Variation in per capita interaction strength: Thresholds due to nonlinear dynamics and nonequilibrium conditions

I measured the strength of interaction between a marine herbivore and its growing resource over a realistic range of absolute and relative abundances. The herbivores (hermit crabs: Pagurus spp.) have slow and/or weak functional and numerical responses to epiphytic diatoms (Isthmia nervosa), which show logistic growth in the absence of consumers. By isolating this interaction in containers in the field, I mimicked many of the physical and biological variables characteristic of the intertidal while controlling the densities of focal species. The per capita effects of consumers on the population dynamics of their resource (i.e., interaction strength) were defined by using the relationship between hermit crab density and proportional change in the resource. When this relationship is fit by a Weibull function, a single parameter distinguishes constant interaction strength from one that varies as a function of density. Constant interaction strength causes the proportion of diatoms to fall linearly or proportionally as hermit crab density increases whereas per capita effects that increase with density cause an accelerating decline. Although many mathematical models of species interactions assume linear dynamics and invariant parameters, at least near equilibrium, the per capita effects of hermit crabs on diatoms varied substantially, apparently crossing a threshold from weak to strong when consumption exceeded resource production. This threshold separates a domain of coexistence from one of local extinction of the resource. Such thresholds may help explain trophic cascades, resource compensation, and context-dependent interaction strengths, while indicating a way to predict trophic effects, despite nonlinearities, as a function of vital rates.

Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

A long marine history of carbon cycle modulation by orbital-climatic changes

Pacing of the marine carbon cycle by orbital forcing during the Pliocene and Pleistocene Ice Ages [past 2.5 million years (Myr)] is well known. As older deep-sea sediment records are being studied at greater temporal resolution, it is becoming clear that similar fluctuations in the marine carbon system have occurred throughout the late Mesozoic and Tertiary, despite the absence of large continental ice sheets over much of this time. Variations in both the organic and the calcium carbonate components of the marine carbon system seem to have varied cyclically in response to climate forcing, and carbon and carbonate time series appear to accurately characterize the frequency spectrum of ancient climatic change. For the past 35 Myr, much of the variance in carbonate content carries the “polar” signal of obliquity [41,000 years (41 kyr)] forcing. Over the past 125 Myr, there is evidence from marine sediments of the continued role of precessional (≈21 kyr) climatic cycles. Repeat patterns of sedimentation at about 100, 400, and 2,400 kyr, the modulation periods of precession, persistently enter into marine carbon cycle records as well. These patterns suggest a nonlinear response of climate and/or the sedimentation of organic carbon and carbonates to precessional orbital perturbations. Nonlinear responses of the carbon system may help to amplify relatively weak orbital insolation anomalies into more significant climatic perturbations through positive feedback effects. Nonlinearities in the carbon cycle may have transformed orbital-climatic cycles into long-wavelength features on time scales comparable to the residence times of carbon and nutrient elements in the ocean.

Putting ion channels to work: Mechanoelectrical transduction, adaptation, and amplification by hair cells

As in other excitable cells, the ion channels of sensory receptors produce electrical signals that constitute the cellular response to stimulation. In photoreceptors, olfactory neurons, and some gustatory receptors, these channels essentially report the results of antecedent events in a cascade of chemical reactions. The mechanoelectrical transduction channels of hair cells, by contrast, are coupled directly to the stimulus. As a consequence, the mechanical properties of these channels shape our hearing process from the outset of transduction. Channel gating introduces nonlinearities prominent enough to be measured and even heard. Channels provide a feedback signal that controls the transducer's adaptation to large stimuli. Finally, transduction channels participate in an amplificatory process that sensitizes and sharpens hearing.