Hi Yan,
I'm useless in R, so I won't comment on that aspect of your email...


I just posted a fix on a branch of dendropy.  The algorithm that DendroPy uses 
is basically stepwise addition of leaves. The code we had pruned the polytomy 
down to having 2 children, and then adding leaves back randomly in the subtree 
that subtends the node that had been the polytomy.

We (dendropy folks) had just failed to include the "root" of the original 
polytomy as an attachment point for a new node. So, that method was 
conceptually correct, but implemented in a buggy way.

The star-decomposition-like method (pinching off pairs of children) doesn't 
work for equiprobable topologies. I think that (if you added branch lengths 
during simulation) that method will give you an equiprobable distribution over 
labelled histories (where the depth of the nodes you are pinching off matters) 
rather than topologies. That pinching off pairs is essentially what we do when 
simulating coalescent histories.

I hope that helps, but I'm definitely being sloppy in my description. So don't 
hesitate to let me know if this explanation doesn't make sens.

all the best,
Mark

Mark Holder

mthol...@gmail.com
mthol...@ku.edu
http://phylo.bio.ku.edu/mark-holder

==============================================
Department of Ecology and Evolutionary Biology
University of Kansas
6031 Haworth Hall
1200 Sunnyside Avenue
Lawrence, Kansas 66045

lab phone:  785.864.5789
fax (shared): 785.864.5860
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________________________________
From: R-sig-phylo <r-sig-phylo-boun...@r-project.org> on behalf of Yan Wong 
<y...@pixie.org.uk>
Sent: Friday, June 26, 2020 4:46 PM
To: r-sig-phylo@r-project.org <r-sig-phylo@r-project.org>
Subject: [R-sig-phylo] Breaking polytomies such that all topologies are 
equiprobable

I�m trying to figure out how to randomly resolve polytomies such that there is 
an equal probability of any topology being generated. I thought that the ape 
function �multi2di� did this, but when I have tried it repeatedly with a 
4-tomy, multi2di seems to produce the 3 balanced trees [((a,b),(c,d)) ; 
((a,c),(b,d)); ((a,d),(b,c))] twice as often as the 12 possible unbalanced 
dichotomous 4-tip rooted topologies. The R code I�ve used to produce the sample 
topologies is something like this:

do.call(c, lapply(1:100000, function(x) multi2di(starTree(c('a','b','c','d')))))

Firstly, is this expected, or am I doing something wrong (if expected, it would 
be useful to note this in the docs)? Secondly, is there an function somewhere 
that *will* break polytomies to produce equiprobable topologies? If not, 
thirdly, is there an algorithm that will do this? I think the standard 
�repeatedly pick 2 random edges from the polytomy node and pair them off� 
results in the non-equiprobable distribution that I find using multi2di. I 
think I�ve found a similar problem with the Dendropy algorithm, which does 
claim to result in equiprobable topologies, and have posted to their mailing 
list in case I�m misunderstanding something.

Cheers

Yan Wong
Big Data Institute, Oxford University
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