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**vegan** FAQ
=============

This document contains answers to some of the most frequently asked
questions about R package **vegan**.

> This work is licensed under the Creative Commons Attribution 3.0
> License. To view a copy of this license, visit
> <http://creativecommons.org/licenses/by/3.0/> or send a letter to
> Creative Commons, 543 Howard Street, 5th Floor, San Francisco,
> California, 94105, USA.
>
> Copyright © 2008-2016 vegan development team

------------------------------------------------------------------------

Introduction
------------

------------------------------------------------------------------------

### What is **vegan**?

**Vegan** is an R package for community ecologists. It contains the most
popular methods of multivariate analysis needed in analysing ecological
communities, and tools for diversity analysis, and other potentially
useful functions. **Vegan** is not self-contained but it must be run
under R statistical environment, and it also depends on many other R
packages. **Vegan** is [free
software](http://www.gnu.org/philosophy/free-sw.html) and distributed
under [GPL2 license](http://www.gnu.org/licenses/gpl.html).

------------------------------------------------------------------------

### What is R?

R is a system for statistical computation and graphics. It consists of a
language plus a run-time environment with graphics, a debugger, access
to certain system functions, and the ability to run programs stored in
script files.

R has a home page at <https://www.R-project.org/>. It is [free
software](http://www.gnu.org/philosophy/free-sw.html) distributed under
a GNU-style [copyleft](http://www.gnu.org/copyleft/copyleft.html), and
an official part of the [GNU](http://www.gnu.org/) project (“GNU S”).

------------------------------------------------------------------------

### How to obtain **vegan** and R?

Both R and latest release version of **vegan** can be obtained through
[CRAN](https://cran.r-project.org). Unstable development version of
**vegan** can be obtained through
[GitHub](https://github.com/vegandevs/vegan). Formerly **vegan** was
developed in [R-Forge](http://r-forge.r-project.org/projects/vegan/),
but after moving to [GitHub](https://github.com/vegandevs/vegan) the
R-Forge repository may be out of date.

------------------------------------------------------------------------

### What R packages **vegan** depends on?

**Vegan** depends on the **permute** package which will provide advanced
and flexible permutation routines for **vegan**. The **permute** package
is developed together with **vegan** in
[GitHub](https://github.com/gavinsimpson/permute).

Some individual **vegan** functions depend on packages **MASS**,
**mgcv**, **parallel**, **cluster**, **lattice** and **tcltk**. These
all are base or recommended R packages that should be available in
every R installation.  **Vegan** declares these as suggested or
imported packages, and you can install **vegan** and use most of its
functions without these packages.

**Vegan** is accompanied with a supporting package **vegan3d** for
three-dimensional and dynamic plotting. The **vegan3d** package needs
non-standard packages **rgl** and **scatterplot3d**.

------------------------------------------------------------------------

### What other packages are available for ecologists?

CRAN [Task Views](https://cran.r-project.org/web/views/) include
entries like `Environmetrics`, `Multivariate` and `Spatial` that
describe several useful packages and functions. If you install R package
**ctv**, you can inspect Task Views from your R session, and
automatically install sets of most important packages.

------------------------------------------------------------------------

### What other documentation is available for **vegan**?

**Vegan** is a fully documented R package with standard help pages.
These are the most authoritative sources of documentation (and as a
last resource you can use the force and the read the source, as
**vegan** is open source). **Vegan** package ships with other
documents which can be read with `browseVignettes("vegan")`
command. The documents included in the **vegan** package are

-   **Vegan** `NEWS`
-   This document (`FAQ-vegan`).
-   Short introduction to basic ordination methods in **vegan**
    (`intro-vegan`).
-   Introduction to diversity methods in **vegan**
    (`diversity-vegan`).
-   Discussion on design decisions in **vegan** (`decision-vegan`).
-   Description of variance partition procedures in function `varpart`
    (`partitioning`).

Web documents outside the package include:

-   <https://github.com/vegandevs/vegan>: **vegan** homepage.
-   <http://cc.oulu.fi/~jarioksa/opetus/metodi/vegantutor.pdf>:
    **vegan** tutorial.

------------------------------------------------------------------------

### Is there a Graphical User Interface (GUI) for **vegan**?

Roeland Kindt has made package **BiodiversityR** which provides a GUI
for **vegan**. The package is available at
[CRAN](https://cran.r-project.org/package=BiodiversityR).
It is not a mere GUI for **vegan**, but adds some new functions and
complements **vegan** functions in order to provide a workbench for
biodiversity analysis. You can install **BiodiversityR** using
`install.packages("BiodiversityR")` or graphical package management menu
in R. The GUI works on Windows, MacOS X and Linux.

