Re: [R-sig-phylo] phylogenetic signal different from BM and random

[Liam J. Revell]

Hello Florian.

I would agree that the value of K you have observed is very low. Since K 
is a standardized variance ratio, this suggest that (controlling for the 
phylogeny) most of the variance is partitioned within, rather than 
between, clades.


That being said, on large trees even small values of K can be 
significant. For instance, if you try the following:


phylosig(tree<-pbtree(n=1000),
x<-fastBM(phytools:::lambdaTree(tree,0.2)),
test=TRUE)

only a very small number of simulations are required to produce one that 
is significant and that has a very small value of K.


Enrico's recommendation to check against picante::phylosignal is wise. 
In my tests, the two functions produce values of K that are identical 
and value of P that are highly similar. (The latter are from 
permutation, so they are not expected to be precisely the same.)


- Liam

Liam J. Revell, Associate Professor of Biology
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://blog.phytools.org

On 12/1/2016 12:32 PM, enrico.reze...@roehampton.ac.uk wrote:

Dear Florian,
following Ted's comment:

1) Is the data you are analyzing normally distributed? It is possible that you 
detect significant signal with a very low K in datasets that deviate 
substantially from normality. Note that under Brownian motion you'd expect 
something like a  normal distibution of the phenotypic data, hence you may want 
to transform you data prior to the analysis of phylogenetic signal

2) You can run the same test with the package picante to ensure that results 
are consistent across packages (i.e., not a bug).

Cheers
Enrico



On 12/1/16 14:19, Theodore Garland wrote:

Dear Florian,

A K values of 0.041 is very small.  It is hard for me to imagine that the
randomizaton test for the presence of phylogenetic signal (Blomberg et al.
2003), which is based on the MSE not K, is significant.  I cannot vouch for
what those R packages are doing.  I would suggest that you get the authors
of those packages to run your data for you and see what's up.

sincerely,
Ted


On Thu, Dec 1, 2016 at 1:41 AM, Menzel, Dr. Florian 
<menz...@uni-mainz.de><mailto:menz...@uni-mainz.de>
wrote:


Dear Ted,

yes. I have a trait with K = 0.041. According to randomization tests, K
differs from the random expectation (p= 0.001; test from Blomberg et al.
2003, computed with 'phylosig' from the phylosig package) AND from the
expectation under a Brownian Motion model (also p=0.001; simulated using
'brownie.lite'/'paintSubTree'). I had similar results for some more
traits.

Does this mean that there is less phylogenetic signal than expected under
Brownian Motion, but more than expected at random? Or does it mean that the
trait evolves even faster than expected at random, i.e. that closely
related taxa differ more than expected from random?

Thanks a lot!

Florian

Dr. Florian Menzel
Department of Evolutionary Biology, Institute of Zoology
University of Mainz
Johannes-von-Müller-Weg 6
55128 Mainz, Germany
phone: 0049-6131-3927848
http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php

Gemeinsam einen Unterschied machen!
www.synagieren.de<http://www.synagieren.de>

'For every complex problem there is an answer that is clear, simple, and
wrong.' (Henry Louis Mencken)


--
*Von:* Theodore Garland 
<theodore.garl...@ucr.edu><mailto:theodore.garl...@ucr.edu>
*Gesendet:* Mittwoch, 30. November 2016 18:38
*An:* Menzel, Dr. Florian
*Cc:* r-sig-phylo@r-project.org<mailto:r-sig-phylo@r-project.org>
*Betreff:* Re: [R-sig-phylo] phylogenetic signal different from BM and
random

Dear Florian,

What do you mean, exactly?  Do you mean the K statistics is, say, about
0.5, and that the randomizaton test for phylogenetic signal (Blomberg et
al. 2003), which is based on the MSE not K, is significant, indicating that
you do have some degree of signal (more than zero)?

