Diet and trophic ecology of the tiger shark (Galeocerdo cuvier) from South African waters

Knowledge of the diet and trophic ecology of apex predators is key for the implementation of effective ecosystem as well as species-based management initiatives. Using a combination of stomach content data and stable isotope analysis (δ15N and δ13C) the current study provides information on size-based and sex-specific variations in diet, trophic position (TP) and foraging habitat of tiger sharks (Galeocerdo cuvier) caught in the KwaZulu-Natal Sharks Board bather protection program. This study presents the longest time-series and most detailed analysis of stomach content data for G. cuvier worldwide. Prey identified from 628 non-empty stomachs revealed a size-based shift in diet. Reptiles, birds, mysticetes, and large shark species increased in dietary importance with G. cuvier size, concomitant with a decrease in smaller prey such as batoids and teleosts. Seasonal and decadal shifts in diet driven primarily by changes in the importance of elasmobranchs and mammal (cetacean) prey were recorded for medium sized (150-220 cm) G. cuvier. Both stomach content and stable isotope analysis indicated that G. cuvier is a generalist feeder at the population level. Size-based δ13C profiles indicated a movement to offshore foraging habitats by larger G. cuvier. Calculated TP varied by method ranging from 4.0 to 5.0 (TPSCA for stomach contents) and from 3.6 to 4.5 (TPscaled and TPadditive for δ15N). Large (> 220 cm) G. cuvier did not feed at discrete trophic levels, but rather throughout the food web. These data provide key information on the ecological role of G. cuvier to improve the accuracy of regional food web modelling. This will enable a better understanding of the ecological impacts related to changes in the abundance of this predator

The last frontier: Catch records of white sharks (carcharodon carcharias) in the northwest pacific ocean

White sharks are highly migratory apex predators, globally distributed in temperate, sub-tropical, and tropical waters. Knowledge of white shark biology and ecology has increased recently based on research at known aggregation sites in the Indian, Atlantic, and Northeast Pacific Oceans; however, few data are available for the Northwest Pacific Ocean. This study provides a meta-analysis of 240 observations of white sharks from the Northwest Pacific Ocean between 1951 and 2012. Records comprise reports of bycatch in commercial fisheries, media accounts, personal communications, and documentation of shark-human interactions from Russia (n = 8), Republic of Korea (22), Japan (129), China (32), Taiwan (45), Philippines (1) and Vietnam (3). Observations occurred in all months, excluding October-January in the north (Russia and Republic of Korea) and July-August in the south (China, Taiwan, Philippines, and Vietnam). Population trend analysis indicated that the relative abundance of white sharks in the region has remained relatively stable, but parameterization of a 75% increase in observer effort found evidence of a minor decline since 2002. Reliably measured sharks ranged from 126–602 cm total length (TL) and 16–2530 kg total weight. The largest shark in this study (602 cm TL) represents the largest measured shark on record worldwide. For all countries combined the sex ratio was non-significantly biased towards females (1∶1.1; n = 113). Of 60 females examined, 11 were confirmed pregnant ranging from the beginning stages of pregnancy (egg cases) to near term (140 cm TL embryos). On average, 6.0±2.2 embryos were found per litter (maximum of 10) and gestation period was estimated to be 20 months. These observations confirm that white sharks are present in the Northwest Pacific Ocean year-round. While acknowledging the difficulties of studying little known populations of a naturally low abundance species, these results highlight the need for dedicated research to inform regional conservation and management planning

Variable δ15N Diet-Tissue Discrimination Factors among Sharks: Implications for Trophic Position, Diet and Food Web Models

