  -0.10030236281  0.039336944245 -0.050133809209 -0.013650266348  0.030936268285
3  -0.00189993911 -0.001147952734  0.013503447194  0.012011736860  0.006199503153
4  -0.23107137032  0.017170290126  0.022282248093 -0.005392612792  0.042208335824
5   0.08401290834 -0.197277645404 -0.208081746479  0.142381544796  0.009046744912
6   0.05954403021  0.127489871590 -0.073283125535 -0.025272096839  0.010578503228
7   0.12642290946 -0.052232268283 -0.057558285243  0.035020854632  0.151701029465
8   0.10144271665 -0.095990226546 -0.012643732944 -0.034131211524 -0.085917379936
9  -0.13799278633  0.166888623105 -0.072845742333  0.059205424439 -0.023137704395
10 -0.20075787163 -0.110118066006 -0.058258007961 -0.076564633497 -0.025259139660
11  0.08502821640  0.056741781296  0.069252398508  0.026809553047 -0.072983418776
12 -0.26142606460 -0.081116519509  0.068074632278 -0.068960843274  0.014359483696
13  0.10929101893 -0.113442354380  0.010290075316 -0.087205322781  0.127911781954
14  0.05418826419  0.056792833546 -0.101069363236 -0.066314475601 -0.009021090850
15  0.01002821687  0.111603394481 -0.080981931773  0.073957974889 -0.037058692027
16  0.17163352729  0.136319300543  0.015080513545 -0.234460895500 -0.034937950432
17  0.03719521799  0.040264493211  0.008953128593  0.149334015750 -0.148583650503
18  0.06416433425 -0.096221881798  0.006200815476 -0.081833642670 -0.119123141298
19 -0.01197600800 -0.072103659890  0.099638238257 -0.021250395252  0.037799817469
20  0.03419850918  0.197679390536  0.069185519034  0.073377090669  0.118659773979
21 -0.08766014130  0.070288487425 -0.059778356269 -0.018101052674 -0.031542237915
22  0.01250784500 -0.149846702455  0.065171266229  0.019202232509 -0.055732270775
23  0.03518787777 -0.037009128711  0.034279948497  0.048746278406  0.110656309760
            Axis.11         Axis.12        Axis.13          Axis.14          Axis.15
1  -0.0771717188901  0.077812751475 -0.03187609406  0.0747993853439  0.0229458889079
2   0.0841374212898 -0.055389020205 -0.02693409203  0.0319426406035  0.0320850008010
3  -0.0379881711385  0.056771671469 -0.02083562147 -0.0596874914358  0.0166059756231
4   0.0680942813806  0.007603277406 -0.09018362834  0.0008408010569 -0.0427540870683
5  -0.0191102746926  0.113171638751 -0.02733883261  0.0543010296619  0.0272783561690
6  -0.0166339515141 -0.069720937732 -0.10382147589  0.0462979719501 -0.0251310005164
7   0.0679684067238  0.031038310577 -0.01817899508 -0.0777996506194  0.0002150316207
8  -0.0409222323760 -0.085803776447  0.04581164872  0.0506505185248 -0.0011925694844
9   0.0167152262695  0.086763162142  0.08664456446  0.0248674574887 -0.0203362959273
10 -0.0824635294075  0.025159387676  0.02701204871  0.0061483979561  0.0276462124724
11  0.0731475047807  0.029825065777  0.07634609000 -0.0641719338721  0.0248279835189
12 -0.0304303075437 -0.014805107052  0.01006553732 -0.0166592573395  0.0033160138076
13  0.0720795336929 -0.074968839510  0.06994219518  0.0752736672419 -0.0110965392231
14 -0.1611182860690 -0.047986408422 -0.01215291090 -0.0300863187059  0.0469379915693
15 -0.0297391084593 -0.069422763715  0.01646501394 -0.0416294147041  0.0165421357061
16  0.0428994073724  0.109991608182 -0.01765826852  0.0169448267595 -0.0033367662936
17  0.0940098057162 -0.058997154393 -0.03445082756  0.0083719005343 -0.0064022798770
18 -0.0216478876730  0.024205741116 -0.04575699834 -0.0435289098724 -0.0564733030486
19  0.0791786453877 -0.025491404524 -0.02418808296 -0.0327928713180  0.1028824232478
20 -0.0880331530917 -0.046846550385  0.02203677020  0.0056706103703 -0.0009173536798
21  0.0574310241043  0.033080221105  0.05027730005  0.0336015217004 -0.0115034884680
22 -0.0001278653959 -0.073378980009  0.02858229553 -0.0354879874747 -0.0553896798084
23 -0.0502747704666  0.027388106717  0.02019236364 -0.0278668938503 -0.0867496500490
            Axis.16         Axis.17
1   3.191437526e-02 -0.023395733393
2   6.107752417e-02 -0.008850538502
3   2.617688718e-02  0.084685887761
4   1.366959325e-02  0.006507392414
5  -5.902123959e-03 -0.001998963742
6  -3.766980936e-02 -0.008545967425
7   2.171755581e-02 -0.015933656584
8  -2.516961373e-02  0.043161774728
9  -5.266172427e-02 -0.009495218628
10  4.746237933e-03 -0.010641406097
11  3.365931620e-02 -0.011706550393
12 -6.011788656e-05 -0.006035505526
13  2.562162053e-02  0.013117182227
14  2.901001748e-02 -0.041566765294
15  5.752265878e-03 -0.011251749630
16 -8.056615254e-03 -0.021018230875
17  4.719126563e-03 -0.005503134976
18 -2.583076013e-03  0.034924191941
19 -9.550496510e-02  0.001061124666
20 -7.400224395e-03  0.040838534494
21  1.736720210e-02  0.015715475865
22 -6.481545128e-03 -0.041454110064
23 -3.394190726e-02 -0.022614032964

$trace
[1] 5.402188477

attr(,"class")
[1] "pcoa"

biplot(lemminvert.pco,lab=lemminvert$manag)

Improve plot

Plots used for QK use the ggplot classic theme, with some tweaks. Tweaks are consolidated into theme_QK; use this theme for figures and tweak the theme to avoid repetitive code changes.

devtools::source_url("https://raw.githubusercontent.com/mjkeough/mjkeough.github.io/refs/heads/main/R/appearance.R")  #Graphics tweaks

Get labels back on

# extract coordinates
a<-as.data.frame(lemminvert.pco$vectors)
# Need to get management types on this plot
a<-cbind(lemminvert[c(1:3)],a)   #Add site names & symbols from original data file
br=c("nm","li","nf","yf")     #Categories from original file; define as object to avoid retyping
la=c("None", "Light", "No fish", "Young fish")   #Labels; define here to avoid retyping
p2<-ggplot(data=a, aes(x=Axis.1, y=Axis.2, shape=manag, ) )+
  geom_point()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=sym4,
                     name="Management",
                     breaks=br,
                     labels=la,
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )+
  theme_qk()+
  theme(legend.position = "top")
p2

# colour version using viridis palette d
p2a<-ggplot(data=a, aes(x=Axis.1, y=Axis.2, color=manag, ) )+
  geom_point()+
  labs(y="MDS2", x="MDS1")+
  scale_color_viridis_d(
                     name="Management",
                     breaks=br,
                     labels=la,
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )+
  theme_qk()+
  theme(legend.position = "top")
p2a