A. Hector, Y. Hautier, P. Saner, L. Wacker, R. Bagchi, J. Joshi, M. Scherer-Lorenzen, E. M. Spehn, E. Bazeley-White, M. Weilenmann, M. C. Caldeira, P. G. Dimitrakopoulos, J. A. Finn, K. Huss-Danell, A. Jumpponen, C. P. Mulder, C. Palmborg, J. S. Pereira, A. S. D. Siamantziouras, A. C. Terry, A. Y. Troumbis, B. Schmid, and M. Loreau. 2010. General stabilizing effects of plant diversity on grassland productivity through population asynchrony and overyielding. Ecology 91:2213–2220.


Supplement

The data sets used in the paper with detailed descriptions.
Ecological Archives
E091-155-S1
.

Copyright


Authors
File list (downloads)
Description


Author(s)

Corresponding author: Andy Hector
Institute of Evolutionary Biology and Environmental Studies
University of Zurich
Winterthurerstrasse 190
CH-8057 Zurich
Switzerland
E-mail: ahector@uwinst.uzh.ch

Yann Hautier
Institute of Evolutionary Biology and Environmental Studies
University of Zurich
Winterthurerstrasse 190
CH-8057 Zurich
Switzerland

Philippe Saner
Institute of Evolutionary Biology and Environmental Studies
University of Zurich
Winterthurerstrasse 190
CH-8057 Zurich
Switzerland

Luca Wacker
Institute of Evolutionary Biology and Environmental Studies
University of Zurich
Winterthurerstrasse 190
CH-8057 Zurich
Switzerland

Robert Bagchi
Department of Zoology
University of Oxford
Tinbergen Building
South Parks Road
Oxford OX1 3PS
UK

Jasmin Joshi
Institute of Evolutionary Biology and Environmental Studies
University of Zurich
Winterthurerstrasse 190
CH-8057 Zurich
Switzerland
Secondary address:
Biodiversity Research/Systematic Botany
Institute of Biochemistry and Biology,
University of Potsdam
Maulbeerallee 1
D-14469 Potsdam
Germany

Michael Scherer-Lorenzen
University of Freiburg
Faculty of Biology, Geobotany
Schaenzlestrasse 1
D-79104 Freiburg
Germany

Eva M. Spehn
Institute of Botany
University of Basel
Schoenbeinstrasse 6
CH-4056 Basel
Switzerland

Ellen Bazeley-White
Natural Environmental Research Council (NERC)
Centre for Population Biology
Imperial College London
Silwood Park Campus
Ascot, Berkshire GB-SL57PY
UK

Maja Weilenmann
Institute of Evolutionary Biology and Environmental Studies
University of Zurich
Winterthurerstrasse 190
CH-8057 Zurich
Switzerland

Maria C. Caldeira
Centro de Estudos Florestais
Instituto Superior de Agronomia
Universidade Técnica de Lisboa
Tapada da Ajuda, 1349-017 Lisboa
Portugal

Panayiotis G. Dimitrakopoulos
Biodiversity Conservation Laboratory
Department of Environment
University of the Aegean
GR-811 00 Mytilene
Greece

John A. Finn
Teagasc
Environment Research Centre
Johnstown Castle
Wexford
Ireland

Kerstin Huss-Danell
Department of Agricultural Research for Northern Sweden
Swedish University of Agricultural Sciences (SLU)
SE-90183 Umeå
Sweden

Ari Jumpponen
Department of Forest Ecology and Management
Swedish University of Agricultural Sciences
S-90183 Umeå
Sweden
Secondary address: Department of Agricultural Research for Northern Sweden
Swedish University of Agricultural Sciences (SLU)
SE-90183 Umeå
Present address: Division of Biology
433 Ackert Hall
Kansas State University
Manhattan
Kansas 66506
USA

Christa P. Mulder
Department of Agricultural Research for Northern Sweden
Swedish University of Agricultural Sciences (SLU)
SE-90183 Umeå
Secondary address:
Department of Forest Ecology and Management
Swedish University of Agricultural Sciences
S-90183 Umeå
Sweden
Current address: Institute of Arctic Biology and Department of Biology and Wildlife
University of Alaska Fairbanks
Fairbanks
AK 99775
USA

