Fraser et al. (Reports, 17 July 2015, p. 302) report a unimodal relationship between productivity and species richness at regional and global scales, which they contrast with the results of Adler et al. (Reports, 23 September 2011, p. 1750). However, both data sets, when analyzed correctly, show clearly and consistently that productivity is a poor predictor of local species richness

Adler, Peter

Anderson, T.

Bakker, Jonathan

Biederman, Lori

Borer, Elizabeth

Brown, Cynthia

Buckley, Yvonne

Chu, Chengjin

Collins, Scott

Crawley, Michael

Fay, Philip

Firn, Jennifer

Grace, James

Gruner, Daniel

Hagenah, Nicole

Harpole, W.

Hautier, Yann

Seabloom, Eric

Tredennick, Andrew

Williams, Ryan

English

Fraser et al. (Reports, 17 July 2015, p. 302) report a unimodal relationship between productivity and species richness at regional and global scales, which they contrast with the results of Adler et al. (Reports, 23 September 2011, p. 1750). However, both data sets, when analyzed correctly, show clearly and consistently that productivity is a poor predictor of local species richness.This article is published as Tredennick, Andrew T., Peter B. Adler, James B. Grace, W. Stanley Harpole, Elizabeth T. Borer, Eric W. Seabloom, T. Michael Anderson et al. "Comment on “Worldwide evidence of a unimodal relationship between productivity and plant species richness”." Science 351, no. 6272 (2016): 457-457. doi: 10.1126/science.aad623.</p

Digital Repository @ Iowa State University (ISU)

