Point sets on the sphere S2\mathbb{S}^2 with small spherical cap discrepancy

In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical Fibonacci lattices converges with order $N^{-1/2}$. Such point sets are therefore useful for numerical integration and other computational simulations. The proof uses an area-preserving Lambert map. A detailed analysis of the level curves and sets of the pre-images of spherical caps under this map is given

Population status of 14 shark species caught in the protective gillnets off KwaZulu-Natal beaches, South Africa, 1978 - 2003

Shark nets have been set off the beaches of KwaZulu–Natal, South Africa, since 1952 to reduce the risk of shark attack. The nets fish in fixed localities 400 m from shore and both directly affect local shark populations and act as fisheries-independent monitoring devices. Reliable catch information at the species level was available for the period 1978–2003. Trends in catch rate and size were used to assess the population status of 14 commonly caught shark species. In addition, a demographic modelling approach was used in conjunction with the catch information to assess the potential effect of the nets on populations. Catch rates of four species (Carcharhinus leucas, C. limbatus, Sphyrna lewini and S. mokarran) showed a significant decline, as did the mean or median length of three species (Carcharhinus amboinensis, C. limbatus and female Carcharodon carcharias). For three species that showed declining catch rates or length the potential effect of the shark nets was assessed to be low, suggesting that other sources of catch were responsible for the declining status. The potential effect of the shark nets was assessed to be high for two species (Carcharhinus obscurus and Carcharias taurus, neither of which showed declines in catch rate or length), because of very low intrinsic rates of population increase

Stable isotope profiles of large marine predators: Viable indicators of trophic position, diet, and movement in sharks?

Understanding the role of predators is challenging but critical for ecosystem management. For community dynamics, predator-specific size-based variation in diet, trophic position, and habitat use are rarely accounted for. Using two applied tools (stable isotopes and stomach content data), we examined inter- and intra-species ontogenetic variability in diet (stomach contents), trophic position (TPSIA for δ15N and TPSCA for stomach contents), and habitat use (δ13C) of two large sharks, the scalloped hammerhead ( Sphyrna lewini ) and the dusky ( Carcharhinus obscurus ). Stomach contents identified size-based and gender-specific shifts in diet indicating resource partitioning for and between species. Calculated TP for the two sharks varied by method, either TPSIA or TPSCA and with species, size, and gender, but were complicated by differing baselines and broad functional prey groups, respectively. TP increased with size for S. lewini, but was low in large C. obscurus compared with small sharks. Size-based δ13C profiles indicated habitat partitioning by sex in S. lewini and a movement to shelf edge foraging in large C. obscurus. These results demonstrate that predators exert proportional size-based effects on multiple components of the marine system that are further complicated by species- and gender-specific strategies. </jats:p