A Feynman integral via higher normal functions

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 surface. This result is shown to be a particular case of Deligne's conjectures relating values of L-functions inside the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications. Version to appear in Compositio Mathematic

String loop corrections to the universal hypermultiplet

We study loop corrections to the universal dilaton supermultiplet for type IIA strings compactified on Calabi-Yau threefolds. We show that the corresponding quaternionic kinetic terms receive non-trivial one-loop contributions proportional to the Euler number of the Calabi-Yau manifold, while the higher-loop corrections can be absorbed by field redefinitions. The corrected metric is no longer Kahler. Our analysis implies in particular that the Calabi-Yau volume is renormalized by loop effects which are present even in higher orders, while there are also one-loop corrections to the Bianchi identities for the NS and RR field strengths.Comment: 30 pages, harvmac, 1 figure. v2: minor typos corrected. Version to appear in Classical and Quantum Gravit

Only true pelagics mix : comparative phylogeography of deepwater bathybatine cichlids from Lake Tanganyika

In the absence of dispersal barriers, species with great dispersal ability are expected to show little, if at all, phylogeographic structure. The East African Great Lakes and their diverse fish faunas provide opportunities to test this hypothesis in pelagic fishes, which are presumed to be highly mobile and unrestricted in their movement by physical barriers. Here, we address the link between panmixis and pelagic habitat use by comparing the phylogeographic structure among four deepwater cichlid species of the tribe Bathybatini from Lake Tanganyika. We show that the mitochondrial genealogies (based on the most variable part or the control region) of the four species are very shallow (0.8–4% intraspecific divergence across entire distribution ranges) and that all species experienced recent population growth. A lack of phylogeographic structure in the two eupelagic species, Bathybates fasciatus and B. leo, was consistent with expectations and with findings in other pelagic cichlid species. Contrary to expectations, a clear phylogeographic structure was detected in the two benthopelagic species, B. graueri and Hemibates stenosoma. Differences in genetic diversity between eupelagic and benthopelagic species may be due to differences in their dispersal propensity, mediated by their respective predatory niches, rather than precipitated by external barriers to dispersal.Peer reviewe

The first next-generation sequencing approach to the mitochondrial phylogeny of African monogenean parasites (Platyhelminthes: Gyrodactylidae and Dactylogyridae)

Abstract Background Monogenean flatworms are the main ectoparasites of fishes. Representatives of the species-rich families Gyrodactylidae and Dactylogyridae, especially those infecting cichlid fishes and clariid catfishes, are important parasites in African aquaculture, even more so due to the massive anthropogenic translocation of their hosts worldwide. Several questions on their evolution, such as the phylogenetic position of Macrogyrodactylus and the highly speciose Gyrodactylus, remain unresolved with available molecular markers. Also, diagnostics and population-level research would benefit from the development of higher-resolution genetic markers. We aim to offer genetic resources for work on African monogeneans by providing mitogenomic data of four species (two belonging to Gyrodactylidae, two to Dactylogyridae), and analysing their gene sequences and gene order from a phylogenetic perspective. Results Using Illumina technology, the first four mitochondrial genomes of African monogeneans were assembled and annotated for the cichlid parasites Gyrodactylus nyanzae, Cichlidogyrus halli, Cichlidogyrus mbirizei (near-complete mitogenome) and the catfish parasite Macrogyrodactylus karibae (near-complete mitogenome). Complete nuclear ribosomal operons were also retrieved, as molecular vouchers. The start codon TTG is new for Gyrodactylus and for Dactylogyridae, as is the incomplete stop codon TA for Dactylogyridae. Especially the nad2 gene is promising for primer development. Gene order was identical for protein-coding genes and differed between the African representatives of these families only in a tRNA gene transposition. A mitochondrial phylogeny based on an alignment of nearly 12,500 bp including 12 protein-coding and two ribosomal RNA genes confirms that the Neotropical oviparous Aglaiogyrodactylus forficulatus takes a sister group position with respect to the other gyrodactylids, instead of the supposedly ‘primitive’ African Macrogyrodactylus. Inclusion of the African Gyrodactylus nyanzae confirms the paraphyly of Gyrodactylus. The position of the African dactylogyrid Cichlidogyrus is unresolved, although gene order suggests it is closely related to marine ancyrocephalines. Conclusions The amount of mitogenomic data available for gyrodactylids and dactylogyrids is increased by roughly one-third. Our study underscores the potential of mitochondrial genes and gene order in flatworm phylogenetics, and of next-generation sequencing for marker development for these non-model helminths for which few primers are available

