Build morphospaces using a variety of multivariate methods, and depict shape variation represented by the resulting ordination axes.
mspace(
shapes,
axes = c(1, 2),
links = NULL,
template = NULL,
FUN = stats::prcomp,
p = NULL,
k = NULL,
nh = 5,
nv = 4,
mag = 1,
invax = NULL,
asp = NA,
rescale = TRUE,
xlim = NULL,
ylim = NULL,
xlab = NULL,
ylab = NULL,
adj_frame = c(1, 1),
rot.models = 0,
size.models = 1,
asp.models = 1,
col.models = "#708095",
bg.models = NULL,
lwd.models = 1,
alpha.models = 1,
points = FALSE,
cex.ldm = 1,
col.ldm = "black",
plot = TRUE,
models = TRUE,
...
)Arguments
- shapes
Shape data.
- axes
Numeric of length 1 (univariate morphospace) or 2 (bivariate morphospace), indicating the axes to be plotted.
- links
A list with the indices of the coordinates defining the wireframe (following the format used in
Morpho).- template
Either a 2-column matrix with landmarks/semilandmarks and template curves coordinates (for 2D shape data) or a
"mesh3d"object representing the mean shape of the sample (for 3D shape data). See details below.- FUN
The function (method) to be used for ordination of shape variation. Supported alternatives include
prcomp,phy_prcomp,bg_prcompandpls_shapes.- p
Numeric, indicating the number of landmarks/semilandmarks used (only for landmark data in 2-margin matrices format).
- k
Numeric, indicating the number of cartesian dimensions of landmarks/semilandmarks (only for landmark data in 2-margin matrices format).
- nh
Positive integer; number of shape models along the x axis.
- nv
Positive integer; number of shape models along the y axis.
- mag
Numeric; magnifying factor for shape models.
- invax
Optional integer indicating which of the axes provided in
axesneeds to be inverted (options are1,2orc(1,2)).- rescale
Logical; whether to re-scale background shape models so shape variation is shown more clearly.
- xlim, ylim, xlab, ylab, asp
Standard arguments passed to the generic plot function.
- adj_frame
Numeric of length 2, providing a posteriori scaling factors for the width and height of the frame, respectively.
- rot.models
Numeric; angle (in degrees) to rotate shape models.
- size.models
Numeric; size factor for shape models.
- asp.models
Numeric; the y/x aspect ratio of shape models.
- col.models
Color for wireframes/outlines.
- bg.models
Background color for outlines/meshes.
- lwd.models
Integer; width of the lines in wireframes/outlines.
- alpha.models
Numeric; transparency factor for background models (3D only).
- points
Logical; whether to plot the scatter points.
- cex.ldm
Numeric; size of landmarks/semilandmarks in the background models.
- col.ldm
Color of landmarks/semilandmarks in the background models.
- plot
Logical; whether to plot morphospace.
- models
Logical; whether to plot background shape models.
- ...
Further arguments passed to
FUN.
Value
An object of class "mspace", which is a list containing:
$ordination: a list with the output from the ordination method used, styled in the
prcompformat (typically containing at least an$x,$rotation, and$centerslots. Also contains the type of data ($datype) and ordination method ($ordtype) used.$projected: a list containing the elements that have been projected into the morphospace stored in the
"mspace"object. Initially includes only the background shape models ($shapemodels), but more elements can be added using theproj_*family of functions.$plotinfo: a list containing the graphical parameters used to create the plot. Passed to
plot_mspaceto regenerate morphospaces.
Details
This function is the heart of the morphospace workflow. It
computes a new ordination space from a sample of normalized shapes using
eigenanalysis-based multivariate methods (supported alternatives include
PCA, between groups PCA, phylogenetic PCA, two-block PLS); it will also
generate a series of shape models depicting the range of variation. The
resulting "mspace" object stores all the information necessary to
project and/or retrieve new shapes into the ordination space. The output
of mspace can be expanded using the proj_* family of
functions and the %>% operator from magrittr.
For landmark data, representation of shape variation can be further
aided by providing a template, which contains additional geometric
features from the structure the landmark/semilandmarks were placed upon.
Templates will be warped using TPS interpolation to produce the set of
background shape models. For 2D landmark data, templates must be provided
as a 2-column matrix containing the actual landmarks/semilandmarks,
followed by the coordinates defining a curve or set of curves, separated
from the former and from each other by a row of NAs
(see build_template2d). For 3D landmark data, the template
must be a "mesh3d" object corresponding to the actual mean
shape of the sample (which can be obtained using
expected_shapes + Morpho::tps3d(); see examples below).
See also
Examples
##2D Landmark data
#load and extract relevant data and information
data("tails")
shapes <- tails$shapes
species <- tails$data$species
links <- tails$links
tree <- tails$tree
#generate morphospace using the basic sample of shapes, PCA as ordination
#method and the links between landmarks provided for backround models
mspace(shapes, links = links, mag = 0.7, axes = c(1,2), points = TRUE)