------------------------------------------------------------------------

### How to cite **vegan**?

Use command `citation("vegan")` in R to see the recommended citation to
be used in publications.

------------------------------------------------------------------------

### How to build **vegan** from sources?

In general, you do not need to build **vegan** from sources, but binary
builds of release versions are available through
[CRAN](https://cran.r-project.org/) for Windows and MacOS X. If you use
some other operating systems, you may have to use source packages.
**Vegan** is a standard R package, and can be built like instructed in R
documentation. **Vegan** contains source files in C and FORTRAN, and you
need appropriate compilers (which may need more work in Windows and
MacOS X).

------------------------------------------------------------------------

### Are there binaries for devel versions?

[R-Forge](http://r-forge.r-project.org/projects/vegan/) runs daily tests
on the devel package, and if passed, it builds source package together
with Windows binaries. However, the R-Forge may be out of date, because
**vegan** is mainly developed in
[GitHub](https://github.com/vegandevs/vegan). You can install R-Forge
packages within R with command
`install.packages("vegan", repos="http://r-forge.r-project.org/")`. If
you use GUI menu entry, you must select or define the R-Forge
repository.

------------------------------------------------------------------------

### How to report a bug in **vegan**?

If you think you have found a bug in **vegan**, you should report it to
**vegan** maintainers or developers. The preferred forum to report bugs
is [GitHub](https://github.com/vegandevs/vegan/issues). The bug report
should be so detailed that the bug can be replicated and corrected.
Preferably, you should send an example that causes a bug. If it needs a
data set that is not available in R, you should send a minimal data set
as well. You also should paste the output or error message in your
message. You also should specify which version of **vegan** you used.

Bug reports are welcome: they are the only way to make **vegan**
non-buggy.

Please note that you shall not send bug reports to R mailing lists,
since **vegan** is not a standard R package.

------------------------------------------------------------------------

### Is it a bug or a feature?

It is not necessarily a bug if some function gives different results
than you expect: That may be a deliberate design decision. It may be
useful to check the documentation of the function to see what was the
intended behaviour. It may also happen that function has an argument to
switch the behaviour to match your expectation. For instance, function
`vegdist` always calculates quantitative indices (when this is
possible). If you expect it to calculate a binary index, you should use
argument `binary = TRUE`.

------------------------------------------------------------------------

### Can I contribute to **vegan**?

**Vegan** is dependent on user contribution. All feedback is welcome. If
you have problems with **vegan**, it may be as simple as incomplete
documentation, and we shall do our best to improve the documents.

Feature requests also are welcome, but they are not necessarily
fulfilled. A new feature will be added if it is easy to do and it looks
useful, or if you submit code.

If you can write code yourself, the best forum to contribute to vegan is
[GitHub](https://github.com/vegandevs/vegan).

------------------------------------------------------------------------

Ordination
----------

------------------------------------------------------------------------

### I have only numeric and positive data but **vegan** still complains

You are wrong! Computers are painfully pedantic, and if they find
non-numeric or negative data entries, you really have them. Check your
data. Most common reasons for non-numeric data are that row names were
read as a non-numeric variable instead of being used as row names (check
argument `row.names` in reading the data), or that the column names were
interpreted as data (check argument `header = TRUE` in reading the
data). Another common reason is that you had empty cells in your input
data, and these were interpreted as missing values.

------------------------------------------------------------------------

### Can I analyse binary or cover class data?

Yes. Most **vegan** methods can handle binary data or cover abundance
data. Most statistical tests are based on permutation, and do not make
distributional assumptions. There are some methods (mainly in diversity
analysis) that need count data. These methods check that input data are
integers, but they may be fooled by cover class data.

------------------------------------------------------------------------

### Why dissimilarities in **vegan** differ from other sources?

Most commonly the reason is that other software use presence–absence
data whereas **vegan** used quantitative data. Usually **vegan** indices
are quantitative, but you can use argument `binary = TRUE` to make them
presence–absence. However, the index name is the same in both cases,
although different names usually occur in literature. For instance,
Jaccard index actually refers to the binary index, but **vegan** uses
name `"jaccard"` for the quantitative index, too.

