@article {Byrnes2022.03.17.484802,
	title = {Understandable Multifunctionality Measures Using Hill Numbers},
	journal = {bioRxiv},
	year = {2022},
	publisher = {Cold Spring Harbor Laboratory},
	abstract = {In ecology, multifunctionality measures the simultaneous provision of multiple ecosystem functions. If species diversity describes the variety of species that together build the ecosystem, multifunctionality attempts to describe the variety of functions these species perform. A range of methods have been proposed to quantify multifunctionality, successively attempting to alleviate problems that have been identified with the previous methods. This has led to a proliferation of more-or-less closely related metrics which, however, lack an overarching theoretical framework. Here we borrow from the comprehensive framework of species diversity to derive a new metric of multifunctionality. Analogously to the effective number of species used to quantify species diversity, the metric we propose is influenced both by the number of functions as well as, crucially, the evenness of performance levels across functions. In addition, the effective multifunctionality also considers the average level at which the functions are performed. The result is a measure of the cumulative performance of the system were all functions provided equally. The framework allows for the inclusion of the correlation structure among functions, thus allowing to account for non-independence between functions. We show that the average metric is a special case of the newly proposed metric when all functions are uncorrelated and performed at equal levels. We hope that by providing a new metric of multifunctionality anchored in the rigorous framework of species diversity based on effective numbers, we will overcome the considerable skepticism that the larger community of ecologists has built against indices of multifunctionality. We thereby hope to help popularize this important concept which, as biological diversity, describes a fundamental property of ecosystems and thus lies at the heart of ecology.Competing Interest StatementThe authors have declared no competing interest.},
	doi = {10.1101/2022.03.17.484802},
	url = {https://www.biorxiv.org/content/early/2022/03/19/2022.03.17.484802},
	author = {Byrnes, Jarrett E. K. and Roger, Fabian and Bagchi, Robert}
}
@article {hautier_general_2020,
	title = {General destabilizing effects of eutrophication on grassland productivity at multiple spatial scales},
	journal = {Nature Communications},
	volume = {11},
	number = {1},
	year = {2020},
	month = {dec},
	pages = {5375},
	abstract = {Abstract Eutrophication is a widespread environmental change that usually reduces the stabilizing effect of plant diversity on productivity in local communities. Whether this effect is scale dependent remains to be elucidated. Here, we determine the relationship between plant diversity and temporal stability of productivity for 243 plant communities from 42 grasslands across the globe and quantify the effect of chronic fertilization on these relationships. Unfertilized local communities with more plant species exhibit greater asynchronous dynamics among species in response to natural environmental fluctuations, resulting in greater local stability (alpha stability). Moreover, neighborhood communities that have greater spatial variation in plant species composition within sites (higher beta diversity) have greater spatial asynchrony of productivity among communities, resulting in greater stability at the larger scale (gamma stability). Importantly, fertilization consistently weakens the contribution of plant diversity to both of these stabilizing mechanisms, thus diminishing the positive effect of biodiversity on stability at differing spatial scales. Our findings suggest that preserving grassland functional stability requires conservation of plant diversity within and among ecological communities.},
	issn = {2041-1723},
	doi = {10.1038/s41467-020-19252-4},
	url = {https://www.nature.com/articles/s41467-020-19252-4},
	author = {Hautier, Yann and Zhang, Pengfei and Loreau, Michel and Wilcox, Kevin R. and Seabloom, Eric W. and Borer, Elizabeth T. and Byrnes, Jarrett E. K. and Koerner, Sally E. and Komatsu, Kimberly J. and Lefcheck, Jonathan S. and Hector, Andy and Adler, Peter B. and Alberti, Juan and Arnillas, Carlos A. and Bakker, Jonathan D. and Brudvig, Lars A. and Bugalho, Miguel N. and Cadotte, Marc and Caldeira, Maria C. and Carroll, Oliver and Crawley, Mick and Collins, Scott L. and Daleo, Pedro and Dee, Laura E. and Eisenhauer, Nico and Eskelinen, Anu and Fay, Philip A. and Gilbert, Benjamin and Hansar, Amandine and Isbell, Forest and Knops, Johannes M. H. and MacDougall, Andrew S. and McCulley, Rebecca L. and Moore, Joslin L. and Morgan, John W. and Mori, Akira S. and Peri, Pablo L. and Pos, Edwin T. and Power, Sally A. and Price, Jodi N. and Reich, Peter B. and Risch, Anita C. and Roscher, Christiane and Sankaran, Mahesh and Sch{\"u}tz, Martin and Smith, Melinda and Stevens, Carly and Tognetti, Pedro M. and Virtanen, Risto and Wardle, Glenda M. and Wilfahrt, Peter A. and Wang, Shaopeng}
}
