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Predicting coexistence in experimental ecological communities

A Publisher Correction to this article was published on 09 January 2020

This article has been updated


The study of experimental communities is fundamental to the development of ecology. Yet, for most ecological systems, the number of experiments required to build, model or analyse the community vastly exceeds what is feasible using current methods. Here, we address this challenge by presenting a statistical approach that uses the results of a limited number of experiments to predict the outcomes (coexistence and species abundances) of all possible assemblages that can be formed from a given pool of species. Using three well-studied experimental systems—encompassing plants, protists, and algae with grazers—we show that this method predicts the results of unobserved experiments with high accuracy, while making no assumptions about the dynamics of the systems. These results demonstrate a fundamentally different way of building and quantifying experimental systems, requiring far fewer experiments than traditional study designs. By developing a scalable method for navigating large systems, this work provides an efficient approach to studying highly diverse experimental communities.

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Fig. 1: Predicting unobserved experimental outcomes.
Fig. 2: Results for three experimental systems.
Fig. 3: Comparison of B within the plant and herbivore–algae datasets.
Fig. 4: Comparison of B in the protist system across the six temperatures.
Fig. 5: Predicting multiple endpoints out-of-fit.

Data availability

The data and code needed to replicate the central findings of this work are available at

Change history

  • 09 January 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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We thank S. Kuebbing, C. Rakowski, F. Pennekamp and O. Petchey for making their data available and for comments on earlier drafts of this manuscript. We thank C. Serván, M. Pascual, J. Bergelson, E. Baskerville, G. Barabás and E. Friedlander for assistance and suggestions throughout this study.

Author information




D.S.M., Z.R.M. and S.A. conceived this study and developed the methods. D.S.M. collected and analysed the data, and wrote the supplementary data analysis. S.A. and Z.R.M. wrote the Supplementary Information and Methods and implemented the simulations. All authors contributed to the writing of the manuscript and assisted with revisions.

Corresponding author

Correspondence to Daniel S. Maynard.

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The authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Simulation results for a Generalized Lotka-Volterra (GLV) competitive system.

For each combination of the four competitors (c1 to c4, colours), we ran 96 simulations starting from different initial conditions. Each panel shows the location of the simulations’ endpoints (solid circles), as well as the true location of the equilibria for the system (crosses, computed analytically). Experiments resulting in a lack of coexistence are represented as half-points at the bottom of the graph. The predictions obtained using our method are reported using open symbols. There are two cases: we use circles for predictions of (locally) stable endpoints, and triangles for unstable ones; the stability is calculated under the assumption of Lotka-Volterra dynamics and equal growth rates. For this system, as expected, we recover a perfect fit for the positive densities. We can also correctly predict the lack of coexistence among triplets. We predict perfectly the position of the four-species equilibrium, and correctly classify it as unstable, despite having used growth rates that differ substantially from each other.

Extended Data Fig. 2 Simulation results for a GLV competitive system exhibiting a limit cycle.

Colours and symbols are as in Fig. 17. Notable features of this system are: competitors might (c1-c2, c2-c3) or might not (c1-c3, c1-c4) coexist in pairs. However, in one case a feasible but unstable equilibrium exists (c1-c3, correctly predicted by our method), while in the other there is no feasible equilibrium (c1-c4, also correctly predicted). The system including c1-c3-c4 shows dependence on initial conditions (some trajectories collapse to another system, while others converge to equilibrium), signaling a locally (but not globally) stable equilibrium. The method correctly identifies the position of the 4-species equilibrium surrounded by the limit cycle. However, it suggests stability for the equilibrium, while it must be unstable to give rise to the stable limit cycle. The misclassification stems from the fact that in the calculation of stability, we consider growth rates to be equal (because we cannot infer growth rates from endpoints), while this is not the case here.

Extended Data Fig. 3 Simulation results for competition with Allee effects, in which competitors cannot grow when rare.

This system exhibits multistability in all cases (half-points at the bottom of each graph signal trajectories that resulted in extinctions). Despite the fact that the model contains cubic terms (while our method can deal only with quadratic terms), the in-fit is excellent, in all cases fitting the location of the endpoints perfectly. Experiments in which the species do not coexist are however misclassified—while there exist equilibria close to the prediction, they are unstable, rather than stable as predicted by our method.

Extended Data Fig. 4 Simulation results for a system of facultative mutualism between two classes of competitors.

Plants are denoted by p, and animals are denoted by a. Despite the non-linear functional response, the method predicts the location of the endpoints (all characterized by equilibrium dynamics) almost perfectly. The method also correctly predicts the lack of coexistence between the two plants (panel p1-p2).

Extended Data Fig. 5 Simulation results for a consumer-resource system.

Two resources and two consumers are simulated in all possible combinations, giving rise to cases of coexistence at equilibrium, stable limit cycles, or extinctions. In all cases, the proposed method predicts the location of the equilibria of the nonlinear system quite perfectly, making the correct inference for all cases in which species cannot coexist.

Extended Data Fig. 6 Simulation results for a system characterized by higher-order interactions.

Despite the strong effect of HOIs, the recovered solution is close to all endpoints. Moreover, the method correctly predicts that coexistence between c1 and c2, or c1, c2 and c3 is precluded. The method however predicts coexistence between two triplets, despite simulations showing that either no feasible equilibrium exists, or it is unstable.

Extended Data Fig. 7 Quality of fit for different experimental designs.

We simulated a 6-species GLV model, in which all 63 possible assemblages lead to coexistence. We measured abundances at these endpoints by adding noise, and producing five ‘replicates’. For each design, we use the specified number of assemblages to fit the model, and predict out-of-fit the abundance of all species at all other endpoints. Designs that produce qualitatively wrong predictions (that is, predicting a lack of coexistence for assemblages that do in fact coexist) are represented as vertical bars at the bottom of each boxplot. The horizontal dashed line marks the performance of the monoculture + leave-one-outs design, which fares among the best despite using only 12 assemblages to predict the remaining 51.

Extended Data Fig. 8 The quality-of-fit for the protist system at 15 °C as a function of the sampling day.

Rather than sample the community at days 15-17, as in the main text, we ‘ended’ the experiment at the indicated day, ±2 days, and fit the model with the corresponding endpoints. These results demonstrate that there is a clear initial period where the model fits poorly due to transient dynamics; followed by a stable period between days 10 and 20 where the approach performs well; followed by a period where the quality of fit starts to deteriorate as the species decline in abundances. The point in red denotes the point used in the main analysis, independently identified by quantifying when total biomass of the community stabilized.

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Supplementary Figs. 1–26, methods and data analysis.

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Maynard, D.S., Miller, Z.R. & Allesina, S. Predicting coexistence in experimental ecological communities. Nat Ecol Evol 4, 91–100 (2020).

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