subject:"\[R\] monte carlo simulations in permanova in vegan package"

Re: [R] monte carlo simulations in permanova in vegan package

2015-10-30 Thread Sean Porter

Thank you Jari,

It seems now that my question is morphing more into a statistical one, and
perhaps not appropriate for R-help list, so apologies. Yes we are talking
about the latest versions of the vegan and permute packages. 

When there are an insufficient number of permutations available due to low
sample sizes apparently an alternative is to use the result given in
Anderson & Robinson (2003) regarding the asymptotic permutation of the
numerator (or denominator) of the test statistic under permutation. And I
quote from Anderson et al. 2008 "It is demonstrated that each of the sums of
squares has, under permutation, an asymptotic distribution that is a linear
form in chi-square variables, where the coefficients are actually the
eigenvalues from a PCO of the resemblance matrix. Thus, chi-square variables
can be drawn randomly and independently, using Monte Carlo sampling, and
these can be combined with the eigenvalues to construct the asymptotic
permutation distribution for each of the numerator and denominator and,
thus,  for the entire pseudo-F statistic, in the event that too few actual
unique permutations exist."

Anderson, Gorley & Clarke. 2008. PERMANOVA+ for PRIMER: Guide to software
and statistical models.
Anderson & Robinson 2003. Generalised discriminant analysis based on
distances. Australian and New Zealand Journal of Statistics. 45: 301-318

I am sure you already know this! The above is what I am trying to do in the
vegan package though.. 

Apologies if I am missing something and if what you have said still applies
(that is not appropriate to exceed the possible number of permutations), I
am not a statistician..so any help/clarity would be welcome.. 

Regards, sean

-Original Message-
From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Jari Oksanen
Sent: 29 October 2015 03:23 PM
To: r-h...@stat.math.ethz.ch
Subject: Re: [R] monte carlo simulations in permanova in vegan package

Sean Porter  ori.org.za> writes:

> I am trying to run a PERMANOVA in the vegan package with an 
> appropriate number of permutations (see example below), ideally .
> Obviously that number of permutations does not exists so I would like 
> to use Monte Carlo permutation tests to derive the probability value, 
> as is done in the commercial package PERMANOVA+ for PRIMER. How can I 
> adapt my code so that adonis will do so ? Many thanks, Sean
[...clip...]
> 
> > permanova <- adonis(species ~ time, data = time, permutations=999,
> method="bray")
> 
> 'nperm' > set of all permutations; Resetting 'nperm'.
> 
I assume we are talking about the latest version of vegan and permute
packages. In that case you really should switch to complete enumeration if
you request exceeds the number of distinct permutations. As people have told
you, you should be satisfied with that because there are no more distinct
permutations. Alternatively, you need more data.

If you mean by Monte Carlo that the same that you have a sampling with
return instead of permutation, or that the same observation can appear
several times and therefore some other unit is missing, then there are two
pieces of advice:

1. You should not do so.
2. If you want to do so, you can generate your resampling matrices by hand
and use that matrix as the argument of permutations=. See the documentations
(?adonis) which tells how to do so.

Cheers, Jari Oksanen

__
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https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

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and provide commented, minimal, self-contained, reproducible code.

Re: [R] monte carlo simulations in permanova in vegan package

2015-10-30 Thread Sean Porter

Thank you Jari,

It seems now that my question is morphing more into a statistical one, and
perhaps not appropriate for R-help list, so apologies. Yes we are talking
about the latest versions of the vegan and permute packages. 

When there are an insufficient number of permutations available due to low
sample sizes apparently an alternative is to use the result given in
Anderson & Robinson (2003) regarding the asymptotic permutation of the
numerator (or denominator) of the test statistic under permutation. And I
quote from Anderson et al. 2008 "It is demonstrated that each of the sums of
squares has, under permutation, an asymptotic distribution that is a linear
form in chi-square variables, where the coefficients are actually the
eigenvalues from a PCO of the resemblance matrix. Thus, chi-square variables
can be drawn randomly and independently, using Monte Carlo sampling, and
these can be combined with the eigenvalues to construct the asymptotic
permutation distribution for each of the numerator and denominator and,
thus,  for the entire pseudo-F statistic, in the event that too few actual
unique permutations exist."