#increase magnification factor x2:
mspace(shapes, links = links, mag = 1.5, axes = c(1,2), points = TRUE)
#plot PCs 1 and 3
mspace(shapes, links = links, mag = 1.5, axes = c(1,3), points = TRUE)
#generate morphospace using the basic sample of shapes, bgPCA as ordination
#method and links between landmarks for backround models
mspace(shapes, links = links, FUN = bg_prcomp, groups = species, mag = 0.7,
axes = c(1,2), invax = 1, points = TRUE)
#generate morphospace using species' consensus shapes, phylogenetic PCA as
#ordination method, and links between landmarks for background models
sp_shapes <- expected_shapes(shapes, species)
mspace(sp_shapes, links = links, FUN = phy_prcomp, tree = tree, mag = 0.7,
axes = c(1,2), points = TRUE)
#just create a morphospace without plotting, save into an object, and inspect
morphosp <- mspace(shapes, links = links, mag = 0.7, axes = c(1,2),
plot = FALSE)
morphosp #general info about the object
#> $ordination
#> Standard deviations (1, .., p=18):
#> [1] 1.426796e-01 6.321339e-02 4.091110e-02 2.872601e-02 1.824931e-02
#> [6] 4.559347e-03 3.059025e-03 5.031532e-09 1.317611e-09 1.153049e-09
#> [11] 4.623420e-10 3.776080e-10 7.165267e-11 2.933615e-11 1.265950e-16
#> [16] 5.341159e-17 3.393677e-17 2.055923e-17
#>
#> Rotation (n x k) = (18 x 18):
#> PC1 PC2 PC3 PC4 PC5
#> [1,] 5.329790e-02 8.002048e-02 -1.709637e-01 1.265618e-01 1.406825e-02
#> [2,] -1.091359e-01 -6.336836e-02 -1.476722e-01 -3.597230e-01 5.881560e-03
#> [3,] 5.329790e-02 8.002047e-02 -1.709637e-01 1.265618e-01 1.406824e-02
#> [4,] 1.091359e-01 6.336838e-02 1.476722e-01 3.597230e-01 -5.881565e-03
#> [5,] -1.594368e-02 4.310034e-02 -2.712629e-01 -1.088825e-01 5.512276e-02
#> [6,] -1.200565e-01 -6.674838e-02 -1.981826e-01 -4.658059e-01 8.099550e-03
#> [7,] -1.594367e-02 4.310032e-02 -2.712629e-01 -1.088826e-01 5.512275e-02
#> [8,] 1.200565e-01 6.674838e-02 1.981826e-01 4.658059e-01 -8.099558e-03
#> [9,] 4.399310e-01 -2.437591e-01 1.046615e-01 -7.443912e-02 -2.401147e-01
#> [10,] 1.491255e-01 -4.527562e-02 -3.582521e-01 2.091877e-01 4.400596e-01
#> [11,] -1.402353e-01 3.900430e-01 3.237856e-01 -9.539350e-02 2.210315e-01
#> [12,] -8.906164e-02 3.528576e-01 -3.026366e-01 1.450829e-01 -4.375836e-01
#> [13,] -6.740999e-01 -5.388095e-01 2.755919e-02 3.043067e-01 -1.002155e-01
#> [14,] 1.213818e-08 -5.804990e-08 1.742740e-09 -4.185695e-09 -6.954021e-08
#> [15,] -1.402353e-01 3.900430e-01 3.237856e-01 -9.539349e-02 2.210314e-01
#> [16,] 8.906166e-02 -3.528576e-01 3.026367e-01 -1.450830e-01 4.375835e-01
#> [17,] 4.399310e-01 -2.437590e-01 1.046615e-01 -7.443910e-02 -2.401147e-01
#> [18,] -1.491256e-01 4.527570e-02 3.582521e-01 -2.091876e-01 -4.400595e-01
#> PC6 PC7 PC8 PC9 PC10
#> [1,] 3.873318e-01 -2.839641e-01 6.844942e-02 -1.343475e-01 5.317757e-03
#> [2,] 4.313873e-01 3.710349e-01 8.266175e-03 -2.096390e-01 -7.185979e-02
#> [3,] 3.873318e-01 -2.839641e-01 -6.844942e-02 1.343475e-01 -5.317734e-03
#> [4,] -4.313872e-01 -3.710349e-01 8.266271e-03 -2.096391e-01 -7.185976e-02
#> [5,] -3.788867e-01 2.954505e-01 7.161155e-02 -1.523507e-01 -4.158114e-03
#> [6,] -1.409452e-01 -4.403843e-01 -3.423388e-02 -1.224052e-01 -7.244692e-02
#> [7,] -3.788867e-01 2.954504e-01 -7.161158e-02 1.523508e-01 4.158112e-03
#> [8,] 1.409451e-01 4.403843e-01 -3.423401e-02 -1.224051e-01 -7.244695e-02
#> [9,] -7.248319e-03 5.735233e-03 -6.846511e-02 4.452142e-01 3.906315e-01
#> [10,] 1.332297e-02 -1.110412e-02 5.147953e-01 2.195411e-01 -5.820761e-03
#> [11,] 5.513743e-03 -7.924600e-03 1.502191e-01 2.157964e-01 -1.812457e-01
#> [12,] -1.038896e-02 8.736658e-03 -2.142650e-01 -1.060949e-01 4.104824e-01
#> [13,] -1.342107e-02 -1.859391e-02 2.759643e-08 -1.286248e-08 1.131728e-08
#> [14,] -3.361147e-08 -1.053959e-07 -5.491251e-01 4.371960e-01 -5.207098e-01
#> [15,] 5.513722e-03 -7.924593e-03 -1.502192e-01 -2.157964e-01 1.812457e-01
#> [16,] 1.038894e-02 -8.736649e-03 -2.142651e-01 -1.060949e-01 4.104824e-01
#> [17,] -7.248325e-03 5.735291e-03 6.846524e-02 -4.452143e-01 -3.906316e-01
#> [18,] -1.332291e-02 1.110418e-02 5.147953e-01 2.195411e-01 -5.820767e-03
#> PC11 PC12 PC13 PC14 PC15
#> [1,] 1.730067e-01 -3.233298e-01 -5.188721e-01 2.539011e-01 -0.325553105
#> [2,] -8.288127e-02 -5.220660e-02 2.995904e-01 3.698919e-01 0.093261498
#> [3,] -1.730066e-01 3.233298e-01 5.188722e-01 -2.539012e-01 -0.323367909
#> [4,] -8.288127e-02 -5.220657e-02 2.995904e-01 3.698918e-01 -0.097186118
#> [5,] 1.942253e-01 -4.656138e-01 2.320760e-01 -3.901983e-01 -0.263614501
#> [6,] -1.710533e-01 1.970719e-01 -2.928273e-01 -3.823447e-01 0.103666897
#> [7,] -1.942253e-01 4.656137e-01 -2.320759e-01 3.901983e-01 -0.261207126
#> [8,] -1.710534e-01 1.970720e-01 -2.928273e-01 -3.823447e-01 -0.106167718
#> [9,] -1.204181e-01 -1.422919e-01 -9.770668e-03 2.531368e-03 0.241836819
#> [10,] -7.985019e-02 -8.677288e-02 -6.041668e-03 2.232092e-03 0.335682314
#> [11,] 5.228479e-01 2.462699e-01 2.676087e-02 -4.819639e-03 0.227184620
#> [12,] 3.186053e-01 8.566835e-02 1.320289e-02 -6.650989e-04 0.255882941
#> [13,] -8.116942e-09 8.768308e-09 -2.498804e-08 1.590465e-08 0.197833429
#> [14,] 3.035895e-02 -2.875216e-01 -2.784881e-02 2.177175e-02 0.004030102
#> [15,] -5.228479e-01 -2.462700e-01 -2.676093e-02 4.819678e-03 0.232955252
