"Ungulate numbers fluctuate substantially without wolves; we expect that one of the impacts of wolves will be to alter the magnitude of these fluctuations."(266)

"Satiation operates in an inverse density-dependent fashion such that, as prey increase from moderate to high density, fewer prey will be killed per capita."(266-7)

"Under natural regulation, the northern Yellowstone elk herd increased to approximately twenty thousand animals, declined by approximately 7,500 during the winter of 1988-89, and subsequently increased to more than twenty thousand"(267)

"Since they were released in 1995, wolves have killed elk in the park at a relatively high rate."(267)

"when stochastic perturbations influence the vegetation, by knowing vegetation biomass, we can predict most of the variance in herbivore numbers; in contrast, knowledge of predator numbers does not help much in predicting ungulate numbers."(277)

"When noise enters at the bottom with stochastic vegetation, our regression analysis would lead us to conclude that predators are not having much of an effect relative to the vegetation. But when stochastic variation perturbs the system from the top, our analysis of the time series would lead us to believe that the system is governed by top-down processes."(278)

"The dichotomy of top-down vs. bottom-up regulation is overly simplistic. The interaction of top-down and bottom-up processes is what shapes population dynamics."(279)

"As our analysis demonstrates, the source of variation in the system can shape conclusions about what factors are controlling the population. Because winter severity has such large influences in causing year-to-year variation in elk population size in Yellowstone before wolf recovery, we find it difficult to imagine that winter severity will not continue to be a major source of population fluctuations even in the face of wolf predation."(279)

"We are concerned that the results of McLaren and Peterson (1994) (suggesting that moose populations on Royale Isle are largely determined by wolf predation) might be generalized to imply that wolves dominate in the dynamics of ungulate population, and that it therefore follows that wolf control efforts are generally necessary. Our results demonstrate that results of the sort presented by McLaren and Peterson (1994) are likely to reflect the sources of stochastic variance in the particular system rather than the importance of top-down control by wolves."(280)

"Because ungulate densities must fall below the satiation thresholds for the predator functional response before we can discern whether or not predation is regulating, we would caution against implementing wolf culls prematurely."(280)