A Phenomenological Approach to Interactive Knot Diagrams.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

No evidence for effects of infection with the amphibian chytrid fungus on populations of yellow-bellied toads.

The parasitic chytrid fungus Batrachochytrium dendrobatidis (Bd) can cause the lethal disease chytridiomycosis in amphibians and therefore may play a role in population declines. The yellow-bellied toad Bombina variegata suffered strong declines throughout western and northwestern parts of its range and is therefore listed as highly endangered for Germany and the federal state of Hesse. Whether chytridiomycosis may play a role in the observed local declines of this strictly protected anuran species has never been tested. We investigated 19 Hessian yellow-bellied toad populations for Bd infection rates, conducted capture-mark-recapture studies in 4 of them over 2 to 3 yr, examined survival histories of recaptured infected individuals, and tested whether multi-locus heterozygosity of individuals as well as expected heterozygosity and different environmental variables of populations affect probabilities of Bd infection. Our results show high prevalence of Bd infection in Hessian yellow-bellied toad populations, but although significant decreases in 2 populations could be observed, no causative link to Bd as the reason for this can be established. Mass mortalities or obvious signs of disease in individuals were not observed. Conversely, we show that growth of Bd-infected populations is possible under favorable habitat conditions and that most infected individuals could be recaptured with improved body indices. Neither genetic diversity nor environmental variables appeared to affect Bd infection probabilities. Hence, genetically diverse amphibian specimens and populations may not automatically be less susceptible for Bd infection.