Package 'temporalEF'

Asymmetric temporal eigenfunctions

Description

Generate a set of asymmetric temporal eigenfunctions

Usage

ate(x, ...)

## Default S3 method:
ate(x, N, weight = FALSE, FUN = NULL, link0 = TRUE, ...)

## S3 method for class 'ate'
print(x, digits = 3, ...)

## S3 method for class 'ate'
scores(x, choices, ...)

## S3 method for class 'ate'
eigenvals(x, ...)

Arguments

x	an R object. For ate currently only a sorted vector of time points. For the print method an object of class "ate".
...	additional arguments passed to FUN.
N	numeric; the number of eigenvectors to return. If not supplied, N is taken from the appropriate dimension of x; for the default method, this is the length of x.
weight	logical; should a weighting matrix be generated and applied to the link matrix?
FUN	a function to be applied to the weighting matrix. Ignored if weight is FALSE.
link0	logical; should the link from t[0] be included?
digits	numeric; number of digits to display in output.
choices	numeric; vector indicating which eigenfunctions to return.

Details

The asymmetric eigenvector map (AEM) is a recently proposed method for describing orthongonal spatial functions for use in multivariate ordination. AEMs are asymmetric because they apply a directionality to the spatial dependencies modelled by the eigenfunctions. Asymmetric temporal eigenfunctions (ATEs) implement the AEM idea to model patterns of temporal dependence; i.e. a single spatial dimension.

Author(s)

Gavin L. Simpson

Examples

tp <- seq_len(10)
tefs <- ate(tp)
tefs.I <- moranI(tefs)
plot(tefs.I)

---

Extract temporal eigenfunctions

Description

Simple extractor function to access temporal eigenfunctions from various objects. Currently methods for class(es) '"ate"', '"pctn"', and '"tef"' are provided.

Usage

eigenfuns(x, ...)

## S3 method for class 'ate'
eigenfuns(x, take = NULL, ...)

## S3 method for class 'pctn'
eigenfuns(x, take = NULL, ...)

## S3 method for class 'tef'
eigenfuns(x, take = NULL, ...)

Arguments

x	the object from which to extract temporal eigenfunctions
...	additional arguments passed to methods
take	numeric; which eigenfunctions should be returned

Value

A data frame with one column per eigenfunction

Author(s)

Gavin L. Simpson

---

Build an asymmetric link matrix

Description

Creates an asymmetric link matrix from provided time points.

Usage

makeLinks(tp, link0 = TRUE, dimnames = TRUE)

Arguments

tp	numeric vector of sorted time points
link0	logical; should the link from t[0] be included?
dimnames	logical; should dimnames be attached to the link matrix?

Value

binary matrix of links between time points. The object is a square asymmetric matrix with length(tp) rows and columns. Rows represent the tp time points, and columns are the network links between timepoints.

Author(s)

Gavin L. Simpson

See Also

makeWeights for a matching weight matrix.

Examples

tp <- seq_len(10)
makeLinks(tp)

---

Diagonal weight matrix for time points

Description

A diagonal matrix of weights based on the inverse of time duration between time points.

Usage

makeWeightMat(tp, FUN = NULL, link0 = TRUE, dimnames = TRUE, ...)

Arguments

tp	numeric vector of sorted time points
FUN	a function to apply
link0	logical; should the link from t[0] be included?
dimnames	logical; should dimnames by attached to the matrix?
...	optional arguments passed to FUN

Value

a diagonal matrix of weights with dimensions length(tp) - 1

Author(s)

Gavin L. Simpson

Examples

tp <- seq_len(10)
makeWeightMat(tp)

---

Temporal weight matrix

Description

Build a temporal weighting matrix

Usage

makeWeights(tp, FUN = NULL, link0 = TRUE, dimnames = TRUE, ...)

Arguments

tp	numeric vector of sorted time points
FUN	a function to apply
link0	logical; should the link from t[0] be included?
dimnames	logical; should dimnames by attached to the matrix?
...	optional arguments passed to FUN

Value

a square, symmetric matrix of weights.

