# plot.cca: Plot or Extract Results of Constrained Correspondence... In vegan: Community Ecology Package

## Description

Functions to plot or extract results of constrained correspondence analysis (`cca`), redundancy analysis (`rda`) or constrained analysis of principal coordinates (`capscale`).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```## S3 method for class 'cca' plot(x, choices = c(1, 2), display = c("sp", "wa", "cn"), scaling = "species", type, xlim, ylim, const, correlation = FALSE, hill = FALSE, ...) ## S3 method for class 'cca' text(x, display = "sites", labels, choices = c(1, 2), scaling = "species", arrow.mul, head.arrow = 0.05, select, const, axis.bp = TRUE, correlation = FALSE, hill = FALSE, ...) ## S3 method for class 'cca' points(x, display = "sites", choices = c(1, 2), scaling = "species", arrow.mul, head.arrow = 0.05, select, const, axis.bp = TRUE, correlation = FALSE, hill = FALSE, ...) ## S3 method for class 'cca' scores(x, choices = c(1,2), display = c("sp","wa","cn"), scaling = "species", hill = FALSE, ...) ## S3 method for class 'rda' scores(x, choices = c(1,2), display = c("sp","wa","cn"), scaling = "species", const, correlation = FALSE, ...) ## S3 method for class 'cca' summary(object, scaling = "species", axes = 6, display = c("sp", "wa", "lc", "bp", "cn"), digits = max(3, getOption("digits") - 3), correlation = FALSE, hill = FALSE, ...) ## S3 method for class 'summary.cca' print(x, digits = x\$digits, head = NA, tail = head, ...) ## S3 method for class 'summary.cca' head(x, n = 6, tail = 0, ...) ## S3 method for class 'summary.cca' tail(x, n = 6, head = 0, ...) ```

## Arguments

 `x, object` A `cca` result object. `choices` Axes shown. `display` Scores shown. These must include some of the alternatives `species` or `sp` for species scores, `sites` or `wa` for site scores, `lc` for linear constraints or “LC scores”, or `bp` for biplot arrows or `cn` for centroids of factor constraints instead of an arrow. `scaling` Scaling for species and site scores. Either species (`2`) or site (`1`) scores are scaled by eigenvalues, and the other set of scores is left unscaled, or with `3` both are scaled symmetrically by square root of eigenvalues. Corresponding negative values can be used in `cca` to additionally multiply results with √(1/(1-λ)). This scaling is know as Hill scaling (although it has nothing to do with Hill's rescaling of `decorana`). With corresponding negative values in `rda`, species scores are divided by standard deviation of each species and multiplied with an equalizing constant. Unscaled raw scores stored in the result can be accessed with `scaling = 0`. The type of scores can also be specified as one of `"none"`, `"sites"`, `"species"`, or `"symmetric"`, which correspond to the values `0`, `1`, `2`, and `3` respectively. Arguments `correlation` and `hill` in `scores.rda` and `scores.cca` respectively can be used in combination with these character descriptions to get the corresponding negative value. `correlation, hill` logical; if `scaling` is a character description of the scaling type, `correlation` or `hill` are used to select the corresponding negative scaling type; either correlation-like scores or Hill's scaling for PCA/RDA and CA/CCA respectively. See argument `scaling` for details. `type` Type of plot: partial match to `text` for text labels, `points` for points, and `none` for setting frames only. If omitted, `text` is selected for smaller data sets, and `points` for larger. `xlim, ylim` the x and y limits (min,max) of the plot. `labels` Optional text to be used instead of row names. `arrow.mul` Factor to expand arrows in the graph. Arrows will be scaled automatically to fit the graph if this is missing. `head.arrow` Default length of arrow heads. `select` Items to be displayed. This can either be a logical vector which is `TRUE` for displayed items or a vector of indices of displayed items. `const` General scaling constant to `rda` scores. The default is to use a constant that gives biplot scores, that is, scores that approximate original data (see `vignette` on ‘Design Decisions’ with `browseVignettes("vegan")` for details and discussion). If `const` is a vector of two items, the first is used for species, and the second item for site scores. `axis.bp` Draw `axis` for biplot arrows. `axes` Number of axes in summaries. `digits` Number of digits in output. `n, head, tail` Number of rows printed from the head and tail of species and site scores. Default `NA` prints all. `...` Parameters passed to other functions.

## Details

Same `plot` function will be used for `cca` and `rda`. This produces a quick, standard plot with current `scaling`.

