Theoretical microbial ecology without species

Ecosystems are commonly conceptualized as networks of interacting species. However, partitioning natural diversity of organisms into discrete units is notoriously problematic and mounting experimental evidence raises the intriguing question whether this perspective is appropriate for the microbial world. Here an alternative formalism is proposed that does not require postulating the existence of species as fundamental ecological variables and provides a naturally hierarchical description of community dynamics. This formalism allows approaching the species problem from the opposite direction. While the classical models treat a world of imperfectly clustered organism types as a perturbation around well-clustered species, the presented approach allows gradually adding structure to a fully disordered background. The relevance of this theoretical construct for describing highly diverse natural ecosystems is discussed.

Figure 1

Clustering organisms into discrete species is often problematic (b). Rather than describing the natural world as a deviation from a perfectly clustered case (a), this work proposes a theoretical construct where structure can be gradually added to a fully disordered ecology without species (c).

Figure 2

Coarse-graining degrees of freedom through clustering. (a) The most common approach to coarse graining the description of an ecosystem is by merging branches of a phylogenetic tree. (b) Elementary clustering operation where the abundances of two rabbit varieties are combined into a single degree of freedom.

Figure 3

For a well-clustered set of phenotypes, the eigenmode representation captures the hierarchy of phenotype similarity. (a) Pathway presence matrix for 12 phenotypes, generated as variations on three core phenotypes (colored lines); phenotypes carrying a given pathway (shown in yellow) are able to metabolize the respective resource. The tree represents hierarchical clustering based on Hamming distance. The dotted transect corresponds to the clear grouping into three clusters. Under MacArthur's model, resource competition in this ecosystem leads to a unique stable equilibrium. (b) Spectral structure of the ecosystem shown in (a), in the vicinity of its equilibrium point. Shown on the left are the eigenvalues of the Jacobian. All eigenvalues are negative, corresponding to a stable equilibrium; shown is the absolute value. On the right are the eigenvectors, ordered by decreasing $\left|\lambda \right|$; each is a linear combination of 12 phenotypes and is difficult to interpret directly. (c) Same eigenvectors, projected into pathway expression space. It is now clear that the three dominant modes span the three core phenotypes [colored lines as in (a)]. The fourth mode (arrowhead) corresponds to a subdivision of the first cluster [compare with (a)].

Figure 4

Smooth interpolation between two unrelated clustering patterns into, respectively, two and three effective species. (a) Pathway presence matrix [same format as in Fig. 3] for 11 phenotypes. Their preference for resources 1–3 induces a grouping into three clusters, but the remaining pathways induce a conflicting clustering pattern (with only two groups). (b) If the supply of resources 1–3 is low, community dynamics exhibits two dominant modes, reflecting the two-cluster structure. (c) As the supply of these resources is increased, the preference for resources 1–3 becomes the more relevant clustering criterion for describing the dynamics. (d) The same 11 phenotypes now behave as a community of three effective species. Unlike a speciation event, where the uncertainty in defining the number of species is merely a matter of the desired level of detail (cf. Fig. 3), the intermediate regime of (c) interpolates between unrelated clustering patterns (not nested).

Figure 5

Constructing a model case of an ecology without species. (a) Multipatch extension of MacArthur's resource competition model. Externally supplied resources are split between $P$ patches harboring separate communities (here $P=3$). Patch boundaries are assumed to be (weakly) permeable to resources, but not organisms (see [41] for details). In this cartoon, phenotypes are represented by circles; size signifies abundance, while colors correspond to resources consumed. (b) Phenotype-phenotype interaction matrix for a particular realization of the model with $N=20$ resources and $P=15$ patches; the 298 coexisting phenotypes are ordered by patch. Organisms in the same patch interact more strongly than across patches, leading to a block-diagonal structure. (c) The top $P$ eigenmodes reflect the $P$-patch structure of the habitat. Modes 2 through $P$ have vanishingly small projection into the pathway expression space: they represent interpatch dynamics and are hidden from an external observer who cannot resolve individual patches. (d) The shape of the eigenvalue distribution is independent of $P$ (left); modes hidden from an external observer (2 through $P$) are omitted. The unique dominant mode is the collective mode (arrowhead). The remainder of the spectrum follows a dense distribution with no gap, reflecting the unstructured background of interacting phenotypes.

Figure 6

Weakly structured ecology as a perturbation of the no-species regime. (a) When the phenotype pool is modified to introduce an anticorrelation between the first and last pathways, the spectrum acquires a mode reflecting this structure (highlighted). This new mode is the dominant observable mode (after the collective mode). (b) The leading observable eigenmodes remain at the same position in the spectrum (arrowheads) and retain their structure (right). The rest of the spectrum follows the same distribution as in the unstructured regime [shaded; compare with Fig. 5].