A test of alternative models of diversification in tropical rainforests: Ecological gradients vs. rainforest refugia

Comparison of mitochondrial and morphological divergence in eight populations of a widespread leaf-litter skink is used to determine the relative importance of geographic isolation and natural selection in generating phenotypic diversity in the Wet Tropics Rainforest region of Australia. The populations occur in two geographically isolated regions, and within each region, in two different habitats (closed rainforest and tall open forest) that span a well characterized ecological gradient. Morphological differences among ancient geographic isolates (separated for several million years, judging by their mitochondrial DNA sequence divergence) were slight, but morphological and life history differences among habitats were large and occurred despite moderate to high levels of mitochondrial gene flow. A field experiment identified avian predation as one potential agent of natural selection. These results indicate that natural selection operating across ecological gradients can be more important than geographic isolation in similar habitats in generating phenotypic diversity. In addition, our results indicate that selection is sufficiently strong to overcome the homogenizing effects of gene flow, a necessary first step toward speciation in continuously distributed populations. Because ecological gradients may be a source of evolutionary novelty, and perhaps new species, their conservation warrants greater attention. This is particularly true in tropical regions, where most reserves do not include ecological gradients and transitional habitats.

On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models.

Most models of tumorigenesis assume that the tumor grows by increased cell division. In these models, it is generally supposed that daughter cells behave as do their parents, and cell numbers have clear potential for exponential growth. We have constructed simple mathematical models of tumorigenesis through failure of programmed cell death (PCD) or differentiation. These models do not assume that descendant cells behave as their parents do. The models predict that exponential growth in cell numbers does sometimes occur, usually when stem cells fail to die or differentiate. At other times, exponential growth does not occur: instead, the number of cells in the population reaches a new, higher equilibrium. This behavior is predicted when fully differentiated cells fail to undergo PCD. When cells of intermediate differentiation fail to die or to differentiate further, the values of growth parameters determine whether growth is exponential or leads to a new equilibrium. The predictions of the model are sensitive to small differences in growth parameters. Failure of PCD and differentiation, leading to a new equilibrium number of cells, may explain many aspects of tumor behavior--for example, early premalignant lesions such as cervical intraepithelial neoplasia, the fact that some tumors very rarely become malignant, the observation of plateaux in the growth of some solid tumors, and, finally, long lag phases of growth until mutations arise that eventually result in exponential growth.