[Vegan-commits] r1708 - pkg/vegan/inst/doc
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Wed Aug 10 14:44:15 CEST 2011
Author: jarioksa
Date: 2011-08-10 14:44:14 +0200 (Wed, 10 Aug 2011)
New Revision: 1708
Modified:
pkg/vegan/inst/doc/decision-vegan.Rnw
pkg/vegan/inst/doc/diversity-vegan.Rnw
pkg/vegan/inst/doc/intro-vegan.Rnw
Log:
fix Rnw for jss.cls
Modified: pkg/vegan/inst/doc/decision-vegan.Rnw
===================================================================
--- pkg/vegan/inst/doc/decision-vegan.Rnw 2011-08-10 05:48:12 UTC (rev 1707)
+++ pkg/vegan/inst/doc/decision-vegan.Rnw 2011-08-10 12:44:14 UTC (rev 1708)
@@ -9,6 +9,7 @@
%\usepackage[T1]{fontenc}
\usepackage{sidecap}
\renewcommand{\floatpagefraction}{0.8}
+\renewcommand{\cite}{\citep}
\author{Jari Oksanen}
\title{Design decisions and implementation details in vegan}
@@ -19,12 +20,12 @@
}
\Keywords{nestdness, matrix temperature, community null models, scaling of PCA and RDA, WA
and LC scores}
-
+%% hijack Address for version info
\Address{$ $Id$ $
processed with vegan
\Sexpr{packageDescription("vegan", field="Version")}
in \Sexpr{R.version.string} on \today}
-\Footername{This version}
+\Footername{About this version}
%% need no \usepackage{Sweave.sty}
\begin{document}
@@ -76,15 +77,16 @@
outside the fill line or absences within the fill line.}
\end{SCfigure}
The function can be implemented in many ways following the general
-principles. Rodr{\'i}guez-Giron{\'e}s and Santamaria \cite{RodGir06}
-have seen the original code and reveal more details of calculations,
-and their explanation is the basis of the implementation in
-\pkg{vegan}. However, there are still some open issues, and
-probably \pkg{vegan} function \code{nestedtemp} will never
+principles. \citet{RodGir06} have seen the original code and reveal
+more details of calculations, and their explanation is the basis of
+the implementation in \pkg{vegan}. However, there are still some open
+issues, and probably \pkg{vegan} function \code{nestedtemp} will never
exactly reproduce results from other programs, although it is based on
-the same general principles. I try to give main computation details in
-this documents --- all details can be seen in the source code of
-\code{nestedtemp}.
+the same general principles.\footnote{function \code{nestedness} in
+ the \pkg{bipartite} package is a direct port of the original
+ \proglang{BINMATNEST} program of \citet{RodGir06}.} I try to give
+main computation details in this document --- all details can be seen
+in the source code of \code{nestedtemp}.
\begin{itemize}
\item Species and sites are put into unit square \citep{RodGir06}. The
@@ -119,7 +121,7 @@
y = (1-(1-x)^p)^{1/p}
\end{equation}
This is similar to the equation suggested by
- \cite[eq. 4]{RodGir06}, but omits all terms dependent on the
+ \citet[eq. 4]{RodGir06}, but omits all terms dependent on the
numbers of species or sites, because I could not understand why
they were needed. The differences are visible only in small data
sets. The $y$ and $x$ are the coordinates in the unit square, and
@@ -151,11 +153,11 @@
``Springer'' in German which is very appropriate as Springer was the
publisher of the paper on ``knight's tour''} has a history:
a piece in a certain position could only have entered from some
-candidate squares. The filling of incidence matrix has not such a history:
+candidate squares. The filling of incidence matrix has no history:
if we know that the item last added was in certain row and column, we
have no information to guess which of the filled items was entered
previously. A consequence of dealing with a different problem is that
-\cite{GotelliEnt01} does not give many hints on implementing a fill
+\citet{GotelliEnt01} do not give many hints on implementing a fill
algorithm as a community null model.