Author(s)

Gavin L. Simpson

See Also

makeLinks for a matching link matrix

Examples

tp <- seq_len(10)
makeWeights(tp)

---

Weight vector for time points

Description

A vector of weights based on the inverse of time duration between time points.

Usage

makeWeightVec(tp, FUN = NULL, link0 = TRUE, names = TRUE, ...)

Arguments

tp	numeric vector of sorted time points
FUN	a function to apply
link0	logical; should the link from t[0] be included?
names	logical; should names by attached to the vector?
...	optional arguments passed to FUN

Value

a matrix of weights of length length(tp) - 1

Author(s)

Gavin L. Simpson

Examples

tp <- seq_len(10)
makeWeightVec(tp)

---

Moran's I for temporal eigenfunctions

Description

Calculate Moran's I for tempoeral eigenfunctions and assess significant of Moran's I values via a parametric test that assumes asymptotic normality or a permutation test.

Usage

moranI(x, ...)

## S3 method for class 'ate'
moranI(x, permute = FALSE, alternative = c("two.sided",
  "greater", "less"), nperm = 999, ...)

Arguments

x	an R object of class "ate".
...	additional arguments passed to methods.
permute	logical; test $I$ via a permutation test
alternative	character; the type of test to perform. The default is "two.sided", which allows for both positive and negative spatial correlation (values of $I$). If you anticipate only one of positive or negative spatial association then you can specify "greater" or "less", respectively, as the alternative hypothesis.
nperm	numeric; number of permutations to perform in permutation test if requested.

Value

Numeric vector of Moran's I statistics

Author(s)

Gavin L. Simpson

---

Principal coordinates of temporal neighbours

Description

Computes the classic PCNM by the principal coordinate analysis of a truncated distance matrix, but for a one-dimensional process.

Usage

pctn(x, ...)

## Default S3 method:
pctn(x, threshold, distfun = dist, ...)

## S3 method for class 'pctn'
print(x, digits = 3, ...)

## S3 method for class 'pctn'
scores(x, choices, ...)

## S3 method for class 'pctn'
eigenvals(x, ...)

Arguments

x	an R object. For pctn currently only a sorted vector of time points.
...	additional arguments passed to other methods or on to distfun.
threshold	numeric; threshold beyond which the temporal separation of smaples is considered equal. The default if no value is supplied is to find the largest temporal separation between any two points. Separations greater than the threshold are given a notional separation of 4 times threshold.
distfun	function or character string naming a function that will be used to compute the temporal seperation between samples. Defaults to dist for the Euclidean distance. See Details for further information.
digits	numeric; number of digits to display in output.
choices	numeric; vector indicating which eigenfunctions to return.

Details

The default distance coefficient used to compute temporal separation is the Euclidean distance. If you want to use a different coefficient, you can supply a suitable function to argument distfun. This should be a function that returns an object of class "dist" or a square symmetric matrix that can be coerced to one. Arguments can be passed to distfun via ....

Author(s)

Gavin L. Simpson

Examples

tp <- seq_len(50)
mod <- pctn(tp)
mod

---

Plot asymmetric temporal eigenfunctions

Description

A multi-panel layout showing the calculated tempoeral eigenfunctions.

Usage

## S3 method for class 'ate'
plot(x, pages = 1, ylim, ylab = nams, xlab = "",
  ask = FALSE, ...)

Arguments

x	an object of class "ate"
pages	numeric; the number of pages over which to spread the plots of the individual eigenfunction
ylim	numeric vector of limits for the y-axis
xlab, ylab	x and y-axis labels
ask	logical; should plotting be paused between pages?
...	additional arguments passed to plot

Value

A plot on the currently active device

Author(s)

Gavin L. Simpson

See Also

ate for creating ATE objects

Examples

tp <- seq_len(50)
mod <- ate(tp)
plot(mod, pages = 2)

---

Plot Moran's I statistics for temporal eigenfunctions

Description

A plot of Moran's I versus time.

Usage

## S3 method for class 'moranI'
plot(x, alpha = 0.05, type = "b",
  xlab = "Eigenfunctions", ylab = "Moran's I", pch = 21, bg = "red",
  col = "black", ...)

