Fig. 3: The role of super-generalist species in the emergence of power-law degree distributions.
From: Power laws in species’ biotic interaction networks can be inferred from co-occurrence data
Top, different possibilities for the relationship between the number of potential interactions and the number of realized links in the network of biotic interactions. The yellow line shows the pattern observed in the data analysed in this study, where generalist species in terms of potential interactions realize a disproportionate large number of those links in the network of biotic interactions. The non-linearity of this relationship makes the non-proportionality across species explicit. This relationship between potential and realized (biotic) interactions highlights the strong generalism of the species both in terms of their abiotic niche (that is, larger occupancy in space and thus larger co-occurrence with other species) and their biotic niche (that is, more biotic interactions among those co-occurring with them). We call these species super-generalists. The grey and green dashed lines represent two other possible cases: a constant proportion of realized links across species and the case where specialist species would realize a larger proportion of the potential links. Bottom, the consequences of these patterns for the shift in the network degree distribution from co-occurrence to biotic interactions. Given that super-generalist species keep a larger proportion of their potential links than specialist species, the degree distribution changes from an exponential in the co-occurrence network to a power law in the network of biotic interactions (yellow line), where the probability of finding a species in the network with a large number of links is higher than in the other cases (grey and green dashed lines). If the interaction degree of species was roughly proportional to the co-occurrence degree, the respective degree distributions would keep the same functional form. The interaction degree distribution would thus be a simple rescaling of the one for co-occurrences. An exponential would remain an exponential, and a power law would remain a power law (see Supplementary Text 2 for a mathematical demonstration).