Cheers,
Ted

Theodore Garland, Jr., Distinguished Professor

Department of Biology

University of California, Riverside

Riverside, CA 92521

Office Phone:  (951) 827-3524

Facsimile:  (951) 827-4286 (not confidential)

Email:  tgarl...@ucr.edu<mailto:tgarl...@ucr.edu>

http://www.biology.ucr.edu/people/faculty/Garland.html

http://scholar.google.com/citations?hl=en=iSSbrhwJ


Director, UCR Institute for the Development of  
<http://idea.ucr.edu/>Educational
Applications <http://idea.ucr.edu/>


Editor in Chief, *Physiological and Biochemical Zoology
<http://www.press.uchicago.edu/ucp/journals/journal/pbz.html>*


Fail Lab: Episode One

http://testtube.com/faillab/zoochosis-episode-one-evolution

http://www.youtube.com/watch?v=c0msBWyTzU0



On Wed, Nov 30, 2016 at 8:50 AM, Menzel, Dr. Florian 
<menz...@uni-mainz.de<mailto:menz...@uni-mainz.de>

wrote:



Dear all,

I am analysing phylogenetic signal using Blomberg's K. For several of my
traits (univ

Re: [R-sig-phylo] phylogenetic signal different from BM and random

[Enrico.Rezende]

Dear Florian,
following Ted's comment:

1) Is the data you are analyzing normally distributed? It is possible that you 
detect significant signal with a very low K in datasets that deviate 
substantially from normality. Note that under Brownian motion you'd expect 
something like a  normal distibution of the phenotypic data, hence you may want 
to transform you data prior to the analysis of phylogenetic signal

2) You can run the same test with the package picante to ensure that results 
are consistent across packages (i.e., not a bug).

Cheers
Enrico



On 12/1/16 14:19, Theodore Garland wrote:

Dear Florian,

A K values of 0.041 is very small.  It is hard for me to imagine that the
randomizaton test for the presence of phylogenetic signal (Blomberg et al.
2003), which is based on the MSE not K, is significant.  I cannot vouch for
what those R packages are doing.  I would suggest that you get the authors
of those packages to run your data for you and see what's up.

sincerely,
Ted


On Thu, Dec 1, 2016 at 1:41 AM, Menzel, Dr. Florian 
<menz...@uni-mainz.de><mailto:menz...@uni-mainz.de>
wrote:

> Dear Ted,
>
> yes. I have a trait with K = 0.041. According to randomization tests, K
> differs from the random expectation (p= 0.001; test from Blomberg et al.
> 2003, computed with 'phylosig' from the phylosig package) AND from the
> expectation under a Brownian Motion model (also p=0.001; simulated using
> 'brownie.lite'/'paintSubTree'). I had similar results for some more
> traits.
>
> Does this mean that there is less phylogenetic signal than expected under
> Brownian Motion, but more than expected at random? Or does it mean that the
> trait evolves even faster than expected at random, i.e. that closely
> related taxa differ more than expected from random?
>
> Thanks a lot!
>
> Florian
>
> Dr. Florian Menzel
> Department of Evolutionary Biology, Institute of Zoology
> University of Mainz
> Johannes-von-Müller-Weg 6
> 55128 Mainz, Germany
> phone: 0049-6131-3927848
> http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php
>
> Gemeinsam einen Unterschied machen!
> www.synagieren.de<http://www.synagieren.de>
>
> 'For every complex problem there is an answer that is clear, simple, and
> wrong.' (Henry Louis Mencken)
>
>
> --
> *Von:* Theodore Garland 
> <theodore.garl...@ucr.edu><mailto:theodore.garl...@ucr.edu>
> *Gesendet:* Mittwoch, 30. November 2016 18:38
> *An:* Menzel, Dr. Florian
> *Cc:* r-sig-phylo@r-project.org<mailto:r-sig-phylo@r-project.org>
> *Betreff:* Re: [R-sig-phylo] phylogenetic signal different from BM and
> random
>
> Dear Florian,
>
> What do you mean, exactly?  Do you mean the K statistics is, say, about
> 0.5, and that the randomizaton test for phylogenetic signal (Blomberg et
> al. 2003), which is based on the MSE not K, is significant, indicating that
> you do have some degree of signal (more than zero)?
>
> Cheers,
> Ted
>
> Theodore Garland, Jr., Distinguished Professor
>
> Department of Biology
>
> University of California, Riverside
>
> Riverside, CA 92521
>
> Office Phone:  (951) 827-3524
>
> Facsimile:  (951) 827-4286 (not confidential)
>
> Email:  tgarl...@ucr.edu<mailto:tgarl...@ucr.edu>
>
> http://www.biology.ucr.edu/people/faculty/Garland.html
>
> http://scholar.google.com/citations?hl=en=iSSbrhwJ
>
>
> Director, UCR Institute for the Development of  
> <http://idea.ucr.edu/>Educational
> Applications <http://idea.ucr.edu/>
>
>
> Editor in Chief, *Physiological and Biochemical Zoology
> <http://www.press.uchicago.edu/ucp/journals/journal/pbz.html>*
>
>
> Fail Lab: Episode One
>
> http://testtube.com/faillab/zoochosis-episode-one-evolution
>
> http://www.youtube.com/watch?v=c0msBWyTzU0
>
>
>
> On Wed, Nov 30, 2016 at 8:50 AM, Menzel, Dr. Florian 
> <menz...@uni-mainz.de<mailto:menz...@uni-mainz.de>
> > wrote:
>
>> Dear all,
>>
>> I am analysing phylogenetic signal using Blomberg's K. For several of my
>> traits (univariate, continuous), the signal strongly deviates both from
>> random and from the Brownian Motion.
>>
>>
>> I am unsure how to interpret this. Can you give me some advice what this
>> could mean?
>>
>>
>> Thanks a lot!
>>
>>
>> Florian
>>
>>
>> Dr. Florian Menzel
>> Department of Evolutionary Biology, Institute of Zoology
>> University of Mainz
>> Johannes-von-Müller-Weg 6
>> 55128 Mainz, Germany
>> phone: 0049-6131-3927848
>> http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php
>>
>> Gemeinsam einen Unterschied machen!
>> www.synag