Anderson, Gorley & Clarke. 2008. PERMANOVA+ for PRIMER: Guide to software
and statistical models.
Anderson & Robinson 2003. Generalised discriminant analysis based on
distances. Australian and New Zealand Journal of Statistics. 45: 301-318

I am sure you already know this! The above is what I am trying to do in the
vegan package though.. 

Apologies if I am missing something and if what you have said still applies
(that is not appropriate to exceed the possible number of permutations), I
am not a statistician..so any help/clarity would be welcome.. 

Regards, sean

-Original Message-
From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Jari Oksanen
Sent: 29 October 2015 03:23 PM
To: r-h...@stat.math.ethz.ch
Subject: Re: [R] monte carlo simulations in permanova in vegan package

Sean Porter  ori.org.za> writes:

> I am trying to run a PERMANOVA in the vegan package with an 
> appropriate number of permutations (see example below), ideally . 
> Obviously that number of permutations does not exists so I would like 
> to use Monte Carlo permutation tests to derive the probability value, 
> as is done in the commercial package PERMANOVA+ for PRIMER. How can I 
> adapt my code so that adonis will do so ? Many thanks, Sean
[...clip...]
> 
> > permanova <- adonis(species ~ time, data = time, permutations=999,
> method="bray")
> 
> 'nperm' > set of all permutations; Resetting 'nperm'.
> 
I assume we are talking about the latest version of vegan and permute
packages. In that case you really should switch to complete enumeration if
you request exceeds the number of distinct permutations. As people have told
you, you should be satisfied with that because there are no more distinct
permutations. Alternatively, you need more data.

If you mean by Monte Carlo that the same that you have a sampling with
return instead of permutation, or that the same observation can appear
several times and therefore some other unit is missing, then there are two
pieces of advice:

1. You should not do so.
2. If you want to do so, you can generate your resampling matrices by hand
and use that matrix as the argument of permutations=. See the documentations
(?adonis) which tells how to do so.

Cheers, Jari Oksanen

__
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

__
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Re: [R] monte carlo simulations in permanova in vegan package

2015-10-29 Thread Jari Oksanen

Sean Porter  ori.org.za> writes:

> I am trying to run a PERMANOVA in the vegan package with an appropriate
> number of permutations (see example below), ideally . Obviously that
> number of permutations does not exists so I would like to use Monte Carlo
> permutation tests to derive the probability value, as is done in the
> commercial package PERMANOVA+ for PRIMER. How can I adapt my code so that
> adonis will do so ? Many thanks, Sean
[...clip...]
> 
> > permanova <- adonis(species ~ time, data = time, permutations=999,
> method="bray")
> 
> 'nperm' > set of all permutations; Resetting 'nperm'.
> 
I assume we are talking about the latest version of vegan and permute
packages. In that case you really should switch to complete enumeration
if you request exceeds the number of distinct permutations. As people
have told you, you should be satisfied with that because there are no
more distinct permutations. Alternatively, you need more data.

If you mean by Monte Carlo that the same that you have a sampling with
return instead of permutation, or that the same observation can appear
several times and therefore some other unit is missing, then there are two
pieces of advice:

1. You should not do so.
2. If you want to do so, you can generate your resampling matrices
by hand and use that matrix as the argument of permutations=. See
the documentations (?adonis) which tells how to do so.