Cecilia Palmborg
Department of Agricultural Research for Northern Sweden
Swedish University of Agricultural Sciences (SLU)
SE-90183 Umeå

João S. Pereira
Centro de Estudos Florestais
Instituto Superior de Agronomia
Universidade Técnica de Lisboa
Tapada da Ajuda, 1349-017 Lisboa
Portugal

Akis S.D. Siamantziouras
Biodiversity Conservation Laboratory
Department of Environment
University of the Aegean
GR-811 00 Mytilene
Greece

Andrew C. Terry
Department of Animal and Plant Sciences
University of Sheffield
South Yorkshire GB-S10 2TN
UK
Present address: Environment Department
University of York
Heslington
York YO10 5DD
UK

Andreas Y. Troumbis
Biodiversity Conservation Laboratory
Department of Environment
University of the Aegean
GR-811 00 Mytilene
Greece

Bernhard Schmid
Institute of Evolutionary Biology and Environmental Studies
University of Zurich
Winterthurerstrasse 190
CH-8057 Zurich
Switzerland

Michel Loreau
Department of Biology
McGill University
1205 ave Docteur Penfield
Montreal
Québec H3A 1B1
Canada


File list

1.
BiodepthStability.zip
2.
BiodepthSpeciesBiomass.txt
3.
BiodepthSpeciesCodes.txt
4.
BiodepthSpeciesNames.txt
5.
BiodepthBiomass.txt
6.
TemporalCVs.txt
7.
TemporalCVsRandomized.txt
8.
SpatialCVs.txt
9.
CVandMeanDbar.txt
10.
TempCVCovar2Mix.txt
11.
RankBiomass.txt
12.
Eveness.txt

Description

1. BiodepthStability.zip contains 11 data files described below. Data files are in ASCII format (tab-delimited text files).

2. BiodepthSpeciesBiomass.txt contains 5802 datapoints with the following variables:
year:
variable for year of experiment 1 to 3
site: factor for site with 8 levels: Germany, Portugal, Switzerland, Greece, Ireland, Sweden, Sheffield (UK), Silwood (UK)
block: factor for blocks within each site with 15 levels (A to O), two levels per site except Portugal with one level only
plot: factor to distinguish each plot at each site with 480 levels
sr: variable for sown species richness with levels 1, 2, 3, 4, 8, 11, 12, 14, 16, 18, 32
fr: variable for sown functional richness with levels 1, 2, 3
fgc: factor for functional group composition. g for grass, f for forb and l for legume , levels 1-7, 1=g, 2=f, 3=l, 4=gf, 5=gl, 6=fl, 7=gfl
mix.nest: variable treating same composition from different sites as different "ecotypes", levels 1-235 (fully nested within sites)
mix: variable for identical species compositions, levels 1-200 (partially crossed)
grass,forb,legume: contrasts for functional groups presence in a mixture, levels 0 or 1 (No,Yes)
funct: factor for the three functional groups grasses, forbs and legumes, three levels g, f, l and NA (for community level responses)
GRASS,FORB,LEG: individual functional group contrasts, levels 0 or 1 (No,Yes)
species: factor to distinguish each species, identical Linnean species at different sites are coded as different "ecotype" species, 186 levels, species coding see below
biomass: aboveground biomass in g/m2 on species over the first three years

3. BiodepthSpeciesCodes.txt contains:
speciescode: factor to distinguish each species, identical Linnean species at different sites are coded as different "ecotype" species, 186 levels, species coding: First letter stands for functional group (g=grass, h=herb, l=legume) followed by site number (1-8), followed by the first three letters of genus then the first three letters of the specific name and then a number to distinguish any doubles in the data set (non present in this data set)
genus: Linnean genus
species: Linnean species name
 
4. BiodepthSpeciesNames.txt contains:
abbrevation: the first three letters of genus then the first three letters of the specific name
genus: Linnean genus
species: Linnean species name