The application of stable isotopes to characterize the complexities of a species foraging behavior and trophic relationships is dependent on assumptions of δ(15)N diet-tissue discrimination factors (∆(15)N). As ∆(15)N values have been experimentally shown to vary amongst consumers, tissues and diet composition, resolving appropriate species-specific ∆(15)N values can be complex. Given the logistical and ethical challenges of controlled feeding experiments for determining ∆(15)N values for large and/or endangered species, our objective was to conduct an assessment of a range of reported ∆(15)N values that can hypothetically serve as surrogates for describing the predator-prey relationships of four shark species that feed on prey from different trophic levels (i.e., different mean δ(15)N dietary values). Overall, the most suitable species-specific ∆(15)N values decreased with increasing dietary-δ(15)N values based on stable isotope Bayesian ellipse overlap estimates of shark and the principal prey functional groups contributing to the diet determined from stomach content analyses. Thus, a single ∆(15)N value was not supported for this speciose group of marine predatory fishes. For example, the ∆(15)N value of 3.7‰ provided the highest percent overlap between prey and predator isotope ellipses for the bonnethead shark (mean diet δ(15)N = 9‰) whereas a ∆(15)N value < 2.3‰ provided the highest percent overlap between prey and predator isotope ellipses for the white shark (mean diet δ(15)N = 15‰). These data corroborate the previously reported inverse ∆(15)N-dietary δ(15)N relationship when both isotope ellipses of principal prey functional groups and the broader identified diet of each species were considered supporting the adoption of different ∆(15)N values that reflect the predators' δ(15)N-dietary value. These findings are critical for refining the application of stable isotope modeling approaches as inferences regarding a species' ecological role in their community will be influenced with consequences for conservation and management actions

Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

Dynamical derivation of Bode's law

In a planetary or satellite system, idealized as n small bodies in initially coplanar, concentric orbits around a large central body, obeying Newtonian point-particle mechanics, resonant perturbations will cause dynamical evolution of the orbital radii except under highly specific mutual relationships, here derived analytically apparently for the first time. In particular, the most stable situation is achieved (in this idealized model) only when each planetary orbit is roughly twice as far from the Sun as the preceding one, as observed empirically already by Titius (1766) and Bode (1778) and used in both the discoveries of Uranus (1781) and the Asteroid Belt (1801). ETC.Comment: 27 page

Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models

Strategies intended to resolve the problem of time in quantum gravity by means of emergent or hidden timefunctions are considered in the arena of relational particle toy models. In situations with `heavy' and `light' degrees of freedom, two notions of emergent semiclassical WKB time emerge; these are furthermore equivalent to two notions of emergent classical `Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach, in a geometric phase formalism, extended to include linear constraints, and with particular care to make explicit those approximations and assumptions used. I propose a new iterative scheme for this in the cosmologically-motivated case with one heavy degree of freedom. I find that the usual semiclassical quantum cosmology emergence of time comes hand in hand with the emergence of other qualitatively significant terms, including back-reactions on the heavy subsystem and second time derivatives. I illustrate my analysis by taking it further for relational particle models with linearly-coupled harmonic oscillator potentials. As these examples are exactly soluble by means outside the semiclassical approach, they are additionally useful for testing the justifiability of some of the approximations and assumptions habitually made in the semiclassical approach to quantum cosmology. Finally, I contrast the emergent semiclassical timefunction with its hidden dilational Euler time counterpart.Comment: References Update

Ranks of twists of elliptic curves and Hilbert's Tenth Problem

In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses we can find many twists with trivial Mordell-Weil group, and (assuming the Shafarevich-Tate conjecture) many others with infinite cyclic Mordell-Weil group. Using work of Poonen and Shlapentokh, it follows from our results that if the Shafarevich-Tate conjecture holds, then Hilbert's Tenth Problem has a negative answer over the ring of integers of every number field.Comment: Minor changes. To appear in Inventiones mathematica

PACS: 32.30.-r, 32.60.+i, 32.70

Abstract: We have measured light shifts, also known as AC Stark shifts, as a function of laser intensity in cold Rubidium atoms by observing sub-natural linewidth gain and loss features in the transmission spectrum of a weak probe beam passing through the atomic sample. The observed energy-level shifts for atoms in a magneto-optical trap (MOT) are found to be consistently higher than that obtained in optical molasses (i.e., when the magnetic field gradient in the MOT is turned off). Using a simple model of a multilevel Rubidium atom interacting with pump and probe beams, we have calculated the theoretical light shift as a function of intensity. A comparison of these calculated values with the light shift data obtained for molasses reveals good agreement between experiment and theory. Further, our model elucidates the role of the Zeeman shifts arising from the magnetic field gradient in the observed probe transmission spectrum for the MOT. A qualitative plot of the transmission spectrum of a probe beam through a fictitious sample of cold J = 1 → J = 2 atoms showing probe absorption at the sum of the pump frequency ω pump and δ , where δ is the difference of the light shifts between the |J = 1,mJ = 0 and the |J = 1,mJ = ± 1 ground state Zeeman sublevels. Probe gain is depicted at ω pump -δ . Se