The dynamical theory of food webs has been based typically on local stabili
ty analysis. The relevance of local stability to food web properties has be
en questioned because local stability holds only in the immediate vicinity
of the equilibrium and provides no information about the size of the basin
of attraction. Local stability does not guarantee persistence of food webs
in stochastic environments. Moreover, local stability excludes more complex
dynamics such as periodic and chaotic behaviors, which may allow persisten
ce. Global stability and permanence could be better criteria of community p
ersistence. Our simulation analysis suggests that these three stability mea
sures are qualitatively consistent in that all three predict decreasing sta
bility with increasing complexity. Some new predictions on how stability de
pends on food web configurations are generated here: a consumer-victim link
has a smaller effect on the probabilities of stability, as measured by all
three stability criteria, than a pair of recipient-controlled and donor-co
ntrolled links; a recipient-controlled link has a larger effect on the prob
abilities of local stability and permanence than a donor-controlled link, w
hile they have the same effect on the probability of global stability; food
webs with equal proportions of donor-controlled and recipient-con trolled
links are less stable than those with different proportions. (C) 2001 Acade
mic Press.