Another reason may be that indices indeed are defined differently,
because people use same names for different indices.

------------------------------------------------------------------------

### Why NMDS stress is sometimes 0.1 and sometimes 10?

Stress is a proportional measure of badness of fit. The proportions can
be expressed either as parts of one or as percents. Function `isoMDS`
(**MASS** package) uses percents, and function `monoMDS` (**vegan**
package) uses proportions, and therefore the same stress is 100 times
higher in `isoMDS`. The results of `goodness` function also depend on
the definition of stress, and the same `goodness` is 100 times higher in
`isoMDS` than in `monoMDS`. Both of these conventions are equally
correct.

------------------------------------------------------------------------

### I get zero stress but no convergent solutions in `metaMDS`

Most common reason is that you have too few observations for your NMDS.
For `n` observations (points) and `k` dimensions you need to estimate
`n*k` parameters (ordination scores) using `n*(n-1)/2` dissimilarities.
For `k` dimensions you must have `n > 2*k + 1`, or for two dimensions at
least six points. In some degenerate situations you may need even a
larger number of points. If you have a lower number of points, you can
find an undefined number of perfect (stress is zero) but different
solutions. Conventional wisdom due to Kruskal is that you should have
`n > 4*k + 1` points for `k` dimensions. A typical symptom of
insufficient data is that you have (nearly) zero stress but no two
convergent solutions. In those cases you should reduce the number of
dimensions (`k`) and with very small data sets you should not use
`NMDS`, but rely on metric methods.

It seems that local and hybrid scaling with `monoMDS` have similar lower
limits in practice (although theoretically they could differ). However,
higher number of dimensions can be used in metric scaling, both with
`monoMDS` and in principal coordinates analysis (`cmdscale` in
**stats**, `wcmdscale` in **vegan**).

------------------------------------------------------------------------

### Zero dissimilarities in isoMDS

Function `metaMDS` uses function `monoMDS` as its default method for
NMDS, and this function can handle zero dissimilarities. Alternative
function `isoMDS` cannot handle zero dissimilarities. If you want to use
`isoMDS`, you can use argument `zerodist = "add"` in `metaMDS` to handle
zero dissimilarities. With this argument, zero dissimilarities are
replaced with a small positive value, and they can be handled in
`isoMDS`. This is a kluge, and some people do not like this. A more
principal solution is to remove duplicate sites using R command
`unique`. However, after some standardizations or with some
dissimilarity indices, originally non-unique sites can have zero
dissimilarity, and you have to resort to the kluge (or work harder with
your data). Usually it is better to use `monoMDS`.

------------------------------------------------------------------------

### I have heard that you cannot fit environmental vectors or surfaces to NMDS results which only have rank-order scores

Claims like this have indeed been at large in the Internet, but they are
based on grave misunderstanding and are plainly wrong. NMDS ordination
results are strictly metric, and in **vegan** `metaMDS` and `monoMDS`
they are even strictly Euclidean. The method is called “non-metric”
because the Euclidean distances in ordination space have a non-metric
rank-order relationship to community dissimilarities. You can inspect
this non-linear step curve using function `stressplot` in **vegan**.
Because the ordination scores are strictly Euclidean, it is correct to
use **vegan** functions `envfit` and `ordisurf` with NMDS results.

------------------------------------------------------------------------

### Where can I find numerical scores of ordination axes?

Normally you can use function `scores` to extract ordination scores for
any ordination method. The `scores` function can also find ordination
scores for many non-**vegan** functions such as for `prcomp` and
`princomp` and for some **ade4** functions.

In some cases the ordination result object stores raw scores, and the
axes are also scaled appropriate when you access them with `scores`. For
instance, in `cca` and `rda` the ordination object has only so-called
normalized scores, and they are scaled for ordination plots or for other
use when they are accessed with `scores`.

------------------------------------------------------------------------

### How the RDA results are scaled?

The scaling or RDA results indeed differ from most other software
packages. The scaling of RDA is such a complicated issue that it cannot
be explained in this FAQ, but it is explained in a separate pdf document
on “Design decision and implementation details in vegan” that you can
read with command `browseVignettes("vegan")`.