Cheers, Jari Oksanen

__
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[R] monte carlo simulations in permanova in vegan package

2015-10-27 Thread Sean Porter

Dear colleagues,

 

I am trying to run a PERMANOVA in the vegan package with an appropriate
number of permutations (see example below), ideally . Obviously that
number of permutations does not exists so I would like to use Monte Carlo
permutation tests to derive the probability value, as is done in the
commercial package PERMANOVA+ for PRIMER. How can I adapt my code so that
adonis will do so ? Many thanks, Sean

 

> permanova <- adonis(species ~ time, data = time, permutations=99,
method="bray")

> permanova

 

Call:

adonis(formula = species ~ time, data = time, permutations = 99,  method
= "bray") 

 

Permutation: free

Number of permutations: 99

 

Terms added sequentially (first to last)

 

  Df SumsOfSqs  MeanSqs F.Model  R2 Pr(>F)   

time   1  0.070504 0.070504  123.65 0.96866   0.01 **

Residuals  4  0.002281 0.000570 0.03134  

Total  5  0.072785  1.0  

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 

 

> permanova <- adonis(species ~ time, data = time, permutations=999,
method="bray")

'nperm' > set of all permutations; Resetting 'nperm'.

 

 

 

 


[[alternative HTML version deleted]]

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and provide commented, minimal, self-contained, reproducible code.

Re: [R] monte carlo simulations in permanova in vegan package

2015-10-27 Thread stephen sefick

The example code works, and reports  permutations. Can you provide more
information?

data(dune)
data(dune.env)
adonis(dune ~ Management*A1, data=dune.env, permutations=)



On Tue, Oct 27, 2015 at 3:56 AM, Sean Porter  wrote:

> Dear colleagues,
>
>
>
> I am trying to run a PERMANOVA in the vegan package with an appropriate
> number of permutations (see example below), ideally . Obviously that
> number of permutations does not exists so I would like to use Monte Carlo
> permutation tests to derive the probability value, as is done in the
> commercial package PERMANOVA+ for PRIMER. How can I adapt my code so that
> adonis will do so ? Many thanks, Sean
>
>
>
> > permanova <- adonis(species ~ time, data = time, permutations=99,
> method="bray")
>
> > permanova
>
>
>
> Call:
>
> adonis(formula = species ~ time, data = time, permutations = 99,
> method
> = "bray")
>
>
>
> Permutation: free
>
> Number of permutations: 99
>
>
>
> Terms added sequentially (first to last)
>
>
>
>   Df SumsOfSqs  MeanSqs F.Model  R2 Pr(>F)
>
> time   1  0.070504 0.070504  123.65 0.96866   0.01 **
>
> Residuals  4  0.002281 0.000570 0.03134
>
> Total  5  0.072785  1.0
>
> ---
>
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>
>
>
>
> > permanova <- adonis(species ~ time, data = time, permutations=999,
> method="bray")
>
> 'nperm' > set of all permutations; Resetting 'nperm'.
>
>
>
>
>
>
>
>
>
>
> [[alternative HTML version deleted]]
>
> __
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>



-- 
Stephen Sefick
**
Auburn University
Biological Sciences
331 Funchess Hall
Auburn, Alabama
36849
**
sas0...@auburn.edu
http://www.auburn.edu/~sas0025
**

Let's not spend our time and resources thinking about things that are so
little or so large that all they really do for us is puff us up and make us
feel like gods.  We are mammals, and have not exhausted the annoying little
problems of being mammals.

-K. Mullis

"A big computer, a complex algorithm and a long time does not equal
science."

  -Robert Gentleman

[[alternative HTML version deleted]]

__
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Re: [R] monte carlo simulations in permanova in vegan package

2015-10-27 Thread Cade, Brian

Sean:  There are only 20 possible combinations, 6!/(3! x 3!), so you just
need to enumerate them completely (no Monte Carlo approximation required).
I don't know if permanova() can do this but you can do it with the mrpp()
functions and argument (,exact=TRUE) in Blossom package for R.