Description and ecophysiology of a new species of Syndesmis Silliman, 1881 (Rhabdocoela: Umagillidae) from the sea urchin Evechinus chloroticus (Valenciennes, 1846) Mortensen, 1943 in New Zealand

A new rhabdocoel of the genus Syndesmis Silliman, 1881 (Umagillidae) is described from the intestine of the New Zealand sea urchin Evechinus chloroticus (Valenciennes, 1846) Mortensen, 1943a. This new species, Syndesmis kurakaikina n. sp., is morphologically distinct and can easily be recognised by its very long (+/- 1 mm) styles and its bright-red colour. In addition to providing a formal description, we present some observations on reproduction and life history of this new species. Fecundity is comparable to that of other umagillids and the rate of egg production and development increases with temperature. Hatching in this species is induced by intestinal fluids of its host. Relevant to global warming, we assessed the effect of temperature on survival, fecundity, and development. The tests indicate that Syndesmis kurakaikina n. sp. is tolerant of a wide range of temperatures (11-25 degrees C) and that its temperature optimum lies between 18.0 and 21.5 degrees C. Egg viability is, however, significantly compromised at the higher end of this temperature range, with expelled egg capsules often being deformed and showing increasingly lower rates of hatching. Given this, a rise in global temperature might increase the risk of Syndesmis kurakaikina n. sp. infecting new hosts and would possibly facilitate the spread of these endosymbionts.Peer reviewe

The Monogenean Parasite Fauna of Cichlids: A Potential Tool for Host Biogeography

We discuss geographical distribution and phylogeny of Dactylogyridea (Monogenea) parasitizing Cichlidae to elucidate their hosts' history. Although mesoparasitic Monogenea (Enterogyrus spp.) show typical vicariant distribution, ectoparasitic representatives from different continents are not considered sister taxa, hence their distribution cannot result from vicariance alone. Because of the close host-parasite relationship, this might indicate that present-day cichlid distribution may also reflect dispersal through coastal or brackish waters. Loss of ectoparasites during transoceanic migration, followed by lateral transfer from other fish families might explain extant host-parasite associations. Because of its mesoparasitic nature, hence not subject to salinity variations of the host's environment, Enterogyrus could have survived marine migrations, intolerable for ectoparasites. Host-switches and salinity transitions may be invoked to explain the pattern revealed by a preliminary morphological phylogeny of monogenean genera from Cichlidae and other selected Monogenea genera, rendering the parasite distribution explicable under both vicariance and dispersal. Testable hypotheses are put forward in this parasitological approach to cichlid biogeography. Along with more comprehensive in-depth morphological phylogeny, comparison with molecular data, clarifying dactylogyridean evolution on different continents and from various fish families, and providing temporal information on host-parasite history, are needed to discriminate between the possible scenarios

Toward a Global Phylogeny of the “Living Fossil" Crustacean Order of the Notostraca

Tadpole shrimp (Crustacea, Notostraca) are iconic inhabitants of temporary aquatic habitats worldwide. Often cited as prime examples of evolutionary stasis, surviving representatives closely resemble fossils older than 200 mya, suggestive of an ancient origin. Despite significant interest in the group as ‘living fossils’ the taxonomy of surviving taxa is still under debate and both the phylogenetic relationships among different lineages and the timing of diversification remain unclear. We constructed a molecular phylogeny of the Notostraca using model based phylogenetic methods. Our analyses supported the monophyly of the two genera Triops and Lepidurus, although for Triops support was weak. Results also revealed high levels of cryptic diversity as well as a peculiar biogeographic link between Australia and North America presumably mediated by historic long distance dispersal. We concluded that, although some present day tadpole shrimp species closely resemble fossil specimens as old as 250 mya, no molecular support was found for an ancient (pre) Mesozoic radiation. Instead, living tadpole shrimp are most likely the result of a relatively recent radiation in the Cenozoic era and close resemblances between recent and fossil taxa are probably the result of the highly conserved general morphology in this group and of homoplasy