#> [16,] 3.186053e-01 8.566833e-02 1.320294e-02 -6.651340e-04 -0.247082993
#> [17,] 1.204181e-01 1.422919e-01 9.770605e-03 -2.531327e-03 0.249434499
#> [18,] -7.985016e-02 -8.677286e-02 -6.041595e-03 2.232045e-03 -0.326525220
#> PC16 PC17 PC18
#> [1,] 0.32604254 0.10397685 -0.02489960
#> [2,] 0.01402703 0.14239211 -0.44107791
#> [3,] 0.33341527 -0.06649184 0.05971565
#> [4,] 0.01263839 0.13989382 -0.44107204
#> [5,] 0.32611973 0.11346748 -0.02920833
#> [6,] 0.01649981 0.08697891 -0.41350974
#> [7,] 0.33424295 -0.07435453 0.06402056
#> [8,] 0.01496981 0.08422631 -0.41350328
#> [9,] 0.32106789 0.32259039 -0.12971788
#> [10,] 0.03781676 -0.36480391 -0.18779327
#> [11,] 0.32403672 0.25111802 -0.09434213
#> [12,] 0.03663362 -0.35191557 -0.19470662
#> [13,] 0.33353719 0.02559396 0.01739194
#> [14,] 0.03355199 -0.32635978 -0.20902145
#> [15,] 0.34350776 -0.19908435 0.12912403
#> [16,] 0.03296627 -0.35851347 -0.19469113
#> [17,] 0.34670358 -0.27014835 0.16449882
#> [18,] 0.03298830 -0.37349074 -0.18777287
#>
#> $projected
#> $projected$shapemodels
#> , , 1
#>
#> [,1] [,2]
#> [1,] 0.29487356 -5.534341e-02
#> [2,] 0.29487355 5.534344e-02
#> [3,] 0.25762935 -6.149401e-02
#> [4,] 0.25762934 6.149404e-02
#> [5,] -0.33371019 -3.657116e-01
#> [6,] -0.25284485 -2.801279e-01
#> [7,] 0.06810435 -9.088825e-09
#> [8,] -0.25284489 2.801279e-01
#> [9,] -0.33371022 3.657116e-01
#>
#> , , 2
#>
#> [,1] [,2]
#> [1,] 0.299722574 -6.527253e-02
#> [2,] 0.299722564 6.527257e-02
#> [3,] 0.256178807 -7.241669e-02
#> [4,] 0.256178796 7.241672e-02
#> [5,] -0.293685498 -3.521442e-01
#> [6,] -0.265603388 -2.882307e-01
#> [7,] 0.006775098 -7.984499e-09
#> [8,] -0.265603418 2.882307e-01
#> [9,] -0.293685535 3.521442e-01
#>
#> , , 3
#>
#> [,1] [,2]
#> [1,] 0.30457159 -7.520166e-02
#> [2,] 0.30457158 7.520169e-02
#> [3,] 0.25472826 -8.333936e-02
#> [4,] 0.25472825 8.333939e-02
#> [5,] -0.25366081 -3.385769e-01
#> [6,] -0.27836192 -2.963335e-01
#> [7,] -0.05455415 -6.880174e-09
#> [8,] -0.27836195 2.963335e-01
#> [9,] -0.25366084 3.385768e-01
#>
#> , , 4
#>
#> [,1] [,2]
#> [1,] 0.3094206 -8.513079e-02
#> [2,] 0.3094206 8.513082e-02
#> [3,] 0.2532777 -9.426204e-02
#> [4,] 0.2532777 9.426207e-02
#> [5,] -0.2136361 -3.250095e-01
#> [6,] -0.2911205 -3.044363e-01
#> [7,] -0.1158834 -5.775848e-09
#> [8,] -0.2911205 3.044362e-01
#> [9,] -0.2136362 3.250095e-01
#>
#> , , 5
#>
#> [,1] [,2]
#> [1,] 0.3142696 -9.505991e-02
#> [2,] 0.3142696 9.505995e-02
#> [3,] 0.2518272 -1.051847e-01
#> [4,] 0.2518272 1.051847e-01
#> [5,] -0.1736114 -3.114421e-01
#> [6,] -0.3038790 -3.125391e-01
#> [7,] -0.1772127 -4.671522e-09
#> [8,] -0.3038790 3.125390e-01
#> [9,] -0.1736115 3.114421e-01
#>
#> , , 6
#>
#> [,1] [,2]
#> [1,] 0.30150830 -6.059747e-02
#> [2,] 0.30150829 6.059751e-02
#> [3,] 0.26120294 -6.702833e-02
#> [4,] 0.26120292 6.702835e-02
#> [5,] -0.35392101 -3.694655e-01
#> [6,] -0.22050518 -2.508714e-01
#> [7,] 0.02342998 -1.390192e-08
#> [8,] -0.22050521 2.508714e-01
#> [9,] -0.35392104 3.694655e-01
#>
#> , , 7
#>
#> [,1] [,2]
#> [1,] 0.30635732 -7.052660e-02
#> [2,] 0.30635731 7.052663e-02
#> [3,] 0.25975239 -7.795100e-02
#> [4,] 0.25975238 7.795103e-02
#> [5,] -0.31389632 -3.558982e-01
#> [6,] -0.23326371 -2.589742e-01
#> [7,] -0.03789927 -1.279760e-08
#> [8,] -0.23326375 2.589742e-01
#> [9,] -0.31389635 3.558981e-01
#>
#> , , 8
#>
#> [,1] [,2]
#> [1,] 0.31120633 -8.045573e-02
#> [2,] 0.31120632 8.045576e-02
#> [3,] 0.25830184 -8.887368e-02
#> [4,] 0.25830183 8.887371e-02
#> [5,] -0.27387163 -3.423308e-01
#> [6,] -0.24602225 -2.670770e-01
#> [7,] -0.09922852 -1.169327e-08
#> [8,] -0.24602228 2.670769e-01
#> [9,] -0.27387166 3.423308e-01
#>
#> , , 9
#>
#> [,1] [,2]
#> [1,] 0.3160553 -9.038485e-02
#> [2,] 0.3160553 9.038489e-02
#> [3,] 0.2568513 -9.979636e-02
#> [4,] 0.2568513 9.979639e-02
#> [5,] -0.2338469 -3.287634e-01
#> [6,] -0.2587808 -2.751798e-01
#> [7,] -0.1605578 -1.058895e-08
#> [8,] -0.2587808 2.751797e-01
#> [9,] -0.2338470 3.287634e-01
#>
#> , , 10
#>
#> [,1] [,2]
#> [1,] 0.3209044 -1.003140e-01
#> [2,] 0.3209044 1.003140e-01
#> [3,] 0.2554007 -1.107190e-01
#> [4,] 0.2554007 1.107191e-01
#> [5,] -0.1938222 -3.151961e-01
#> [6,] -0.2715393 -2.832825e-01
#> [7,] -0.2218870 -9.484619e-09
#> [8,] -0.2715393 2.832825e-01
#> [9,] -0.1938223 3.151960e-01
#>
#> , , 11
#>
#> [,1] [,2]
#> [1,] 0.30814305 -6.585154e-02
#> [2,] 0.30814304 6.585158e-02
#> [3,] 0.26477652 -7.256264e-02
#> [4,] 0.26477650 7.256267e-02
#> [5,] -0.37413183 -3.732195e-01
#> [6,] -0.18816551 -2.216149e-01
#> [7,] -0.02124438 -1.871502e-08
#> [8,] -0.18816554 2.216149e-01
#> [9,] -0.37413186 3.732195e-01
#>
#> , , 12
#>
#> [,1] [,2]
#> [1,] 0.31299207 -7.578067e-02
#> [2,] 0.31299205 7.578070e-02
#> [3,] 0.26332597 -8.348532e-02
#> [4,] 0.26332596 8.348535e-02
#> [5,] -0.33410714 -3.596521e-01
#> [6,] -0.20092404 -2.297177e-01
#> [7,] -0.08257363 -1.761069e-08
#> [8,] -0.20092407 2.297176e-01
#> [9,] -0.33410717 3.596521e-01
#>
#> , , 13
#>
#> [,1] [,2]
#> [1,] 0.3178411 -8.570979e-02
#> [2,] 0.3178411 8.570983e-02
#> [3,] 0.2618754 -9.440799e-02
#> [4,] 0.2618754 9.440802e-02
#> [5,] -0.2940824 -3.460847e-01
#> [6,] -0.2136826 -2.378205e-01
#> [7,] -0.1439029 -1.650637e-08
#> [8,] -0.2136826 2.378204e-01
#> [9,] -0.2940825 3.460847e-01
#>
#> , , 14
#>
#> [,1] [,2]
#> [1,] 0.3226901 -9.563892e-02
