Searching for balance: stability and equilibria of food webs

Abstract

How complexity of food webs relates to stability has been a subject of many studies. Often,

unweighted connectance is used to express complexity. Unweighted connectance is

measured as the proportion of realized links in the network. Weighted connectance, on the

other hand, takes link weights (fluxes or feeding rates) into account and captures the shape

of the flux distribution. Here, we used weighted connectance to revisit the relation between

complexity and stability. We used 15 real soil food webs and determined the feeding rates

and the interaction strength matrices. We calculated both versions of connectance, and

related these structural properties to food web stability. We also determined the skewness

of both flux and interaction strength distributions with the Gini coefficient. We found no

relation between unweighted connectance and food web stability, but weighted connectance

was positively correlated with stability. This finding challenges the notion that complexity

may constrain stability, and supports the ‘complexity begets stability’ notion. The positive

correlation between weighted connectance and stability implies that the more evenly flux

rates were distributed over links, the more stable the webs were. This was confirmed by the

Gini coefficients of both fluxes and interaction strengths. However, the most even

distributions of this dataset still were strongly skewed towards small fluxes or weak

interaction strengths. Thus, incorporating these distribution with many weak links via

weighted instead of unweighted food web measures can shed new light on classical

theories