5. BiodepthBiomass.txt contains:
year:
variable for year of experiment 1 to 3
site: factor for site with 8 levels: Germany, Portugal, Switzerland, Greece, Ireland, Sweden, Sheffield (UK), Silwood (UK)
block: factor for blocks within each site with 15 levels (A to O), two levels per site except Portugal with one level only
plot: factor to distinguish each plot at each site with 480 levels
sr: variable for sown species richness with levels 1, 2, 3, 4, 8, 11, 12, 14, 16, 18, 32
fr: variable for sown functional richness with levels 1, 2, 3
fgc: factor for functional group composition. g for grass, f for forb and l for legume , levels 1-7, 1=g, 2=f, 3=l, 4=gf, 5=gl, 6=fl, 7=gfl
mix.nest: variable treating same composition from different sites as different "ecotypes", levels 1-235 (fully nested within sites)
mix: variable for identical species compositions, levels 1-200 (partially crossed)
grass,forb,legume: contrasts for functional groups presence in a mixture, levels 0 or 1 (No,Yes)
funct: factor for the three functional groups grasses, forbs and legumes, three levels g, f, l and NA (for community level responses)
GRASS,FORB,LEG: individual functional group contrasts, levels 0 or 1 (No,Yes)
species: factor to distinguish each species, identical Linnean species at different sites are coded as different "ecotype" species, 187 levels (with NA)
level: factor to distinguish stability measures at the species (Species), functional groups (Group) or mixture (Community) level
biomass: aboveground biomass in g/m2 on species, functional group and community level over the first three years

6. TemporalCVs.txt contains:
site: factor for site with 8 levels: Germany, Portugal, Switzerland, Greece, Ireland, Sweden, Sheffield (UK), Silwood (UK)
sr: variable for sown species richness with levels 1, 2, 3, 4, 8, 11, 12, 14, 16, 18, 32
mix.nest: variable treating same composition from different sites as different "ecotypes"
level: factor to distinguish stability measures at the species (Species), functional groups (Group) or mixture (Community) level
tempCV: temporal coefficient of variation (ratio of the standard deviation, σ, to the mean, μ, expressed as percentage) of total aboveground biomass on species, functional group and community level over the first three years
tempSD: standard deviation of total aboveground biomass on species, functional group and community level over the first three years

tempMean: mean of total aboveground biomass on species, functional group and community level over the first three years 

7. TemporalCVsRandomized.txt contains:
site: factor for site with 8 levels: Germany, Portugal, Switzerland, Greece, Ireland, Sweden, Sheffield (UK), Silwood (UK)
sr: variable for sown species richness with levels 1, 2, 3, 4, 8, 11, 12, 14, 16, 18, 32
mix.nest: variable treating same composition from different sites as different "ecotypes"
level: factor to distinguish stability measures at the species (Species), functional groups (Group) or mixture (Community) level
tempCV
: temporal coefficient of variation (ratio of the standard deviation, σ, to the mean, μ, expressed as percentage) of total aboveground biomass on species and community level over the first three years calculated after randomly assigning the two replicate plots of each mixture to either the population CV or the community CV omitting the functional group level.

8. SpatialCVs.txt contains:
year: variable for year of experiment 1 to 3
site: factor for site with 8 levels: Germany, Portugal, Switzerland, Greece, Ireland, Sweden, Sheffield (UK), Silwood (UK)
sr: variable for sown species richness with levels 1, 2, 3, 4, 8, 11, 12, 14, 16, 18, 32
mix.nest: variable treating same composition from different sites as different "ecotypes"
level: factor to distinguish stability measures at the species (Species), functional groups (Group) or mixture (Community) level

9. CVandMeanDbar.txt contains:
site: factor for site with 8 levels: Germany, Portugal, Switzerland, Greece, Ireland, Sweden, Sheffield (UK), Silwood (UK)
mix.nest: variable treating same composition from different sites as different "ecotypes"
tempCV: temporal coefficient of variation of total aboveground biomass on species, functional group and community level
meanDbar: Dbar quantifies the deviation of mixtures yields from the average of monocultures yields (a measure for overyielding, Loreau 1998). Average over the three years and took the natural log after adding one to remove zeros