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  ca...@usgs.gov <brian_c...@usgs.gov>
tel:  970 226-9326


On Tue, Oct 27, 2015 at 7:42 AM, Sean Porter <spor...@ori.org.za> wrote:

> Hi Stephen and others,
>
>
>
> I am trying to run a one-way permanova where I have only 2 levels in the
> factor “time”, and each level contains only 3 replicates. So because I have
> such few observations (6 in total) and levels (2) there are not enough
> possible permutations to get a reasonable test (i.e. (2*3)!/ [2!(3!)^2].
>  That is why for example if I run the analysis with only 99 permutations it
> completes the task. However, if I set the number of permutations to
> anything larger it returns the message “'nperm' > set of all permutations;
> Resetting 'nperm'.” as the number of possible permutations exceeds the
> number set by the argument “permutations=”. In PERMANOVA + for PRIMER there
> is a way of dealing with this issue – by using Monte Carlo simulations to
> generate the p value with a reasonable number of permutations. Hopefully
> this clarifies my situation and aim?
>
>
>
> I was therefore hoping there was a way of coding for the Monte-Carlo
> permutation procedure into adonis?
>
>
>
> Thanks for your help!
>
>
>
> From: stephen sefick [mailto:ssef...@gmail.com]
> Sent: 27 October 2015 03:11 PM
> To: Sean Porter
> Cc: r-help@r-project.org
> Subject: Re: [R] monte carlo simulations in permanova in vegan package
>
>
>
> The example code works, and reports  permutations. Can you provide
> more information?
>
>
>
> data(dune)
> data(dune.env)
> adonis(dune ~ Management*A1, data=dune.env, permutations=)
>
>
>
>
>
> On Tue, Oct 27, 2015 at 3:56 AM, Sean Porter <spor...@ori.org.za> wrote:
>
> Dear colleagues,
>
>
>
> I am trying to run a PERMANOVA in the vegan package with an appropriate
> number of permutations (see example below), ideally . Obviously that
> number of permutations does not exists so I would like to use Monte Carlo
> permutation tests to derive the probability value, as is done in the
> commercial package PERMANOVA+ for PRIMER. How can I adapt my code so that
> adonis will do so ? Many thanks, Sean
>
>
>
> > permanova <- adonis(species ~ time, data = time, permutations=99,
> method="bray")
>
> > permanova
>
>
>
> Call:
>
> adonis(formula = species ~ time, data = time, permutations = 99,
> method
> = "bray")
>
>
>
> Permutation: free
>
> Number of permutations: 99
>
>
>
> Terms added sequentially (first to last)
>
>
>
>   Df SumsOfSqs  MeanSqs F.Model  R2 Pr(>F)
>
> time   1  0.070504 0.070504  123.65 0.96866   0.01 **
>
> Residuals  4  0.002281 0.000570 0.03134
>
> Total  5  0.072785  1.0
>
> ---
>
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>
>
>
>
> > permanova <- adonis(species ~ time, data = time, permutations=999,
> method="bray")
>
> 'nperm' > set of all permutations; Resetting 'nperm'.
>
>
>
>
>
>
>
>
>
>
> [[alternative HTML version deleted]]
>
> __
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>
>
>
>
>
>
> --
>
> Stephen Sefick
> **
> Auburn University
> Biological Sciences
> 331 Funchess Hall
> Auburn, Alabama
> 36849
> **
> sas0...@auburn.edu
> http://www.auburn.edu/~sas0025
> **
>
> Let's not spend our time and resources thinking about things that are so
> little or so large that all they really do for us is puff us up and make us
> feel like gods.  We are mammals, and have not exhausted the annoying little
> problems of being mammals.
>
> -K. Mullis
>
> "A big computer, a complex algorithm and a long time does not equal
> science."
>
>

Re: [R] monte carlo simulations in permanova in vegan package

2015-10-27 Thread stephen sefick

Look at the permute package. I believe this functionality is there.