The `plot` function sets colours (`col`), plotting characters (`pch`) and character sizes (`cex`) to certain standard values. For a fuller control of produced plot, it is best to call `plot` with `type="none"` first, and then add each plotting item separately using `text.cca` or `points.cca` functions. These use the default settings of standard `text` and `points` functions and accept all their parameters, allowing a full user control of produced plots.

Environmental variables receive a special treatment. With `display="bp"`, arrows will be drawn. These are labelled with `text` and unlabelled with `points`. The arrows have basically unit scaling, but if sites were scaled (`scaling` `"sites"` or `"symmetric"`), the scores of requested axes are adjusted relative to the axis with highest eigenvalue. With `scaling = "species"` or `scaling = "none"`, the arrows will be consistent with vectors fitted to linear combination scores (`display = "lc"` in function `envfit`), but with other scaling alternatives they will differ. The basic `plot` function uses a simple heuristics for adjusting the unit-length arrows to the current plot area, but the user can give the expansion factor in `mul.arrow`. With `display="cn"` the centroids of levels of `factor` variables are displayed (these are available only if there were factors and a formula interface was used in `cca` or `rda`). With this option continuous variables still are presented as arrows and ordered factors as arrows and centroids.

If you want to have still a better control of plots, it is better to produce them using primitive `plot` commands. Function `scores` helps in extracting the needed components with the selected `scaling`.

Function `summary` lists all scores and the output can be very long. You can suppress scores by setting `axes = 0` or `display = NA` or `display = NULL`. You can display some first or last (or both) rows of scores by using `head` or `tail` or explicit `print` command for the `summary`.

Palmer (1993) suggested using linear constraints (“LC scores”) in ordination diagrams, because these gave better results in simulations and site scores (“WA scores”) are a step from constrained to unconstrained analysis. However, McCune (1997) showed that noisy environmental variables (and all environmental measurements are noisy) destroy “LC scores” whereas “WA scores” were little affected. Therefore the `plot` function uses site scores (“WA scores”) as the default. This is consistent with the usage in statistics and other functions in R (`lda`, `cancor`).

## Value

The `plot` function returns invisibly a plotting structure which can be used by function `identify.ordiplot` to identify the points or other functions in the `ordiplot` family.

## Author(s)

Jari Oksanen

`cca`, `rda` and `capscale` for getting something to plot, `ordiplot` for an alternative plotting routine and more support functions, and `text`, `points` and `arrows` for the basic routines.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```data(dune) data(dune.env) mod <- cca(dune ~ A1 + Moisture + Management, dune.env) plot(mod, type="n") text(mod, dis="cn") points(mod, pch=21, col="red", bg="yellow", cex=1.2) text(mod, "species", col="blue", cex=0.8) ## Limited output of 'summary' head(summary(mod), tail=2) ## Scaling can be numeric or more user-friendly names ## e.g. Hill's scaling for (C)CA scrs <- scores(mod, scaling = "sites", hill = TRUE) ## or correlation-based scores in PCA/RDA scrs <- scores(rda(dune ~ A1 + Moisture + Management, dune.env), scaling = "sites", correlation = TRUE) ```

