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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