What Does A Likelihood Ratio Test Of 0 Mean? ( R:Phylosig {Phytools}. P-Value=0)?

Question

[Alice]

Hello, biostars!

I use phytools to analyse phylogenetic signal in different tree topologies. In likelihood ratio test with likelihoods for Pagel's lambda I recieve p-value=0 in all my topologies (1000 trees). Not 0.000, or something like that, just 0. I understand, that it indicates highly significant LRT result. But I'm in doubt, is it theoretically possible? And what does it mean from mathematical point of view?

Answer 1

[Istvan Albert]

I have seen this in different circumstances and I think this simply means that the value is low enough that it is pushing the limits of floating point representation for the method as implemented.

For example if say that limit is 1E-16 then later if two values appear to be computed to be 1E-20 and 1E-30 both may be reported as 0 as they are past the limit. Now whether or not this is the right approach is debatable but some methods do it. See if yours is such.

Answer 2

[liamjrevell]

The other commenter is correct that this is due to limitations on floating point representation as implemented. I have modified some of the calculations so that even lower p-values can be represented (http://blog.phytools.org/2013/03/small-update-to-phylosig.html). This update will be in the next release of phytools.