Tag Archives: PERMNOVA

Custom multivariate spread of variance

Recently I had to deal with reviewing some figures I prepared for a manuscript that my colleagues and I submitted for publication.

One figure in particular needed a little bit of “re-styling”. It was the representation of the multivariate-spread of variance using a Principal Component Analysis. My dataset was fairly complex with two species of large reptiles sampled across three years.

The default graphical output produced using plot() is shown below.

With a nice explanatory caption the image could work, but it probably would be best to try and make it from scratch. I struggled a while to figure out the appropriate code to make an image that could deliver the important and appropriate information. I eventually stumbled upon this post that gave me a bunch of good ideas on how to develop my own code to make better graphics.

The main idea is that I wanted to graphically represent the distinction between the two different species sampled across multiple years. I also wanted to highlight differences between sexes. Below is the code and thought process that I followed!

First, the data. To make the example reproducible I used dput() from my R! session and copied the data. The code block below creates two objects: cent and vect. It is just numbers. Feel free to use them to reproduce the example.

cent <- structure(list(grps = structure(c(1L, 7L, 4L, 9L, 2L, 8L, 5L, 10L, 3L, 6L, 11L), 
                          .Label = c("P.F.2012", "P.F.2014", "P.F.2015", 
                          "P.M.2012", "P.M.2014", "P.M.2015", "Y.F.2012", "Y.F.2014", "Y.M.2012", 
                          "Y.M.2014", "Y.M.2015"), class = "factor"), PCoA1 = c(-0.232308295213946, 
                          -0.139600907716025, -0.23871740447522, -0.13289458216504, 0.447510859027901, 
                          0.408846369396462, 0.421557222881589, 0.420000775027015, 0.126708509926023, 
                          0.162432592104704, 0.173235470911422), PCoA2 = c(-0.0767320953158099, 
                          -0.0309422674481247, -0.0595237554222932, 0.0521870006926146, 
                          -0.0196829955701272, -0.0966715610040982, -0.0116833317430039, 
                          -0.126017773437853, 0.472363514000923, 0.526616708002587, 0.410527734672885
                          )), row.names = c("P.F.2012", "Y.F.2012", "P.M.2012", "Y.M.2012", 
                          "P.F.2014", "Y.F.2014", "P.M.2014", "Y.M.2014", "P.F.2015", "P.M.2015", 
                          "Y.M.2015"), class = "data.frame")