The backtracking is implemented in two stages in \pkg{vegan}: filling and
@@ -182,7 +184,7 @@
Because there is no record of history, this does not sound like a
backtracking, but it still fits the general definition of
backtracking: ``try something, and if it fails, try something
- else'' \cite{Sedgewick90}.
+ else'' \citep{Sedgewick90}.
\end{enumerate}
@@ -302,7 +304,7 @@
There is no natural way of scaling species and site scores to each
other. The eigenvalues in redundancy and principal components
-analysis are scale-dependent and change when the the data are
+analysis are scale-dependent and change when the data are
multiplied by a constant. If we have percent cover data, the
eigenvalues are typically very high, and the scores scaled by
eigenvalues will have much wider dispersion than the orthonormal set.
@@ -311,10 +313,10 @@
scores scaled by eigenvalues will have a narrower dispersion. For
graphical biplots we should be able to fix the relations of row and
column scores to be invariant against scaling of data. The solution
-in R standard function \code{biplot} is to scale site and species
+in \proglang{R} standard function \code{biplot} is to scale site and species
scores independently, and typically very differently, but plot each
independently to fill the graph area. The solution in \proglang{Canoco} and
-and \code{rda} is to use proportional eigenvalues $\lambda_k / \sum
+\code{rda} is to use proportional eigenvalues $\lambda_k / \sum
\lambda_k$ instead of original eigenvalues. These proportions are
invariant with scale changes, and typically they have a nice range for
plotting two data sets in the same graph.
@@ -327,7 +329,7 @@
the scaling constant to any desired values. It is also possible to
have two separate scaling constants: the first for the species, and
the second for sites and friends, and this allows getting scores of
-other software or R functions (Table \ref{tab:rdaconst}).
+other software or \proglang{R} functions (Table \ref{tab:rdaconst}).
\begin{table}
\caption{\label{tab:rdaconst} Values of the \code{const} argument in
\textbf{vegan} to get the scores that are equal to those from
@@ -339,8 +341,8 @@
& \textbf{Scaling} &\textbf{Species constant} & \textbf{Site constant} \\
\pkg{vegan} & any & $\sqrt[4]{(n-1) \sum \lambda_k}$ & $\sqrt[4]{(n-1) \sum \lambda_k}$\\
\code{prcomp}, \code{princomp} & \code{1} & $1$ & $\sqrt{(n-1) \sum_k \lambda_k}$\\
-\texttt{Canoco 3} & \code{-1, -2, -3} & $\sqrt{n-1}$ & $\sqrt{n}$\\
-\texttt{Canoco 4} & \code{-1, -2, -3} & $\sqrt{m}$ & $\sqrt{n}$
+\proglang{Canoco\,v3} & \code{-1, -2, -3} & $\sqrt{n-1}$ & $\sqrt{n}$\\
+\proglang{Canoco\,v4} & \code{-1, -2, -3} & $\sqrt{m}$ & $\sqrt{n}$
\end{tabular}
\end{table}
@@ -363,8 +365,7 @@
the rest. This is better done with directly centred analysis.