Arguments

x	an object of class moranI.
alpha	numeric; level of significance
type	character; the type of plotting to use. See plot.default.
xlab	the label for the x-axis of the plot.
ylab	the label for the y-axis of the plot.
pch	the plotting character to use
bg	fill colour of points
col	border colour of points
...	additional arguments passed to plot.

Value

A plot on the current device

Author(s)

Gavin L. Simpson

---

Plot PCTN eigenfunctions

Description

A multi-panel layout showing the calculated tempoeral eigenfunctions.

Usage

## S3 method for class 'pctn'
plot(x, pages = 1, ylim, ylab = nams, xlab = "",
  ask = FALSE, ...)

Arguments

x	an object of class "pctn"
pages	numeric; the number of pages over which to spread the plots of the individual eigenfunctions
ylim	numeric vector of limits for the y-axis
xlab, ylab	x and y-axis labels
ask	logical; should plotting be paused between pages?
...	additional arguments passed to plot

Value

A plot on the currently active device

Author(s)

Gavin L. Simpson

See Also

pctn for creating PCTN objects

Examples

tp <- seq_len(50)
mod <- pctn(tp)
plot(mod, pages = 2)

---

A time lag analysis plot.

Description

A plot of $\sqrt{\mathrm{lag}}$ against compositional dissimilarity.

Usage

## S3 method for class 'timelagAnalysis'
plot(x, ...)

Arguments

x	an object of class "timelagAnalysis", the result of a call to timelag.
...	additional arguments passed to plot.

Details

TODO - smoothers etc.

Value

Invisibly returns its input x.

Author(s)

Gavin L. Simpson

Examples

## load analogue for Abernethy data set & distance()
if (require("analogue")) {

## Load Abernethy Forest data set
data("abernethy", package = "analogue")
## Load Abernethy Forest data set

## Remove the Depth and Age variables
abernethy2 <- abernethy[, -(37:38)]

## time lag analysis
dij <- as.dist(distance(abernethy2, method = "chord"))
tla <- timelag(dij)
plot(tla, pch = 19)
}

---

Temporal eigenfunction ordination

Description

Fits an ordination using temporal eigenfunctions as constraints.

Usage

tef(x, ...)

## Default S3 method:
tef(x, index, method = c("ate", "aem", "pctn", "pcnm"),
  ordination = c("rda"), ...)

Arguments

x	community data matrix or data frame
...	additional arguments passed to other methods. Arguments are also passed to the function generating the temporal eigenfunctions and the constrained ordination function.
index	numeric; the time ordering of the samples from which temporal eigenfunctions will be computed
method	character; which method to use to create the temporal eigenfunctions
ordination	character; the name of the constrained ordination function, from the vegan package to use. Only rda is support currently.

Details

TODO

Value

An object of class "tef", a list with the following components:

ordination

the fitted constrained ordination.

tefs

the computed set of temporal eigenfunctions.

Author(s)

Gavin L. Simpson

---

Time lag analysis

Description

Time lag analysis for a multivariate data set

Usage

timelag(x, ...)

## S3 method for class 'dist'
timelag(x, ...)

Arguments

x	an R object. Only objects of class "dist" are currently supported.
...	additional arguments passed to other methods.

Details

Time lag analysis involves computing the compositional dissimilarity between samples at lag 1, at lag 2, etc, then the least squares slope between $\sqrt{\mathrm{lag}}$ and dissimilarity.

Value

Returns an object of class "timelagAnalysis", a list with components

data

data frame; unpacked set of lags (Lag) and compositional dissimilarities (Distance).

Author(s)

Gavin L. Simpson

Examples

## load analogue for Abernethy data set & distance()
if (require("analogue")) {

## Load Abernethy Forest data set
data("abernethy", package = "analogue")
## Load Abernethy Forest data set

## Remove the Depth and Age variables
abernethy2 <- abernethy[, -(37:38)]

## time lag analysis
dij <- as.dist(distance(abernethy2, method = "chord"))
tla <- timelag(dij)
head(tla[[1]])
}

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