10. TempCVCovar2Mix.txt contains:
site: factor for site with 8 levels: Germany, Portugal, Switzerland, Greece, Ireland, Sweden, Sheffield (UK), Silwood (UK)
mix.nest: variable treating same composition from different sites as different "ecotypes"
Corr: temporal correlation between pairs of species in two-species plots
CV: temporal CV

11. RankBiomass.txt contains:
site: factor for site with 5 levels: Germany, Portugal, Greece, Ireland, Silwood (UK), which had reference plots
plot: factor to distinguish each plot at each site
sr: variable for sown species richness with levels  4, 8, 11, 14, 16, 18, NA ("Not available" for the reference plots)
fr: variable for sown functional richness with levels 1, 2, 3, NA (for the reference plots)
type: two levels of plot types, reference (REF) or experimental (EXP)
rank: species rank in biomass production within plot

biomass: total aboveground biomass in g/m2 of year 2

12. Eveness.txt contains:
site: factor for site with 5 levels: Germany, Portugal, Greece, Ireland, Silwood (UK), which had reference plots
plot: factor to distinguish each plot at each site
type: two levels of plot types, reference (REF) or experimental (EXP)
eveness: reciprocal Simpson’s index divided by the number of species (Magurran 2003) calculated by replacing number of individuals with biomass of species per plot

Abstract

Insurance effects of biodiversity can stabilize the functioning of multispecies ecosystems against environmental variability when differential species’ responses lead to asynchronous population dynamics. When responses are not perfectly positively correlated declines in some populations are compensated by increases in others smoothing variability in ecosystem productivity. This variance reduction effect of biodiversity is analogous to the risk-spreading benefits of diverse investment portfolios in financial markets.
We use data from the BIODEPTH network of grassland biodiversity experiments to perform a general test for stabilizing effects of plant diversity on the temporal variability of individual species, functional groups and aggregate communities. We tested three potential mechanisms: reduction of temporal variability through population asynchrony; enhancement of long-term average performance through positive selection effects; and increases in the temporal mean due to overyielding.
Our results support a stabilizing effect of diversity on the temporal variability of grassland aboveground annual net primary production through two mechanisms. Two-species communities with greater population asynchrony were more stable in their average production over time due to compensatory fluctuations. Overyielding also stabilized productivity by increasing levels of average biomass production relative to temporal variability. However, there was no evidence for a performance enhancing effect on the temporal mean through positive selection effects. In combination with previous work, our results suggest that stabilizing effects of diversity on community productivity through population asynchrony and overyielding appear to be a general in grassland ecosystems.

Key words: BIODEPTH project; biodiversity; ecosystem functioning; insurance effect; overyielding; stability.

Metadata

Class I: Data set descriptors
Title or Theme of Data set: “BIODEPTH stability”
Name of Dataset Originator/Owner: “Andy Hector”
Citation for Data use: “Data provided by the BIODEPTH project”
Data Abstract(purpose or context): “Ecosystem process responses to manipulation of plant diversity in European grasslands”
E-mail Address of Data set Contact: “ahector@uwinst.uzh.ch”
Key words: ”Biodiversity, grasslands, stability, diversity”
Research Period: “ 19950501 19991231”
Location: “see Methods”
Location: “see Methods ”
Phone Number of Data set Contact: “00 44 (0)1 635 4804”
Address1 of Data set Contact: “Institute of Evolutionary Biology and Environmental Studies”
Address2 of Data set Contact: “University of Zurich”
Address3 of Data set Contact: “Winterthurerstrasse 190, Zurich 8057, Switzerland”