TECHNICAL COMMENT◥PLANT ECOLOGYComment on “Worldwide evidence of aunimodal relationship betweenproductivity and plant species richness”Andrew T. Tredennick,1*† Peter B. Adler,1† James B. Grace,2† W. Stanley Harpole,3†Elizabeth T. Borer,4† Eric W. Seabloom,4† T. Michael Anderson,5 Jonathan D. Bakker,6Lori A. Biederman,7 Cynthia S. Brown,8 Yvonne M. Buckley,9 Chengjin Chu,10 Scott L. Collins,11Michael J. Crawley,12 Philip A. Fay,13 Jennifer Firn,14 Daniel S. Gruner,15 Nicole Hagenah,16Yann Hautier,17 Andy Hector,18 Helmut Hillebrand,19 Kevin Kirkman,16Johannes M. H. Knops,20 Ramesh Laungani,21 Eric M. Lind,4 Andrew S. MacDougall,22Rebecca L. McCulley,23 Charles E. Mitchell,24 Joslin L Moore,25 John W. Morgan,26John L. Orrock,27 Pablo L. Peri,28 Suzanne M. Prober,29 Anita C. Risch,30Martin Schütz,30 Karina L. Speziale,31 Rachel J. Standish,32 Lauren L. Sullivan,4Glenda M. Wardle,33 Ryan J. Williams,34 Louie H. Yang35Fraser et al. (Reports, 17 July 2015, p. 302) report a unimodal relationship betweenproductivity and species richness at regional and global scales, which they contrast withthe results of Adler et al. (Reports, 23 September 2011, p. 1750). However, both data sets,when analyzed correctly, show clearly and consistently that productivity is a poor predictorof local species richness.Fraser et al. (1) collected a worldwide dataset to examine the relationship betweenproductivity and species richness at globaland local scales. They present their resultsas a direct contrast with the results ofAdler et al. (2). However, their presentationobscures substantial areas of agreement, andwhere results between the two studies do differ,problems in Fraser et al.’s statistical analysisamplify the apparent differences.The most important area of agreement is thelow explanatory power of the “humped-backmodel” (HBM), in which species richness peaksat intermediate productivity and declines at lowand high productivity. Fraser et al. fit a bivariaterelationship between productivity and diversitythat accounts for less than 1% of the observedvariation in species richness in their data (Table 1,marginal R2s for the Fraser et al. data set). Thesame is true for an analysis of the Adler et al.data set using a generalized linear mixed model(GLMM) with a block nested within-site random-effects structure (Table 1, marginal R2s for theAdler et al. data set). Thus, the analyses in bothAdler et al. and Fraser et al. demonstrate thatproductivity is an uninformative predictor ofrichness for most grasslands. A combined anal-ysis using both data sets yields similar results(Table 1).A second point of agreement is the difficultyof inferring process from bivariate patterns. TheHBM can arise through a wide array of mech-anisms (3, 4), meaning that the detection of aunimodal pattern does not provide evidence forany particular mechanism.Adler et al. argued, “[e]cologists should focuson fresh, mechanistic approaches to understand-ing the multivariate links between productivityand richness” (2). Fraser et al. also concluded“more work is needed to determine the under-lying causal mechanisms that drive the uni-modal pattern” and called for “additional effortsto understand the multivariate drivers of speciesrichness.”The key disagreement between Fraser et al.and Adler et al. concerns the statistical signifi-cance of the quadratic term that determines thedownward concavity of the richness productivityrelationship. Adler et al. found little evidence fora concave-down relationship at the site scale (2%of 48 sites) [figure 2 in (2)] and at the globalscale reported a significant effect but noted thatit was sensitive to choices about which sites toinclude in the analysis [figure 3 in (2)]. In con-trast, Fraser et al. found that 68% of 28 site-levelrelationships were significantly concave-down[figure 2A in (1)], and in a global extent regres-sion, across all sites, the negative quadratic termhad a significant, and robust, P value. However,their analysis at the site level is flawed, and thepresentation of the global regression in theirmain figure is misleading.The site-level regressions reported by Fraseret al. and displayed in their figure 2A do not in-clude the proper random-effects structure. An im-portant feature of the Fraser et al. design wasexplicitly selecting areas (i.e., grids) to sampleacross productivity gradients within sites, whereasAdler et al. located blocks of plots randomly withrespect to local productivity gradients. To properlyreflect their sampling design, in which each “grid”of quadrats was located at one point along thewithin-site productivity gradient, each site-levelRESEARCHSCIENCE sciencemag.org 29 JANUARY 2016 • VOL 351 ISSUE 6272 457-a1Department of Wildland Resources and the Ecology Center,Utah State University, 5230 Old Main, Logan, UT 84322,USA. 2U.S. Geological Survey, Wetland and AquaticResearch Center, 700 Cajundome Boulevard, Lafayette,LA 70506, USA. 3Department of Physiological Diversity,Helmholtz Center for Environmental Research – UFZ,Permoserstrasse 15, 04318 Leipzig, Germany. 4Departmentof Ecology, Evolution, and Behavior, University of Minnesota,St. Paul, MN 55108, USA. 5Department of Biology,Wake Forest University, Box 7325 Reynolda Station,Winston-Salem, NC 27109, USA. 6School of Environmentaland Forest Sciences, University of Washington, 3501NE 41st Street, Box 354115, Seattle, WA 98195, USA.7Ecology, Evolution and Organismal Biology, lowa StateUniversity, 251 Bessey Hall, Ames, IA 50010, USA.8Department of Bioagricultural Sciences and PestManagement, Colorado State University, 307 UniversityAvenue, Fort Collins, CO 80523, USA. 9School of NaturalSciences, Trinity College Dublin, University of Dublin,Zoology, Dublin 2, Ireland. 