Please excuse my brevity; this message was sent from my telephone.
On Oct 27, 2015 10:55 AM, "Cade, Brian" <ca...@usgs.gov> wrote:

> Sean:  There are only 20 possible combinations, 6!/(3! x 3!), so you just
> need to enumerate them completely (no Monte Carlo approximation required).
> I don't know if permanova() can do this but you can do it with the mrpp()
> functions and argument (,exact=TRUE) in Blossom package for R.
>
> Brian
>
> Brian S. Cade, PhD
>
> U. S. Geological Survey
> Fort Collins Science Center
> 2150 Centre Ave., Bldg. C
> Fort Collins, CO  80526-8818
>
> email:  ca...@usgs.gov <brian_c...@usgs.gov>
> tel:  970 226-9326
>
>
> On Tue, Oct 27, 2015 at 7:42 AM, Sean Porter <spor...@ori.org.za> wrote:
>
> > Hi Stephen and others,
> >
> >
> >
> > I am trying to run a one-way permanova where I have only 2 levels in the
> > factor “time”, and each level contains only 3 replicates. So because I
> have
> > such few observations (6 in total) and levels (2) there are not enough
> > possible permutations to get a reasonable test (i.e. (2*3)!/ [2!(3!)^2].
> >  That is why for example if I run the analysis with only 99 permutations
> it
> > completes the task. However, if I set the number of permutations to
> > anything larger it returns the message “'nperm' > set of all
> permutations;
> > Resetting 'nperm'.” as the number of possible permutations exceeds the
> > number set by the argument “permutations=”. In PERMANOVA + for PRIMER
> there
> > is a way of dealing with this issue – by using Monte Carlo simulations to
> > generate the p value with a reasonable number of permutations. Hopefully
> > this clarifies my situation and aim?
> >
> >
> >
> > I was therefore hoping there was a way of coding for the Monte-Carlo
> > permutation procedure into adonis?
> >
> >
> >
> > Thanks for your help!
> >
> >
> >
> > From: stephen sefick [mailto:ssef...@gmail.com]
> > Sent: 27 October 2015 03:11 PM
> > To: Sean Porter
> > Cc: r-help@r-project.org
> > Subject: Re: [R] monte carlo simulations in permanova in vegan package
> >
> >
> >
> > The example code works, and reports  permutations. Can you provide
> > more information?
> >
> >
> >
> > data(dune)
> > data(dune.env)
> > adonis(dune ~ Management*A1, data=dune.env, permutations=)
> >
> >
> >
> >
> >
> > On Tue, Oct 27, 2015 at 3:56 AM, Sean Porter <spor...@ori.org.za> wrote:
> >
> > Dear colleagues,
> >
> >
> >
> > I am trying to run a PERMANOVA in the vegan package with an appropriate
> > number of permutations (see example below), ideally . Obviously that
> > number of permutations does not exists so I would like to use Monte Carlo
> > permutation tests to derive the probability value, as is done in the
> > commercial package PERMANOVA+ for PRIMER. How can I adapt my code so that
> > adonis will do so ? Many thanks, Sean
> >
> >
> >
> > > permanova <- adonis(species ~ time, data = time, permutations=99,
> > method="bray")
> >
> > > permanova
> >
> >
> >
> > Call:
> >
> > adonis(formula = species ~ time, data = time, permutations = 99,
> > method
> > = "bray")
> >
> >
> >
> > Permutation: free
> >
> > Number of permutations: 99
> >
> >
> >
> > Terms added sequentially (first to last)
> >
> >
> >
> >   Df SumsOfSqs  MeanSqs F.Model  R2 Pr(>F)
> >
> > time   1  0.070504 0.070504  123.65 0.96866   0.01 **
> >
> > Residuals  4  0.002281 0.000570 0.03134
> >
> > Total  5  0.072785  1.0
> >
> > ---
> >
> > Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> >
> >
> >
> >
> >
> > > permanova <- adonis(species ~ time, data = time, permutations=999,
> > method="bray")
> >
> > 'nperm' > set of all permutations; Resetting 'nperm'.
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > [[alternative HTML version deleted]]
> >
> > __
> > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
&g

