Working with laws, regularities and singularities in biology: The evolution of mammalian red blood cell size as a case study

Phylogenetic comparative methods have been used in recent literature to work with laws and test for regularities (evolutionary associations of quantitative features) and evolutionary singularities (features that evolved in a single taxon). We analyzed these uses epistemologically, taking the evolution of red-blood-cell mean corpuscular volume (MCV) in mammals as a case study. For this, we considered three hypotheses: (i) in the absence of natural selection, other forces or constraints acting on the variation of MCV, MCV variance increases with evolutionary time, as predicted by biology's first law. Our results show that MCV evolves following Brownian motion which, according to Donsker's theorem, is the limit of the random walks on which the law is based on; (ii) MCV decreases as mass-independent basal-metabolic-rate increases, probably because smaller red-blood-cells are more efficient than larger ones at delivering oxygen in tissues. We show evidence for such evolutionary association so we are facing a regularity; (iii) outliers to the latter regularity (extreme MCV values) are evolutionary singularities. We show evidence for a significant difference between the value predicted by an inference model and that observed in Tragulus javanicus. Although at first sight laws and regularities have more in common with each other than with evolutionary singularities, they are fundamentally different: "biology's first law" is based on a priori, mathematical reasoning, whereas the regularity hypothesis is based on empirical data. Regularities and evolutionary singularities are two sides of the same coin, the latter appearing as the exceptions that, so to say, prove the rule.