Food web assembly rules

In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. Yet, fundamental understanding, even of minimal conditions for coexistence, is lacking. Using the generalized Lotka-Volterra equations, we show that sustainable coexistence necessitates a nonzero determinant of the interaction matrix, a requirement that is equivalent to demanding that each species is part of a non-overlapping pairing. In cases where nonzero determinant cannot be achieved, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, these assembly rules specify sustainable combinations. In neighboring levels, the rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with empirical data the constraints predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and increase robustness in food webs. We further explore how concomitant predation, caused by consumption of parasites by their hosts’ predators, adds further possibilities of non-overlapping pairing and thereby supports coexistence.