random skewers and allometry

[morphmet_moderator]

----- Forwarded message from Milos Blagojevic -----

Date: Fri, 8 Jun 2012 06:20:22 -0400
From: Milos Blagojevic
Reply-To: Milos Blagojevic
Subject: random skewers and allometry
To: morphmet

Dear Morphometricians,

Considering the ever-lasting question of size vs. shape variability in the collections of linear measurements I came across these two contrasting papers.

1. Berner, D., 2011. Size correction in biology: how reliable are approaches based on (common) principal component analysis? Oecologia 166, 961–971.
2. McCoy, M.W., Bolker, B.M., Osenberg, C.W., Miner, B.G., Vonesh, J.R., 2006. Size correction: comparing morphological traits among populations and environments. Oecologia 148, 547–554.

Both of them suggest that the decision on whether to factor-out size variability should be made on the basis of inter-population comparison (if there are multiple populations). My question is that common principal components analysis, although providing covariance matrix similarity with tests, could be substituted with random skewers method of Cheverud? Now in that substitution we would lost CPC1 which could be used for, i.e. Burnaby`s back projection (if all populations share the same size/shape relationship). Could random skewers coefficient be used as a proxy of similarity in determining whether major axes of variability run parallel or diverge or are the same? If all of these coefficients be sufficiently high (although robust test is lacking) would it be safe to assume that whole sample PC1 axis is a well-fit representation of size variability, that could be used for either regression or Burnaby projection?

Best regards,
Milos Blagojevic, Ph.D. student,
Department of Biology and Ecology,
Faculty of Science, Kragujevac, Serbia.
email: paulidealist.kg.ac.rs; paulideali...@gmail.com; spearsata...@hotmail.com

----- End forwarded message -----