#> [2,] 0.3226901 9.563896e-02
#> [3,] 0.2604249 -1.053307e-01
#> [4,] 0.2604249 1.053307e-01
#> [5,] -0.2540578 -3.325174e-01
#> [6,] -0.2264411 -2.459232e-01
#> [7,] -0.2052321 -1.540204e-08
#> [8,] -0.2264411 2.459232e-01
#> [9,] -0.2540578 3.325174e-01
#>
#> , , 15
#>
#> [,1] [,2]
#> [1,] 0.3275391 -1.055680e-01
#> [2,] 0.3275391 1.055681e-01
#> [3,] 0.2589743 -1.162533e-01
#> [4,] 0.2589743 1.162534e-01
#> [5,] -0.2140331 -3.189500e-01
#> [6,] -0.2391996 -2.540260e-01
#> [7,] -0.2665614 -1.429772e-08
#> [8,] -0.2391997 2.540260e-01
#> [9,] -0.2140331 3.189500e-01
#>
#> , , 16
#>
#> [,1] [,2]
#> [1,] 0.31477780 -7.110561e-02
#> [2,] 0.31477778 7.110564e-02
#> [3,] 0.26835010 -7.809696e-02
#> [4,] 0.26835009 7.809698e-02
#> [5,] -0.39434265 -3.769734e-01
#> [6,] -0.15582583 -1.923584e-01
#> [7,] -0.06591874 -2.352812e-08
#> [8,] -0.15582587 1.923584e-01
#> [9,] -0.39434267 3.769734e-01
#>
#> , , 17
#>
#> [,1] [,2]
#> [1,] 0.3196268 -8.103473e-02
#> [2,] 0.3196268 8.103477e-02
#> [3,] 0.2668996 -8.901963e-02
#> [4,] 0.2668995 8.901966e-02
#> [5,] -0.3543180 -3.634060e-01
#> [6,] -0.1685844 -2.004612e-01
#> [7,] -0.1272480 -2.242379e-08
#> [8,] -0.1685844 2.004611e-01
#> [9,] -0.3543180 3.634060e-01
#>
#> , , 18
#>
#> [,1] [,2]
#> [1,] 0.3244758 -9.096386e-02
#> [2,] 0.3244758 9.096390e-02
#> [3,] 0.2654490 -9.994231e-02
#> [4,] 0.2654490 9.994234e-02
#> [5,] -0.3142933 -3.498387e-01
#> [6,] -0.1813429 -2.085640e-01
#> [7,] -0.1885772 -2.131946e-08
#> [8,] -0.1813429 2.085639e-01
#> [9,] -0.3142933 3.498387e-01
#>
#> , , 19
#>
#> [,1] [,2]
#> [1,] 0.3293248 -1.008930e-01
#> [2,] 0.3293248 1.008930e-01
#> [3,] 0.2639985 -1.108650e-01
#> [4,] 0.2639984 1.108650e-01
#> [5,] -0.2742686 -3.362713e-01
#> [6,] -0.1941014 -2.166667e-01
#> [7,] -0.2499065 -2.021514e-08
#> [8,] -0.1941015 2.166667e-01
#> [9,] -0.2742686 3.362713e-01
#>
#> , , 20
#>
#> [,1] [,2]
#> [1,] 0.3341739 -1.108221e-01
#> [2,] 0.3341738 1.108222e-01
#> [3,] 0.2625479 -1.217877e-01
#> [4,] 0.2625479 1.217877e-01
#> [5,] -0.2342439 -3.227040e-01
#> [6,] -0.2068600 -2.247695e-01
#> [7,] -0.3112357 -1.911081e-08
#> [8,] -0.2068600 2.247695e-01
#> [9,] -0.2342439 3.227039e-01
#>
#>
#>
#> $plotinfo
#> $plotinfo$p
#> [1] 9
#>
#> $plotinfo$k
#> [1] 2
#>
#> $plotinfo$links
#> $plotinfo$links[[1]]
#> [1] 1 3 5 6 7 8 9 4 2
#>
#>
#> $plotinfo$template
#> NULL
#>
#> $plotinfo$axes
#> [1] 1 2
#>
#> $plotinfo$nh
#> [1] 5
#>
#> $plotinfo$nv
#> [1] 4
#>
#> $plotinfo$mag
#> [1] 0.7
#>
#> $plotinfo$xlim
#> NULL
#>
#> $plotinfo$ylim
#> NULL
#>
#> $plotinfo$asp
#> [1] NA
#>
#> $plotinfo$rescale
#> [1] TRUE
#>
#> $plotinfo$adj_frame
#> [1] 1 1
#>
#> $plotinfo$asp.models
#> [1] 1
#>
#> $plotinfo$rot.models
#> [1] 0
#>
#> $plotinfo$size.models
#> [1] 1
#>
#> $plotinfo$lwd.models
#> [1] 1
#>
#> $plotinfo$bg.models
#> NULL
#>
#> $plotinfo$col.models
#> [1] "#708095"
#>
#> $plotinfo$alpha.models
#> [1] 1
#>
#> $plotinfo$cex.ldm
#> [1] 1
#>
#> $plotinfo$col.ldm
#> [1] "black"
#>
#> $plotinfo$models
#> [1] TRUE
#>
#> $plotinfo$rotation_matrix
#> NULL
#>
#>
#> attr(,"class")
#> [1] "mspace"
names(morphosp) #slots
#> [1] "ordination" "projected" "plotinfo"
#load wing data for a quick demo with templates
data("wings")
shapes <- wings$shapes
links <- wings$links
template <- wings$template
#generate morphospace using links
mspace(shapes, links = links, mag = 3, axes = c(1,2), points = TRUE)
#> Error in shapes_mat(shapes): object 'data2d' not found
#generate morphospace using template
mspace(shapes, template = template, mag = 3, axes = c(1,2), points = TRUE)
#> Error in shapes_mat(shapes): object 'data2d' not found
##3D Landmark data
if (FALSE) {
#load data and packages and extract relevant data and information
library(Morpho)
library(geomorph)
data("shells3D")
shapes <- shells3D$shapes
mesh_meanspec <- shells3D$mesh_meanspec
#generate morphospace. This is interactive, you need to rotate the shape by
#yourself and then press enter into the console.
mspace(shapes, mag = 1, axes = c(1,2), col.ldm = "black", cex.ldm = 2,
points = TRUE)
#generate morphospace using a mesh template that improves visualization:
#first, get shape corresponding to shells3D$mesh_meanspec using
#geomorph::findMeanSpec
meanspec_id <- findMeanSpec(shapes)
meanspec_shape <- shapes[,,meanspec_id]
#then get the consensus shape and warp the sample mesh to get the mesh
#corresponding to the consensus using Morpho::tps3d
meanshape <- expected_shapes(shapes)
meanmesh <- tps3d(x = mesh_meanspec , refmat = meanspec_shape,
tarmat = meanshape)
#finally, generate morphospace providing template (this function used the
#mesh warped to the mean shape of the entire sample, hence the previous
#lines)
morphosp_3d <- mspace(shapes, mag = 1, axes = c(1,2), template = meanmesh,
bg.models = "gray", nh = 4, nv = 4, cex.ldm = 0,
points = TRUE)
#inspect the contents of the object
morphosp_3d
}
##Outline data
#load and extract relevant data and information
data("shells")
shapes <- shells$shapes$coe
#generate morphospace using all the raw variation
mspace(shapes, mag = 1, axes = c(1,2), nh = 5, nv = 4, size.models = 1,
rescale = FALSE, asp.models = 1, bg.model = "light gray")
#shapes in the background can be rescaled to avhieve a (slightly) better
#visualization. Also, save the ordination into an object.
