Two degrees of separation in complex food webs

Abstract

Feeding relationships can cause invasions, extirpations, and population fluctuations of a species to dramatically affect other species within a variety of natural habitats. Empirical evidence suggests that such strong effects rarely propagate through food webs more than three links away from the initial perturbation. However, the size of these spheres of potential influence within complex communities is generally unknown. Here, we show for that species within large communities from a variety of aquatic and terrestrial ecosystems are on average two links apart, with >95% of species typically within three links of each other. Species are drawn even closer as network complexity and, more unexpectedly, species richness increase. Our findings are based on seven of the largest and most complex food webs available as well as a food-web model that extends the generality of the empirical results. These results indicate that the dynamics of species within ecosystems may be more highly interconnected and that biodiversity loss and species invasions may affect more species than previously thought.

Figure 1

Characteristic path length D of the seven empirical webs listed in Table 1 (●), error bars showing mean ± 2 SD for niche model webs with the same S and C as the empirical webs, and curves showing mean D vs. C for niche model webs with S = 20, 100, and 1,000. Log-log plot shows the approximate power-law relationship between mean D of niche model webs and C for all S. The seven empirical webs are, from left to right, Ythan Estuary (S = 78), Chesapeake Bay (S = 31), St. Martin Island (S = 42), Little Rock Lake (S = 92), Bridge Brook Lake (S = 25), Coachella Valley (S = 29), and Skipwith Pond (S = 25). Because the niche model is a stochastic model, previously described Monte Carlo techniques (5) were used to measure the mean and SD of the niche model predictions, and errors are normalized by the SD of the model prediction (Table 1). The mean normalized error is −0.02 model SD, which is very close to zero as expected when the model fits the data. The SD of the errors is 1.4, showing slightly greater variability of normalized error than the theoretically expected SD of 1 (5). A null model that randomly arranges trophic links while maintaining empirically observed S and C (5) fits the data much worse as indicated by a normalized error mean of −2.6 and SD of 5.4.

Figure 2

Distributions of distances (d) between species pairs for the seven webs listed in Table 1. The histograms are normalized to show the fraction of species pairs at each distance.

Figure 3

Sensitivity of D among niche model webs to S. Lines connect the means from 1,000 iterations for each level of S and C.

Figure 4

Fraction of species pairs with d ≤ 3 in niche model webs as a function of species number (S) and connectance (C). Adjacent lines designate isopleths that are 0.025 apart. Most empirical webs fall above and to the right of the 0.95 isopleth.