Spatial variance of mobile aquatic organisms: capelin and cod in Newfoundland coastal waters

摘要

Spatial variance in the distribution of aquatic mobile organisms differs from that of passive tracers such as phytoplankton or water temperature. On average, spatial variance of phytoplankton scales with sample unit as $L^2$ or equivalently with frequency as $f^{-2}$. Limited evidence suggests that spatial variance in the distribution of mobile organisms is concentrated at relatively small scales, with little increase over larger scales: spatial variance scales as $f^{-1}$ or less. We investigated whether spatial variance in distributions of a mobile predator, Atlantic cod (Gadus morhua), and a schooling prey, capelin (Mallotus villosus), also scale with frequency as $f^{-1}$. Acoustic surveys showed that at short time scales spatial variance in cod and capelin densities, as measured by spectral density, peaked at various scales ranging from 20 m to 10 km. At longer time scales, spatial variance of cod scaled as $f^{-1.08}$ at resolutions finer than 90 m, while scaling as $f^{-0.18}$ at coarser scales. Spatial variance of capelin scaled as $f^{-1.1}$ at resolutions finer than 400 m, while scaling as $f^{-0.21}$ at coarser scales. Spatial variance plots of krill and marine birds showed similar transitions from shallow to steep scaling. Shoaling, schooling and the aggregative response by predators to concentrations of prey were three processes hypothesized to influence spatial variance in distributions of mobile organisms. Numerical experiments showed that shoaling injects variance at large to intermediate scales, resulting in scalings flatter than $f^{-1}$. Additional experiments showed that schooling produces a transition from shallow to steep scaling as frequency increases. Spatial variance patterns in cod density were not due to aggregative responses by the predator to concentrations of capelin: there was no association, on average, at resolution scales from 20 m to 10 km. Exponent values for aquatic or terrestrial mobile organisms are predicted to be approximately two at the scale of an individual organism, 0.2 at scales that contain aggregations, and two at scales larger than that of populations. These findings suggest that relations between mobile organisms and large scale habitat variables will be difficult to detect, that stratified survey designs used to estimate commercial population sizes will be inefficient, and that rates of interaction between predator and prey will be underestimated if local observations are averaged over the spatial scale of the population.