Class II: Research Origin Descriptors
Research Project Title: “BIODEPTH: BIOdiversity and Ecosystem Processes in Terrestrial Herbaceous ecosystems”
Name of Principle Investigator: “Prof. Dr. Andy Hector (for Prof. John H. Lawton)”
Address1 of Principle Investigator: “Institute of Evolutionary Biology and Environmental Studies”
Address2 of Principle Investigator: “University of Zurich”
Address3 of Principle Investigator: “Winterthurerstrasse 190, Zurich 8057, Switzerland”
Email Address of Principle Investigator: “ahector@uwinst.uzh.ch”
Phone Number of Principle Investigator: “00 44 (0)1 635 4804”
Scope and Purpose of Research Programme: “Biodiversity and ecosystem functioning experiments in European grasslands”
Research Abstract: “see Abstract”
Citation for Funding Agency: “European Commission, Framework IV Environment and Climate programme (ENV-CT95-0008)”
Research Site description: “see Methods”
Research Site size: “see Methods”
Habitat Characteristics: “Grassland”
Geology: “see Methods”
Hydrology: “see Methods”
History: “see Methods”
Climate: “see Methods”
Experimental Design: “Gradients of species and functional-group richness (numbers) nested within eight sites. Richness gradients repeated within sites in two blocks to replicate species composition”
Permanent Plot Characteristics: “see Methods”
Sampling Regime: “see Methods”
Field/Laboratory Methods: “see Methods”
Instrumentation: “see Methods”
Taxonomy and Systematics: “Follows Flora Europaea”
Personnel: “see Methods”

Class III: Data Set Status and Accessibility
Date of Last Data Update: “7 January 2002”
Date of Last Data Archival: “7 January 2002”
Date of Last Data Metadata Update and Current Status: “This data set: 28 January 2009 (it does not include some additional variables and data from later years (>3) measured only at a one or a few sites”
Status of Data Quality Assurance Checking: “See Methods”
Where Data Reside: “Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Switzerland”
Data Access Contact: “Andy Hector”
Address1 of Data set Contact: “Institute of Evolutionary Biology and Environmental Studies”
Address2 of Data set Contact: “University of Zurich”
Address3 of Data set Contact: “Winterthurerstrasse 190, CH-8057 Zurich”
Email Address of Data set Contact “ahector@uwinst.unizh.ch”
Phone Number of Data set Contact: “+41 (0) 1 635 5711”
Intellectual Property Restrictions: “Cite as below”
Expiration Date of Restrictions: “NA”
How the Data Should be Cited: “Hector et al. (2009: supplement) in text and the full citation should be to the original article, Hector et al. 2009. Diversity and stability: A multisite test of the insurance hypothesis using experimental grassland communities. Ecological Archives ##:#####.”
Disclaimers: “Data correct at dates given above but later additions and corrections may still continue to be made”
Cost for Data: “None”

Class IV: Data Set Structural Descriptors
Unique File Name: “BiodepthStability.zip”
File Size: “121 KB”
File Type: “txt, tab delimited”
Alphanumeric Case Attributes: “”
Special Characters: “NA = not available (missing values)”
Authentication Procedures: “”

Methods

Study sites

This study was carried out at eight European locations: Bayreuth, Germany; Cork, Ireland; Lupsingen, Switzerland; Lezirias, Portugal; Umeå, Sweden; Lesbos, Greece; and in Sheffield and at Silwood Park (Ascot, near London) in the UK. Sites differed widely in climate, soil conditions, and other major environmental factors - further information can be found in the main article associated with this supplement and by Spehn et al. 2005 and in Hector et al. (1999). The following references give more detailed information on the individual sites: Switzerland (Diemer et al. 1997, Joshi et al. 2000, Koricheva et al. 2000, Spehn et al. 2000a, Spehn et al. 2000b, Diemer and Schmid 2001; Pfisterer and Schmid 2002; Pfisterer, Diemer and Schmid 2003; Pfisterer et al. 2004), Sweden (Mulder et al. 1999, Koricheva et al. 2000, Jumpponen et al. 2002, Mulder et al. 2002) Germany (Scherer-Lorenzen et al. 2003), Greece (Troumbis et al. 2000, Troumbis et al. 2002), Portugal (Caldeira et al. 2001) and Silwood Park (Hector et al. 2000, Hector et al. 2001; Otway, Hector and Lawton 2005).

