Fisher waves: An individual-based stochastic model.

The propagation of a beneficial mutation in a spatially extended population is usually studied using the phenomenological stochastic Fisher-Kolmogorov-Petrovsky-Piscounov (SFKPP) equation. We derive here an individual-based, stochastic model founded on the spatial Moran process where fluctuations are treated exactly. The mean-field approximation of this model leads to an equation that is different from the phenomenological FKPP equation. At small selection pressure, the front behavior can be mapped into a Brownian motion with drift, the properties of which can be derived from the microscopic parameters of the Moran model. Finally, we generalize the model to take into account dispersal kernels beyond migration to nearest neighbors. We show how the effective population size (which controls the noise amplitude) and the diffusion coefficient can both be computed from the dispersal kernel.

Neutron fluctuations: The importance of being delayed.

The neutron population in a nuclear reactor is subject to fluctuations in time and in space due to the competition of diffusion by scattering, births by fission events, and deaths by absorptions. As such, fission chains provide a prototype model for the study of spatial clustering phenomena. In order for the reactor to be operated in stationary conditions at the critical point, the population of prompt neutrons instantaneously emitted at fission must be in equilibrium with the much smaller population of delayed neutrons, emitted after a Poissonian time by nuclear decay of the fissioned nuclei. In this work, we will show that the delayed neutrons, although representing a tiny fraction of the total number of neutrons in the reactor, actually have a key impact on the fluctuations, and their contribution is very effective in quenching the spatial clustering.

Neutral clustering in a simple experimental ecological community.

The spatial distribution of most species in ecosystems is nonuniform. New theories try to explain patterns observed at multiple scales in terms of neutral processes such as birth, death, and migration. We have devised an experimental, niche-free ecosystem where the amplitude of neutral patchiness can be precisely measured. Spatial distribution of species in this system is extremely clustered. We demonstrate that this clustering is entirely attributed to neutral causes and show that the most basic properties of life can provoke intricate spatial structures without clues from the environment.

Species abundance distribution and population dynamics in a two-community model of neutral ecology.

Explicit formulas for the steady-state distribution of species in two interconnected communities of arbitrary sizes are derived in the framework of Hubbell's neutral model of biodiversity. Migrations of seeds from both communities as well as mutations in both of them are taken into account. These results generalize those previously obtained for the "island-continent" model and they allow an analysis of the influence of the ratio of the sizes of the two communities on the dominance/diversity equilibrium. Exact expressions for species abundance distributions are deduced from a master equation for the joint probability distribution of species in the two communities. Moreover, an approximate self-consistent solution is derived. It corresponds to a generalization of previous results and it proves to be accurate over a broad range of parameters. The dynamical correlations between the abundances of a species in both communities are also discussed.

Precise domain specification in the developing Drosophila embryo.

A simple morphogen gradient based on the protein bicoid is insufficient to explain the precise (i.e., similar in all embryos) setting of anteroposterior gene expression domains in the early Drosophila embryo. We present here an alternative model, based on quantitative data, which accounts for all of our observations. The model also explains the robustness of hunchback boundary setting in unnatural environments such as published recently [Luccheta, Nature 434, 1134 (2005)]. The model is based on the existence of a secondary gradient correlated to bicoid through protein degradation by the same agent.

Analytical solution of a neutral model of biodiversity.

The unified neutral model of biodiversity proposed by S. Hubbell is solved analytically: The distributions of species abundance in the metacommunity and in a local community are calculated exactly as a function of speciation and migration rates and of the size of the community. In the limit of large population sizes the densities of species of given relative abundance are found to be given by universal functions depending only on two parameters.

Clustering in neutral ecology.

The "neutral ecology" model assumes that all organisms in the same trophic level have the same death, duplication, migration and mutation rates and are subjected to a zero sum rule. We show by exact analytical methods that under the assumption of this model, organisms tend to aggregate and form clusters. At dimensions less than or equal to 2, cluster size grows in average and one specie will dominate the whole ecosystem if enough time is allocated. At dimension d=3 (or higher), an equilibrium is reached and cluster sizes are distributed as a power law.

Clustering of diffusing organisms.

Recently, a "Brownian bugs" model has been proposed as a possible explanation for the clustering of organisms such as planktons [W.R. Young, A.J. Roberts, and G. Stuhne, Nature (London) 412, 328 (2001)]. In this model, diffusing organisms die and give birth with equal probabilities and are independent of each other. The clustering phenomenon is due to the discreteness of birth and death events and cannot be explained in the framework of the continuous model of population dynamics. We show by exact calculation that at dimensions smaller than or equal to 2, this simple mechanism is enough to provoke aggregations of the organisms. At dimensions higher than 2, the clustering phenomenon disappears, but reproductive fluctuations can still be large compared to diffusive ones.

Elasticity measurements show the existence of thin rigid cores inside mitotic chromosomes.

Chromosome condensation is one of the most critical steps during cell division. However, the structure of condensed mitotic chromosomes is poorly understood. In this paper we describe a new approach based on elasticity measurements for studying the structure of in vitro assembled mitotic chromosomes in Xenopus egg extract. The approach is based on a unique combination of measurements of both longitudinal deformability and bending rigidity of whole chromosomes. By using specially designed micropipettes, the chromosome force-extension curve was determined. Analysis of the curvature fluctuation spectrum allowed for the measurement of chromosome bending ridigity. The relationship between the values of these two parameters is very specific: the measured chromosome flexibility was found to be 2,000 times lower than the flexibility calculated from the experimentally determined Young modulus. This requires the chromosome structure to be formed of one or a few thin rigid elastic axes surrounded by a soft envelope. The properties of these axes are well-described by models developed for the elasticity of titin-like molecules. Additionally, the deformability of in vitro assembled chromosomes was found to be very similar to that of native somatic chromosomes, thus demonstrating the existence of an essentially identical structure.

Elasticity and structure of eukaryote chromosomes studied by micromanipulation and micropipette aspiration.

The structure of mitotic chromosomes in cultured newt lung cells was investigated by a quantitative study of their deformability, using micropipettes. Metaphase chromosomes are highly extensible objects that return to their native shape after being stretched up to 10 times their normal length. Larger deformations of 10 to 100 times irreversibly and progressively transform the chromosomes into a "thin filament," parts of which display a helical organization. Chromosomes break for elongations of the order of 100 times, at which time the applied force is around 100 nanonewtons. We have also observed that as mitosis proceeds from nuclear envelope breakdown to metaphase, the native chromosomes progressively become more flexible. (The elastic Young modulus drops from 5,000 +/- 1,000 to 1,000 +/- 200 Pa.) These observations and measurements are in agreement with a helix-hierarchy model of chromosome structure. Knowing the Young modulus allows us to estimate that the force exerted by the spindle on a newt chromosome at anaphase is roughly one nanonewton.