Low dimensionality of supraspinally induced force fields

Recent experiments using electrical and N-methyl-d-aspartate microstimulation of the spinal cord gray matter and cutaneous stimulation of the hindlimb of spinalized frogs have provided evidence for a modular organization of the frog’s spinal cord circuitry. A “module” is a functional unit in the spinal cord circuitry that generates a specific motor output by imposing a specific pattern of muscle activation. The output of a module can be characterized as a force field: the collection of the isometric forces generated at the ankle over different locations in the leg’s workspace. Different modules can be combined independently so that their force fields linearly sum. The goal of this study was to ascertain whether the force fields generated by the activation of supraspinal structures could result from combinations of a small number of modules. We recorded a set of force fields generated by the electrical stimulation of the vestibular nerve in seven frogs, and we performed a principal component analysis to study the dimensionality of this set. We found that 94% of the total variation of the data is explained by the first five principal components, a result that indicates that the dimensionality of the set of fields evoked by vestibular stimulation is low. This result is compatible with the hypothesis that vestibular fields are generated by combinations of a small number of spinal modules.

Temporal variation, dormancy, and coexistence: A field test of the storage effect

Theoretical models suggest that overlapping generations, in combination with a temporally fluctuating environment, may allow the persistence of competitors that otherwise would not coexist. Despite extensive theoretical development, this “storage effect” hypothesis has received little empirical attention. Herein I present the first explicit mathematical analysis of the contribution of the storage effect to the dynamics of competing natural populations. In Oneida Lake, NY, data collected over the past 30 years show a striking negative correlation between the water-column densities of two species of suspension-feeding zooplankton, Daphnia galeata mendotae and Daphnia pulicaria. I have demonstrated competition between these two species and have shown that both possess long-lived eggs that establish overlapping generations. Moreover, recruitment to this long-lived stage varies annually, so that both daphnids have years in which they are favored (for recruitment) relative to their competitor. When the long-term population growth rates are calculated both with and without the effects of a variable environment, I show that D. galeata mendotae clearly cannot persist without the environmental variation and prolonged dormancy (i.e., storage effect) whereas D. pulicaria persists through consistently high per capita recruitment to the long-lived stage.