Ecological modelling approaches for predicting emergent properties in microbial communities

Abstract

Recent studies have brought forward the critical role of emergent properties in shaping microbial communities and the ecosystems of which they are a part. Emergent properties-patterns or functions that cannot be deduced linearly from the properties of the constituent parts-underlie important ecological characteristics such as resilience, niche expansion and spatial self-organization. While it is clear that emergent properties are a consequence of interactions within the community, their non-linear nature makes mathematical modelling imperative for establishing the quantitative link between community structure and function. As the need for conservation and rational modulation of microbial ecosystems is increasingly apparent, so is the consideration of the benefits and limitations of the approaches to model emergent properties. Here we review ecosystem modelling approaches from the viewpoint of emergent properties. We consider the scope, advantages and limitations of Lotka-Volterra, consumer-resource, trait-based, individual-based and genome-scale metabolic models. Future efforts in this research area would benefit from capitalizing on the complementarity between these approaches towards enabling rational modulation of complex microbial ecosystems.

Figure 1. Examples of emergent properties arising from community complexity.

A. Stability and resilience. Interactions among community members can buffer against biotic and/or abiotic perturbations leading back to stable compositional state [82, 113, 136]. Blue arrow indicates a perturbation event. B. Phenotypes. Emergent functions such as substrate utilization, biomass production, cross-protection, result from the cooperation between community members. [104, 110, 139]. C. Persistence. Strains that would otherwise face competitive exclusion can coexist via, for instance, the intermediary of a cross-fed metabolite secreted by another community member [84, 88, 175]. D. Self-organisation. Balance between competitive and cooperative interactions can lead to spatial patterning, such as the formation of clonal patches [30, 47, 141].

Figure 2. Model types commonly used for studying emergent properties of microbial communities.

Shown equations in A-D are examples, and could be varied to be more realistic by, for instance, making growth rates non-linearly dependent on resource availability (e.g., via Monod-like kinetics, as in panel C), or by introducing species-specific carrying capacities to make growth logistic. Parts of the equation that correspond to elements in the conceptual diagram are matched by colour, whereas grey elements are those not explicitly present in the shown equations. See Supplementary Table 1 for further details including notations used. A uniform background colour represents a homogenous (and closed) environment. In panels A & B, populations and/or resources are shown as groups for the purpose of illustration, but the model assumes spatiotemporally homogeneous distribution (effectively rendering the system like a well-stirred reactor). We further note that the boundaries between different model types are not rigid, and each model type can be extended beyond their typical application.

Figure 3. Choosing a suitable modelling approach.

The flow diagram indicates the model choice trajectory, starting with the available input parameters till the emergent properties that can be potentially modelled. The dotted line marks the potential for inferring interaction coefficients from omics data (e.g., co-occurrence networks predicted by genome-scale metabolic models), albeit without being indicative of direct and density-dependent interactions. Top-down models are those that consider communities in terms of population-averages, whereas bottom-up models simulate communities at individual level. The shown model types and their links to parameters and emergent properties are based on their common forms and applications. The model types can be adapted to be informed by additional parameters and be made suitable to model other emergent properties than indicated. For instance, genome-scale metabolic models can be used to study spatial patterns [160].