I have morphometric measurements for a trait across various animal taxa, and would like to study the relationship between the size of this trait, and the animals' body size. In theory, I can account for the non-independence of the data with phylogenetic methods, such as independent contrasts. However, I have very different groups in my tree (for example insects and lizards), and even within more closely related groups, the structures are often not homologous. Does this present a problem for independent contrasts/phylogenetic least squares? For example, the structure is not homologous between ants and flies, yet every (sensible?) tree would treat a fly as more similar to an ant than to any lizard. Is this justified if structures are analogous? If not, are there any ways to deal with this problem?
When you calculate the PICs of a trait, you are making a statement about how that trait evolved. The purpose of PICs is to account for phylogenetic non-independence. However, when you are comparing two analogous traits, those two traits are in fact phylogenetically independent of each other; they do not share a common origin. Thus, I think it would be an error to perform PICs on analogous traits because those traits do not share an evolutionary origin.
How to deal with this problem would depend on the specific question you are asking. One thing to do would be to perform PICs on each trait independently on just the portion of the tree that that trait occurs so you are not comparing analogous traits.
You've probably already read this, but I recommend that anyone who hasn't check out Felsenstein's 1985 paper describing the PIC method.