Re: [R] monte carlo simulations in permanova in vegan package

2015-10-27 Thread Sean Porter

Hi Stephen and others,

I am trying to run a one-way permanova where I have only 2 levels in the factor 
“time”, and each level contains only 3 replicates. So because I have such few 
observations (6 in total) and levels (2) there are not enough possible 
permutations to get a reasonable test (i.e. (2*3)!/ [2!(3!)^2].   That is why 
for example if I run the analysis with only 99 permutations it completes the 
task. However, if I set the number of permutations to anything larger it 
returns the message “'nperm' > set of all permutations; Resetting 'nperm'.” as 
the number of possible permutations exceeds the number set by the argument 
“permutations=”. In PERMANOVA + for PRIMER there is a way of dealing with this 
issue – by using Monte Carlo simulations to generate the p value with a 
reasonable number of permutations. Hopefully this clarifies my situation and 
aim?

I was therefore hoping there was a way of coding for the Monte-Carlo 
permutation procedure into adonis?  

Thanks for your help!

From: stephen sefick [mailto:ssef...@gmail.com] 
Sent: 27 October 2015 03:11 PM
To: Sean Porter
Cc: r-help@r-project.org
Subject: Re: [R] monte carlo simulations in permanova in vegan package

The example code works, and reports  permutations. Can you provide more 
information? 

data(dune)
data(dune.env)
adonis(dune ~ Management*A1, data=dune.env, permutations=)

On Tue, Oct 27, 2015 at 3:56 AM, Sean Porter <spor...@ori.org.za> wrote:

Dear colleagues,

I am trying to run a PERMANOVA in the vegan package with an appropriate
number of permutations (see example below), ideally . Obviously that
number of permutations does not exists so I would like to use Monte Carlo
permutation tests to derive the probability value, as is done in the
commercial package PERMANOVA+ for PRIMER. How can I adapt my code so that
adonis will do so ? Many thanks, Sean

> permanova <- adonis(species ~ time, data = time, permutations=99,
method="bray")

> permanova

Call:

adonis(formula = species ~ time, data = time, permutations = 99,  method
= "bray")

Permutation: free

Number of permutations: 99

Terms added sequentially (first to last)

  Df SumsOfSqs  MeanSqs F.Model  R2 Pr(>F)

time   1  0.070504 0.070504  123.65 0.96866   0.01 **

Residuals  4  0.002281 0.000570 0.03134

Total  5  0.072785  1.0

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> permanova <- adonis(species ~ time, data = time, permutations=999,
method="bray")

'nperm' > set of all permutations; Resetting 'nperm'.

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-- 

Stephen Sefick
**
Auburn University 
Biological Sciences  
331 Funchess Hall   
Auburn, Alabama
36849   
**
sas0...@auburn.edu  
http://www.auburn.edu/~sas0025 
**

Let's not spend our time and resources thinking about things that are so little 
or so large that all they really do for us is puff us up and make us feel like 
gods.  We are mammals, and have not exhausted the annoying little problems of 
being mammals.

-K. Mullis

"A big computer, a complex algorithm and a long time does not equal science."

  -Robert Gentleman

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R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Re: [R] monte carlo simulations in permanova in vegan package

Re: [R] monte carlo simulations in permanova in vegan package

Re: [R] monte carlo simulations in permanova in vegan package

[R] monte carlo simulations in permanova in vegan package

Re: [R] monte carlo simulations in permanova in vegan package

Re: [R] monte carlo simulations in permanova in vegan package

Re: [R] monte carlo simulations in permanova in vegan package

Re: [R] monte carlo simulations in permanova in vegan package

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