vect <- structure(list(group = structure(c(3L, 4L, 1L, 2L, 2L, 2L, 1L, 
              3L, 4L, 4L, 2L, 2L, 2L, 2L, 2L, 2L, 4L, 2L, 4L, 4L, 3L, 3L, 1L, 
              3L, 2L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 4L, 3L, 1L, 3L, 3L, 3L, 3L, 
              3L, 3L, 2L, 4L, 2L, 4L, 4L, 4L, 4L, 3L, 3L, 3L, 3L, 1L, 1L, 3L, 
              1L, 1L, 3L, 3L, 4L, 4L, 4L, 2L, 2L, 3L, 3L, 1L, 3L, 3L, 4L, 3L, 
              1L, 3L, 1L, 4L, 3L, 4L, 3L, 4L, 2L, 4L, 2L, 1L, 3L, 4L, 3L, 4L, 
              3L, 4L, 4L, 3L, 1L, 3L, 2L, 3L, 4L, 1L, 4L, 2L, 2L, 2L, 1L, 4L, 
              2L, 2L, 4L, 4L, 4L, 3L, 4L, 3L, 3L, 3L, 3L, 2L, 3L, 3L, 3L, 3L, 
              3L, 2L, 4L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 3L, 1L, 
              4L, 3L, 3L, 2L, 2L, 1L, 3L, 1L, 2L, 2L, 4L, 4L, 2L, 2L, 1L, 8L, 
              8L, 6L, 8L, 6L, 7L, 5L, 7L, 7L, 8L, 8L, 7L, 7L, 7L, 7L, 5L, 7L, 
              7L, 7L, 7L, 8L, 5L, 8L, 8L, 7L, 5L, 7L, 7L, 8L, 8L, 5L, 5L, 5L, 
              5L, 6L, 6L, 8L, 5L, 8L, 8L, 8L, 8L, 5L, 5L, 6L, 5L, 6L, 8L, 8L, 
              7L, 5L, 5L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 6L, 9L, 10L, 11L, 9L, 
              11L, 11L, 9L, 11L, 11L, 11L, 10L, 11L, 11L, 10L, 11L, 10L, 10L), 
              .Label = c("P.F.2012", "Y.F.2012", "P.M.2012", "Y.M.2012", 
              "P.F.2014", "Y.F.2014", "P.M.2014", "Y.M.2014", "P.F.2015", "P.M.2015", 
              "Y.M.2015"), class = "factor"), PCoA1 = c(-0.230399563384464, 
              -0.134660213481351, -0.203754629089395, -0.256544903538633, -0.0963269236640878, 
              -0.0694337387298244, -0.281789671494329, -0.186386572449756, 
              -0.225180773660388, -0.171370571290936, -0.185937653177261, -0.0313349898106232, 
              -0.177414154493466, -0.286788004227091, -0.057096258535677, 0.0311506121862437, 
              0.00737219333238985, -0.23944399904694, 0.0250201000172532, -0.124498498733216, 
              -0.318666093918789, -0.263058322357503, -0.30437379108452, -0.317716787227452, 
              -0.22936858056337, -0.324020128865818, -0.156284741626089, -0.234488238994369, 
              -0.322947505553436, -0.269254541985182, -0.202171132788021, -0.184842644761263, 
              -0.195859234992588, -0.282295012488084, -0.207769950061687, -0.0432998408453922, 
              -0.278422767726366, -0.00425519745151709, -0.341252606885391, 
              -0.314974083712529, -0.322809684519165, -0.0261828937940813, 
              -0.111006443736141, -0.129545880345861, -0.144589704542049, -0.215927245615552, 
              -0.172530265813857, 0.0341339808656641, -0.301776947671195, -0.33372174237259, 
              -0.186333103181287, -0.197020579486089, -0.178341113926678, -0.277170972770639, 
              -0.250578381488708, -0.198668672218084, -0.260180040538445, -0.231282025822095, 
              -0.316097034833028, -0.168722470602506, -0.175171067223132, -0.214789024421525, 
              -0.215777252772746, -0.230687622399837, -0.216584634169675, -0.290464154917697, 
              -0.217674204709272, -0.309944103911973, -0.334205206599481, -0.110429776451595, 
              -0.26762240366662, -0.131455593967047, -0.168378287926015, -0.295041743014695, 
              -0.241407574594379, -0.230288558216916, -0.254831792720723, -0.124513765659242, 
              0.100275505577226, -0.134938432890682, -0.0558328735565296, -0.252848991866849, 
              -0.164579672506183, -0.197494806897518, -0.141098827666042, -0.254971309037345, 
              -0.167242702726603, -0.23236613623913, 0.0395174244388881, -0.239609836805462, 
              -0.276340875811544, -0.143108361747883, -0.211025748926658, -0.181045470349234, 
              -0.253458918772677, -0.173851745508372, -0.226500308336377, -0.125557875115246, 
              -0.100646606550761, 0.1292556268151, -0.190044071510094, -0.239993579830368, 
              -0.196185432695898, -0.169723453666052, 0.0840757691524504, -0.0828552732030694, 
              -0.18867602251596, -0.240262651678313, -0.240562707504407, -0.195571582299229, 
              -0.29368079508683, -0.189669520157007, -0.106469206939931, -0.159254877744035, 