------------------------------------------------------------------------

### Ordination fails with “Error in La.svd”

Constrained ordination (`cca`, `rda`, `capscale`) will sometimes fail
with error message
`Error in La.svd(x, nu, nv): error code 1 from Lapack routine 'dgesdd'.`

It seems that the basic problem is in the `svd` function of `LAPACK`
that is used for numerical analysis in R. `LAPACK` is an external
library that is beyond the control of package developers and R core team
so that these problems may be unsolvable. It seems that the problems
with the `LAPACK` code are so common that even the help page of `svd`
warns about them

Reducing the range of constraints (environmental variables) helps
sometimes. For instance, multiplying constraints by a constant \< 1.
This rescaling does not influence the numerical results of constrained
ordination, but it can complicate further analyses when values of
constraints are needed, because the same scaling must be applied there.
We can only hope that this problem is fixed in the future versions of R
and `LAPACK`.

------------------------------------------------------------------------

### Variance explained by ordination axes.

In general, **vegan** does not directly give any statistics on the
“variance explained” by ordination axes or by the constrained axes. This
is a design decision: I think this information is normally useless and
often misleading. In community ordination, the goal typically is not to
explain the variance, but to find the “gradients” or main trends in the
data. The “total variation” often is meaningless, and all proportions of
meaningless values also are meaningless. Often a better solution
explains a smaller part of “total variation”. For instance, in
unstandardized principal components analysis most of the variance is
generated by a small number of most abundant species, and they are easy
to “explain” because data really are not very multivariate. If you
standardize your data, all species are equally important. The first axes
explains much less of the “total variation”, but now they explain all
species equally, and results typically are much more useful for the
whole community. Correspondence analysis uses another measure of
variation (which is not variance), and again it typically explains a
“smaller proportion” than principal components but with a better result.
Detrended correspondence analysis and nonmetric multidimensional scaling
even do not try to “explain” the variation, but use other criteria. All
methods are incommensurable, and it is impossible to compare methods
using “explanation of variation”.

If you still want to get “explanation of variation” (or a deranged
editor requests that from you), it is possible to get this information
for some methods:

-   Eigenvector methods: Functions `rda`, `cca` and `capscale` give the
    variation of conditional (partialled), constrained (canonical) and
    residual components, but you must calculate the proportions by hand.
    Function `eigenvals` extracts the eigenvalues, and
    `summary(eigenvals(ord))` reports the proportions explained in the
    result object `ord`. Function `RsquareAdj` gives the R-squared and
    adjusted R-squared (if available) for constrained components.
    Function `goodness` gives the same statistics for individual species
    or sites (species are unavailable with `capscale`). In addition,
    there is a special function `varpart` for unbiased partitioning of
    variance between up to four separate components in redundancy
    analysis.
-   Detrended correspondence analysis (function `decorana`). The total
    amount of variation is undefined in detrended correspondence
    analysis, and therefore proportions from total are unknown and
    undefined. DCA is not a method for decomposition of variation, and
    therefore these proportions would not make sense either.
-   Nonmetric multidimensional scaling. NMDS is a method for nonlinear
    mapping, and the concept of of variation explained does not make
    sense. However, 1 - stress\^2 transforms nonlinear stress into
    quantity analogous to squared correlation coefficient. Function
    `stressplot` displays the nonlinear fit and gives this statistic.

------------------------------------------------------------------------

### Can I have random effects in constrained ordination or in `adonis`?

No. Strictly speaking, this is impossible. However, you can define
models that respond to similar goals as random effects models, although
they strictly speaking use only fixed effects.

Constrained ordination functions `cca`, `rda` and `capscale` can have
`Condition()` terms in their formula. The `Condition()` define partial
terms that are fitted before other constraints and can be used to remove
the effects of background variables, and their contribution to
decomposing inertia (variance) is reported separately. These partial
terms are often regarded as similar to random effects, but they are
still fitted in the same way as other terms and strictly speaking they
are fixed terms.

Function `adonis` evaluates terms sequentially. In a model with
right-hand-side `~ A + B` the effects of `A` are evaluated first, and
the effects of `B` after removing the effects of `A`. Sequential tests
are also available in `anova` function for constrained ordination
results by setting argument `by = "term"`. In this way, the first terms
can serve in a similar role as random effects, although they are fitted
in the same way as all other terms, and strictly speaking they are fixed
terms.

All permutation tests in **vegan** are based on the **permute** package
that allows constructing various restricted permutation schemes. For
instance, you can set levels of `plots` or `blocks` for a factor
regarded as a random term.

