Persistence and flow reliability in simple food webs

Abstract

Twenty-five model food webs can be designed from five points (species) and five links (trophic interactions), if they contain a single top-predator (i.e. sink webs). According to a simple topological approach, we presented elsewhere a reliability theoretical analysis of this set of food web graphs. The question addressed here is how network flow reliability is related to the dynamical behavior and stability of these ‘model communities’. We simulated the behavior of these webs and calculated their persistence, according to four models: (1) with symmetrical interaction coefficients between species; (2) with asymmetrical interaction coefficients and lower death rates for predators; and (3) with absolutely and (4) relatively perturbed, formerly persistent parameter sets of the asymmetrical model. We used both Lotka–Volterra (LV) and Holling II-type equations (with switching effect). Thus, we had eight persistence values for each web. Persistence (a dynamical property) and flow reliability (a structural property) were analyzed. We found that (1) reliable flow pattern is associated with high persistence in the Holling models, while the LV models predict no consistent correlations; (2) in asymmetrical situations, persistence is always much higher (in both LV and Holling models); and (3) the predictions of Holling models (versus LV models) are much less sensitive to local perturbations. Based on these results, we conclude that (1) reliable network flows can contribute to persistence only if switching is possible; (2) asymmetrical interactions increase persistence, independently of the switching effect but it indicates persistence in Holling II model; (3) switching makes the relationship much more predictable between structure and dynamics. Thus, the network design is less useful predictor of persistence without switching effect but well can ensure dynamical stability under the conditions of the Holling II model. We have presented how various dynamical models predict different behavior of modelled communities characterized by the same structure and complexity. Complementing dynamical with structural analysis may further increase our understanding of persistence in food webs.