Re: [R-sig-phylo] phylogenetic signal different from BM and random

[Theodore Garland]

Dear Florian,

A K values of 0.041 is very small.  It is hard for me to imagine that the
randomizaton test for the presence of phylogenetic signal (Blomberg et al.
2003), which is based on the MSE not K, is significant.  I cannot vouch for
what those R packages are doing.  I would suggest that you get the authors
of those packages to run your data for you and see what's up.

sincerely,
Ted


On Thu, Dec 1, 2016 at 1:41 AM, Menzel, Dr. Florian <menz...@uni-mainz.de>
wrote:

> Dear Ted,
>
> yes. I have a trait with K = 0.041. According to randomization tests, K
> differs from the random expectation (p= 0.001; test from Blomberg et al.
> 2003, computed with 'phylosig' from the phylosig package) AND from the
> expectation under a Brownian Motion model (also p=0.001; simulated using
> 'brownie.lite'/'paintSubTree'). I had similar results for some more
> traits.
>
> Does this mean that there is less phylogenetic signal than expected under
> Brownian Motion, but more than expected at random? Or does it mean that the
> trait evolves even faster than expected at random, i.e. that closely
> related taxa differ more than expected from random?
>
> Thanks a lot!
>
> Florian
>
> Dr. Florian Menzel
> Department of Evolutionary Biology, Institute of Zoology
> University of Mainz
> Johannes-von-Müller-Weg 6
> 55128 Mainz, Germany
> phone: 0049-6131-3927848
> http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php
>
> Gemeinsam einen Unterschied machen!
> www.synagieren.de
>
> 'For every complex problem there is an answer that is clear, simple, and
> wrong.' (Henry Louis Mencken)
>
>
> --
> *Von:* Theodore Garland <theodore.garl...@ucr.edu>
> *Gesendet:* Mittwoch, 30. November 2016 18:38
> *An:* Menzel, Dr. Florian
> *Cc:* r-sig-phylo@r-project.org
> *Betreff:* Re: [R-sig-phylo] phylogenetic signal different from BM and
> random
>
> Dear Florian,
>
> What do you mean, exactly?  Do you mean the K statistics is, say, about
> 0.5, and that the randomizaton test for phylogenetic signal (Blomberg et
> al. 2003), which is based on the MSE not K, is significant, indicating that
> you do have some degree of signal (more than zero)?
>
> Cheers,
> Ted
>
> Theodore Garland, Jr., Distinguished Professor
>
> Department of Biology
>
> University of California, Riverside
>
> Riverside, CA 92521
>
> Office Phone:  (951) 827-3524
>
> Facsimile:  (951) 827-4286 (not confidential)
>
> Email:  tgarl...@ucr.edu
>
> http://www.biology.ucr.edu/people/faculty/Garland.html
>
> http://scholar.google.com/citations?hl=en=iSSbrhwJ
>
>
> Director, UCR Institute for the Development of  
> <http://idea.ucr.edu/>Educational
> Applications <http://idea.ucr.edu/>
>
>
> Editor in Chief, *Physiological and Biochemical Zoology
> <http://www.press.uchicago.edu/ucp/journals/journal/pbz.html>*
>
>
> Fail Lab: Episode One
>
> http://testtube.com/faillab/zoochosis-episode-one-evolution
>
> http://www.youtube.com/watch?v=c0msBWyTzU0
>
>
>
