Damian, It is an interesting question and a very common one, and I have some suggestions (which I think will cause a few other people to chime in). However, before you focus too much on whether you need to consider the issue of what to do when you have seperate shape ~ size relationships across different groups or species, it is worth asking (beyond just significance testing) whether any differences in those relationships are meaningful across the range of observed sizes in your data. There are (at least) two points I suggest considering.
1 - If you have sufficiently large sample sizes, truly trivial differences in the "slope" (really the vector of coefficients associated with the size predictor) may be significantly different. So a common thing to examine next is whether the direction of effects are that different. There are a variety of ways of examining this, but perhaps the easiest is examining the vector correlation (or the angle which can be derived from the correlation) between the allometric vectors for species A and B. If the vector correlation between them is "close" to 1 (or the angle close to 0), then you be able to assume common allometry. There are a few things to consider along with this, but this is a good starting place. One thing that is hard to pin down is how "close" to 1 is "close enough". This can depend on the range of sizes within and among species among other considerations. If you were working on Drosophila wings I can tell you from experience that generally above about 0.93 or 0.95 and you are probably ok making this assumption, but I am not prepared to generalize this. 2 - As always, just as a double check, did you account for the effects of phylogeny in the assessment? If not, take care about what the "significance" really means. 3 - In general for ontogenic or evolutionary allometry, it is generally recommended to use logCS. Hopefully you have done this. The effect of this means that you are examining proportional differences, not absolute differences. But for such interspecific comparisons, I believe (rest of morphmet chime in...) that this is generally reasonable. If you are dealing with a very large size range this can be very useful, BUT if you have some VERY small individuals in the mix, it can cause some issues in terms of mean- variance relationships (but there are corrections for this). So what happens if after all of this (using logCS, accounting for effects of phylogeny) the vector correlations between shape and size are substantially different between species? Well, it will depend on exactly what you may wish to do. One reasonably sensible thing you can do is predict shape values for individuals of each species at comparable sizes (say at mean size for species A, and then again for mean size of species B) along their species specific shape ~ size relationships (but from a single unified model) and assess shape differences (magnitudes etc). In combination with some bootstrapping you can use this to generate plausible distributions of shape differences given these (there is a bit more to it, but hopefully the idea is clear). If you are a Bayesian (and even if you are not), there are some clever ways of integrating over the posterior distribution for these. If you have other goals, let us know. -- You received this message because you are subscribed to the Google Groups "Morphmet" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/morphmet2/e2e38c0b-cd5c-486c-88d9-f882189c79dbo%40googlegroups.com.