-\section{Why to use weighted averages scores instead of linear
- combinations in constrained ordination}
+\section{Weighted average and linear combination scores}
Constrained ordination methods such as Constrained Correspondence
Analysis (CCA) and Redundancy Analysis (RDA) produce two kind of site
Modified: pkg/vegan/inst/doc/diversity-vegan.Rnw
===================================================================
--- pkg/vegan/inst/doc/diversity-vegan.Rnw 2011-08-10 05:48:12 UTC (rev 1707)
+++ pkg/vegan/inst/doc/diversity-vegan.Rnw 2011-08-10 12:44:14 UTC (rev 1708)
@@ -1,28 +1,28 @@
% -*- mode: noweb; noweb-default-code-mode: R-mode; -*-
%\VignetteIndexEntry{Diversity analysis in vegan}
-\documentclass[article,a4paper,10pt,nojss]{jss}
-%\usepackage{ucs}
-%\usepackage[utf8x]{inputenc}
-%\usepackage[T1]{fontenc}
+\documentclass[article,nojss]{jss}
+\usepackage{ucs}
+\usepackage[utf8x]{inputenc}
+\usepackage[T1]{fontenc}
\usepackage{sidecap}
\usepackage{amsmath}
+\usepackage{amssymb} % \gtrapprox
-\title{Vegan: ecological diversity}
-\author{Jari Oksanen}
-\Abstract{
- }
-\Keywords{diversity, Shannon, R{\'e}nyi, Hill number, Tsallis,
- rarefaction, species accumulation, beta diversity, species
+\title{Vegan: ecological diversity} \author{Jari Oksanen}
+\Abstract{ }
+\Keywords{diversity, Shannon, Simpson, R{\'e}nyi, Hill number,
+ Tsallis, rarefaction, species accumulation, beta diversity, species
abundance, Fisher alpha, Fisher logarithmic series, Preston
- log-normal model, extended richness, taxonomic diversity, functional
- divesity, species pool}
+ log-normal model, species abundance models, Whittaker plots,
+ extended richness, taxonomic diversity, functional divesity, species
+ pool}
%% misuse next for scm data
\Address{$ $Id$ $
processed with vegan \Sexpr{packageDescription("vegan", field="Version")}
in \Sexpr{R.version.string} on \today}
-\Footername{This version}
+\Footername{About this version}
%% need no \usepackage{Sweave}
\begin{document}
@@ -42,13 +42,13 @@
analysis of ecological communities. This document gives an
introduction to the latter. Ordination methods are covered in other
documents. Many of the diversity functions were written by Roeland
-Kindt and Bob O'Hara.
+Kindt, Bob O'Hara and P{\'e}ter S{\'o}lymos.
Most diversity methods assume that data are counts of individuals.
The methods are used with other data types, and some people argue that
biomass or cover are more adequate than counts of individuals of
variable sizes. However, this document mainly uses a data set with
-counts: stem counts of trees on $1$ha plots in the Barro Colorado
+counts: stem counts of trees on $1$\,ha plots in the Barro Colorado
Island. The following steps make these data available for the
document:
<<>>=
@@ -76,7 +76,7 @@
@
which finds diversity indices for all sites.
-\pkg{vegan} does not have indices for evenness (equitability), but
+\pkg{Vegan} does not have indices for evenness (equitability), but
the most common of these, Pielou's evenness $J = H'/\log(S)$ is easily
found as:
<<>>=
@@ -85,7 +85,8 @@
where \code{specnumber} is a simple \pkg{vegan} function to find
the numbers of species.
-\pkg{vegan} also can estimate R\'{e}nyi diversities of order $a$:
+\pkg{vegan} also can estimate series of R\'{e}nyi and Tsallis
+diversities. R{\'e}nyi diversity of order $a$ is:
\begin{equation}
H_a = \frac{1}{1-a} \log \sum_{i=1}^S p_i^a
\end{equation}
@@ -93,8 +94,18 @@
diversity indices are special cases of Hill numbers: $N_0 = S$, $N_1 =
\exp(H')$, $N_2 = D_2$, and $N_\infty = 1/(\max p_i)$. The
corresponding R\'{e}nyi diversities are $H_0 = \log(S)$, $H_1 = H'$, $H_2 =
-- \log(\sum p_i^2)$, and $H_\infty = - \log(\max p_i)$. We select a
-random subset of five sites for R\'{e}nyi diversities:
+- \log(\sum p_i^2)$, and $H_\infty = - \log(\max p_i)$.
+Tsallis diversity of order $q$ is:
+\begin{equation}
+ H_q = \frac{1}{q-1} \left(1 - \sum_{i=1}^S p^q \right) \, .
+\end{equation}
+This corresponds to common diversity indices: $H_0 = S-1$, $H_1 = H'$,
+and $H_2 = D_2$, and can be converted to the Hill number:
+\begin{equation}
+ N_q = (1 - (q-1) H_q )^\frac{1}{1-q} \, .
