Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We study the long time behaviour of solutions with initial conditions close to a stable, B=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function B(t,x), plus an H^1-small fluctuation.Comment: 19 page

Testing the robustness of primary production models in shallow coastal areas: a case study

In this paper we investigate the robustness of a dynamic model, which describes the dynamic of the seagrass Zostera marina, with respect to the inter-annual variability of the two main forcing functions of primary production models in eutrophicated environments. The model was previously applied to simulate the seasonal evolution of this species in the Lagoon of Venice during a specific year and calibrated against time series of field data. In the this paper, we present and discuss the results which were obtained by forcing the model using time series of site-specific daily values concerning the solar radiation intensity and water temperature. The latter was estimated by means of a regression model, whose input variable was a site-specific time series of the air temperature. The regression model was calibrated using a year-long time series of hourly observations. The Z marina model was first partially recalibrated against the same data set that was used in the original paper. Subsequently, the model was forced using a 7-year-long time series of the driving functions, in order to check the reliability of its long-term predictions. Even though the calibration gave satisfactory results, the multi-annual trends of the output variables were found to be in contrast with the observed evolution of the seagrass biomasses. Since detailed information about the air temperature and solar radiation are often available, these findings suggest that the testing of the ecological consistency of the evolution of primary production models in the long term would provide additional confidence in their results, particularly in those cases in which the scarcity of field data does not allow one to perform a formal corroboration/validation of these models

Contrasting Patterns of Transposable-Element Insertion Polymorphism and Nucleotide Diversity in Autotetraploid and Allotetraploid Arabidopsis Species

It has been hypothesized that polyploidy permits the proliferation of transposable elements, due to both the masking of deleterious recessive mutations and the breakdown of host silencing mechanisms. We investigated the patterns of insertion polymorphism of an Ac-like transposable element and nucleotide diversity at 18 gene fragments in the allotetraploid Arabidopsis suecica and the autotetraploid A. arenosa. All identified insertions were fixed in A. suecica, and many were clearly inherited from the parental species A. thaliana or A. arenosa. These results are inconsistent with a rapid increase in transposition associated with hybrid breakdown but support the evidence from nucleotide polymorphism patterns of a recent single origin of this species leading to genomewide fixations of transposable elements. In contrast, most insertions were segregating at very low frequencies in A. arenosa samples, showing a significant departure from neutrality in favor of purifying selection, even when we account for population subdivision inferred from sequence variation. Patterns of nucleotide variation at reference genes are consistent with the TE results, showing evidence for higher effective population sizes in A. arenosa than in related diploid taxa but a near complete population bottleneck associated with the origins of A. suecica