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 Behavioural and Genetic Mating System of the Sand Tiger Shark, Carcharias taurus, an Intrauterine Cannibal

Sand tiger sharks (Carcharias taurus) have an unusual mode of reproduction, whereby the first embryos in each of the paired uteri to reach a certain size (‘hatchlings’) consume all of their smaller siblings during gestation (‘embryonic cannibalism’ or EC). If females commonly mate with multiple males (‘behavioural polyandry’) then litters could initially have multiple sires. It is possible, however, that EC could exclude of all but one of these sires from producing offspring thus influencing the species genetic mating system (‘genetic monogamy’). Here, we use microsatellite DNA profiling of mothers and their litters (n = 15, from two to nine embryos per litter) to quantify the frequency of behavioural and genetic polyandry in this system. We conservatively estimate that nine of the females we examined (60%) were behaviourally polyandrous. The genetic mating system was characterized by assessing sibling relationships between hatchlings and revealed only 40 per cent genetic polyandry (i.e. hatchlings were full siblings in 60% of litters). The discrepancy stemmed from three females that were initially fertilized by multiple males but only produced hatchlings with one of them. This reveals that males can be excluded even after fertilizing ova and that some instances of genetic monogamy in this population arise from the reduction in litter size by EC. More research is needed on how cryptic post-copulatory and post-zygotic processes contribute to determining paternity and bridging the behavioural and genetic mating systems of viviparous species

Breakdown of Lindstedt Expansion for Chaotic Maps

In a previous paper of one of us [Europhys. Lett. 59 (2002), 330--336] the validity of Greene's method for determining the critical constant of the standard map (SM) was questioned on the basis of some numerical findings. Here we come back to that analysis and we provide an interpretation of the numerical results by showing that no contradiction is found with respect to Greene's method. We show that the previous results based on the expansion in Lindstedt series do correspond to the transition value but for a different map: the semi-standard map (SSM). Moreover, we study the expansion obtained from the SM and SSM by suppressing the small divisors. The first case turns out to be related to Kepler's equation after a proper transformation of variables. In both cases we give an analytical solution for the radius of convergence, that represents the singularity in the complex plane closest to the origin. Also here, the radius of convergence of the SM's analogue turns out to be lower than the one of the SSM. However, despite the absence of small denominators these two radii are lower than the ones of the true maps for golden mean winding numbers. Finally, the analyticity domain and, in particular, the critical constant for the two maps without small divisors are studied analytically and numerically. The analyticity domain appears to be an perfect circle for the SSM analogue, while it is stretched along the real axis for the SM analogue yielding a critical constant that is larger than its radius of convergence.Comment: 12 pages, 3 figure

Mechanical similarity as a generalization of scale symmetry

In this paper we study the symmetry known as mechanical similarity (LMS) and present for any monomial potential. We analyze it in the framework of the Koopman-von Neumann formulation of classical mechanics and prove that in this framework the LMS can be given a canonical implementation. We also show that the LMS is a generalization of the scale symmetry which is present only for the inverse square potential. Finally we study the main obstructions which one encounters in implementing the LMS at the quantum mechanical level.Comment: 9 pages, Latex, a new section adde

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

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

Spatio-temporal genetic tagging of a cosmopolitan planktivorous shark provides insight to gene flow, temporal variation and site-specific re-encounters

Migratory movements in response to seasonal resources often influence population structure and dynamics. Yet in mobile marine predators, population genetic consequences of such repetitious behaviour remain inaccessible without comprehensive sampling strategies. Temporal genetic sampling of seasonally recurring aggregations of planktivorous basking sharks, Cetorhinus maximus, in the Northeast Atlantic (NEA) affords an opportunity to resolve individual re-encounters at key sites with population connectivity and patterns of relatedness. Genetic tagging (19 microsatellites) revealed 18% of re-sampled individuals in the NEA demonstrated inter/multi-annual site-specific re-encounters. High genetic connectivity and migration between aggregation sites indicate the Irish Sea as an important movement corridor, with a contemporary effective population estimate (Ne) of 382 (CI = 241–830). We contrast the prevailing view of high gene flow across oceanic regions with evidence of population structure within the NEA, with early-season sharks off southwest Ireland possibly representing genetically distinct migrants. Finally, we found basking sharks surfacing together in the NEA are on average more related than expected by chance, suggesting a genetic consequence of, or a potential mechanism maintaining, site-specific re-encounters. Long-term temporal genetic monitoring is paramount in determining future viability of cosmopolitan marine species, identifying genetic units for conservation management, and for understanding aggregation structure and dynamics

Convex central configurations of the 4-body problem with two pairs of equal masses

Agraïments: The first and third authors are partially supported by FAPEMIG grant APQ-001082/14. The third author is partially supported by CNPq grant 472321/2013-7 and by FAPEMIG grant PPM-00516-15. The second and third autors are supported by CAPES CSF-PVE grant 88881.030454/2013-01.MacMillan and Bartky in 1932 proved that there is a unique isosceles trapezoid central configuration of the 4--body problem when two pairs of equal masses are located at adjacent vertices. After this result the following conjecture was well known between people working on central configurations: The isosceles trapezoid is the unique convex central configuration of the planar 4--body problem when two pairs of equal masses are located at adjacent vertices. We prove this conjecture

Critical Perspective: Named Reactions Discovered and Developed by Women

Named organic reactions. As chemists, we’re all familiar with them: who can forget the Diels−Alder reaction? But how much do we know about the people behind the names? For example, can you identify a reaction named for a woman? How about a reaction discovered or developed by a woman but named for her male adviser? Our attempts to answer these simple questions started us on the journey that led to this Account. We introduce you to four reactions named for women and nine reactions discovered or developed by women. Using information obtained from the literature and, whenever possible, through interviews with the chemists themselves, their associates, and their advisers, we paint a more detailed picture of these remarkable women and their outstanding accomplishments. Some of the women you meet in this Account include Irma Goldberg, the only woman unambiguously recognized with her own named reaction. Gertrude Maud Robinson, the wife of Robert Robinson, who collaborated with him on several projects including the Piloty−Robinson pyrrole synthesis. Elizabeth Hardy, the Bryn Mawr graduate student who discovered the Cope rearrangement. Dorothee Felix, a critical member of Albert Eschenmoser’s research lab for over forty years who helped develop both the Eschenmoser−Claisen rearrangement and the Eschenmoser−Tanabe fragmentation. Jennifer Loebach, the University of Illinois undergraduate who was part of the team in Eric Jacobsen’s lab that discovered the Jacobsen−Katsuki epoxidation. Keiko Noda, a graduate student in Tsutomu Katsuki’s lab who also played a key role in the development of the Jacobsen−Katsuki epoxidation. Lydia McKinstry, a postdoc in Andrew Myers’s lab who helped develop the Myers asymmetric alkylation. Rosa Lockwood, a graduate student at Boston College whose sole publication is the discovery of the Nicholas reaction. Kaori Ando, a successful professor in Japan who helped develop the Roush asymmetric alkylation as a postdoc at MIT. Bianka Tchoubar, a critically important member of the organic chemistry community in France who developed the Tiffeneau−Demjanov rearrangement. The accomplishments of the women in this Account illustrate the key roles women have played in the discovery and development of reactions used daily by organic chemists around the world. These pioneering chemists represent the vanguard of women in the field, and we are confident that many more of the growing number of current and future female organic chemists will be recognized with their own named reactions