> On Wed, Nov 30, 2016 at 8:50 AM, Menzel, Dr. Florian <menz...@uni-mainz.de
> > wrote:
>
>> Dear all,
>>
>> I am analysing phylogenetic signal using Blomberg's K. For several of my
>> traits (univariate, continuous), the signal strongly deviates both from
>> random and from the Brownian Motion.
>>
>>
>> I am unsure how to interpret this. Can you give me some advice what this
>> could mean?
>>
>>
>> Thanks a lot!
>>
>>
>> Florian
>>
>>
>> Dr. Florian Menzel
>> Department of Evolutionary Biology, Institute of Zoology
>> University of Mainz
>> Johannes-von-Müller-Weg 6
>> 55128 Mainz, Germany
>> phone: 0049-6131-3927848
>> http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php
>>
>> Gemeinsam einen Unterschied machen!
>> www.synagieren.de<http://www.synagieren.de>
>>
>> 'For every complex problem there is an answer that is clear, simple, and
>> wrong.' (Henry Louis Mencken)
>>
>> [[alternative HTML version deleted]]
>>
>>
>> ___
>> R-sig-phylo mailing list - R-sig-phylo@r-project.org
>> https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
>> Searchable archive at http://www.mail-archive.com/r-
>> sig-ph...@r-project.org/
>>
>
>

[[alternative HTML version deleted]]

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https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/

Re: [R-sig-phylo] phylogenetic signal different from BM and random

[Menzel, Dr. Florian]

Dear Ted,

yes - I have a trait with K = 0.041. It differs significantly from random 
expectation (p = 0.001, command phylosig, package phylosig and command 
phylosignal, package picante). But it also differs from the Brownian motion 
model (p = 0.001, simulated with brownie.lite and fastBM). I obtained similar 
results for other traits, too.


Does this mean that the trait has less phylogenetic signal than expected under 
Brownian motion, but more than expected from random, or does that mean that 
closely related species are even more different than expected from random (i.e. 
'negative' phylogenetic signal)? I am not sure how to interpret these results...


Thanks a lot for your help!


Florian


Dr. Florian Menzel
Department of Evolutionary Biology, Institute of Zoology
University of Mainz
Johannes-von-M�ller-Weg 6
55128 Mainz, Germany
phone: 0049-6131-3927848
http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php

Gemeinsam einen Unterschied machen!
www.synagieren.de<http://www.synagieren.de>

'For every complex problem there is an answer that is clear, simple, and 
wrong.' (Henry Louis Mencken)



Von: Theodore Garland <theodore.garl...@ucr.edu>
Gesendet: Mittwoch, 30. November 2016 18:38
An: Menzel, Dr. Florian
Cc: r-sig-phylo@r-project.org
Betreff: Re: [R-sig-phylo] phylogenetic signal different from BM and random

Dear Florian,

What do you mean, exactly?  Do you mean the K statistics is, say, about 0.5, 
and that the randomizaton test for phylogenetic signal (Blomberg et al. 2003), 
which is based on the MSE not K, is significant, indicating that you do have 
some degree of signal (more than zero)?