+\end{equation}
+
+We select a random subset of five sites for R\'{e}nyi diversities:
<<>>=
k <- sample(nrow(BCI), 6)
R <- renyi(BCI[k,])
@@ -132,26 +143,26 @@
rarefied from $N$ to $n$ individuals is:
\begin{equation}
\label{eq:rare}
-\hat S_n = \sum_{i=1}^S (1 - p_i),\, \text{where} \quad p_i = {N-x_i
+\hat S_n = \sum_{i=1}^S (1 - q_i),\quad \text{where} \quad q_i = {N-x_i
\choose n} \Bigm /{N \choose n}
\end{equation}
where $x_i$ is the count of species $i$, and ${N \choose n}$ is the
binomial coefficient, or the number of ways we can choose $n$ from
-$N$, and $p_i$ give the probabilities that species $i$ does not occur in a
+$N$, and $q_i$ give the probabilities that species $i$ does \emph{not} occur in a
sample of size $n$. This is defined only when $N-x_i > n$, but for
-other cases $p_i = 0$ or the species is sure to occur in the sample.
+other cases $q_i = 0$ or the species is sure to occur in the sample.
The variance of rarefied richness is:
\begin{equation}
\label{eq:rarevar}
-s^2 = p_i (1-p_i) + 2 \sum_{i=1}^S \sum_{j>i} \left[ {N- x_i - x_j
+s^2 = q_i (1-q_i) + 2 \sum_{i=1}^S \sum_{j>i} \left[ {N- x_i - x_j
\choose n} \Bigm / {N
- \choose n} - p_i p_j\right]
+ \choose n} - q_i q_j\right]
\end{equation}
Equation \ref{eq:rarevar} actually is of the same form as the variance
of sum of correlated variables:
\begin{equation}
-\mathrm{var} \left(\sum x_i \right) = \sum \mathrm{var}(x_i) - 2 \sum_{i=1}^S
-\sum_{j>i} \mathrm{cov}(x_i, x_j)
+\VAR \left(\sum x_i \right) = \sum \VAR (x_i) + 2 \sum_{i=1}^S
+\sum_{j>i} \COV (x_i, x_j)
\end{equation}
The number of stems per hectare varies in our
@@ -165,7 +176,8 @@
@
Rarefaction curves often are seen as an objective solution for
comparing species richness with different sample sizes. However, rank
-orders typically differ among different rarefaction sample sizes.
+orders typically differ among different rarefaction sample sizes,
+rarefaction curves can cross.
As an extreme case we may rarefy sample size to two individuals:
<<>>=
@@ -190,7 +202,7 @@
Simple diversity indices only consider species identity: all different
species are equally different. In contrast, taxonomic and functional
-diversity indices see how different two different species
+diversity indices judge the differences of species
are. Taxonomic and functional diversities are used in different fields
of science, but they really have very similar reasoning, and either
could be used either with taxonomic or functional properties of
@@ -207,7 +219,7 @@
These equations give the index values for a single site, and summation
goes over species $i$ and $j$, and $\omega$ are the taxonomic
distances among taxa, $x$ are species abundances, and $n$ is the total
-abundance for a site. With presence absence data, both indices
+abundance for a site. With presence--absence data, both indices
reduce to the same index called $\Delta^+$, and for this it is
possible to estimate standard deviation. There are two indices
derived from $\Delta^+$: it can be multiplied with species
@@ -284,7 +296,7 @@
Diversity indices may be regarded as variance measures of species
abundance distribution. We may wish to inspect abundance
-distributions more directly. \pkg{vegan} has functions for
+distributions more directly. \pkg{Vegan} has functions for
Fisher's log-series and Preston's log-normal models, and in addition
several models for species abundance distribution.
@@ -314,7 +326,7 @@
\end{SCfigure}
We already saw $\alpha$ as a diversity index. Now we also obtained
estimate of standard error of $\alpha$ (these also are optionally
-available in \code{fisherfit}). The standard errors are based on
+available in \code{fisher.alpha}). The standard errors are based on
the second derivatives (curvature) of log-likelihood at the solution
of $\alpha$. The distribution of $\alpha$ is often non-normal
and skewed, and standard errors are of not much use. However,
@@ -335,7 +347,13 @@
There are two alternative functions for the log-normal model:
\code{prestonfit} and \code{prestondistr}. Function
\code{prestonfit} uses traditionally binning approach, and is burdened
-with arbitrary choices of binning limits and treatment of ties.
