Abstract
How the 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.
Highlights
Food webs are networks of species linked via trophic interactions that in a simple way describe the biodiversity and feeding relations in ecosystems
We found no relation between unweighted connectance, C, and food web stability expressed as diagonal strength, s, in the 15 real soil food webs (Spearman rank correlation test: ρ = 0.11, P > 0.5, corrected for 5 ties)
Some food webs had a value of m that was very close to the minimum value of 1 (Fig. 1), that is, these webs had practically one link per node when link weights were taken into account
Summary
Food webs are networks of species linked via trophic interactions that in a simple way describe the biodiversity and feeding relations in ecosystems. Depending on definitions of stability, methods to construct theoretical food webs, Theor Ecol (2016) 9:49–58 or usage of empirical food web data or structures, some studies confirmed the negative relation between food web complexity and stability (Gardner and Ashby 1970; May 1972; Pimm 1979; Chen and Cohen 2001), but others found that highly connected food webs could still be stable (DeAngelis 1975; Haydon 2000; Dunne et al 2002)
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