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Higher-order interactions capture unexplained complexity in diverse communities

Nature Ecology & Evolution volume 1, Article number: 0062 (2017) Cite this article

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Abstract

Natural communities are well known to be maintained by many complex processes. Despite this, the practical aspects of studying them often require some simplification, such as the widespread assumption that direct, additive competition captures the important details about how interactions between species impact community diversity. More complex non-additive ‘higher-order’ interactions are assumed to be negligible or absent. Notably, these assumptions are poorly supported and have major consequences for the accuracy with which patterns of natural diversity are modelled and explained. We present a mathematically simple framework for incorporating biologically meaningful complexity into models of diversity by including non-additive higher-order interactions. We further provide empirical evidence that such higher-order interactions strongly influence species’ performance in natural plant communities, with variation in seed production (as a proxy for per capita fitness) explained dramatically better when at least some higher-order interactions are considered. Our study lays the groundwork for a long-overdue shift in how species interactions are used to study the diversity of natural communities.

Interactions between entities are central to the functionality of systems across science, whether socioeconomic, atomic, chemical or biological. In natural systems, for example, species interactions are biologically and mathematically integral to explaining patterns of diversity1–4. Mechanistically, it is believed that interactions between species, and competitive interactions in particular, are of central importance to coexistence and food-web dynamics and are core drivers of community-level diversity1,3,5–7. Typically, individual-based fitness models are used to incorporate the effects of species interactions into coexistence and diversity models7–11; this approach is commonly used in plant and marine-focused studies7,11–13 while also being conceptually appropriate for other types of communities5,8. Despite their extensive applicability, these models often do a surprisingly poor job of accurately explaining empirically observed fitness outcomes14–16. This may be because of the common assumption that additive competitive interactions between species pairs capture all of the important details of species interactions and are thus the only interactions typically incorporated into fitness models4,17–19.

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Figure 1: Effects of direct interactions and HOIs on individual fecundity.
Figure 2: Examples of predicted fecundities for three species pairs using direct-interactions-only (dashed line) and the full HOI-inclusive model (solid line).
Figure 3: Decomposition of the observed impacts of direct and higher-order effects on the fecundity of six focal species.

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Acknowledgements

This project was made possible by funding awarded to M.M.M. by the Australian Research Council (DP140100574 and FT140100498) and to D.B.S. from the Royal Society of New Zealand (UOC-1101 and a Rutherford Discovery Fellowship). We thank H. R. Lai, X. Loy, C. Wainwright and J. HilleRisLambers for help with data collection and J. HilleRisLambers, J. Dwyer, J. Tylianakis and the Mayfield and Stouffer labs for constructive comments. We also thank X. Loy for the art used to create Supplementary Fig. 1.

Author information

Authors and Affiliations

  1. The University of Queensland, School of Biological Sciences, Brisbane, 4072, Queensland, Australia

    Margaret M. Mayfield

  2. Centre for Integrative Ecology, University of Canterbury, School of Biological Sciences, Christchurch, Canterbury 8041, New Zealand

    Daniel B. Stouffer

Authors
  1. Margaret M. Mayfield
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  2. Daniel B. Stouffer
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Contributions

Authors are equal contributors to this paper. M.M.M. and D.B.S. conceived of the project and the framework together. M.M.M. collected and provided all data (with acknowledged help) and D.B.S. conducted all analyses. M.M.M. led the joint effort of writing the manuscript.

Corresponding authors

Correspondence to Margaret M. Mayfield or Daniel B. Stouffer.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Methods; Supplementary Figs 1–3; Supplementary Tables 1–4; Supplementary References. (PDF 2093 kb)

Supplementary Data 1

Full dataset analysed in this study. This file contains an R list object, called fecundity.data, made up of six data frames (one per focal species). Within these data frames, each row (with unique identifier) contains the data for a single focal plant. The first four columns provide the following information: “Seed”: the number of seeds produced by focal plant; “focal”: focal species name; “site”: site code (B = Bendering, K = Kunjin); and “quadrat”: quadrat number. All remaining columns report densities of each potential competitor species, listed by name. Values in these “competitor” columns are abundances within the 7.5 cm radius “neighbourhood” around the focal plant. This file is also accessible from Dryad. (ZIP 0 kb)

Supplementary Data 2

This Rdata file contains an example dataset usable with Supplementary Code 2. Note that this file does not include all of the data used to generate the results presented in this paper but is simplified to better help users become familiar with our model-fitting R code. Our full dataset is available through Dryad and as Supplementary Data 1. (ZIP 14 kb)

Supplementary Code 1

This file includes the model-fitting code for our regression framework. It includes the function needed to fit fecundity models based on the following model formulations: the full and intermediate forms of the negative binomial model (Table 1 and Supplementary Table 3), a Poissonian form (not included in results), the negative binomial with quadrat included as a random effect, and the linear form and the inverse forms all presented in Supplementary Table 2. Notes for running this code with our full dataset (Supplementary Data 1) or the simpler and smaller example dataset (Supplementary Data 2) are provided at the beginning of the files. (TXT 6 kb)

Supplementary Code 2

This file provides a sample workflow for data analysis from this paper. The provided code fits the null-no competition, direct-competitive only and the full HOI-inclusive negative binomial models (equation (1)). It is designed to run with the example data file (Supplementary Data 2). This code runs much faster (when using the example data) than Supplementary Code 1 with the full dataset. (TXT 0 kb)

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Mayfield, M., Stouffer, D. Higher-order interactions capture unexplained complexity in diverse communities. Nat Ecol Evol 1, 0062 (2017). https://doi.org/10.1038/s41559-016-0062

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