Abstract: We have recently proposed the revised spherical cap harmonic analysis (R-SCHA) modeling technique. The new mathematical functions represent faithfully the spatial variations of potential fields in a restricted area. In this paper, we tackle the inverse problem and outline the efficiency of the new basis functions with respect to real magnetic data. Processing simultaneously repeat stations, observatory, aeromagnetic, and CHAMP satellite data provides our first vector lithospheric field model over France, which extends from surface to 500 km of altitude. The magnetic field is represented with a minimum horizontal spatial representation of 40 km at the mean Earth radius. The magnetic lithospheric map consistency is confirmed with a comparison to known geological features. The model variation with altitude also suggests that the major French magnetic anomaly, the Paris basin anomaly, is produced by a deep-rooted geological structure. These results demonstrate the superiority of regional modeling over global modeling for delineating small-scale details in the lithospheric field. In view of forthcoming satellite missions, like Swarm, the revised spherical cap harmonic analysis method will help to accurately represent the lithospheric field for more detailed geological interpretations.

Abstract: The Traill island model of Gilg et al. (2003) is a landmark attempt at mechanistic modelling of the cyclic population dynamics of rodents, focusing on a high Arctic community. It models the dynamics of one prey, the collared lemming, and four predators : the stoat, the Arctic fox, the long-tailed skua and the snowy owl. In the present short note, we first summarize how the model works in light of theory on seasonally forced predator-prey systems, with a focus on the temporal dynamics of predation rates. We show notably how the impact of generalist predation, which is able here to initiate population declines, differs slightly from that of generalist predation in other mechanistic models of rodent-mustelid interactions such as Turchin & Hanski (1997). We then provide a low-dimensional approximation with a single generalist predator compartment that mimics the essential features of the Traill island model: cycle periodicity, amplitude, shape, as well as generalist-induced declines. This simpler model should be broadly applicable to model other lemming populations that predominantly grow under the snow during the winter period. Matlab computer codes for Gilg et al. (2003), its two-dimensional approximation, as well as alternative lemming population dynamics models are provided.