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.

Network structure and the biology of populations

“…The above analyses [53,54] would suggest not, and this view is supported by recent studies of three different marine ecosystems, which 'substantiate previously reported results for estuarine, fresh-water and terrestrial datasets, [suggesting] that food webs from different types of ecosystems with variable diversity and complexity share fundamental structural and ordering characteristics' [59].…”

“…As emphasised over 30 years ago [2], real food webs are not randomly assembled, and so the first question is: what patterns, if any, are there in the degree distributions, diameters and clustering coefficients of interacting species in ecosystems? Two recent analyses [53,54] of 16 high-resolution food webs from aquatic and terrestrial ecosystems (with total nodes from 25 to 172) strongly suggest 'two degrees of separation', in the sense that more than '95% of species [are] typically within three links of each other' [54]. These degree distributions are not random Erdos-Renyi ones, although whether they are exponential, scale-free, or something else is the subject of debate [9,20].…”

The smallest of all worlds: Pollination networks

“…In the small food webs analysed by Dunne et al (2002), /lS also increases with N. However, the relationship appears negative for the larger food webs (Table 3). In Williams In Dunne et al (2002), //lSS ¼ 2.18, and in Williams et al (2002), //lSS ¼ 1.93, which is considerably longer than in 1-mode pollination networks (1.60). However, Williams et al (2002) also stress that ''the two degrees of separation'' may overestimate distances, because food webs only take trophic interactions into account.…”

“…Baraba´si et al, 2000;Albert and Baraba´si, 2001) has been applied to two types of ecological webs, viz. food webs Montoya and Sole´, 2002;Williams et al, 2002) and mutualistic networks . Network properties of these two types of webs have, however, never been compared.…”

“…In general, networks with short distance or path length between their nodes and highly clustered nodes are termed small worlds (for definitions see later). Although path length between taxa in food webs is short, food webs do not truly qualify as small worlds because their taxa are not highly clustered Williams et al, 2002). We extend this analysis to include non-food webs, mutualistic networks, in order to make broad generalizations about ecological webs.…”