Testing the Cambrian explosion hypothesis by using a molecular dating technique

Molecular studies have the potential to shed light on the origin of the animal phyla by providing independent estimates of the divergence times, but have been criticized for failing to account adequately for variation in rate of evolution. A method of dating divergence times from molecular data addresses the criticisms of earlier studies and provides more realistic, but wider, confidence intervals. The data are not compatible with the Cambrian explosion hypothesis as an explanation for the origin of metazoan phyla, and provide additional support for an extended period of Precambrian metazoan diversification.

The influence of the flow of the reacting gas on the conditions for a thermal explosion

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

The thermal explosion revisited

The classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction α of its wall is ideally thermally conducting while the remaining fraction 1−α is thermally isolated. Partial isolation of the wall naturally reduces the critical radius of the vessel. Most interesting is the case when the structure of the boundary is a periodic one, so that the alternating conductive α and isolated 1−α parts of the boundary occupy together the segments 2π/N (N is the number of segments) of the boundary. A numerical investigation is performed. It is shown that at small α and large N, the critical radius obeys a scaling law with the coefficients depending on N. For large N, the result is obtained that in the central core of the vessel the temperature distribution is axisymmetric. In the boundary layer near the wall having the thickness ≈2πr0/N (r0 is the radius of the vessel), the temperature distribution varies sharply in the peripheral direction. The temperature distribution in the axisymmetric core at the critical value of the vessel radius is subcritical.

The Cambrian “explosion”: Slow-fuse or megatonnage?

Clearly, the fossil record from the Cambrian period is an invaluable tool for deciphering animal evolution. Less clear, however, is how to integrate the paleontological information with molecular phylogeny and developmental biology data. Equally challenging is answering why the Cambrian period provided such a rich interval for the redeployment of genes that led to more complex bodyplans.