morphosp_F <- mspace(shapes, mag = 1, axes = c(1,2), nh = 5, nv = 4,
size.models = 1, asp.models = 1,
bg.model = "light gray")
#inspect the contents of the object
morphosp_F
#> $ordination
#> Standard deviations (1, .., p=28):
#> [1] 6.630556e-02 1.568822e-02 1.215250e-02 7.867647e-03 5.781898e-03
#> [6] 4.838864e-03 3.833776e-03 2.799163e-03 2.464360e-03 2.276466e-03
#> [11] 1.835531e-03 1.660593e-03 1.437697e-03 1.307675e-03 1.189539e-03
#> [16] 1.096859e-03 9.622907e-04 9.226957e-04 8.089497e-04 6.210718e-04
#> [21] 5.645506e-04 5.086423e-04 4.254094e-04 3.988798e-04 3.712252e-04
#> [26] 1.462905e-16 6.380812e-18 6.380812e-18
#>
#> Rotation (n x k) = (28 x 28):
#> PC1 PC2 PC3 PC4 PC5
#> A1 -4.145867e-16 -1.191235e-15 9.759333e-17 -3.797246e-15 1.809422e-15
#> A2 4.967593e-02 2.694393e-01 -4.307776e-02 1.206682e-01 2.920123e-01
#> A3 -1.233233e-01 6.942753e-02 1.925656e-01 -2.499869e-01 3.808477e-02
#> A4 2.307683e-02 1.945512e-01 3.955441e-02 1.840008e-01 4.964924e-02
#> A5 -3.872792e-02 2.454062e-02 1.274860e-01 -1.606762e-01 1.183256e-01
#> A6 -7.667248e-03 1.922569e-02 5.116191e-02 1.212619e-01 -1.984051e-02
#> A7 -1.945484e-02 -6.183420e-03 2.117076e-02 3.813111e-02 1.069016e-01
#> B1 0.000000e+00 0.000000e+00 0.000000e+00 -6.938894e-18 -1.110223e-16
#> B2 3.554575e-02 6.172861e-02 -3.195165e-01 -1.462292e-01 2.950328e-01
#> B3 -2.126920e-02 -4.329129e-02 -4.322680e-03 3.890679e-02 -3.274894e-01
#> B4 3.615945e-02 5.969358e-02 -2.672780e-01 -1.876653e-02 2.742349e-02
#> B5 -3.841112e-03 5.080481e-03 3.965784e-02 -6.294367e-02 -3.059885e-01
#> B6 1.569429e-02 4.457797e-02 -1.185847e-01 7.269871e-02 -8.589280e-02
#> B7 9.926818e-03 2.595143e-02 1.777325e-02 -6.881232e-02 -1.366775e-01
#> C1 0.000000e+00 0.000000e+00 -3.786532e-29 -2.584939e-26 -2.646978e-23
#> C2 -2.287316e-02 -1.418314e-01 7.134584e-01 4.019630e-01 1.726615e-01
#> C3 1.981945e-02 -6.678444e-02 3.557905e-02 6.077091e-02 6.288789e-01
#> C4 -4.323135e-03 -8.031176e-02 -6.456261e-02 -2.534568e-01 2.567122e-01
#> C5 -1.070913e-02 -7.573176e-02 -4.987594e-02 1.549285e-01 -4.496193e-02
#> C6 1.605667e-02 -1.441231e-02 -1.207840e-01 -2.083253e-02 1.129421e-01
#> C7 3.871858e-03 -2.982786e-02 -1.247524e-02 -6.056039e-02 -1.069186e-01
#> D1 -9.789602e-01 9.506505e-02 -2.991922e-02 -1.240679e-02 3.609252e-02
#> D2 5.872731e-02 8.420255e-01 4.275123e-02 2.310457e-01 -7.132373e-02
#> D3 1.067527e-01 2.123677e-01 4.304113e-01 -5.817454e-01 8.896310e-03
#> D4 -3.164236e-02 -2.150858e-01 9.061582e-02 1.556738e-01 -1.604395e-01
#> D5 2.829798e-02 -1.003312e-01 -1.349586e-01 3.056239e-01 1.252519e-01
#> D6 -3.034388e-03 -1.069726e-01 2.673224e-02 -1.375360e-01 5.227142e-02
#> D7 1.138204e-02 -5.489064e-02 -6.226012e-02 1.541128e-01 -4.708304e-02
#> PC6 PC7 PC8 PC9 PC10
#> A1 -2.780008e-15 2.993438e-15 -5.752998e-15 2.161461e-15 -2.455056e-15
#> A2 1.013843e-01 -6.456342e-02 -2.316411e-01 -1.561421e-01 -1.165065e-02
#> A3 3.106781e-02 -1.849404e-01 -5.718159e-02 -1.581259e-01 7.359405e-02
#> A4 -1.030835e-01 -2.972308e-01 2.896924e-03 7.738609e-02 -1.203209e-02
#> A5 -9.908202e-02 -2.773935e-02 -3.514089e-01 -7.836970e-02 -3.563651e-02
#> A6 4.227112e-02 -3.230348e-01 -1.339148e-01 1.937922e-01 6.227356e-02
#> A7 -1.864407e-01 -5.140715e-02 -3.621102e-01 -9.643957e-02 -6.583327e-02
#> B1 -8.326673e-17 1.665335e-16 1.110223e-16 4.163336e-16 6.591949e-16
#> B2 5.075439e-02 1.443643e-01 7.138144e-02 4.540165e-01 -5.237024e-01
#> B3 1.450441e-01 -1.292530e-01 -1.256444e-02 -4.173355e-02 -1.959371e-01
#> B4 -3.104690e-01 1.853690e-01 -4.343516e-02 6.778478e-02 -2.582614e-01
#> B5 1.924746e-01 9.372113e-02 -1.226202e-01 1.983177e-01 8.105937e-02
#> B6 -3.246718e-01 1.363179e-01 1.333348e-01 5.694759e-02 -3.726453e-02
#> B7 7.847210e-02 1.995397e-01 -9.952343e-02 2.587674e-01 1.456932e-01
#> C1 -1.694066e-21 -5.421011e-20 -3.469447e-18 -5.551115e-17 0.000000e+00
#> C2 1.331164e-01 3.167495e-01 5.399447e-02 1.188869e-01 -3.339325e-01
#> C3 -1.498743e-01 -1.197196e-01 2.666627e-01 6.261250e-02 3.915079e-01
#> C4 5.323909e-01 -3.349549e-01 6.171582e-02 1.315641e-01 -1.964546e-01
#> C5 -4.329519e-02 -3.389040e-01 7.257201e-02 -4.886240e-01 -4.792306e-01
#> C6 -6.215177e-02 1.148534e-01 -2.938718e-01 -8.281409e-02 -2.630238e-02
#> C7 1.599750e-01 -2.720376e-02 -7.561588e-02 2.762308e-02 8.267170e-02
#> D1 -4.626522e-02 3.761851e-02 -1.826942e-03 3.978805e-02 -2.780241e-02
#> D2 1.347824e-01 -6.131090e-02 1.764722e-02 1.088604e-01 1.096183e-02
#> D3 -3.692986e-01 -7.247460e-02 -8.933700e-02 5.754474e-02 -1.732526e-01
#> D4 -2.818844e-01 -4.946173e-01 -8.240244e-02 5.158041e-01 -1.100814e-02
#> D5 -2.190711e-02 3.832099e-02 -5.661963e-01 5.377325e-02 1.578862e-02
#> D6 2.298868e-01 2.744182e-02 -3.178936e-01 4.167844e-02 6.240215e-02
#> D7 -1.368140e-01 -1.161372e-01 9.360319e-02 2.151035e-02 -2.312622e-02
#> PC11 PC12 PC13 PC14 PC15
#> A1 -4.345987e-15 4.265594e-15 1.226918e-14 2.380328e-14 -4.591606e-15
#> A2 -1.839682e-01 -2.740361e-01 7.323514e-01 -1.295474e-01 1.416244e-01
#> A3 2.480443e-01 -1.528192e-01 -1.810449e-01 2.487820e-01 6.507206e-01
#> A4 6.062471e-02 -9.726789e-02 -5.107899e-02 -1.433534e-01 -1.319825e-01
