Supplementary Methods:

Estimating functional uniqueness

We estimated the functional uniqueness of each species in a food web using an established measure of species originality (Pavoine et al. 2005). This measure of functional uniqueness, which we call FU, is based on the apportionment of quadratic entropy, as proposed by Rao (1982). The functional uniqueness of species i, FUi, is calculated as:

FUi = di• / d••

where, di• = Σj dij , d•• =Σj di• and dij is the measure of functional trait dissimilarity between species i and species j used by Pavoine et al.(2005). This definition of functional uniqueness can be related back to the expected dissimilarity between two randomly chosen species (i.e. Rao’s quadratic entropy, QE = Σijpipj dij, where pi is the relative abundance of species i), since setting the relative abundance of each species equal to its functional uniqueness (pi = FUi) can be shown to maximise this expected dissimilarity. Note that this definition of functional uniqueness does not identify features that are strictly unique to one species (see Pavoine et al. 2005 for a detailed explanation of methods for calculating species originality).

The functional traits used to estimate FU were body mass, mobility and trophic height. Body mass is a continuous variable, measured as average species mass in grams. Mobility is a discrete variable, where a value of 1 is given to sessile or free-floating organisms, 2 is associated with crawling organisms, 3 relates to crawlers with the ability to swim, and 4 equates to free-swimmers. Trophic height is determined from the food web of all predator-prey links. It is calculated as the short-weighted trophic level (TL), which is the mean of the shortest TL and the prey-averaged TL (1 + the mean TL of all the consumer’s trophic resources). Short-weighted TL has been shown to estimate flow-based TL to within a quarter of a TL (Williams & Martinez 2004).

Estimating interaction strength

Here, we define interaction strength as the direct effect per unit biomass of one species on another. This can be the negative effect of a predator feeding on a prey or the positive effect, in terms of energy transfer, of the prey on the predator. We estimated the direct effect of each predator j on its prey i based on established allometric predator-prey relationships (see O'Gorman et al. 2010), such that:

where Mj is the body mass of predator j, sj is the number of prey species consumed by predator jand the exponent of -0.25 is based on allometric scaling relationships to approximate basal metabolic rate per unit biomass (Brown & Gillooly 2003). The intercept b is the scaling constant, which only changes the magnitude of the interaction strength, and it is set to 0.01 here. Note that the denominator, sj, is derived from a preference of predator j for prey i. Here, it is assumed that the predator spreads its feeding effort evenly among its prey species if the density of each species, X, scales inversely with body mass, M, as X ~ M-1(Brown & Gillooly 2003), leading to all prey species having equal biomass (see O'Gorman et al. 2010). If detailed information exists on the preference of predators for different types of prey, this will lead to more accurate predictions of interaction strengths between individual predator-prey pairs. Here, we are interested in the mean interaction strength of a species in the system, so individual predator-prey interaction strengths are less important.

To estimate the direct effect of the prey on the predator, we assumed an ecological efficiency, e, equal to 0.1 reflecting a 10% transfer of energy between trophic levels (Brown & Gillooly 2003), hence . We calculated the mean absolute direct effect (MDE) of species i as Σj ( |aij| + |aji| ) / n, where n is the number of its direct interactions (note that we take absolute values so that positive and negative interaction strengths do not tend to cancel each other out).

References:

Brown J.H. & Gillooly J.F. (2003). Ecological food webs: High-quality data facilitate theoretical unification. Proceedings of the National Academy of Sciences of the United States of America, 100, 1467-1468.

O'Gorman E.J., Jacob U., Jonsson T. & Emmerson M.C. (2010). Interaction strength, food web topology and the relative importance of species in food webs. Journal of Animal Ecology, 79, 682-692.

Pavoine S., Ollier S. & Dufour A.B. (2005). Is the originality of a species measurable? Ecology Letters, 8, 579-586.

Rao C.R. (1982). Diversity and dissimilarity coefficients - a unified approach. Theoretical Population Biology, 21, 24-43.

Williams R.J. & Martinez N.D. (2004). Limits to trophic levels and omnivory in complex food webs: Theory and data. American Naturalist, 163, 458-468.

Table S1. Food web statistics for three natural ecosystems: WS = Weddell Sea; LH = Lough Hyne; and CCR = Caribbean Coral Reef. For taxa, numbers in brackets indicate the proportion of taxa resolved to species level. For basal, intermediate and top taxa, numbers in brackets signify the proportion of taxa belonging to those categories.

WS / LH / CCR
Taxa / 490 (0.996) / 345 (0.971) / 247 (0.834)
Links / 16041 / 5030 / 3288
Connectance / 0.067 / 0.042 / 0.054
Basal taxa / 65 (0.132) / 48 (0.139) / 5 (0.020)
Intermediate taxa / 392 (0.800) / 284 (0.823) / 241 (0.976)
Top taxa / 33 (0.067) / 13 (0.038) / 1 (0.004)

Figure S1. Food web diagrams highlighting the complexity of the study systems. Nodes are arranged in the vertical plane according to trophic height and are coloured according to trophic position, with top predators darkest and basal resources lightest. (a), (b) and (c) are experimental communities with 10, 4 and 0 manipulated predator species richness, respectively. The remaining webs are natural communities: (d) the Weddell Sea, (e) the entire Lough Hyne web and (f) a Caribbean Coral Reef. Food web diagrams were rendered using Network3D (copyright Microsoft Research and PEaCE Lab).

Figure S2.The distribution of slopes (a, d, g), r2 values (b, e, h) and intercepts (c, f, i) from the linear regressions of log10(FU) against log10(MDE) for the 210 experimental food webs, after excluding mobility (a-c: dotted lines), body mass (d-f: dashed lines) and food web links (g-i: solid lines) from the estimation of functional uniqueness. Probability densities were calculated using a Gaussian kernel density estimator. This analysis shows that no single trait is driving the observed relationship between FU and MDE for the 210 experimental food webs.

Figure S3.The relationship between functional uniqueness (FU) and interaction strength (MDE) in three natural ecosystems: (a) the Weddell Sea; (b) Lough Hyne; and (c) a Caribbean Coral Reef.

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