Energy flux determines stability in generalized food web motifs

Background/Question/Methods

Characterizing the factors that determine the stability of biological communities is a long standing issue in ecology. Theory from two species consumer-resource models suggests that increased energy flux decreases stability. However, real food webs consist of complex networks of interaction, the structure of which may have an important influence on the effect that energy flux has on food web stability. To address this, we explored the effect of increased energy flux at various trophic levels on the stability of different food web motifs. Previous theoretical work on food web stability made assumptions about the specific functional forms of interactions, which are known to have important consequences for the stability of the system. While in some cases there is justification for the use of a particular functional form, in other cases there is not. Furthermore, there is likely variation in the form of interactions both within and across different food webs. We performed simulations using the newly proposed method of generalized modeling, which allows the simultaneous analysis of broad classes of models without making assumptions about the exact functional form of interactions. This approach makes our results generalizable across a range of assumptions about the nature of species interactions.

Results/Conclusions

We found a significant effect of energy flux on the stability of each of the food web motifs (2 and 3-species chains, intraguild predation, apparent competition, and exploitative competition). Furthermore, the nature of this effect varied across different motifs. In most cases, the mean leading eigenvalue (which is inversely related to stability) had a convex relationship with increasing energy flux to a particular trophic level. However, the mean leading eigenvalue always had a linear relationship with the total energy flux through the system. In the 2-species chain, there was a negative relationship with increasing energy flux, while in the other motifs the relationship was positive. We investigated the volume of the stable region for linear food chains with 2 to 4 species and found that the stability effects of energy flux across trophic levels depended ratio of turnover rates in the levels. Furthermore, the effect of flux to the lowest trophic level was always opposite of that the higher trophic levels. Together, our results suggest that energy flux can have opposite effects on food web stability and underline the need for comprehensive studies that take into account the complex structure of food webs to fully understand their stability.