              -0.252544984788576, -0.181045470349234, -0.251501044444335, -0.14873585609214, 
              -0.341409312007338, -0.29422201212156, 0.00583753495184317, 0.0101775937951025, 
              -0.233187528813313, -0.226864081321846, -0.244494472376726, -0.171210842923591, 
              -0.0595344383338595, -0.0571697905980911, -0.0342463649025507, 
              -0.289206711262372, -0.0433007380702916, -0.24157131439507, -0.181225503601252, 
              -0.298959942537002, -0.248514795038792, -0.279157389102156, -0.231035001544293, 
              -0.234516167629517, -0.0873790575474149, -0.114569468928722, 
              -0.309163789150021, -0.259807938377265, -0.15242487724223, -0.282032055003666, 
              -0.226296767992886, -0.0824717212910516, -0.228792585525858, 
              -0.315322705170076, -0.0386727609378934, -0.237770817011458, 
              0.348112407782663, 0.356305338806301, 0.259899300706282, 0.418475142444894, 
              0.363700298369635, 0.360103274061879, 0.396746129120811, 0.438573922603235, 
              0.382239976357167, 0.388295212367119, 0.300273822578281, 0.364027851104267, 
              0.360612509938702, 0.437527965244732, 0.47438425812642, 0.471126779343484, 
              0.405017558499106, 0.46774443014255, 0.442403233583862, 0.458968573092587, 
              0.464042031205564, 0.451745508543372, 0.466751018499985, 0.445124133569052, 
              0.481801433158007, 0.463260537321389, 0.400227866051992, 0.418509759984409, 
              0.454496511114008, 0.449220367124618, 0.386587934663972, 0.427091644994218, 
              0.450605988088211, 0.441802433298112, 0.384144699353354, 0.452138792538128, 
              0.483330562507924, 0.478196728279581, 0.466356471047664, 0.458880694980997, 
              0.445203812523939, 0.328511120556464, 0.451882416405062, 0.422039425876919, 
              0.434568234897284, 0.456046966754084, 0.429303988670518, 0.396413846996235, 
              0.47022068135355, 0.431215731274915, 0.47275070204514, 0.494238258356094, 
              0.447767018139506, 0.422635825516969, 0.409052142082599, 0.448541432328074, 
              0.435579336028336, 0.373702053711424, 0.470248046885876, 0.432263065254091, 
              0.105801697005539, 0.165491938888967, 0.20183149437323, 0.157063702812224, 
              0.191713328709327, 0.185909449591539, 0.117260129960307, 0.175617881152869, 
              0.113814659221755, 0.113311155284664, 0.156584334899961, 0.162156638432386, 
              0.123828653854679, 0.207413571886514, 0.290935977582346, 0.15476772878197, 
              0.127905386066107), PCoA2 = c(-0.0191341788343272, 0.125168726992728, 
              -0.202390361206006, 0.146490100247817, -0.200301849366383, -0.21201222640355, 
              -0.0494779672831398, -0.064867860513553, 0.216253685647168, 0.0867701091746775, 
              -0.0239106285841686, -0.219393777849861, -0.0230233856717296, 
              -0.0163292155724036, 0.0592152889677712, -0.151617651855222, 
              -0.0212007857869626, 0.115566927346534, -0.164139032263446, 0.0029531837582282, 
              -0.0794717197234781, -0.0293929147442873, -0.110911592901463, 
              -0.12927716953763, 0.117180336391695, -0.0149612458810882, -0.0960266562283222, 
              -0.049729047645075, -0.0682815196170832, -0.155403049889603, 
              -0.0959639620424382, 0.00136368493909292, 0.167474360903015, 
              -0.0890067395142755, -0.0659968504421273, -0.171984415395419, 
              -0.0226301121126082, -0.134899140182382, -0.0652732525645313, 
              -0.0141374766642671, 0.0221177088313266, -0.0277129408215808, 
              -0.0291571032251613, 0.0507403968305617, 0.0783047857485938, 
              0.0835416661450715, 0.125549464068238, -0.095888543364202, 0.023491497876642, 
              -0.0635018258483635, -0.0294487207421573, -0.108823584736146, 
              -0.108034914144809, -0.156157231183656, -0.103386745593316, -0.124905123364418, 
              -0.0133696028998138, 0.0250847436377295, -0.125441363122204, 