A major reason why real random effects models are impossible in most
**vegan** functions is that their tests are based on the permutation of
the data. The data are given, that is fixed, and therefore permutation
tests are basically tests of fixed terms on fixed data. Random effect
terms would require permutations of data with a random component instead
of the given, fixed data, and such tests are not available in **vegan**.

------------------------------------------------------------------------

### Is it possible to have passive points in ordination?

**Vegan** does not have a concept of passive points, or a point that
should only little influence the ordination results. However, you can
add points to eigenvector methods using `predict` functions with
`newdata`. You can first perform an ordination without some species or
sites, and then you can find scores for all points using your complete
data as `newdata`. The `predict` functions are available for basic
eigenvector methods in **vegan** (`cca`, `rda`, `decorana`, for an
up-to-date list, use command `methods("predict")`). You also can
simulate the passive points in R by using low weights to row and columns
(this is the method used in software with passive points). For instance,
the following command makes row 3 “passive”:
`dune[3,] <- 0.001*dune[3,]`.

------------------------------------------------------------------------

### Class variables and dummies

You should define a class variable as an R `factor`, and **vegan** will
automatically handle them with formula interface. You also can define
constrained ordination without formula interface, but then you must code
your class variables by hand.

R (and **vegan**) knows both unordered and ordered factors. Unordered
factors are internally coded as dummy variables, but one redundant level
is removed or aliased. With default contrasts, the removed level is the
first one. Ordered factors are expressed as polynomial contrasts. Both
of these contrasts explained in standard R documentation.

------------------------------------------------------------------------

### How are environmental arrows scaled?

The printed output of `envfit` gives the direction cosines which are the
coordinates of unit length arrows. For plotting, these are scaled by
their correlation (square roots of column `r2`). You can see the scaled
lengths of `envfit` arrows using command `scores`.

The scaled environmental vectors from `envfit` and the arrows for
continuous environmental variables in constrained ordination (`cca`,
`rda`, `capscale`) are adjusted to fill the current graph. The lengths
of arrows do not have fixed meaning with respect to the points (species,
sites), but they can only compared against each other, and therefore
only their relative lengths are important.

If you want change the scaling of the arrows, you can use `text`
(plotting arrows and text) or `points` (plotting only arrows) functions
for constrained ordination. These functions have argument `arrow.mul`
which sets the multiplier. The `plot` function for `envfit` also has the
`arrow.mul` argument to set the arrow multiplier. If you save the
invisible result of the constrained ordination `plot` command, you can
see the value of the currently used `arrow.mul` which is saved as an
attribute of `biplot` scores.

Function `ordiArrowMul` is used to find the scaling for the current
plot. You can use this function to see how arrows would be scaled:


```{r eval=FALSE}
sol <- cca(varespec)
ef <- envfit(sol ~ ., varechem)
plot(sol)
ordiArrowMul(scores(ef, display="vectors"))
```

------------------------------------------------------------------------

### I want to use Helmert or sum contrasts

`vegan` uses standard R utilities for defining contrasts. The default in
standard installations is to use treatment contrasts, but you can change
the behaviour globally setting `options` or locally by using keyword
`contrasts`. Please check the R help pages and user manuals for details.

------------------------------------------------------------------------

### What are aliased variables and how to see them?

Aliased variable has no information because it can be expressed with the
help of other variables. Such variables are automatically removed in
constrained ordination in **vegan**. The aliased variables can be
redundant levels of factors or whole variables.

**Vegan** function `alias` gives the defining equations for aliased
variables. If you only want to see the names of aliased variables or
levels in solution `sol`, use `alias(sol, names.only=TRUE)`.

------------------------------------------------------------------------

### Plotting aliased variables

You can fit vectors or class centroids for aliased variables using
`envfit` function. The `envfit` function uses weighted fitting, and the
fitted vectors are identical to the vectors in correspondence analysis.

------------------------------------------------------------------------

### Restricted permutations in **vegan**

**Vegan** uses **permute** package in all its permutation tests. The
**permute** package will allow restricted permutation designs for time
series, line transects, spatial grids and blocking factors. The
construction of restricted permutation schemes is explained in the
manual page `permutations` in **vegan** and in the documentation of the
**permute** package.

------------------------------------------------------------------------

### How to use different plotting symbols in ordination graphics?

The default ordination `plot` function is intended for fast plotting and
it is not very configurable. To use different plotting symbols, you
should first create and empty ordination plot with
`plot(..., type="n")`, and then add `points` or `text` to the created
empty frame (here `...` means other arguments you want to give to your
`plot` command). The `points` and `text` commands are fully
configurable, and allow different plotting symbols and characters.

