Higher-order effects, continuous species interactions, and trait evolution shape microbial spatial dynamics

Abstract

The assembly and maintenance of microbial diversity in natural communities, despite the abundance of toxin-based antagonistic interactions, presents major challenges for biological understanding. A common framework for investigating such antagonistic interactions involves cyclic dominance games with pairwise interactions. The incorporation of higher-order interactions in such models permits increased levels of microbial diversity, especially in communities in which antibiotic-producing, sensitive, and resistant strains coexist. However, most such models involve a small number of discrete species, assume a notion of pure cyclic dominance, and focus on low mutation rate regimes, none of which well represent the highly interlinked, quickly evolving, and continuous nature of microbial phenotypic space. Here, we present an alternative vision of spatial dynamics for microbial communities based on antagonistic interactions-one in which a large number of species interact in continuous phenotypic space, are capable of rapid mutation, and engage in both direct and higher-order interactions mediated by production of and resistance to antibiotics. Focusing on toxin production, vulnerability, and inhibition among species, we observe highly divergent patterns of diversity and spatial community dynamics. We find that species interaction constraints (rather than mobility) best predict spatiotemporal disturbance regimes, whereas community formation time, mobility, and mutation size best explain patterns of diversity. We also report an intriguing relationship among community formation time, spatial disturbance regimes, and diversity dynamics. This relationship, which suggests that both higher-order interactions and rapid evolution are critical for the origin and maintenance of microbial diversity, has broad-ranging links to the maintenance of diversity in other systems.

Keywords: community assembly; continuous species model; cyclic dominance; eco-evolutionary dynamics; higher-order interactions.

Fig. 1.

A conceptual representation of the model with descriptions of all the parameters involved. See SI Appendix, Supplemental Methods for details about implementation.

Fig. 2.

System dynamics in three example conditions of initial conditions pertaining to different regimes of spatial disturbance behavior (Low, Medium, and High) (A–C). Snapshots of each simulation at different timesteps (10, 100, 250, and 500) are shown in columns 1 through 4. The respective species dynamics (in which different colors represent different species “bins,” SI Appendix, Supplemental Methods) and diversity dynamics are represented in columns 5 and 6, respectively. In columns 5 and 6, the time taken for the simulation to stabilize (i.e., the CFT) is denoted with a vertical red dotted line. The community existing after the system has reached the CFT is termed an eco-evolutionary stable community.

Fig. 3.

Dependence of model dynamics on different parameters and CFT. A shows the variable importance score for all the parameters from an RF classification (with 10,000 trees) on the three categories of spatial disturbance (OOB = 10.2%). B and C denote the variable importance scores from RF regression models (with 10,000 trees) for SD mean and variance, respectively. D, E, and F show the SD mean–variance plots overlaid with mutation size, growth radius, and CFT values of the respective simulations. For A–C, IncNodePurity (used in regression RFs) and MeanDecreaseGini (used in classification RFs) refer to how well a parameter explains the prediction variable in question.

Fig. 4.

Effects of CFT on the spatial diversity dynamics. A depicts the four optimal clusters (groups) of SD mean–variance space found using k-means clustering (SI Appendix, Fig. S3). B shows the results from the PRCC analyses of the four groups and the overall data. C shows the proportion of spatial disturbance regimes present in different groups. D and F show the distribution of the values of mean and variance of Shannon equitability and Simpson’s index, respectively, for a smaller subsample of the runs with points colored by groups from A. E depicts the group-wise histogram of Shannon equitability, and G depicts the histogram of Simpson’s index (for clarity, only the range between 0 and 0.04 is shown).