              0.131097655495749, 0.0836103428858159, 0.128893730469317, 0.167815421817788, 
              0.0777405296869226, 0.0168663114490739, -0.153183408017823, -0.0909348704469186, 
              -0.14021167293329, -0.0930419417310087, 0.0436877074394201, -0.00225319821767063, 
              0.0208146270029163, -0.00351947062266598, -0.16730817534396, 
              0.112557789748311, 0.0554538524404688, 0.181951585244428, 0.0759461647433655, 
              -0.151581431783219, 0.0096728144345489, 0.00330932981991135, 
              0.0960068455025288, -0.0641591706332058, -0.116160652954858, 
              0.147442288553806, 0.0501155209349927, 0.0275555597633417, 0.0888625671566081, 
              -0.0960489308344658, 0.199273481452986, -0.0189884667557609, 
              0.0618505397737743, -0.121028327612638, -0.0857532086504985, 
              -0.138181163935366, 0.0880040030562361, -0.11030465746869, 0.00878921664279682, 
              -0.199213478490711, -0.192215953774544, 0.022790698668874, 0.00383356262477344, 
              0.0935754276044847, -0.139033365702276, -0.103320887221478, 0.0690232335475765, 
              0.0472656020856467, 0.122565635077436, -0.140102298747715, 0.0641482609425624, 
              -0.176810035404832, -0.129649663515281, -0.0855188451064051, 
              -0.096270764279862, 0.109478651834638, -0.0857532086504985, -0.0858316607142512, 
              0.0368213601207682, -0.08334290200728, -0.0475226873282189, -0.145192106265334, 
              -0.11993047751714, -0.00120734838280895, 0.0575022964973828, 
              0.00454727511837668, -0.0280811381260746, 0.00247121743454203, 
              -0.0632716134030262, 0.124461113311219, -0.0761637363883439, 
              -0.0360108098776078, 0.0514130392932943, -0.0812002685815079, 
              -0.113227844995018, -0.0712238451169342, 0.134504778206784, -0.17693508834818, 
              -0.0970853669034015, -0.149542085154106, -0.00416243122148371, 
              -0.0811795737900006, -0.109000675404029, -0.0682005601517485, 
              0.0805657711155904, -0.00787090753563984, 0.0829178244917227, 
              0.110442089573397, 0.059352757695238, -0.171220731291405, -0.0127368984823977, 
              -0.0227265115960453, -0.0675998040040803, 0.0123777264850023, 
              -0.17625254924779, -0.0100481757634364, -0.033285894872971, -0.0577783326325101, 
              -0.0188681370367962, 0.0312342880777784, -0.098387985154546, 
              -0.0256414863685817, 0.0184863552430799, 0.081342134439549, 0.0550790041300113, 
              -0.0504704902398865, -0.0235293808461972, 0.00786459228718106, 
              0.00223796462343852, 0.030677240684701, -0.132949074151751, -0.128201691014533, 
              -0.0356569432107826, -0.176291205991176, -0.174661762085358, 
              -0.0515899060618532, -0.0981136270684708, -0.117463986256326, 
              -0.0706523168174752, -0.118822448801722, -0.126649486059274, 
              -0.0376663033777901, -0.0143437185846975, -0.0748295755480395, 
              -0.100429323740166, -0.0039755823248106, -0.160655309935462, 
              -0.195631974958725, -0.00593748743055577, -0.170527643205115, 
              -0.206854966976772, -0.123689486612512, -0.0830836612792189, 
              0.069991994970583, 0.048571476449164, -0.137897682849205, 0.0316577678958369, 
              -0.0239325410354453, -0.0893762813948878, -0.157903203693157, 
              0.0731082498062617, -0.0213416320051184, 0.0325948844591984, 
              -0.164645976312765, -0.179307495643697, -0.0786658467646943, 
              -0.00843473288236123, -0.164852727234645, 0.00726274039171153, 
              -0.185240419023864, -0.167149003041966, 0.510517771197614, 0.531555184470961, 
              0.457833699032652, 0.422918169057653, 0.433761403813814, 0.438221290363338, 
              0.483654601747502, 0.44751594154082, 0.457785577272894, 0.348138814437302, 
              0.488861204642494, 0.396585995233976, 0.440405884220264, 0.508177282257904, 
              0.274501006140909, 0.55809258587971, 0.546397282761865)), 
              class = "data.frame", row.names = c(NA, -227L))


