prc {vegan} | R Documentation

## Principal Response Curves for Treatments with Repeated Observations

### Description

Principal Response Curves (PRC) are a special case of Redundancy Analysis (`rda`) for multivariate responses in repeated observation design. They were originally suggested for ecological communities. They should be easier to interpret than traditional constrained ordination.

### Usage

    prc(response, treatment, time, ...)
    ## S3 method for class 'prc':
    summary(object, axis = 1, scaling = 2, digits = 4, ...)
    ## S3 method for class 'prc':
    plot(x, species = TRUE, select, scaling = 2, axis = 1, type = "l",
        xlab, ylab, ylim, lty = 1:5, col = 1:6, pch, legpos, cex = 0.8,
        ...)

### Arguments

`response` | Multivariate response data. Typically these are community (species) data. If the data are counts, they probably should be log transformed prior to the analysis.
`treatment` | A factor for treatments.
`time` | An unordered factor defining the observations times in the repeated design.
`object, x` | An `prc` result object.
`axis` | Axis shown (only one axis can be selected).
`scaling` | Scaling of species scores, identical to the `scaling` in `scores.rda`.
`digits` | Number of significant digits displayed.
`species` | Display species scores.
`select` | Vector to select displayed species. This can be a vector of indices or a logical vector which is `TRUE` for the selected species
`type` | Type of plot: `"l"` for lines, `"p"` for points or `"b"` for both.
`xlab, ylab` | Text to replace default axis labels.
`ylim` | Limits for the vertical axis.
`lty, col, pch` | Line type, colour and plotting characters (defaults supplied).
`legpos` | The position of the `legend`. A guess is made if this is not supplied, and `NA` will suppress legend.
`cex` | Character expansion for symbols and species labels.
`...` | Other parameters passed to functions.

### Details

PRC is a special case of `rda` with a single factor for `treatment` and a single factor for `time` points in repeated observations. In vegan, the corresponding `rda` model is defined as `rda(response ~ treatment * time + Condition(time))`. Since the `time` appears twice in the model formula, its main effects will be aliased, and only interaction terms are available, and will be used in PRC. Instead of usual multivariate ordination diagrams, PRC uses canonical (regression) coefficients and species scores for a single axis. All that the current functions do is to provide a special `summary` and `plot` methods that display the `rda` results in the PRC fashion. With default contrasts (`contr.treatment`) the coefficients are contrasts against the first level, and the levels must be arranged so that the first level is the control.

Function `summary` prints the species scores and the coefficients. Function `plot` plots coefficients against `time` using `matplot`, and has similar defaults. The graph (and PRC) is meaningful only if the first `treatment` level is the control, as the results are contrasts to the first level when unordered factors are used. The plot also displays species scores on the right vertical axis using function `linestack`. Typically the number of species is so high that not all can be displayed with the default settings, but users can reduce character size or padding (`air`) in `linestack`, or `select` only a subset of the species. A legend will be displayed unless suppressed with `legpos = NA`, and the functions tries to guess where to put the legend if `legpos` is not supplied.

### Value

The function is a special case of `rda` and returns its result object (see `cca.object`). However, a special `summary` and `plot` methods display returns differently than in `rda`.

### Warning

The first level of `treatment` must be the control, and the treatment contrasts must be used (see `contr.treatment`), so that results are expressed as contrasts to the control. The function works with other contrast types also, but then the user must take care that the resulting coefficients are meaningful. The `time` must be an unordered factor.

### Author(s)

Jari Oksanen

### References

van den Brink, P.J. & ter Braak, C.J.F. (1999). Principal response curves: Analysis of time-dependent multivariate responses of biological community to stress. Environmental Toxicology and Chemistry, 18, 138–148.

### See Also

`rda`, `anova.cca`.

### Examples

    # Chlorpyrifos experiment and experimental design
    data(pyrifos)
    week <- gl(11, 12, labels=c(-4, -1, 0.1, 1, 2, 4, 8, 12, 15, 19, 24))
    dose <- factor(rep(c(0.1, 0, 0, 0.9, 0, 44, 6, 0.1, 44, 0.9, 0, 6), 11))
    # PRC
    mod <- prc(pyrifos, dose, week)
    mod            # RDA
    summary(mod)   # PRC
    logabu <- colSums(pyrifos)
    plot(mod, select = logabu > 100)
    # Permutations should be done only within one week, and we only
    # are interested on the first axis
    anova(mod, strata = week, first=TRUE)

[Package vegan version 1.8-8 Index]