+with arbitrary choices of binning limits and treatment of ties. It
+seems that Preston split ties between adjacent octaves: only half of
+the species observed once were in the first octave, and half were
+transferred to the next octave, and the same for all species at the
+octave limits occuring 2, 4, 8, 16\ldots times. Function
+\code{prestonfit} can either split the ties or keep all limit cases in
+the lower octave.
Function \code{prestondistr} directly
maximizes truncated log-normal likelihood without binning data, and it
is the recommended alternative. Log-normal models usually fit poorly
@@ -516,9 +534,9 @@
where $X$ is the area (size) of the patch or site, and $c$ and $z$ are
parameters. Parameter $c$ is uninteresting, but $z$ gives the
steepness of the species area curve and is a measure of beta
-diversity. In islands, $z$ is typically about $0.3$. This kind of
+diversity. In islands typically $z \approx 0.3$. This kind of
islands can be regarded as subsets of the same community, indicating
-that we really should talk about gradient differences if $z > 0.3$. We
+that we really should talk about gradient differences if $z \gtrapprox 0.3$. We
can find the value of $z$ for a pair of plots using function
\code{betadiver}:
<<>>=
@@ -577,7 +595,7 @@
and $p_i$ are proportions of species. The idea in jackknife seems to
be that we missed about as many species as we saw only once, and the
idea in bootstrap that if we repeat sampling (with replacement) from
-the same data, we miss any many species as we missed originally.
+the same data, we miss as many species as we missed originally.
The variance estimators of Chao is:
\begin{equation}
@@ -607,13 +625,11 @@
@
If the estimation of pool size really works, we should get the same
values of estimated richness if we take a random subset of a half of
-the plots:
+the plots (but this is rarely true):
<<>>=
s <- sample(nrow(BCI), 25)
specpool(BCI[s,])
@
-These typically are even lower than the observed richness
-(\Sexpr{ncol(BCI)} species) at the whole data set.
\subsection{Pool size from a single site}
@@ -658,9 +674,8 @@
maximum (at $\mu$), and $\sigma$ is the width. Function
\code{veiledspec} estimates this integral from a model fitted either
with \code{prestondistr} or \code{prestonfit}, and fits the latter
-if raw site data are given. Log-normal model fits badly, and
-\code{prestonfit} is particularly poor. Therefore the following
-explicitly uses \code{prestondistr}, although this also may fail:
+if raw site data are given. Log-normal model may fit poorly, but we
+can try:
<<>>=
veiledspec(prestondistr(BCI[k,]))
veiledspec(BCI[k,])
Modified: pkg/vegan/inst/doc/intro-vegan.Rnw
===================================================================
--- pkg/vegan/inst/doc/intro-vegan.Rnw 2011-08-10 05:48:12 UTC (rev 1707)
+++ pkg/vegan/inst/doc/intro-vegan.Rnw 2011-08-10 12:44:14 UTC (rev 1708)
@@ -1,9 +1,9 @@
% -*- mode: noweb; noweb-default-code-mode: R-mode; -*-
%\VignetteIndexEntry{Introduction to ordination in vegan}
-\documentclass[article,10pt,nojss]{jss}
-%\usepackage{ucs}
-%\usepackage[utf8x]{inputenc}
-%\usepackage[T1]{fontenc}
+\documentclass[article,nojss]{jss}
+\usepackage{ucs} %% needed for R output: signif stars etc, quotes
+\usepackage[utf8x]{inputenc}
+\usepackage[T1]{fontenc}
\usepackage{sidecap}
\usepackage{amsmath}
@@ -14,7 +14,19 @@
\author{Jari Oksanen}
-\Abstract{ }
+\Abstract{The document describes typical, simple work pathways of
+ vegetation ordination. Unconstrained ordination uses as examples
+ detrended correspondence analysis and non-metric multidimensional
+ scaling, and shows how to interpret their results by fitting
+ environmental vectors and factors or smooth environmental surfaces
