The Suspension of The Ethical in Fear and Trembling

The Suspension of The Ethical in Fear and Tremblin

Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential

We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lam{\'e} functions that describe the orbits bifurcated from the fundamental linear orbit in the vicinity of the bifurcation points, we use perturbation theory to obtain their evolution away from the bifurcation points. As an application, we derive an analytical semiclassical trace formula for the density of states in the separable case, using a uniform approximation for the pitchfork bifurcations occurring there, which allows for full semiclassical quantization. For the non-integrable situations, we show that the uniform contribution of the bifurcating period-one orbits to the coarse-grained density of states competes with that of the shortest isolated orbits, but decreases with increasing chaoticity parameter $\alpha$.Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear in J. Phys. A final version 3; error in eq. (33) corrected and note added in prin

Mimicry as a novel pathway linking biodiversity functions and individual behavioural performances

The feedback of biodiversity on individual trait variation is a poorly explored mechanistic pathway in ecological research. We analysed the relationship between biodiversity and individual performance by focusing on vocal mimicry, a widespread interaction that may serve in intra- and interspecific communication. We studied the songs of two lark species (genus Galerida) that increase the complexity of their song displays by mimicking other birds, and analysed the influence of bird species richness on individual song performance. The diversity of mimicked species and the prevalence of mimicry increased in areas characterized by great α and γ diversity (i.e. where larks experience more diverse encounters with community members, many of them being highly vocal owing to breeding). Conversely, the variability in species-specific song components peaked where larks were abundant, probably matching the complexity of conspecific social milieu. Some trade-offs existed between homo- and heterospecific complexity, suggesting that larks could change from population- to community-driven song variation by tracking the composition of the auditory environment. Mimicry, which serves communication with conspecifics or predators, may mediate interactions, ultimately cascading to aspects of ecological diversity other than those promoting its complexity