The output of a community model depends on how you set its parameters. Thus, analyses of specific parameter settings hardwire the results to specific ecological scenarios. Because more general answers are often of interest, one tradition is to give models a statistical treatment: one summarizes how model parameters vary across species, and then predicts how changing the summary, instead of the individual parameters themselves, would change model output. Arguably the best-known example is the work initiated by May, showing that the properties of a community matrix, encoding effects species have on each other near their equilibrium, determine stability (1,2). More recently, this statistical treatment has also been applied to one of community ecology’s more prickly and slippery subjects: community assembly, which deals with the question “Given some regional species pool, which species will be able to persist together at some local ecosystem?”. Summaries of how species grow and interact in this regional pool predict the fraction of survivors and their relative abundances, the kind of dynamics, and various kinds of stability (3,4). One common characteristic of such statistical treatments is the assumption of disorder: if species do not interact in too structured ways, simple and therefore powerful predictions ensue that often stand up to scrutiny in relatively ordered systems.
In their recent preprint, Miller, Clenet, et al. (5) subscribe to this tradition and consider tractable assembly scenarios (6) to study the outcome of assembly in a metacommunity. They recover a result of remarkable simplicity: roughly half of the species pool makes it into the final assemblage. Their vehicle is Tilman’s classic metacommunity model (7), where colonization rates are traded off with competitive ability. More precisely, in this model, one ranks species according to their colonization rate and attributes a greater competitive strength to lower-ranked species, which makes competition strictly hierarchical and thus departs from the disorder usually imposed by statistical approaches. The authors then leverage the simplicity of the species interaction network implied by this recursive setting to analytically probe how many species survive assembly. This turns out to be a fixed fraction that is distributed according to a Binomial with a mean of 0.5. While these results should not be extrapolated beyond the system at hand (4), they are important for two reasons. First, they imply that, within the framework of metacommunities driven by competition-colonization tradeoffs, richer species pools will produce richer communities: there is no upper bound on species richness, other than the one set by the raw material available for assembly. Second, this conclusion does not rely on simulation or equation solving and is, therefore, a hopeful sign of the palatability of the problem, if formalized in the right way. Their paper then shows that varying some of the settings does not change the main conclusion: changing how colonization rates distribute across species, and therefore the nature of the tradeoff, or the order with which species invade seems not to disrupt the big picture. Only when invaders are created “de novo” during assembly, a scenario akin to “de novo” mutation, a smaller fraction of species will survive assembly.
As always, logical extensions of this study involve complicating the model and then looking if the results stay on par. The manuscript cites switching to other kinds of competition-colonization tradeoffs, and the addition of spatial heterogeneity as two potential avenues for further research. While certainly of merit, alternative albeit more bumpy roads would encompass models with radically different behavior. Most notably, one wonders how priority effects would play out. The current analysis shows that different invasion orders always lead to the same final composition, and therefore the same final species richness, confirming earlier results from models with similar structures (6). In models with priority effects, different invasion orders will surely lead to different compositions at the end. However, if one only cares about how many (and not which) species survive, it is unsure how much priority effects will qualitatively affect assembly. Because priority effects are varied in their topological manifestation (8), an important first step will be to evaluate which kinds of priority effects are compliant with formal analysis.
1. May, R. M. (1972). Will a Large Complex System be Stable? Nature 238, 413–414. https://doi.org/10.1038/238413a0
2. Allesina, S. & Tang, S. (2015). The stability–complexity relationship at age 40: a random matrix perspective. Population Ecology, 57, 63–75. https://doi.org/10.1007/s10144-014-0471-0
3. Bunin, G. (2016). Interaction patterns and diversity in assembled ecological communities. Preprint at http://arxiv.org/abs/1607.04734.
4. Barbier, M., Arnoldi, J.-F., Bunin, G. & Loreau, M. (2018). Generic assembly patterns in complex ecological communities. Proceeding of the National Academy of Sciences, 115, 2156–2161. https://doi.org/10.1073/pnas.1710352115
5. Miller, Z. R., Clenet, M., Libera, K. D., Massol, F. & Allesina, S. (2023). Coexistence of many species under a random competition-colonization trade-off. bioRxiv 2023.03.23.533867, ver 3 peer-reviewed and recommended by PCI Ecology. https://doi.org/10.1101/2023.03.23.533867
6. Serván, C. A. & Allesina, S. (2021). Tractable models of ecological assembly. Ecology Letters, 24, 1029–1037. https://doi.org/10.1111/ele.13702
7. Tilman, D. (1994). Competition and Biodiversity in Spatially Structured Habitats. Ecology, 75, 2–16. https://doi.org/10.2307/1939377
8. Song, C., Fukami, T. & Saavedra, S. (2021). Untangling the complexity of priority effects in multispecies communities. Ecolygy Letters, 24, 2301–2313. https://doi.org/10.1111/ele.13870
DOI or URL of the preprint: https://doi.org/10.1101/2023.03.23.533867
Version of the preprint: 1
Both reviewers highlight the merits of the presented work, but also list a number of suggestions to strengthen the paper. These revolve around two aspects: (1) improving the link between the presented results and empirical systems; (2) explaining how and why the presented results differ from (or confirm) those already available in the published literature. I agree with these suggestions, and personally find the second aspect most important.