+ to the graph. The basic plotting command, and more advanced plotting
+ commands for congested plots are also discussed, as well as adding
+ items such as ellipses, convex hulls, and other items for
+ classes. The constrained ordination uses constrained (canonical)
+ correspondence analysis as an example. It is first shown how a model
+ is defined, then the document discusses model building and
+ signficance tests of the whole analysis, single constraints and
+ axes.}
\Keywords{ordination, correspondence analysis, non-metric
multidimensional scaling, CCA, RDA, NMDS, fitted environmental
@@ -25,7 +37,7 @@
processed with vegan
\Sexpr{packageDescription("vegan", field="Version")}
in \Sexpr{R.version.string} on \today}
-\Footername{This version}
+\Footername{About this version}
%% need no \usepackage{Sweave}
\begin{document}
@@ -43,7 +55,7 @@
\noindent \pkg{vegan} is a package for community ecologists. This
documents explains how the commonly used ordination methods can be
-done in \pkg{vegan}. The document only is a very basic
+performed in \pkg{vegan}. The document only is a very basic
introduction. Another document (\emph{vegan tutorial})
(\url{http://cc.oulu.fi/~jarioksa/opetus/method/vegantutor.pdf}) gives
a longer and more detailed introduction to ordination. The
@@ -55,14 +67,13 @@
\section{Ordination}
The \pkg{vegan} package contains all common ordination methods:
-Principal component analysis (function \code{rda}, or
-\code{prcomp} in the base \textsf{R}), correspondence analysis
-(\code{cca}), detrended correspondence analysis (\code{decorana})
-and a wrapper for non-metric multidimensional scaling
-(\code{metaMDS}). Functions \code{rda} and \code{cca} mainly
-are designed for constrained ordination, and will be discussed later.
-In this chapter I describe functions \code{decorana} and
-\code{metaMDS}.
+Principal component analysis (function \code{rda}, or \code{prcomp} in
+the base \proglang{R}), correspondence analysis (\code{cca}),
+detrended correspondence analysis (\code{decorana}) and a wrapper for
+non-metric multidimensional scaling (\code{metaMDS}). Functions
+\code{rda} and \code{cca} mainly are designed for constrained
+ordination, and will be discussed later. In this chapter I describe
+functions \code{decorana} and \code{metaMDS}.
\subsection{Detrended correspondence analysis}
@@ -85,15 +96,17 @@
\subsection{Non-metric multidimensional scaling}
-Function \code{metaMDS} is a bit special case. The actual
-ordination is performed by function \code{isoMDS} of the \code{MASS}
-package. Function \code{metaMDS} is a wrapper to perform non-metric
+
+Function \code{metaMDS} is a bit special case. The actual ordination
+is performed by function \pkg{vegan} function \code{monoMDS} (or
+alternatively using \code{isoMDS} of the \pkg{MASS} package).
+Function \code{metaMDS} is a wrapper to perform non-metric
multidimensional scaling (\textsc{nmds}) like recommended in community
ordination: it uses adequate dissimilarity measures (function
-\code{vegdist}), then it runs \textsc{nmds} several times with
-random starting configurations, compares results (function
-\code{procrustes}), and stops after finding twice a similar minimum stress
-solution. Finally it scales and rotates the solution, and adds
+\code{vegdist}), then it runs \textsc{nmds} several times with random
+starting configurations, compares results (function
+\code{procrustes}), and stops after finding twice a similar minimum
+stress solution. Finally it scales and rotates the solution, and adds
species scores to the configuration as weighted averages (function
\code{wascores}):
<<>>=
@@ -152,9 +165,9 @@
support functions with the results (\code{points}, \code{text},
\code{identify}).
