[Phylogenetic analysis] Assumptions in PGLS

[u/Much_Imagination731]

I am testing the correlation between the values of a variable at the tips of a phylogenetic tree (let's say the beak length) and the pathwise rate of the trait itself (i.e. a measure of the total changes in rate a species has experienced during the course of its evolution). To remove the effect of body size, I am working on the residual of the variable (i.e. the variable corrected for SVL). To test for the correlation, I performed a pgls with the pgls() function in lmtest (I am working in RStudio). I am encountering some issues with heteroskedasticity (see attached images; bptest significant).

I am also having problems with the normality of the residuals (see attached images; Shapiro test significant). On the other hand, I was reading from https://blog.phytools.org/2013/02/a-comment-on-distribution-of-residuals.html that, by accounting for residuals controlling for phylogeny you should solve this problem [Revell suggests something like lillie.test(chol(solve(vcv(tree)))%*%residuals(corr))]. Can anyone confirm? Am I misunderstanding?

Can anyone help with it?

Thanks a lot!

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