Darwinian gradualism and its limits: The development of Darwin's views on the rate and pattern of evolutionary change

Conclusion The major tenets of the recent hypothesis of punctuated equilibrium are explicit in Darwin's writing. His notes from 1837–1838 contain references to stasis and rapid change. In the first edition of the Origin (1859), Darwin described the importance of isolation of local varieties in the process of speciation. His views on the tempo of speciation were influenced by Hugh Falconer and also, perhaps, by Edward Suess (1831–1914). It is paradoxical that, although both topics were recorded in his unpublished notes of 1837–1838, the second was not explicitly and fully discussed until the fourth edition of the Origin (1866). While no wholly satisfactory explanation of this paradox suggests itself, it seems probable that Falconer's work on the persistence of fossil species of elephant helped Darwin to see the wider significance of the tempo of evolution for his general theory.     

Structural Properties and Complexity of a New Network Class: Collatz Step Graphs

In this paper, we introduce a biologically inspired model to generate complex networks. In contrast to many other construction procedures for growing networks introduced so far, our method generates networks from one-dimensional symbol sequences that are related to the so called Collatz problem from number theory. The major purpose of the present paper is, first, to derive a symbol sequence from the Collatz problem, we call the step sequence, and investigate its structural properties. Second, we introduce a construction procedure for growing networks that is based on these step sequences. Third, we investigate the structural properties of this new network class including their finite scaling and asymptotic behavior of their complexity, average shortest path lengths and clustering coefficients. Interestingly, in contrast to many other network models including the small-world network from Watts & Strogatz, we find that CS graphs become ‘smaller’ with an increasing size.     

Protein diffusion in crowded electrolyte solutions

We report on a combined cold neutron backscattering and spin-echo study of the short-range and long-range nanosecond diffusion of the model globular protein bovine serum albumin (BSA) in aqueous solution as a function of protein concentration and NaCl salt concentration. Complementary small angle X-ray scattering data are used to obtain information on the correlations of the proteins in solution. Particular emphasis is put on the effect of crowding, i.e. conditions under which the proteins cannot be considered as objects independent of each other. We thus address the question at which concentration this crowding starts to influence the static and in particular also the dynamical behaviour. We also briefly discuss qualitatively which charge effects, i.e. effects due to the interplay of charged molecules in an electrolyte solution, may be anticipated. Both the issue of crowding as well as that of charge effects are particularly relevant for proteins and their function under physiological conditions, where the protein volume fraction can be up to approximately 40% and salt ions are ubiquitous. The interpretation of the data is put in the context of existing studies on related systems and of existing theoretical models.