-Function \code{ordirgl} (requires \code{rgl} package) provides
+Function \code{ordirgl} (requires \pkg{rgl} package) provides
dynamic three-dimensional graphics that can be spun around or zoomed
-into with your mouse. Function \code{ordiplot3d} (requires package
+into with your mouse. Function \pkg{ordiplot3d} (requires package
\code{scatterplot3d}) displays simple three-dimensional
scatterplots.
@@ -163,14 +176,14 @@
Ordination plots are often congested: there is a large number of sites
and species, and it may be impossible to display all clearly. In
particular, two or more species may have identical scores and are
-plotted over each other. \pkg{vegan} does not have (yet?)
+plotted over each other. \pkg{Vegan} does not have (yet?)
automatic tools for clean plotting in these cases, but here some
methods you can try:
\begin{itemize}
\item Zoom into graph setting axis limits \code{xlim} and
\code{ylim}. You must typically set both, because \pkg{vegan}
will maintain equal aspect ratio of axes.
-\item Use points and label only some of these with \code{identify}
+\item Use points and add labell only some points with \code{identify}
command.
\item Use \code{select} argument in ordination \code{text} and
\code{points} functions to only show the specified items.
@@ -184,16 +197,17 @@
points and text labels, and tries to optimize the location of the
text to avoid overwriting.
\item Use interactive \code{orditkplot} function that draws both
- points and labels for ordination scores, and allows you to drag labels
- to better positions. You can export the results of the edited graph to
- encapsulated postscript, pdf, png or jpeg files, or copy directly to
- encapsulated postscript, or return the edited positions to R for
- further processing.
+ points and labels for ordination scores, and allows you to drag
+ labels to better positions. You can export the results of the edited
+ graph to encapsulated \proglang{postscript}, \proglang{pdf},
+ \proglang{png} or \proglang{jpeg} files, or copy directly to
+ encapsulated \proglang{postscript}, or return the edited positions
+ to \proglang{R} for further processing.
\end{itemize}
\subsection{Adding items to ordination plots}
-\pkg{vegan} has a group of functions for adding information about
+\pkg{Vegan} has a group of functions for adding information about
classification or grouping of points onto ordination diagrams.
Function \code{ordihull} adds convex hulls, \code{ordiellipse}
adds ellipses of standard deviation, standard error or confidence
@@ -226,15 +240,15 @@
\section{Fitting environmental variables}
-\pkg{vegan} provides two functions for fitting environmental
+\pkg{Vegan} provides two functions for fitting environmental
variables onto ordination:
\begin{itemize}
-\item \code{envfit} fits vectors of continuous variables and
- centroids of levels of class variables (defined as \code{factor}
- in \textsf{R}). The direction of the vector shows the direction of
- the gradient, and the length of the arrow is proportional to the
+\item \code{envfit} fits vectors of continuous variables and centroids
+ of levels of class variables (defined as \code{factor} in
+ \proglang{R}). The arrow shows the direction of the (increasing)
+ gradient, and the length of the arrow is proportional to the
correlation between the variable and the ordination.
-\item \code{ordisurf} (which requires package \code{mgcv}) fits
+\item \code{ordisurf} (which requires package \pkg{mgcv}) fits
smooth surfaces for continuous variables onto ordination using
thinplate splines with cross-validatory selection of smoothness.
\end{itemize}
@@ -271,11 +285,11 @@
\section{Constrained ordination}
-\pkg{vegan} has three methods of constrained ordination:
+\pkg{Vegan} has three methods of constrained ordination:
constrained or ``canonical'' correspondence analysis (function
\code{cca}), redundancy analysis (function \code{rda}) and
-constrained analysis of proximities (function \code{capscale}). All
-these functions also can have a conditioning term that is ``partialled
+distance-based redundancy analysis (function \code{capscale}). All
+these functions can have a conditioning term that is ``partialled
out''. I only demonstrate \code{cca}, but all functions accept
similar commands and can be used in the same way.
@@ -323,7 +337,7 @@
anova(ord)
@
The function actually used was \code{anova.cca}, but you do not need
-to give its name in full, because \textsf{R} automatically chooses the
+to give its name in full, because \proglang{R} automatically chooses the
correct \code{anova} variant for the result of constrained
ordination.
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