THE RESPONSES OF UNSTABLE FOOD-CHAINS TO ENRICHMENT

This article investigates the mean abundances of trophic levels in sim ple models of two- and three-level food chains as a function of the ra te 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 becom e satiated when food density is high. In unstable two-level systems, b ottom level abundance generally increases with increased nutrient inpu t. The abundance of the second level may decrease with increased input . Changes in the intrinsic rate of increase and carrying capacity of t he bottom level can have qualitatively opposite effects on trophic lev el abundances. Refuges for or immigration of the bottom level usually cause both levels to increase in mean abundance with an increased carr ying capacity. A variety of different predator-prey models are discuss ed briefly and the results suggest that increased nutrient input will often increase the abundance of both levels; however, several circumst ances can cause the top level to decrease. In three-level systems, an increased carrying capacity can cause extinction of the top level. Ext inction may or may not be conditional on the initial densities of the three levels. These results may help explain the observed lack of corr elation between productivity and the number of trophic levels in natur al food webs, as well as the lack of very long food chains. The result s suggest that patterns of abundances across productivity gradients ca nnot be used to assess the importance of top-down vs bottom-up effects .