#> A5 4.279499e-02 1.749171e-01 -9.759593e-02 -8.166315e-02 1.537391e-01
#> A6 2.147828e-01 -1.496628e-01 7.551697e-02 1.981710e-01 -9.285114e-02
#> A7 -4.615518e-02 2.631367e-01 -8.476765e-02 -1.935930e-02 -6.591464e-02
#> B1 4.570996e-16 2.428613e-16 4.718448e-16 -8.326673e-17 1.457168e-16
#> B2 2.683042e-01 -3.918806e-02 6.282717e-02 -4.924132e-02 2.090568e-01
#> B3 3.058551e-01 4.404485e-01 1.895473e-01 -4.412080e-01 6.598064e-02
#> B4 6.267032e-03 -1.816977e-02 -1.009169e-01 2.184067e-01 -8.057212e-02
#> B5 1.445395e-01 3.517963e-02 9.174709e-02 -1.863378e-01 1.023943e-01
#> B6 -3.429344e-04 1.220706e-01 2.101522e-01 2.134044e-01 -3.377876e-02
#> B7 -1.068919e-01 9.840762e-02 6.672664e-02 -1.876669e-01 1.983282e-01
#> C1 0.000000e+00 -1.110223e-16 0.000000e+00 5.551115e-17 -2.775558e-17
#> C2 4.180670e-02 -5.906628e-02 -3.078678e-02 3.151490e-02 -1.824770e-02
#> C3 2.993656e-01 2.835657e-01 5.231419e-03 -2.151536e-01 -3.858997e-02
#> C4 -3.729190e-01 1.567638e-01 -1.686247e-01 3.319544e-02 -1.501370e-01
#> C5 1.124663e-01 4.739139e-05 -5.212835e-03 -2.328240e-03 -1.188509e-02
#> C6 2.233585e-01 -4.702286e-01 -3.535133e-01 -4.634911e-01 -1.216107e-01
#> C7 2.616570e-01 -1.689921e-01 5.927968e-02 1.792277e-02 -4.781461e-01
#> D1 -3.250853e-02 1.698652e-02 5.375188e-02 -3.423480e-02 -1.118427e-01
#> D2 6.752760e-02 1.299809e-01 -2.565887e-01 8.555361e-02 -3.893914e-02
#> D3 -6.880644e-02 1.005484e-01 1.336757e-01 -8.086151e-02 -2.504271e-01
#> D4 -1.372106e-01 -1.972610e-01 9.987079e-03 -3.323282e-02 1.017327e-01
#> D5 -1.789824e-01 3.026395e-01 -1.183682e-01 8.455230e-02 4.050802e-02
#> D6 4.189673e-01 5.389308e-02 1.820392e-01 4.441410e-01 -1.970536e-01
#> D7 2.340624e-01 1.712395e-01 8.366953e-02 1.005234e-01 3.869938e-02
#> PC16 PC17 PC18 PC19 PC20
#> A1 -1.899912e-14 -2.172890e-14 -1.279034e-14 1.869127e-14 2.111276e-14
#> A2 1.220080e-01 -3.919735e-02 -2.004076e-02 1.496203e-01 -8.319480e-02
#> A3 9.697858e-02 4.839994e-02 2.108472e-01 3.016087e-01 1.521580e-01
#> A4 2.220384e-01 6.205459e-01 1.345737e-01 -2.286415e-01 4.501114e-01
#> A5 1.085692e-01 1.577262e-01 1.079186e-01 -4.037594e-01 -5.088537e-01
#> A6 -1.364826e-01 1.329546e-01 -1.737396e-02 -3.866638e-02 -9.311926e-02
#> A7 3.198557e-01 -1.214974e-01 1.185982e-01 -4.506417e-02 3.973741e-03
#> B1 7.771561e-16 8.881784e-16 -4.163336e-17 2.359224e-16 5.273559e-16
#> B2 -1.234765e-01 -9.988887e-02 2.129346e-01 -2.466335e-01 5.840385e-02
#> B3 -2.004968e-02 2.453833e-01 -4.411826e-02 2.373243e-01 -1.791235e-01
#> B4 2.009025e-01 3.210507e-01 -1.499769e-01 5.457057e-01 -2.493863e-01
#> B5 2.723467e-03 -1.079123e-01 1.146846e-01 2.126487e-01 2.119157e-01
#> B6 1.239935e-03 8.241446e-02 9.348519e-02 7.359411e-02 1.888746e-01
#> B7 8.722382e-02 1.756774e-02 -2.881041e-01 -8.297122e-02 2.091528e-01
#> C1 -1.283695e-16 0.000000e+00 1.942890e-16 -1.665335e-16 -4.434387e-17
#> C2 9.083409e-02 3.731629e-02 5.144613e-03 1.016154e-01 -1.994954e-02
#> C3 -1.505140e-01 -4.361398e-02 -4.522317e-02 2.108559e-01 -2.565979e-02
#> C4 2.421004e-01 2.884487e-02 -8.453252e-02 1.984662e-01 5.783163e-02
#> C5 -2.740025e-01 -1.847214e-01 -1.250668e-01 -3.208892e-02 1.468671e-01
#> C6 7.673304e-02 -1.075560e-01 -2.787114e-01 1.122107e-01 9.844437e-02
#> C7 1.156927e-01 -1.646125e-01 5.852090e-01 1.468249e-01 -1.194458e-01
#> D1 -2.495586e-02 -2.474009e-02 -3.258483e-02 3.228117e-03 4.047779e-02
#> D2 -8.373482e-02 -2.004358e-01 -1.111514e-01 3.956626e-02 -1.337999e-01
#> D3 -1.309884e-01 -1.326131e-01 -3.947777e-02 8.494160e-02 2.114128e-01
#> D4 -7.769777e-02 -1.661485e-01 -1.156438e-01 9.061928e-02 -2.156912e-01
#> D5 -2.890901e-01 -8.968267e-02 2.067380e-01 1.647016e-01 2.999113e-01
#> D6 -7.881871e-02 1.041951e-01 -4.499378e-01 -9.988014e-02 7.573533e-02
#> D7 6.523618e-01 -4.241764e-01 -1.334154e-01 -1.090747e-01 1.460125e-01
#> PC21 PC22 PC23 PC24 PC25
#> A1 3.589307e-14 2.134660e-14 1.358987e-14 9.489055e-15 6.200933e-16
#> A2 -2.021038e-02 1.067759e-02 -2.459882e-02 -9.576470e-03 -3.400885e-02
#> A3 8.093032e-04 9.878765e-02 2.723979e-02 1.520095e-01 -5.629338e-02
#> A4 -1.222887e-01 -6.456904e-02 -1.803580e-01 -1.674861e-02 -7.485673e-02
#> A5 -3.623120e-01 -4.456572e-02 2.163693e-01 -2.528102e-01 -1.176181e-01
#> A6 3.960497e-01 -2.499741e-01 5.589883e-01 -7.182355e-02 3.323899e-01
#> A7 2.083744e-01 2.708370e-01 -2.378943e-01 1.706790e-01 6.205938e-01
#> B1 1.276756e-15 8.257284e-16 1.009609e-15 4.440892e-16 -3.285133e-17
#> B2 8.109239e-02 2.998456e-03 -7.625143e-02 6.112366e-02 3.099982e-02
#> B3 2.348836e-01 1.536254e-01 2.591228e-02 1.525109e-01 -1.862709e-01
#> B4 -1.364917e-01 -3.177995e-01 -5.558180e-02 -1.494494e-03 7.261212e-02
#> B5 -2.323056e-01 -1.379008e-01 -1.393172e-01 -6.336926e-01 3.307347e-01
#> B6 -1.981196e-01 6.267864e-01 4.504958e-01 -1.648848e-01 4.534145e-03
#> B7 -3.677183e-01 -1.801246e-01 3.015925e-01 5.327998e-01 2.174164e-01
#> C1 2.220446e-16 -2.220446e-16 -1.387779e-16 3.885781e-16 1.474515e-17
#> C2 -2.947744e-02 3.409219e-02 4.885271e-02 -1.579803e-03 4.063635e-03
#> C3 -1.635945e-01 -4.487405e-02 -6.806549e-03 -2.586287e-02 1.026995e-01
#> C4 -7.800595e-02 1.517813e-01 1.929118e-01 -1.105679e-01 -1.634218e-02