10School of Life Sciences,Sun Yat-sen University, Xingang Xi Road 135, Guangzhou,510275, China. 11Department of Biology, University of NewMexico, Albuquerque, NM 87131, USA. 12Department ofBiology, Imperial College London, Silwood Park, Ascot,SL5 7PY, UK. 13Grassland, Soil, and Water ResearchLaboratory, USDA-ARS, 808 East Blackland Road, Temple,TX 76502, USA. 14School of Earth, Environmental andBiological 42 Sciences, Queensland University of Technology(QUT), Gardens Point, Brisbane, Queensland, Australia, 4001.15Department of Entomology, University of Maryland, 4112Plant Sciences, College Park, MD 20742, USA. 16School ofLife Sciences, University of KwaZulu-Natal, 1 Carbis Road,Pietermaritzburg, 3201, South Africa. 17Department ofBiology, Ecology and Biodiversity group, Utrecht University,Padualaan 8, 3584 CH Utrecht, Netherlands. 18Department ofPlant Sciences, University of Oxford, South Parks Road,Oxford, OX1 3RB, UK. 19Institute for Chemistry and Biologyof the Marine Environment, Carl-von-Ossietzky UniversityOldenburg, Schleusenstrasse 1, 26382 Wihlhemshaven,Germany. 20School of Biological Sciences, University ofNebraska, 211 Manter Hall, Lincoln, NE 68588, USA.21Biology Department, Doane College, 1014 Boswell Avenue,Crete, NE 68333, USA. 22Department of Integrative Biology,University of Guelph, 50 Stone Road, Guelph, Ontario,Canada N1G 2W1. 23Department of Plant and Soil Science,University of Kentucky, N-222D Ag Science North, Lexington,KY 40546-0091, USA. 24Department of Biology, University ofNorth Carolina at Chapel Hill, CB#3280, Chapel Hill, NC27599, USA. 25School of Biological Sciences, MonashUniversity, Clayton Campus, Wellington Road, Clayton 3800,Victoria, Australia. 26Department of Ecology, Environmentand Evolution, La Trobe University, Kingsbury Drive,Bundoora 3086, Victoria, Australia. 27Department of Zoology,University of Wisconsin, 430 Lincoln Drive, Madison, WI53706, USA. 28Department of Forestry, Agriculture and Water,Southern Patagonia National University-INTA-CONICET, CC332 (CP 9400), Río Gallegos, Santa Cruz, Patagonia,Argentina. 29Commonwealth Scientific and IndustrialResearch Organisation Land and Water, Private Bag 5,Wembley, WA 6913, Australia. 30Community Ecology, SwissFederal Institute for Forest, Snow and Landscape Research,Zuercherstrasse 111, 8903 Birmensdorf, Switzerland.31Department of Ecology, INIBIOMA (CONICET-UNCO),Quintral 1250, Bariloche (8400), Rio Negro, Argentina.32School of Veterinary and Life Sciences, MurdochUniversity, Perth, Western Australia, 90 South Street,Murdoch, Western Australia 6150. 33School of BiologicalSciences, University of Sydney, Heydon-Laurence Building,A08, University of Sydney, Sydney, NSW, 2006, Australia.34Agricultural and Biosystems Engineering, Iowa StateUniversity, Ames, IA, USA. 35Department of Entomology andNematology, University of California, Davis, One ShieldsAvenue, Davis, CA 95616, USA.*Corresponding author. E-mail: atredenn@gmail.com †Coreauthors that led the analysis and wrote the paper. All otherauthors, listed alphabetically, are Nutrient Network membersand/or coauthors of Adler et al. (2011) who sign our Comment insupport to show consensus among the Nutrient Network.on December 13, 2017 http://science.sciencemag.org/Downloaded from regression requires a random effect of “grid” toaccount for the inherent correlation among plotsnested within a sampling grid. We reran the anal-ysis of Fraser et al. with the grid random effectincluded (5), except for one site (6). When theproper statistical model is used, we find that only29% of 28 site-level regressions are significantlyconcave-down (Fig. 1).Fraser et al. correctly account for their samplingdesign at the global extent by using a GLMMwithgrid nested within site, as reported in their table 1.However, in their figure 2A, they plot the muchmore compelling fit from the statistical modelwithout the random effects. Although still sig-nificant (P < 0.0001), the valid relationship ismuch weaker than the relationship presented byFraser et al. (Fig. 1, heavy black line, and Table 1).Despite Fraser et al.’s assertion that theirresults are diametrically opposed to those pres-ented in Adler et al., the degree of concordanceis impressive. In both data sets, the variance ex-plained by the addition of a quadratic term isvirtually indistinguishable from that of a linearmodel (Table 1). In fact, in both data sets the ran-dom effects of site and grid (block for Adler et al.)explain much more of the variation in speciesrichness than productivity, the supposed mech-anistic driver of species richness (Table 1). Further-more, with the appropriate statistical treatment,the main difference in our results—the strength ofevidence for a significant quadratic term—appearssmaller.A continued focus on this bivariate relation-ship hinders progress toward understanding theunderlying multivariate causal relationship (4)and the development of truly predictive models.It is time to focus on effect sizes and varianceexplained rather than just P values. The title ofAdler et al.’s paper, “Productivity is a poor pre-dictor of plant species richness,” would be aperfectly appropriate title for the Fraser et al.paper, too.457-a 29 JANUARY 2016 • VOL 351 ISSUE 6272 sciencemag.org SCIENCEFig. 