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.

Active control of waves in a cochlear model with subpartitions.

Multiscale asymptotic methods developed previously to study macromechanical wave propagation in cochlear models are generalized here to include active control of a cochlear partition having three subpartitions, the basilar membrane, the reticular lamina, and the tectorial membrane. Activation of outer hair cells by stereocilia displacement and/or by lateral wall stretching result in a frequency-dependent force acting between the reticular lamina and basilar membrane. Wavelength-dependent fluid loads are estimated by using the unsteady Stokes' equations, except in the narrow gap between the tectorial membrane and reticular lamina, where lubrication theory is appropriate. The local wavenumber and subpartition amplitude ratios are determined from the zeroth order equations of motion. A solvability relation for the first order equations of motion determines the subpartition amplitudes. The main findings are as follows: The reticular lamina and tectorial membrane move in unison with essentially no squeezing of the gap; an active force level consistent with measurements on isolated outer hair cells can provide a 35-dB amplification and sharpening of subpartition waveforms by delaying dissipation and allowing a greater structural resonance to occur before the wave is cut off; however, previously postulated activity mechanisms for single partition models cannot achieve sharp enough tuning in subpartitioned models.