------------------------------------------------------------------------

### How to avoid cluttered ordination graphs?

If there is a really high number of species or sites, the graphs often
are congested and many labels are overwritten. It may be impossible to
have complete readable graphics with some data sets. Below we give a
brief overview of tricks you can use. Gavin Simpson’s blog [From the
bottom of the heap](http://www.fromthebottomoftheheap.net) has a series
of articles on “decluttering ordination plots” with more detailed
discussion and examples.

-   Use only points, possibly with different types if you do not need to
    see the labels. You may need to first create an empty plot using
    `plot(..., type="n")`, if you are not satisfied with the default
    graph. (Here and below `...` means other arguments you want to give
    to your `plot` command.)
-   Use points and add labels to desired points using interactive
    `identify` command if you do not need to see all labels.
-   Add labels using function `ordilabel` which uses non-transparent
    background to the text. The labels still shadow each other, but the
    uppermost labels are readable. Argument `priority` will help in
    displaying the most interesting labels (see [Decluttering blog, part
    1](http://www.fromthebottomoftheheap.net/2013/01/12/decluttering-ordination-plots-in-vegan-part-1-ordilabel/)).
-   Use `orditorp` function that uses labels only if these can be added
    to a graph without overwriting other labels, and points otherwise,
    if you do not need to see all labels. You must first create an empty
    plot using `plot(..., type="n")`, and then add labels or points with
    `orditorp` (see [Decluttering
    blog](http://www.fromthebottomoftheheap.net/2013/01/13/decluttering-ordination-plots-in-vegan-part-2-orditorp/)).
-   Use `ordipointlabel` which uses points and text labels to the
    points, and tries to optimize the location of the text to minimize
    the overlap (see [Decluttering
    blog](http://www.fromthebottomoftheheap.net/2013/06/27/decluttering-ordination-plots-in-vegan-part-3-ordipointlabel/)).
-   Ordination `text` and `points` functions have argument `select` that
    can be used for full control of selecting items plotted as text or
    points.
-   Use interactive `orditkplot` function that lets you drag labels of
    points to better positions if you need to see all labels. Only one
    set of points can be used (see [Decluttering
    blog](http://www.fromthebottomoftheheap.net/2013/12/31/decluttering-ordination-in-vegan-part-4-orditkplot/)).
-   Most `plot` functions allow you to zoom to a part of the graph using
    `xlim` and `ylim` arguments to reduce clutter in congested areas.

------------------------------------------------------------------------

### Can I flip an axis in ordination diagram?

Use `xlim` or `ylim` with flipped limits. If you have model
`mod <- cca(dune)` you can flip the first axis with
`plot(mod, xlim = c(3, -2))`.

------------------------------------------------------------------------

### Can I zoom into an ordination plot?

You can use `xlim` and `ylim` arguments in `plot` or `ordiplot` to zoom
into ordination diagrams. Normally you must set both `xlim` and `ylim`
because ordination plots will keep the equal aspect ratio of axes, and
they will fill the graph so that the longer axis will fit.

Dynamic zooming can be done with function `orditkplot`. You can directly
save the edited `orditkplot` graph in various graphic formats, or you
can export the graph object back to R and use `plot` to display the
results.

------------------------------------------------------------------------

Other analysis methods
----------------------

------------------------------------------------------------------------

### Is there TWINSPAN?

No. It may be possible to port TWINSPAN to **vegan**, but it is not
among the **vegan** top priorities. If anybody wants to try porting, I
will be happy to help. TWINSPAN has a very permissive license, and it
would be completely legal to port the function into R.

------------------------------------------------------------------------

### Why restricted permutation does not influence adonis results?

The permutation scheme influences the permutation distribution of the
statistics and probably the significance levels, but does not influence
the calculation of the statistics.

------------------------------------------------------------------------

### How is deviance calculated?

Some **vegan** functions, such as `radfit` use base R facility of
`family` in maximum likelihood estimation. This allows use of several
alternative error distributions, among them `"poisson"` and
`"gaussian"`. The R `family` also defines the deviance. You can see the
equations for deviance with commands like `poisson()$dev` or
`gaussian()$dev`.

In general, deviance is 2 times log.likelihood shifted so that models
with exact fit have zero deviance.

------------------------------------------------------------------------