I am not going to spend too much time describing what the two objects contain. Suffice to say that cent has the “coordinates” (PCoA1 and PCoA2) of centroid values calculated on the raw data stored in vect.

To help the graphical mapping of the data I first modified the data and add a couple of columns for shape and color of variables. I use a for(){} loop and a regular expression grep() with matching patterns to associate the right color/shape with the appropriate value.

# adding colors
# cent is rather small, only 11 entries
# I can specify by hand the various colors I want
cent$colour <- c("pink", "yellow", "deeppink", "gold",
                 "pink", "yellow", "deeppink", "gold",
                 "pink", "deeppink", "gold")
cent$shape <- NA

# I use a matching expression
# to add a shape factor in the right place
cent$shape[grep(".2012", cent$grps)] <- "a"
cent$shape[grep(".2014", cent$grps)] <- "b"
cent$shape[grep(".2015", cent$grps)] <- "c"

# adding empty variables that will be populated later
vect$v_PCoA1 <- NA
vect$v_PCoA2 <- NA
vect$colour <- NA
vect$shape <- NA

# Populating the empty variables with the 
# coordinates of centroids to draw segments
# in the plot 
for (y in 1:length(vect$group)) {
  for (i in 1:length(cent$grps)) {
    if (vect$group[y] == cent$grps[i]) {
      vect$v_PCoA1[y] <-  cent$PCoA1[i]
      vect$v_PCoA2[y] <-  cent$PCoA2[i]
    } 
  }
}

# One more matching expression
# to add a the appropriate color based on 
# species and sex

vect$colour[grep("P.M.", vect$group)] <- "deeppink"
vect$colour[grep("P.F.", vect$group)] <- "pink"
vect$colour[grep("Y.M.", vect$group)] <- "gold"
vect$colour[grep("Y.F.", vect$group)] <- "yellow"

vect$shape[grep(".2012", vect$group)] <- "a"
vect$shape[grep(".2014", vect$group)] <- "b"
vect$shape[grep(".2015", vect$group)] <- "c"

At this point I am almost there. The only one piece that is missing is to create a convex hull for each group of data of interest.

# Calculating the convex hull
# Basically this is a polygon 
hull_2012_1 <- vect[vect$group=="P.M.2012",1:3][chull(vect[vect$group=="P.M.2012",2:3]),]
hull_2012_2 <- vect[vect$group=="P.F.2012",1:3][chull(vect[vect$group=="P.F.2012",2:3]),]
hull_2012_3 <- vect[vect$group=="Y.M.2012",1:3][chull(vect[vect$group=="Y.M.2012",2:3]),]
hull_2012_4 <- vect[vect$group=="Y.F.2012",1:3][chull(vect[vect$group=="Y.F.2012",2:3]),]
hull_2014_1 <- vect[vect$group=="P.M.2014",1:3][chull(vect[vect$group=="P.M.2014",2:3]),]
hull_2014_2 <- vect[vect$group=="P.F.2014",1:3][chull(vect[vect$group=="P.F.2014",2:3]),]
hull_2014_3 <- vect[vect$group=="Y.M.2014",1:3][chull(vect[vect$group=="Y.M.2014",2:3]),]
hull_2014_4 <- vect[vect$group=="Y.F.2014",1:3][chull(vect[vect$group=="Y.F.2014",2:3]),]
hull_2015_1 <- vect[vect$group=="P.M.2015",1:3][chull(vect[vect$group=="P.M.2015",2:3]),]
hull_2015_2 <- vect[vect$group=="P.F.2015",1:3][chull(vect[vect$group=="P.F.2015",2:3]),]
hull_2015_3 <- vect[vect$group=="Y.M.2015",1:3][chull(vect[vect$group=="Y.M.2015",2:3]),]

Now I have everything I need and I can just use ggplot() to make my graph.

ggplot() +
  geom_polygon(data = hull_2012_1, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2012_2, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2012_3, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2012_4, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2014_1, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2014_2, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2014_3, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2014_4, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2015_1, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2015_2, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_polygon(data = hull_2015_3, aes(x = PCoA1, y = PCoA2), 
               colour = "black", alpha = 0, linetype = "dashed", size = .5) +
  geom_segment(data = vect, aes(x=PCoA1, xend = v_PCoA1, y = PCoA2, yend = v_PCoA2),
               alpha = 0.3) +
  geom_point(data = vect, aes(x = PCoA1, y = PCoA2, fill = vect$colour, shape = vect$shape),
             colour = "black", size = 3, stroke = .6, alpha = 0.9,) +
  geom_point(data = cent, aes(x = PCoA1, y = PCoA2, fill = cent$colour, shape = cent$shape),
             colour = "black", size = 6, stroke = 2) + 
  coord_cartesian(xlim = c(-0.4, 0.5), ylim = c(-0.2, 0.6)) +
  scale_fill_manual(name = "Species/Sex",
                    guide = guide_legend(override.aes = list(shape = 22, size = 5)),
                    values = levels(factor(vect$colour)),
                    #breaks = levels(factor(vect$colour)),
                    labels = c("Male pink", "Male yellow",
                               "Female pink", "Female yellow")
  ) +
  scale_shape_manual(name = "Year",
                     guide = guide_legend(override.aes = list(fill = "black", size = 5)),
                     values = c(21, 22, 23),
                     labels = c("2012", "2014", "2015")
  )