#> C5 -3.852870e-01 -1.319400e-01 6.801292e-02 4.349167e-02 2.063755e-01
#> C6 6.848160e-02 2.393497e-01 1.998180e-01 -7.817000e-02 -9.883161e-02
#> C7 -2.926376e-01 -1.857163e-02 6.134254e-02 3.194948e-01 -6.413516e-02
#> D1 7.856010e-03 -4.084181e-02 2.398739e-03 -1.176107e-02 -2.445514e-02
#> D2 -7.282009e-02 9.953296e-02 -3.947124e-02 2.042193e-02 -2.680007e-02
#> D3 1.121186e-01 -1.335174e-01 3.920642e-02 -5.491905e-03 -1.210632e-01
#> D4 -1.783284e-01 1.884614e-01 -2.192730e-01 6.257769e-02 -8.439287e-02
#> D5 4.155993e-02 -1.546762e-01 7.917485e-02 5.506550e-03 -3.261137e-01
#> D6 -1.214536e-01 1.811315e-01 -2.612937e-01 2.006370e-02 -8.226184e-02
#> D7 7.467957e-02 -2.372662e-01 1.169165e-01 -1.038317e-01 -2.819511e-01
#> PC26 PC27 PC28
#> A1 -1.000000e+00 0.000000e+00 0.000000e+00
#> A2 4.041422e-15 -1.911317e-16 -1.160108e-17
#> A3 6.329229e-15 -5.037665e-16 9.877094e-17
#> A4 -2.799879e-14 -4.862059e-16 1.683027e-16
#> A5 -3.897897e-14 5.031204e-16 -2.541313e-16
#> A6 1.717703e-14 -9.005673e-16 -1.074300e-16
#> A7 8.911591e-15 -1.840397e-16 1.757058e-16
#> B1 6.310887e-29 9.873986e-01 -1.582529e-01
#> B2 1.376453e-15 1.505949e-16 6.298184e-17
#> B3 7.239098e-16 -9.699889e-16 1.180546e-16
#> B4 -9.664659e-15 2.625137e-16 -1.736182e-16
#> B5 -1.360095e-14 5.847481e-16 -3.086612e-16
#> B6 2.177313e-14 -1.059694e-15 4.691522e-17
#> B7 -5.784090e-15 -3.825875e-16 1.721837e-16
#> C1 1.577722e-30 -1.582529e-01 -9.873986e-01
#> C2 -4.021627e-16 1.536397e-17 -2.284210e-17
#> C3 -5.610058e-15 9.206869e-18 -1.361220e-17
#> C4 3.934823e-15 -1.557405e-16 -5.108743e-17
#> C5 -4.184904e-15 1.341629e-15 -1.512347e-16
#> C6 2.686532e-15 -2.827997e-16 -2.323644e-17
#> C7 -1.163206e-14 2.502670e-16 1.763991e-16
#> D1 3.039375e-15 3.917758e-17 -6.936966e-19
#> D2 1.281274e-15 3.984417e-16 -3.277438e-17
#> D3 1.894247e-14 2.776728e-17 2.230525e-17
#> D4 -2.175669e-15 4.100776e-16 -2.237382e-18
#> D5 1.843752e-14 4.839094e-17 2.096714e-17
#> D6 1.489228e-14 3.957950e-17 7.453091e-17
#> D7 -4.460525e-16 -3.568529e-16 4.993092e-17
#>
#> $projected
#> $projected$shapemodels
#> A1 A2 A3 A4 A5 A6
#> [1,] 1 -0.006342011 0.08671459 -4.929756e-03 0.021738378 -2.220405e-04
#> [2,] 1 -0.002232144 0.07651161 -3.020527e-03 0.018534278 -8.563793e-04
#> [3,] 1 0.001877723 0.06630864 -1.111298e-03 0.015330179 -1.490718e-03
#> [4,] 1 0.005987590 0.05610566 7.979310e-04 0.012126080 -2.125057e-03
#> [5,] 1 0.010097457 0.04590268 2.707160e-03 0.008921980 -2.759396e-03
#> [6,] 1 0.000504780 0.08847883 1.403505e-05 0.022361986 2.665084e-04
#> [7,] 1 0.004614647 0.07827585 1.923264e-03 0.019157886 -3.678304e-04
#> [8,] 1 0.008724514 0.06807288 3.832493e-03 0.015953787 -1.002169e-03
#> [9,] 1 0.012834381 0.05786990 5.741722e-03 0.012749687 -1.636508e-03
#> [10,] 1 0.016944248 0.04766693 7.650951e-03 0.009545588 -2.270847e-03
#> [11,] 1 0.007351571 0.09024307 4.957826e-03 0.022985593 7.550574e-04
#> [12,] 1 0.011461438 0.08004009 6.867055e-03 0.019781494 1.207186e-04
#> [13,] 1 0.015571305 0.06983712 8.776284e-03 0.016577395 -5.136202e-04
#> [14,] 1 0.019681172 0.05963414 1.068551e-02 0.013373295 -1.147959e-03
#> [15,] 1 0.023791039 0.04943117 1.259474e-02 0.010169196 -1.782298e-03
#> [16,] 1 0.014198362 0.09200731 9.901616e-03 0.023609201 1.243606e-03
#> [17,] 1 0.018308229 0.08180433 1.181085e-02 0.020405102 6.092675e-04
#> [18,] 1 0.022418096 0.07160136 1.372007e-02 0.017201003 -2.507122e-05
#> [19,] 1 0.026527963 0.06139838 1.562930e-02 0.013996903 -6.594100e-04
#> [20,] 1 0.030637830 0.05119541 1.753853e-02 0.010792804 -1.293749e-03
#> A7 B1 B2 B3 B4 B5
#> [1,] 0.009080876 0 -0.0003739261 2.883557e-03 0.001042821 0.0019842750
#> [2,] 0.007471308 0 0.0025669005 1.123880e-03 0.004034421 0.0016664862
#> [3,] 0.005861740 0 0.0055077271 -6.357975e-04 0.007026022 0.0013486973
#> [4,] 0.004252172 0 0.0084485537 -2.395475e-03 0.010017622 0.0010309084
#> [5,] 0.002642604 0 0.0113893803 -4.155152e-03 0.013009223 0.0007131195
#> [6,] 0.008923748 0 0.0011946756 1.783471e-03 0.002559709 0.0021133765
#> [7,] 0.007314180 0 0.0041355022 2.379354e-05 0.005551310 0.0017955876
#> [8,] 0.005704612 0 0.0070763288 -1.735884e-03 0.008542911 0.0014777987
#> [9,] 0.004095044 0 0.0100171554 -3.495561e-03 0.011534511 0.0011600098
#> [10,] 0.002485476 0 0.0129579820 -5.255238e-03 0.014526112 0.0008422210
#> [11,] 0.008766619 0 0.0027632773 6.833846e-04 0.004076598 0.0022424779
#> [12,] 0.007157051 0 0.0057041039 -1.076293e-03 0.007068199 0.0019246890
#> [13,] 0.005547483 0 0.0086449305 -2.835970e-03 0.010059800 0.0016069001
#> [14,] 0.003937915 0 0.0115857571 -4.595647e-03 0.013051400 0.0012891113
#> [15,] 0.002328347 0 0.0145265837 -6.355324e-03 0.016043001 0.0009713224
#> [16,] 0.008609491 0 0.0043318790 -4.167016e-04 0.005593487 0.0023715793
#> [17,] 0.006999923 0 0.0072727056 -2.176379e-03 0.008585088 0.0020537904
#> [18,] 0.005390355 0 0.0102135322 -3.936056e-03 0.011576688 0.0017360015
#> [19,] 0.003780787 0 0.0131543588 -5.695733e-03 0.014568289 0.0014182127
#> [20,] 0.002171219 0 0.0160951854 -7.455411e-03 0.017559890 0.0011004238
#> B6 B7 C1 C2 C3 C4
#> [1,] 0.001128197 0.001767839 0 -0.007252085 -0.0043575189 -0.002306030
#> [2,] 0.002426642 0.002589120 0 -0.009144463 -0.0027177852 -0.002663698
