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.
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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.
The authors declare no competing financial interests.
Supplementary Methods; Supplementary Figs 1–3; Supplementary Tables 1–4; Supplementary References. (PDF 2093 kb)
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)
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)
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)
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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