Statistical structure of host-phage interactions

Abstract

Interactions between bacteria and the viruses that infect them (i.e., phages) have profound effects on biological processes, but despite their importance, little is known on the general structure of infection and resistance between most phages and bacteria. For example, are bacteria-phage communities characterized by complex patterns of overlapping exploitation networks, do they conform to a more ordered general pattern across all communities, or are they idiosyncratic and hard to predict from one ecosystem to the next? To answer these questions, we collect and present a detailed metaanalysis of 38 laboratory-verified studies of host-phage interactions representing almost 12,000 distinct experimental infection assays across a broad spectrum of taxa, habitat, and mode of selection. In so doing, we present evidence that currently available host-phage infection networks are statistically different from random networks and that they possess a characteristic nested structure. This nested structure is typified by the finding that hard to infect bacteria are infected by generalist phages (and not specialist phages) and that easy to infect bacteria are infected by generalist and specialist phages. Moreover, we find that currently available host-phage infection networks do not typically possess a modular structure. We explore possible underlying mechanisms and significance of the observed nested host-phage interaction structure. In addition, given that most of the available host-phage infection networks examined here are composed of taxa separated by short phylogenetic distances, we propose that the lack of modularity is a scale-dependent effect, and then, we describe experimental studies to test whether modular patterns exist at macroevolutionary scales.

Fig. 1.

Schematic of expected host–phage interaction matrices (white cells denote infection). (A) Host–phage interactions are unique (i.e., only one phage infects a given host, and only one host is infected by a given phage). (B) Host–phage interactions are modular (i.e., blocks of phages can infect blocks of bacteria, but cross-block infections are not present). (C) Host–phage interactions are nested (i.e., the generalist phage infects the most sensitive and the most resistant bacteria, whereas the specialist phage infects the host that is infected by the most viruses). (D) Host–phage interactions are random and lack any particular structure. For B–D, a connectance of 0.33 was used so that the expected total number of interactions was the same in each case.

Fig. 2.

Matrix representation of the compiled studies. The rows represent the hosts, and the columns represent the phages. White cells indicate the recorded infections. Note the diversity in the size of these matrices.

Fig. 3.

Two example matrices were resorted to maximize modularity and nestedness. (A and B) The matrix in Left is the original data, the matrix in Center is the output from the modularity algorithm (102), and the matrix in Right is the output from the modified nestedness algorithm (103, 104). Colors represent different communities within the maximal modular configuration. (A) An example of a matrix with significantly elevated modularity and insignificant nestedness. (B) An example of a matrix with insignificant modularity and significantly elevated nestedness.

Fig. 4.

Modularity sorts of the collected studies. Blue labels (20/38) represent studies statistically antimodular, and red labels (6/38) represent studies statistically modular.

Fig. 5.

Nestedness sorts of the collected studies. Red line represents the isocline. Blue labels (0/38) represent studies statistically antinested, and red labels (27/38) represent studies statistically nested.

Fig. 6.

Statistical distribution of modularity and nestedness for random matrices compared with that of the original data. (A) Sorted comparison of modularity of the collected studies vs. random networks. (B) Sorted comparison of nestedness of the collected studies vs. random networks. In both cases, error bars denote 95% confidence intervals based on 10⁵ randomizations.

Fig. 7.

Union of two nested matrices indicates possible host–phage interaction structure at larger, possibly macroevolutionary scales. In this figure, we selected two of the most nested studies and performed a union while presuming that there were no cross-infections of hosts by phages of the other study. In this case, E. coli and cyanobacteria were the host types. (A) Depiction of the original matrices. (B) Randomization of the union matrix. (C) Nested sort of the union matrix. (D) Modularity sort of the union matrix with a nested sort of each module.

Fig. P1.

Matrix representation of 1 of 38 compiled studies of host–phage infection networks (matrix 32 in the text). The rows represent the hosts, and the columns represent the phages. White cells indicate a successful infection. In A, the order of rows and columns corresponds to the formatting in its original published format. In B, the order of rows and columns has been determined automatically to maximize nestedness. The red line represents the isocline for a perfectly nested matrix. In this case, the matrix is significantly nested. Overall, we found 27 of 38 studies to be significantly nested.