Multi-stability and the origin of microbial community types

Abstract

The study of host-associated microbial community composition has suggested the presence of alternative community types. We discuss three mechanisms that could explain these observations. The most commonly invoked mechanism links community types to a response to environmental change; alternatively, community types were shown to emerge from interactions between members of local communities sampled from a metacommunity. Here, we emphasize multi-stability as a third mechanism, giving rise to different community types in the same environmental conditions. We illustrate with a toy model how multi-stability can generate community types and discuss the consequences of multi-stability for data interpretation.

Figure 1

Overview of different mechanisms generating community types. (a) In general, peaks in the landscape of possible community configurations are interpreted as community types. The landscape plot shown here was generated with data from the Flemish Gut Flora Project. It combines a principal coordinates analysis plot, which summarizes community composition in two dimensions, with a density landscape. The latter encodes the frequency of observed community configurations as height. The mountain peaks thus represent alternative community types. The exact mechanism behind these peaks is unknown. (b) The most frequently evoked mechanism for different community types is a continuous response to environmental change. The community type is here represented by a bar plot that depicts the abundance of different species (indicated with colored bars). The probability of detecting different community types depends on the slope of the community response curve. If the slope is steep, transitional community configurations will be harder to find, resulting in separate clusters. (c) Gibson and colleagues recently proposed a model that generates different local communities from a metacommunity through random selection. The local communities differ when interaction strengths between community members are strongly heterogeneous. The model can be adapted to describe the impact of the environment by replacing random selection with habitat filtering. (d) Finally, a multi-stable community can adopt different stable states in the same environmental conditions. A community type switch can be triggered either by adding or removing individuals belonging to species present in the community (vertical arrows) or by changing the environment (bent arrows). However, once the system is pushed across a tipping point (black point), it does not return when original conditions are restored. Instead, it has to be altered beyond another tipping point to go back to its original state. This effect is known as hysteresis.

Figure 2

Toy model for multi-stable communities. (a) The toy model community consists of three species, each of which competes with the other two. (b) The toy model describes the dynamics of each species as a function of its growth rate b_i, its death rate k_i and an inhibition term f_i. The inhibition term models how all species lower the species' growth rate using a Hill function, which takes inhibition coefficients K_ij and the Hill coefficient n (here n=2) as parameters. The interaction coefficients form a matrix, the values of which are shown. The smaller the inhibition coefficients, the stronger the inhibition. (c) Numeric simulation of the model demonstrates that three stable states exist, which depend on the initial abundances of the species. (d) The three bifurcation diagrams show for each species the range of the three stable states. (e) When perturbing the system by temporarily decreasing the growth rate of b₁ below the first tipping point, the green species replaces the blue one as the dominant species in the system. A second perturbation, increasing the growth rate of the blue species beyond the second tipping point, is needed to return to the original state. More details are provided in the Supplementary Material.

Figure 3

Proof-of-concept model for multi-stable communities. (a) The first version of the proof-of-concept model consists of three groups of five weakly interacting species (n=2, K_ij≈1). Each group strongly inhibits the other two groups (n=2, K_ij≈0.5). (b) There are three stable states, each dominated by either the blue, red or green group. Each panel shows the stable distribution of the 15 species for randomly sampled initial abundances. (c) When carrying out simulations with slightly varying growth rates and inhibition coefficients and plotting resulting total group abundances together in a ternary plot, the group structure is clearly visible (upper triangle plot). However, when the inter-group inhibitions are lowered, the distinction between groups lessens (middle triangle). A gradient between two groups can also emerge if their mutual inhibition is lower than their inhibition with the third group (bottom triangle). (d) We also explored a version of the proof-of-concept model without pre-defined group structure, where inhibition coefficients were sampled from an exponential distribution and the Hill coefficient n was set to 4 (inset). When repeating simulations with varying initial abundances and visualizing stable state abundances in a bar plot, distinct groups emerge. The bar plot only colors abundances of the five species that vary the most strongly across groups, whereas more homogeneous species are uniformly colored in gray. (e) As in the toy model, a community type switch can be induced by temporarily increasing the growth rate of a species (species 4 here, cyan curve). The two bar plots depict the abundance distribution before and after community type switching. Since species 4 and 8 inhibit each other, the abundance of species 8 is low in the new stable state (lower bar plot) as compared to the first stable state (upper bar plot). Hysteresis is demonstrated by the fact that the growth rate of species 4 has to be reduced below its original value to return to the original state. More details are provided in the Supplementary Material.