Uncentred correlation coefficient between pairs of empirical food webs for (

*a*) motifs S1–S5 and (

*b*) motifs D1–D8. The uncentred correlation coefficient

*r* measures the degree of similarity between two food webs: a value of

*r* close to 1 indicates high similarity; that close to 0 indicates little similarity; and that close to 1 indicates that the two behave oppositely. (

*c*) Motifs S1–S5 and (

*d*) motifs D1–D8: we show here the fraction of model-generated food webs with uncentred correlation coefficient

*r*≥0.75 when compared to the empirical food webs for the niche (solid circles) and nested-hierarchy (open diamonds) models. When examining the uncentred correlation coefficient, the two models reproduce the empirical profile of over- and under-representation for motifs S1–S5 with similar success (

*c*), with the niche model typically performing only slightly better than the nested-hierarchy model. For motifs D1–D8 (

*d*), however, only the niche model successfully reproduces the empirical patterns, significantly outperforming the nested-hierarchy model. (

*e*) Motifs S1–S5 and (

*f*) motifs D1–D8: we repeat the analysis but also consider the ratio

*d* for the Caribbean Reef food web and the generalized niche model for

. The original niche model (generalized niche model with

*c*=1.0) is unable to fully capture the magnitude of the empirical

*z*-scores for motifs D1–D8; however, the introduction of slight discontiguity in species diets (e.g.

*c*=0.95) allows the generalized niche model to completely capture the motif behaviour exhibited by the Caribbean Reef food web. Note that, in (

*b*) (

*d*) and (

*f*), we only consider the empirical food webs which contain double links.

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