### Example output

```Loading required package: permute
This is vegan 2.4-3

Call:
cca(formula = dune ~ A1 + Moisture + Management, data = dune.env)

Partitioning of mean squared contingency coefficient:
Inertia Proportion
Total          2.1153     1.0000
Constrained    1.1392     0.5385
Unconstrained  0.9761     0.4615

Eigenvalues, and their contribution to the mean squared contingency coefficient

Importance of components:
CCA1   CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
Eigenvalue            0.4483 0.3001 0.14995 0.10733 0.05668 0.04335 0.03345
Proportion Explained  0.2119 0.1419 0.07089 0.05074 0.02680 0.02050 0.01581
Cumulative Proportion 0.2119 0.3538 0.42470 0.47544 0.50223 0.52273 0.53855
CA1     CA2     CA3     CA4     CA5     CA6     CA7
Eigenvalue            0.3064 0.13191 0.11516 0.10947 0.07724 0.07575 0.04871
Proportion Explained  0.1448 0.06236 0.05444 0.05175 0.03652 0.03581 0.02303
Cumulative Proportion 0.6834 0.74574 0.80018 0.85194 0.88845 0.92427 0.94730
CA8     CA9    CA10    CA11     CA12
Eigenvalue            0.03758 0.03106 0.02102 0.01254 0.009277
Proportion Explained  0.01777 0.01468 0.00994 0.00593 0.004390
Cumulative Proportion 0.96506 0.97975 0.98968 0.99561 1.000000

Accumulated constrained eigenvalues
Importance of components:
CCA1   CCA2   CCA3    CCA4    CCA5    CCA6    CCA7
Eigenvalue            0.4483 0.3001 0.1499 0.10733 0.05668 0.04335 0.03345
Proportion Explained  0.3935 0.2635 0.1316 0.09422 0.04976 0.03806 0.02937
Cumulative Proportion 0.3935 0.6570 0.7886 0.88282 0.93258 0.97063 1.00000

Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions

Species scores

CCA1    CCA2     CCA3     CCA4      CCA5     CCA6
Achimill  0.8150  0.4375 -0.11236  0.35595 -0.114763 -0.01972
Agrostol -0.7488 -0.4783  0.03561  0.17039  0.187389  0.23471
Airaprae -0.8186  1.7469  1.04506 -0.28593  0.191836  0.73077
Alopgeni -0.3442 -1.0216  0.37620  0.02296 -0.004041  0.04789
Anthodor  0.3367  0.7694 -0.07602 -0.05421  0.136354  0.42463
Bellpere  0.6535  0.2200  0.03438  0.60436 -0.090469  0.28138
....
Bracruta -0.1309  0.2009 -0.03708 -0.17421 -0.109657  0.04381
Callcusp -1.5181  0.3834 -0.23255  0.15246  0.104239 -0.11424

Site scores (weighted averages of species scores)

CCA1    CCA2     CCA3    CCA4    CCA5    CCA6
1     1.2468 -0.4017  0.91955  0.7292  1.5785 -1.0196
2     0.8622 -0.1641  0.25789  1.7240 -0.7592 -0.6479
3     0.3165 -0.9785  0.82952  0.7451  0.6556  0.3256
4     0.2405 -0.8699  1.07861  1.4103  1.1164  2.4714
5     1.1362  0.2621 -1.10847 -0.9417  0.5630  1.1495
6     1.0575  0.4041 -1.65035 -1.8483  1.0287 -0.1690
....
19   -0.7913  2.7451  2.93017 -1.3851 -0.3932  1.7277
20   -2.0770  1.0113 -0.02581 -0.8949  1.6406 -1.7917

Site constraints (linear combinations of constraining variables)

CCA1    CCA2     CCA3    CCA4    CCA5     CCA6
1     0.7245 -0.3695  1.25652 -0.3678  0.9827 -0.60590
2     0.9033  0.4250  0.03901  1.0557 -1.0860 -1.61234
3     0.4493 -0.6694  0.67765  0.8695  0.9609  1.52307
4     0.4550 -0.6532  0.72768  0.8529  0.9795  1.50218
5     0.9671 -0.2010 -1.93972 -0.5807  0.2582  0.31905
6     1.0805  0.1235 -0.93911 -0.9126  0.6307 -0.09863
....
19   -1.4581  1.6074  1.16812 -0.5305  0.3178 -0.40336
20   -1.4468  1.6399  1.26818 -0.5637  0.3551 -0.44513

Biplot scores for constraining variables

CCA1    CCA2     CCA3     CCA4     CCA5     CCA6
A1           -0.5554 -0.1617 -0.67982  0.10708 -0.17998  0.30507
Moisture.L   -0.9437 -0.1638  0.07974 -0.02238  0.03067 -0.02368
Moisture.Q   -0.1876  0.3571 -0.45352 -0.17237  0.28350 -0.63025
Moisture.C   -0.2069  0.1732  0.10635  0.68203  0.50123  0.35887
ManagementHF  0.3645 -0.1171 -0.42202 -0.67746  0.17212 -0.12317
ManagementNM -0.5855  0.7267 -0.01115 -0.09642 -0.11445  0.27037
ManagementSF -0.1511 -0.6957  0.38543  0.24770  0.29469  0.23829

Centroids for factor constraints

CCA1     CCA2     CCA3     CCA4     CCA5    CCA6
Moisture1     0.9119  0.35388 -0.40013 -0.26218  0.02084 -0.4708
Moisture2     0.5015 -0.06706  0.60222  1.12478  0.33942  1.2024
Moisture4    -0.1522 -1.35873  0.76544 -1.37289 -1.80794  0.3849
Moisture5    -1.3394  0.11972 -0.20942  0.04843  0.39751 -0.3902
ManagementBF  0.8376  0.41614  0.13885  1.40679 -0.97766 -0.9604
ManagementHF  0.5426 -0.17426 -0.62822 -1.00848  0.25622 -0.1834
ManagementNM -1.1010  1.36665 -0.02097 -0.18131 -0.21523  0.5084
ManagementSF -0.2320 -1.06831  0.59183  0.38035  0.45250  0.3659
```

vegan documentation built on Jan. 25, 2018, 9:45 a.m.