A universal scaling law between gray matter and white matter of cerebral cortex

Neocortex, a new and rapidly evolving brain structure in mammals, has a similar layered architecture in species over a wide range of brain sizes. Larger brains require longer fibers to communicate between distant cortical areas; the volume of the white matter that contains long axons increases disproportionally faster than the volume of the gray matter that contains cell bodies, dendrites, and axons for local information processing, according to a power law. The theoretical analysis presented here shows how this remarkable anatomical regularity might arise naturally as a consequence of the local uniformity of the cortex and the requirement for compact arrangement of long axonal fibers. The predicted power law with an exponent of 4/3 minus a small correction for the thickness of the cortex accurately accounts for empirical data spanning several orders of magnitude in brain sizes for various mammalian species, including human and nonhuman primates.

Morphological innovation and developmental genetics

How do the actions of individual genes contribute to the complex morphologies of animals and plants? How widespread are these genes taxonomically? How many genes are involved in the morphological differences observed between species, and can we identify them? To what extent can empirical data and theory be reconciled? We provide an overview of some recent attempts to answer these questions, answers that have taken us to the threshold of understanding the mechanistic basis and evolutionary factors that underlie morphological innovation.

DNA profile match probabilities in a subdivided population: when can subdivision be ignored?

Li and Chakravarti [Li, C.C. & Chakravarti, A. (1994) Hum. Hered. 44, 100-109] compared the probability (MO) of a random match between the two DNA profiles of a pair of individuals drawn from a random-mating population to the probability (MF) of the match between a pair of random individuals drawn from a subdivided population. The level of heterogeneity in this subdivided population is measured by the parameter F, where there is no subdivision when F = 0 and increasing values of F indicate increasing subdivisions. Li and Chakravarti concluded that it is conservative to use the match probability MO, which is derived under the assumption that the two individuals are drawn from a homogeneous random-mating population without subdivision. However, MO may not be always greater than MF, even for biologically reasonable values of F. We explore here those mathematical conditions under which MO is less than MF, and we find that MO is not conservative mainly when there is an allele with a much higher frequency than all the other alleles. When empirical data for both variable number of tandem repeat (VNTR) and short tandem repeat (STR) systems are evaluated, we find that in the majority of cases MO represents a conservative probability of a match, and so the subdivision of human populations may usually be ignored for a random match, although not, of course, for relatives. Loci for which MO is not conservative should be avoided for forensic inference.

Inferring phylogenies from DNA sequences of unequal base compositions.

A new method for computing evolutionary distances between DNA sequences is proposed. Contrasting with classical methods, the underlying model does not assume that sequence base compositions (A, C, G, and T contents) are at equilibrium, thus allowing unequal base compositions among compared sequences. This makes the method more efficient than the usual ones in recovering phylogenetic trees from sequence data when base composition is heterogeneous within the data set, as we show by using both simulated and empirical data. When applied to small-subunit ribosomal RNA sequences from several prokaryotic or eukaryotic organisms, this method provides evidence for an early divergence of the microsporidian Vairimorpha necatrix in the eukaryotic lineage.