The theory of invariants in life history is mostly attributable to Eric Charnov, who also reviewed the key principles in his book, Life History Invariants : Some Explorations of Symmetry in Evolutionary Ecology. In the interim, Charnov has been kind enough to forward a short article he has in press in Oikos, which expresses some of the mathematics underlying the "dimensionless ratios", and some of the reasons they might be expected to be independent of body size.
Now, Charnov and his colleagues have a technical comment in this week's Science:
Nee et al. (Reports, 19 August 2005, p. 1236) used a null model to argue that life history invariants are illusions. We show that their results are largely inconsequential for life history theory because the authors confound two definitions of invariance, and rigorous analysis of their null model demonstrates that it does not match observed data.
Nee and colleagues have a response to the comment, which as you might expect doesn't agree:
Savage et al. describe two different kinds of invariant. The kind they claim to have the greatest biological importance allows the invariant quantities to vary widely, even randomly, between different species. We do not agree that such quantities reveal any deep constraints on evolution.
I have my own perspective on this exchange. Mostly, I come from outside the problem of life history, and my interest in it concerns one small taxonomic group -- the hominids.
Deviations from a regression cannot be used to confirm the regression. Consider Meganthropus.
Charnov E. 1993. Life History Invariants: Some Explorations of Symmetry in Evolutionary Ecology. Oxford University Press, Oxford. Amazon
de Jong G. 2005. Is invariance across animal species just an illusion? Science 309:1193-1195. Full text (subscription required)
Nee S, Colegrave N, West SA, Grafen A. 2005. The illusion of invariant quantities in life histories. Science 309:1236-1239. Full text (subscription required)
Savage VM, White EP, Moses ME, Ernest SKM, Enquist BJ, Charnov EL. 2006. Comment on "The illusion of invariant quantities in life histories. Science 312:198. DOI link