1. Species richness as a function of bio-mass production at the site level (colored lines)and at the global extent (heavy black line).Theseregressions are the same as presented by Fraseret al. except that we included a grid random effectfor the site-level regressions, and we show theproper global extent regression line from a GLMMwith grid nested within site. Nonsignificant regres-sion fits are not plotted.Table 1. Results from global-extent GLMMs for both data sets.Results from regressions with and without a quadratic effect of productivity on species richnessacross all sites. Both models include a random-effects structure of grid nested within site (Fraser et al.) or block nested within site (Adler et al.). Marginal andconditional R2 values estimated using (7, 8). For the combined analysis, we use the same grid (or block) nested within-site random-effects structure and alsoinclude a “study” random effect.Data set Model typeMarginal R2(variance explained byfixed effects)Conditional R2(variance explained byfixed + random effects)Root mean squareerror (in units ofspecies number)Fraser et al. Linear 0.00007 0.84 8.5.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .Fraser et al. Quadratic 0.009 0.84 8.3.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .Adler et al. Linear 0.0007 0.79 7.7.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .Adler et al. Quadratic 0.001 0.78 7.7.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .Combined Linear 0.00005 0.82 8.4.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .Combined Quadratic 0.003 0.82 8.3.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .RESEARCH | TECHNICAL COMMENTon December 13, 2017 http://science.sciencemag.org/Downloaded from REFERENCES AND NOTES1. L. H. Fraser et al., Science 349, 302–305 (2015).2. P. B. Adler et al., Science 333, 1750–1753 (2011).3. J. B. Grace et al., Science 335, 6075 (2012).4. J. B. Grace et al., Nature 529, 10.1038/nature16524 (2016).5. We used the “lme4” package in the statistical programmingenvironment R to fit the GLMMs at the site and global extents.Some models struggled to converge on coefficient estimates, awell-known issue with mixed-effects models. We conducted theanalyses using different optimizers to make sure that our resultsare robust (they are), and we did our own checks of modeldiagnostics to make sure that the warnings could be ignored(they could). Lastly, we fit a hierarchical mixed-effects modelusing a Bayesian approach to make sure we obtained consistentresults (we did). All of our analyses and results can be found onGitHub at http://github.com/atredennick/prodDiv and asrelease v0.1, https://github.com/atredennick/prodDiv/tag/v0.16. There are four sites, out of 28, that have only two grids. In onlyone case did this result in inadequate fits of the GLMM modelwith a “grid” random effect. We therefore fit that one site with ageneralized linear model with no random effects.7. S. Nakagawa, H. Schielzeth, Methods Ecol. Evol. 4, 133–142 (2013).8. J. Lefcheck, R-squared for generalized linear mixed-effectsmodels (2014); https://github.com/jslefche/rsquared.glmmACKNOWLEDGMENTSWe thank L. Fraser and colleagues for making their analyses anddata openly available. D. Johnson, USGS, provided comments onan earlier version of the manuscript. J.B.G. was supported by theUSGS Ecosystems and Climate and Land Use Change Programs.The use of trade, firm, or product names is for descriptivepurposes only and does not imply endorsement by the U.S.Government. USDA is an equal opportunity employer. We alsoacknowledge support from the National Science FoundationResearch Coordination Network (NSF-DEB-1042132) andLong Term Ecological Research (NSF-DEB-1234162 to CedarCreek LTER) programs, and the Institute on the Environment(DG-0001-13).16 October 2015; accepted 17 December 201510.1126/science.aad6236SCIENCE sciencemag.org 29 JANUARY 2016 • VOL 351 ISSUE 6272 457-aRESEARCH | TECHNICAL COMMENTon December 13, 2017 http://science.sciencemag.org/Downloaded from species richness''Comment on ''Worldwide evidence of a unimodal relationship between productivity and plantLouie H. YangRisch, Martin Schütz, Karina L. Speziale, Rachel J. Standish, Lauren L. Sullivan, Glenda M. Wardle, Ryan J. Williams and McCulley, Charles E. Mitchell, Joslin L Moore, John W. Morgan, John L. Orrock, Pablo L. Peri, Suzanne M. Prober, Anita C.Hillebrand, Kevin Kirkman, Johannes M. H. Knops, Ramesh Laungani, Eric M. Lind, Andrew S. MacDougall, Rebecca L. Michael J. Crawley, Philip A. Fay, Jennifer Firn, Daniel S. Gruner, Nicole Hagenah, Yann Hautier, Andy Hector, HelmutAnderson, Jonathan D. Bakker, Lori A. Biederman, Cynthia S. Brown, Yvonne M. Buckley, Chengjin Chu, Scott L. Collins, Andrew T. Tredennick, Peter B. Adler, James B. Grace, W. Stanley Harpole, Elizabeth T. Borer, Eric W. Seabloom, T. MichaelDOI: 10.1126/science.aad6236 (6272), 457.351Science ARTICLE TOOLS http://science.sciencemag.org/content/351/6272/457.1CONTENTRELATED http://science.sciencemag.org/content/sci/349/6245/302.fullhttp://science.sciencemag.org/content/sci/351/6272/457.2.fullREFERENCEShttp://science.sciencemag.org/content/351/6272/457.1#BIBLThis article cites 5 articles, 2 of which you can access for freePERMISSIONS http://www.sciencemag.org/help/reprints-and-permissionsTerms of ServiceUse of this article is subject to the  is a registered trademark of AAAS.Sciencelicensee American Association for the Advancement of Science. No claim to original U.S. Government Works. The title Science, 1200 New York Avenue NW, Washington, DC 20005. 2017 © The Authors, some rights reserved; exclusive (print ISSN 0036-8075; online ISSN 1095-9203) is published by the American Association for the Advancement ofScience on December 13, 2017 http://science.sciencemag.org/Downloaded from 

Comment on “Worldwide evidence of a unimodal relationship between productivity and plant species richness”

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Comment on “Worldwide evidence of a unimodal relationship between productivity and plant species richness”

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