The figures below are from Felsenstein's paper "Phylogenies and the Comparative Method". I was wondering if there was a specific name for this effect where there is an apparant correlation that is actually the result of the data being structured into two separate groups, where there is no correlation within groups but an apparent correlation between groups. "Phylogenetic non-independence" doesn't seem specific enough.
The fact that species are not independent observations because of their specific phylogenetic relationship is sometimes called phylogenetic dependence (see its use in this paper for example).
Most often though, we talk about the existence of such phylogenetic dependence for a particular trait and we talk about phylogenetic signal for this trait.
I think (correct me if I am wrong) you're searching for a name to describe a situation where two quantitative traits correlate along a phylogeny (when you have one data point per species) but not within any of the species of this phylogeny. If this is the case, I don't think you will actually find a name for this pattern as it it is already quite specific. You could eventually say that there is an inter-species correlation between the two traits but not an intra-species correlation.
I think that the answers here are good, and @Remi.b's term is preferable, but the term in the literature appears to most frequently be "phylogenetic non-independence", e.g. here.
I don't care for this term. Why not just "dependence"? But it seems to be what folks use.