Cheers,
Ted


Theodore Garland, Jr., Distinguished Professor

Department of Biology

University of California, Riverside

Riverside, CA 92521

Office Phone:  (951) 827-3524<tel:%28951%29%20827-3524>

Facsimile:  (951) 827-4286<tel:%28951%29%20827-4286> (not confidential)

Email:  tgarl...@ucr.edu<mailto:tgarl...@ucr.edu>

http://www.biology.ucr.edu/people/faculty/Garland.html

http://scholar.google.com/citations?hl=en=iSSbrhwJ


Director, UCR Institute for the Development of <http://idea.ucr.edu/> 
Educational Applications<http://idea.ucr.edu/>


Editor in Chief, Physiological and Biochemical 
Zoology<http://www.press.uchicago.edu/ucp/journals/journal/pbz.html>


Fail Lab: Episode One

http://testtube.com/faillab/zoochosis-episode-one-evolution

http://www.youtube.com/watch?v=c0msBWyTzU0


On Wed, Nov 30, 2016 at 8:50 AM, Menzel, Dr. Florian 
<menz...@uni-mainz.de<mailto:menz...@uni-mainz.de>> wrote:
Dear all,

I am analysing phylogenetic signal using Blomberg's K. For several of my traits 
(univariate, continuous), the signal strongly deviates both from random and 
from the Brownian Motion.


I am unsure how to interpret this. Can you give me some advice what this could 
mean?


Thanks a lot!


Florian


Dr. Florian Menzel
Department of Evolutionary Biology, Institute of Zoology
University of Mainz
Johannes-von-M�ller-Weg 6
55128 Mainz, Germany
phone: 0049-6131-3927848
http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php

Gemeinsam einen Unterschied machen!
www.synagieren.de<http://www.synagieren.de><http://www.synagieren.de>

'For every complex problem there is an answer that is clear, simple, and 
wrong.' (Henry Louis Mencken)

[[alternative HTML version deleted]]


___
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R-sig-phylo@r-project.org<mailto:R-sig-phylo@r-project.org>
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/


[[alternative HTML version deleted]]

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https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/

Re: [R-sig-phylo] phylogenetic signal different from BM and random

[Menzel, Dr. Florian]

Dear Ted,

yes. I have a trait with K = 0.041. According to randomization tests, K differs 
from the random expectation (p= 0.001; test from Blomberg et al. 2003, computed 
with 'phylosig' from the phylosig package) AND from the expectation under a 
Brownian Motion model (also p=0.001; simulated using 
'brownie.lite'/'paintSubTree'). I had similar results for some more traits.


Does this mean that there is less phylogenetic signal than expected under 
Brownian Motion, but more than expected at random? Or does it mean that the 
trait evolves even faster than expected at random, i.e. that closely related 
taxa differ more than expected from random?


Thanks a lot!


Florian


Dr. Florian Menzel
Department of Evolutionary Biology, Institute of Zoology
University of Mainz
Johannes-von-M�ller-Weg 6
55128 Mainz, Germany
phone: 0049-6131-3927848
http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php

Gemeinsam einen Unterschied machen!
www.synagieren.de<http://www.synagieren.de>

'For every complex problem there is an answer that is clear, simple, and 
wrong.' (Henry Louis Mencken)



Von: Theodore Garland <theodore.garl...@ucr.edu>
Gesendet: Mittwoch, 30. November 2016 18:38
An: Menzel, Dr. Florian
Cc: r-sig-phylo@r-project.org
Betreff: Re: [R-sig-phylo] phylogenetic signal different from BM and random

Dear Florian,

What do you mean, exactly?  Do you mean the K statistics is, say, about 0.5, 
and that the randomizaton test for phylogenetic signal (Blomberg et al. 2003), 
which is based on the MSE not K, is significant, indicating that you do have 
some degree of signal (more than zero)?

