A simple explanation for taxon abundance patterns

For taxonomic levels higher than species, the abundance distributions of the number of subtaxa per taxon tend to approximate power laws but often show strong deviations from such laws. Previously, these deviations were attributed to finite-time effects in a continuous-time branching process at the generic level. Instead, we describe herein a simple discrete branching process that generates the observed distributions and find that the distribution's deviation from power law form is not caused by disequilibration, but rather that it is time independent and determined by the evolutionary properties of the taxa of interest. Our model predicts—with no free parameters—the rank-frequency distribution of the number of families in fossil marine animal orders obtained from the fossil record. We find that near power law distributions are statistically almost inevitable for taxa higher than species. The branching model also sheds light on species-abundance patterns, as well as on links between evolutionary processes, self-organized criticality, and fractals.

Cation-pi interactions in aromatics of biological and medicinal interest: electrostatic potential surfaces as a useful qualitative guide.

The cation-pi interaction is an important, general force for molecular recognition in biological receptors. Through the sidechains of aromatic amino acids, novel binding sites for cationic ligands such as acetylcholine can be constructed. We report here a number of calculations on prototypical cation-pi systems, emphasizing structures of relevance to biological receptors and prototypical heterocycles of the type often of importance in medicinal chemistry. Trends in the data can be rationalized using a relatively simple model that emphasizes the electrostatic component of the cation-pi interaction. In particular, plots of the electrostatic potential surfaces of the relevant aromatics provide useful guidelines for predicting cation-pi interactions in new systems.