THE RESPONSES OF UNSTABLE FOOD-CHAINS TO ENRICHMENT

This article investigates the mean abundances of trophic levels in simple models of two- and three-level food chains as a function of the rate of input of nutrients. The analysis concentrates on cases in which the equilibrium point with all species present is unstable. In most of the models, the instability arises because the consumer species become satiated when food density is high. In unstable two-level systems, bottom level abundance generally increases with increased nutrient input. The abundance of the second level may decrease with increased input. Changes in the intrinsic rate of increase and carrying capacity of the bottom level can have qualitatively opposite effects on trophic level abundances. Refuges for or immigration of the bottom level usually cause both levels to increase in mean abundance with an increased carrying capacity. A variety of different predator-prey models are discussed briefly and the results suggest that increased nutrient input will often increase the abundance of both levels; however, several circumstances can cause the top level to decrease. In three-level systems, an increased carrying capacity can cause extinction of the top level. Extinction may or may not be conditional on the initial densities of the three levels. These results may help explain the observed lack of correlation between productivity and the number of trophic levels in natural food webs, as well as the lack of very long food chains. The results suggest that patterns of abundances across productivity gradients cannot be used to assess the importance of top-down vs bottom-up effects.