Cheers,
Ted


Theodore Garland, Jr., Distinguished Professor

Department of Biology

University of California, Riverside

Riverside, CA 92521

Office Phone:  (951) 827-3524<tel:%28951%29%20827-3524>

Facsimile:  (951) 827-4286<tel:%28951%29%20827-4286> (not confidential)

Email:  tgarl...@ucr.edu<mailto:tgarl...@ucr.edu>

http://www.biology.ucr.edu/people/faculty/Garland.html

http://scholar.google.com/citations?hl=en=iSSbrhwJ


Director, UCR Institute for the Development of <http://idea.ucr.edu/> 
Educational Applications<http://idea.ucr.edu/>


Editor in Chief, Physiological and Biochemical 
Zoology<http://www.press.uchicago.edu/ucp/journals/journal/pbz.html>


Fail Lab: Episode One

http://testtube.com/faillab/zoochosis-episode-one-evolution

http://www.youtube.com/watch?v=c0msBWyTzU0


On Wed, Nov 30, 2016 at 8:50 AM, Menzel, Dr. Florian 
<menz...@uni-mainz.de<mailto:menz...@uni-mainz.de>> wrote:
Dear all,

I am analysing phylogenetic signal using Blomberg's K. For several of my traits 
(univariate, continuous), the signal strongly deviates both from random and 
from the Brownian Motion.


I am unsure how to interpret this. Can you give me some advice what this could 
mean?


Thanks a lot!


Florian


Dr. Florian Menzel
Department of Evolutionary Biology, Institute of Zoology
University of Mainz
Johannes-von-M�ller-Weg 6
55128 Mainz, Germany
phone: 0049-6131-3927848
http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php

Gemeinsam einen Unterschied machen!
www.synagieren.de<http://www.synagieren.de><http://www.synagieren.de>

'For every complex problem there is an answer that is clear, simple, and 
wrong.' (Henry Louis Mencken)

[[alternative HTML version deleted]]


___
R-sig-phylo mailing list - 
R-sig-phylo@r-project.org<mailto:R-sig-phylo@r-project.org>
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/


[[alternative HTML version deleted]]

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R-sig-phylo mailing list - R-sig-phylo@r-project.org
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Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/

Re: [R-sig-phylo] phylogenetic signal different from BM and random

[Theodore Garland]

Dear Florian,

What do you mean, exactly?  Do you mean the K statistics is, say, about
0.5, and that the randomizaton test for phylogenetic signal (Blomberg et
al. 2003), which is based on the MSE not K, is significant, indicating that
you do have some degree of signal (more than zero)?

Cheers,
Ted

Theodore Garland, Jr., Distinguished Professor

Department of Biology

University of California, Riverside

Riverside, CA 92521

Office Phone:  (951) 827-3524

Facsimile:  (951) 827-4286 (not confidential)

Email:  tgarl...@ucr.edu

http://www.biology.ucr.edu/people/faculty/Garland.html

http://scholar.google.com/citations?hl=en=iSSbrhwJ


Director, UCR Institute for the Development of
Educational
Applications 


Editor in Chief, *Physiological and Biochemical Zoology
*


Fail Lab: Episode One

http://testtube.com/faillab/zoochosis-episode-one-evolution

http://www.youtube.com/watch?v=c0msBWyTzU0



On Wed, Nov 30, 2016 at 8:50 AM, Menzel, Dr. Florian 
wrote:

> Dear all,
>
> I am analysing phylogenetic signal using Blomberg's K. For several of my
> traits (univariate, continuous), the signal strongly deviates both from
> random and from the Brownian Motion.
>
>
> I am unsure how to interpret this. Can you give me some advice what this
> could mean?
>
>
> Thanks a lot!
>
>
> Florian
>
>
> Dr. Florian Menzel
> Department of Evolutionary Biology, Institute of Zoology
> University of Mainz
> Johannes-von-Müller-Weg 6
> 55128 Mainz, Germany
> phone: 0049-6131-3927848
> http://www.bio.uni-mainz.de/zoo/evobio/73_ENG_HTML.php
>
> Gemeinsam einen Unterschied machen!
> www.synagieren.de
>
> 'For every complex problem there is an answer that is clear, simple, and
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