#> [3,] 0.003725086 0.003410401 0 -0.011036841 -0.0010780515 -0.003021367
#> [4,] 0.005023531 0.004231682 0 -0.012929219 0.0005616822 -0.003379035
#> [5,] 0.006321975 0.005052964 0 -0.014821596 0.0022014159 -0.003736703
#> [6,] 0.002260979 0.002427298 0 -0.010856200 -0.0060545956 -0.004346853
#> [7,] 0.003559424 0.003248579 0 -0.012748578 -0.0044148619 -0.004704521
#> [8,] 0.004857868 0.004069860 0 -0.014640955 -0.0027751282 -0.005062189
#> [9,] 0.006156313 0.004891141 0 -0.016533333 -0.0011353945 -0.005419858
#> [10,] 0.007454757 0.005712422 0 -0.018425711 0.0005043392 -0.005777526
#> [11,] 0.003393762 0.003086756 0 -0.014460314 -0.0077516723 -0.006387675
#> [12,] 0.004692206 0.003908037 0 -0.016352692 -0.0061119386 -0.006745344
#> [13,] 0.005990651 0.004729318 0 -0.018245070 -0.0044722049 -0.007103012
#> [14,] 0.007289095 0.005550599 0 -0.020137448 -0.0028324712 -0.007460681
#> [15,] 0.008587540 0.006371881 0 -0.022029826 -0.0011927374 -0.007818349
#> [16,] 0.004526544 0.003746215 0 -0.018064429 -0.0094487490 -0.008428498
#> [17,] 0.005824989 0.004567496 0 -0.019956807 -0.0078090153 -0.008786167
#> [18,] 0.007123433 0.005388777 0 -0.021849185 -0.0061692816 -0.009143835
#> [19,] 0.008421877 0.006210058 0 -0.023741563 -0.0045295478 -0.009501503
#> [20,] 0.009720322 0.007031339 0 -0.025633941 -0.0028898141 -0.009859172
#> C5 C6 C7 D1 D2
#> [1,] -0.002645628 1.054438e-03 -0.0019663462 -0.4233166 -0.006901607
#> [2,] -0.003531633 2.382864e-03 -0.0016460136 -0.5043095 -0.002042887
#> [3,] -0.004417638 3.711289e-03 -0.0013256809 -0.5853024 0.002815833
#> [4,] -0.005303643 5.039715e-03 -0.0010053483 -0.6662952 0.007674553
#> [5,] -0.006189648 6.368141e-03 -0.0006850157 -0.7472881 0.012533273
#> [6,] -0.004570067 6.882030e-04 -0.0027243097 -0.4209009 0.014495319
#> [7,] -0.005456072 2.016629e-03 -0.0024039771 -0.5018938 0.019354039
#> [8,] -0.006342077 3.345055e-03 -0.0020836445 -0.5828866 0.024212759
#> [9,] -0.007228082 4.673480e-03 -0.0017633118 -0.6638795 0.029071479
#> [10,] -0.008114087 6.001906e-03 -0.0014429792 -0.7448724 0.033930199
#> [11,] -0.006494506 3.219682e-04 -0.0034822733 -0.4184852 0.035892245
#> [12,] -0.007380511 1.650394e-03 -0.0031619406 -0.4994780 0.040750965
#> [13,] -0.008266516 2.978820e-03 -0.0028416080 -0.5804709 0.045609684
#> [14,] -0.009152521 4.307246e-03 -0.0025212753 -0.6614638 0.050468404
#> [15,] -0.010038526 5.635671e-03 -0.0022009427 -0.7424567 0.055327124
#> [16,] -0.008418945 -4.426673e-05 -0.0042402368 -0.4160694 0.057289170
#> [17,] -0.009304950 1.284159e-03 -0.0039199041 -0.4970623 0.062147890
#> [18,] -0.010190955 2.612585e-03 -0.0035995715 -0.5780552 0.067006610
#> [19,] -0.011076960 3.941011e-03 -0.0032792388 -0.6590481 0.071865330
#> [20,] -0.011962965 5.269436e-03 -0.0029589062 -0.7400409 0.076724050
#> D3 D4 D5 D6 D7
#> [1,] -0.07505064 0.0005851296 -0.010442332 0.0021472621 -0.004984709
#> [2,] -0.06621861 -0.0020327555 -0.008101139 0.0018962164 -0.004043032
#> [3,] -0.05738658 -0.0046506407 -0.005759946 0.0016451707 -0.003101356
#> [4,] -0.04855455 -0.0072685258 -0.003418753 0.0013941249 -0.002159679
#> [5,] -0.03972251 -0.0098864110 -0.001077560 0.0011430792 -0.001218003
#> [6,] -0.06965411 -0.0048804699 -0.012991874 -0.0005710456 -0.006379549
#> [7,] -0.06082208 -0.0074983550 -0.010650681 -0.0008220913 -0.005437872
#> [8,] -0.05199005 -0.0101162402 -0.008309488 -0.0010731371 -0.004496196
#> [9,] -0.04315802 -0.0127341253 -0.005968295 -0.0013241828 -0.003554519
#> [10,] -0.03432598 -0.0153520105 -0.003627103 -0.0015752285 -0.002612843
#> [11,] -0.06425758 -0.0103460694 -0.015541416 -0.0032893534 -0.007774389
#> [12,] -0.05542555 -0.0129639546 -0.013200223 -0.0035403991 -0.006832713
#> [13,] -0.04659352 -0.0155818397 -0.010859030 -0.0037914448 -0.005891036
#> [14,] -0.03776149 -0.0181997249 -0.008517837 -0.0040424905 -0.004949359
#> [15,] -0.02892945 -0.0208176100 -0.006176645 -0.0042935362 -0.004007683
#> [16,] -0.05886105 -0.0158116689 -0.018090958 -0.0060076611 -0.009169229
#> [17,] -0.05002902 -0.0184295541 -0.015749765 -0.0062587068 -0.008227553
#> [18,] -0.04119699 -0.0210474392 -0.013408572 -0.0065097525 -0.007285876
#> [19,] -0.03236496 -0.0236653244 -0.011067380 -0.0067607982 -0.006344199
#> [20,] -0.02353292 -0.0262832095 -0.008726187 -0.0070118439 -0.005402523
#>
#>
#> $plotinfo
#> $plotinfo$p
#> [1] 300
#>
#> $plotinfo$k
#> [1] 2
#>
#> $plotinfo$links
#> NULL
#>
#> $plotinfo$template
#> NULL
#>
#> $plotinfo$axes
#> [1] 1 2
#>
#> $plotinfo$nh
#> [1] 5
#>
#> $plotinfo$nv
#> [1] 4
#>
#> $plotinfo$mag
#> [1] 1
#>
#> $plotinfo$xlim
#> NULL
#>
#> $plotinfo$ylim
#> NULL
#>
#> $plotinfo$asp
#> [1] NA
#>
#> $plotinfo$rescale
#> [1] TRUE
#>
#> $plotinfo$adj_frame
#> [1] 1 1
#>
#> $plotinfo$asp.models
#> [1] 1
#>
#> $plotinfo$rot.models
#> [1] 0
#>
#> $plotinfo$size.models
#> [1] 1
#>
#> $plotinfo$lwd.models
#> [1] 1
#>
#> $plotinfo$bg.models
#> [1] "light gray"
#>
#> $plotinfo$col.models
#> [1] "#708095"
#>
#> $plotinfo$alpha.models
#> [1] 1
#>
#> $plotinfo$cex.ldm
#> [1] 1
#>
#> $plotinfo$col.ldm
#> [1] "black"
#>
#> $plotinfo$models
#> [1] TRUE
#>
#> $plotinfo$rotation_matrix
#> NULL
#>
#>
#> attr(,"class")
#> [1] "mspace"