Spatial scales of desert locust gregarization

Central to swarm formation in migratory locusts is a crowding-induced change from a “solitarious” to a “gregarious” phenotype. This change can occur within the lifetime of a single locust and accrues across generations. It represents an extreme example of phenotypic plasticity. We present computer simulations and a laboratory experiment that show how differences in resource distributions, conspicuous only at small spatial scales, can have significant effects on phase change at the population level; local spatial concentration of resource induces gregarization. Simulations also show that populations inhabiting a locally concentrated resource tend to change phase rapidly and synchronously in response to altered population densities. Our results show why information about the structure of resource at small spatial scales should become key components in monitoring and control strategies.

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.

Predicting species diversity in tropical forests

A fundamental question in ecology is how many species occur within a given area. Despite the complexity and diversity of different ecosystems, there exists a surprisingly simple, approximate answer: the number of species is proportional to the size of the area raised to some exponent. The exponent often turns out to be roughly 1/4. This power law can be derived from assumptions about the relative abundances of species or from notions of self-similarity. Here we analyze the largest existing data set of location-mapped species: over one million, individually identified trees from five tropical forests on three continents. Although the power law is a reasonable, zeroth-order approximation of our data, we find consistent deviations from it on all spatial scales. Furthermore, tropical forests are not self-similar at areas ≤50 hectares. We develop an extended model of the species-area relationship, which enables us to predict large-scale species diversity from small-scale data samples more accurately than any other available method.

Multiscale assessment of patterns of avian species richness

The search for a common cause of species richness gradients has spawned more than 100 explanatory hypotheses in just the past two decades. Despite recent conceptual advances, further refinement of the most plausible models has been stifled by the difficulty of compiling high-resolution databases at continental scales. We used a database of the geographic ranges of 2,869 species of birds breeding in South America (nearly a third of the world's living avian species) to explore the influence of climate, quadrat area, ecosystem diversity, and topography on species richness gradients at 10 spatial scales (quadrat area, ≈12,300 to ≈1,225,000 km2). Topography, precipitation, topography × latitude, ecosystem diversity, and cloud cover emerged as the most important predictors of regional variability of species richness in regression models incorporating 16 independent variables, although ranking of variables depended on spatial scale. Direct measures of ambient energy such as mean and maximum temperature were of ancillary importance. Species richness values for 1° × 1° latitude-longitude quadrats in the Andes (peaking at 845 species) were ≈30–250% greater than those recorded at equivalent latitudes in the central Amazon basin. These findings reflect the extraordinary abundance of species associated with humid montane regions at equatorial latitudes and the importance of orography in avian speciation. In a broader context, our data reinforce the hypothesis that terrestrial species richness from the equator to the poles is ultimately governed by a synergism between climate and coarse-scale topographic heterogeneity.

The resource consumption principle: attention and memory in volumes of neural tissue.

In the cerebral cortex, the small volume of the extracellular space in relation to the volume enclosed by synapses suggests an important functional role for this relationship. It is well known that there are atoms and molecules in the extracellular space that are absolutely necessary for synapses to function (e.g., calcium). I propose here the hypothesis that the rapid shift of these atoms and molecules from extracellular to intrasynaptic compartments represents the consumption of a shared, limited resource available to local volumes of neural tissue. Such consumption results in a dramatic competition among synapses for resources necessary for their function. In this paper, I explore a theory in which this resource consumption plays a critical role in the way local volumes of neural tissue operate. On short time scales, this principle of resource consumption permits a tissue volume to choose those synapses that function in a particular context and thereby helps to integrate the many neural signals that impinge on a tissue volume at any given moment. On longer time scales, the same principle aids in the stable storage and recall of information. The theory provides one framework for understanding how cerebral cortical tissue volumes integrate, attend to, store, and recall information. In this account, the capacity of neural tissue to attend to stimuli is intimately tied to the way tissue volumes are organized at fine spatial scales.

Spatial integration and cortical dynamics.

Cells in adult primary visual cortex are capable of integrating information over much larger portions of the visual field than was originally thought. Moreover, their receptive field properties can be altered by the context within which local features are presented and by changes in visual experience. The substrate for both spatial integration and cortical plasticity is likely to be found in a plexus of long-range horizontal connections, formed by cortical pyramidal cells, which link cells within each cortical area over distances of 6-8 mm. The relationship between horizontal connections and cortical functional architecture suggests a role in visual segmentation and spatial integration. The distribution of lateral interactions within striate cortex was visualized with optical recording, and their functional consequences were explored by using comparable stimuli in human psychophysical experiments and in recordings from alert monkeys. They may represent the substrate for perceptual phenomena such as illusory contours, surface fill-in, and contour saliency. The dynamic nature of receptive field properties and cortical architecture has been seen over time scales ranging from seconds to months. One can induce a remapping of the topography of visual cortex by making focal binocular retinal lesions. Shorter-term plasticity of cortical receptive fields was observed following brief periods of visual stimulation. The mechanisms involved entailed, for the short-term changes, altering the effectiveness of existing cortical connections, and for the long-term changes, sprouting of axon collaterals and synaptogenesis. The mutability of cortical function implies a continual process of calibration and normalization of the perception of visual attributes that is dependent on sensory experience throughout adulthood and might further represent the mechanism of perceptual learning.