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?