Trophic links of community food webs.

Abstract

This report describes and explains regularities in the numbers and kinds of trophic links in community food webs. To a first approximation, the mean number of trophic links in a community food web is proportional to the total number of trophic species. The mean number of trophic links between any two categories of trophic species (basal, intermediate, and top) is proportional to the geometric mean number of species in the categories joined. These linear relationships, and scale-invariance in the proportions of basal, intermediate, and top species, make it possible to predict with remarkable precision the proportions of each kind of trophic link among all community food webs. The differences between food webs in constant and in fluctuating environments reflect apparently greater constraints on the trophic organization of food webs in fluctuating environments. PROBLEM AND HYPOTHESESHow does the total number L of links in a web vary as the number S of species increases? At least three hypotheses are plausible. First, the number of potential links increases as S2 because the maximal number of edges in a directed graph on S nodes is S(S-1). If there were a constant probability that any potential link were a real link, the mean E(L) of L would be proportional to S2. Second, if each species could eat or serve as food for only a finite number of other species, regardless of how many species were present in the community, the mean E(L) would be proportional to S. Third, both of the preceding hypotheses might apply over different ranges of values of S. When the number of species in a community is small, L may be constrained only by the availability of potential links and hence vary as S2. When the number of species in a community is large, L may be limited by the potential for interaction of each species and hence vary as S. The same relation between L and S might also arise because field ecologists might be more thorough in recording links when the total number of species in the community is small, but proportionally more prone to omission when the number of species is large.According to these three hypotheses, plots against S, on the abscissa, of (a) the square root of L, (b) L, or (c) some power of L between 1/2 and 1, on the ordinate, should be approximately linear.

The small world inside large metabolic networks

“…The variation in connectivity of both types of graph greatly exceeds that of random graphs. Like networks found in neurobiology and ecology (Cohen & Briand 1984;Murre & Sturdy 1995), metabolic graphs are sparse, i.e. the average degree ( k) of each vertex (metabolite or reaction) is small, of order log n. In a random graph with n nodes and probability p of two nodes being connected the degree of each vertex follows a binomial distribution with variance (n À 1)p(1 À p).…”

Correlation, selection and the evolution of species networks

“…This form of dependence has been observed in ecological field data; predominantly food web structured but also mutualistic networks (Cohen & Briand, 1984) (Olesen & Jordano, 2002) (Montoya & Sole, 2003) (Bascompte, Jordano, Melian, & Olesen, 2003). In a generalised interaction network this relation is thought to represent a delineation of stable and unstable regions of network structure (May, 1974) (McKane, Alonso, & Sole, 2000).…”

A genotype network reveals homoplastic cycles of convergent evolution in influenza A (H3N2) haemagglutinin

“…Casting such data in the form of a network immediately makes many analytical tools from graph theory available [18]. Their use has contributed to fields as different as ecology, systems biology and the social sciences [19][20][21][22][23][24][25]. For example, they can help identify 'modules' of cooperating molecules, interactions in ecological networks that affect their stability, or network properties that can influence the spreading of traits, such as innovations or diseases [19,24,26].…”