Establishment of the experimental communities

The field experiments were established in spring 1995 in Switzerland, autumn 1996 in Portugal, and spring 1996 at all other sites. Plots of at least 2  × 2 m (Switzerland: 2  × 8 m, Sweden: 2.2  × 5.2 m) were seeded with 2000 viable seeds m2 divided equally between the number of species in each plant assemblage. Seeds were locally collected as far as possible, or otherwise purchased from national commercial sources avoiding agricultural cultivars. Prior to sowing, the existing vegetation was removed and the soil seed bank was eliminated by continuous weeding (Switzerland, Sweden), steam sterilization (Germany), heat (soil was covered with black plastic for 2.5 months, Portugal) or methyl-bromide application (UK, Ireland, Greece). To reduce post-application effects of methyl bromide on legumes, an inoculum of Rhizobium was applied. plots were regularly weeded to remove unwanted species emerging from the remaining seed bank or invading from outside. Plots were separated by 1.5 m wide borders sown with slow-growing grass species that were regularly mowed (Switzerland, Germany, Ireland, UK, Sweden, Portugal) or were not separated (Greece). The plots were not fertilized during the experimental period.

Experimental design

We established five levels of species richness, ranging from monocultures to higher diversity mixtures. The highest diversities approximately matched background levels of diversity in comparable semi-natural grasslands at each site (Hector et al. 1999). In addition, we varied the number of functional groups — grasses, nitrogen-fixing legumes and other herbaceous dicots (forbs) — within the different levels of species richness. Further, we constrained our random selection of species from the local pool of grassland species so that all assemblages included grasses. Each particular combination of species richness and number of functional groups, hereafter called a diversity level, was replicated, with several different species compositions, hereafter called an assemblage (both monocultures and mixtures), at each site to separate the effects of species richness from the effects of species identity (Givnish 1994, Tilman 1997, Allison 1999, Schmid et al. 2002). At each site all assemblages were randomly allocated within two replicated blocks (except Portugal with fully randomized plots). In total, the experiment comprised eight sites, 480 plots, and 200 different plant assemblages, with the same assemblage sometimes occurring at more than one site. In addition, at some sites (Portugal, Germany, Greece, Ireland, UK Silwood) we established unmanipulated "reference" plots in neighboring grasslands to provide a natural comparison for the variables measured in our experimental plots.

Data processing and database compilation

Data were collected according to standard protocols established at project meetings and circulated to all data collectors. Data were checked by read-back, followed by tabulation and on-screen plotting to look for outliers. Checked data were emailed to Silwood Park and collated into a relational database using Microsoft Access-97. The database was set up with constraints placed on acceptable column headers and column formats. Data with incorrect headers, column formatting (text numerical, etc.) could not be entered into the database and were returned to sites for further checking until correctly reformatted and entered. This provided a second round of checking. The raw data were then processed (e.g., to produce means per plot) and derived variables (e.g., complementarity and selection effects) calculated. A third round of data checking occurred during data processing and at the first stage of analysis.

The analyses presented use data on net aboveground biomass production (g m-2 year-1) of species from the experimental plots at each of the eight BIODEPTH fieldsites for the three main years of the project (Spehn et al. 2005). The dataset comprises information on 480 plots each containing between 1 and 32 species (and between 1 and 3 plant functioning groups, namely grasses, legumes and other forbs). In total this produces 1934 data points per year, with each data point reporting the biomass of a species in an individual plot. Each monoculture or species mixture was replicated in two identical plots (with a few exceptions: five plant assemblages were replicated 4 times, see Spehn et al. 2005).
To standardise fluctuations relative to changes in mean productivity over time we quantified variability as the coefficient of variation (CV) where CV is the ratio of the standard deviation, σ, to the mean, μ,
expressed as a percentage:
CV = σ/μ ×100
Since a decrease in the CV can result from an increase in the mean, a decrease in the variance (SD), or both, we examine patterns in all three statistics.
Temporal CVs were calculated for the biomass of individual species, for functional groups and for aggregate communities (ecosystem aboveground annual net primary production) over the first three years of the BIODEPTH experiment (longer time series exist for some sites that show similar patterns as long as weeding is maintained; (Pfisterer et al. 2004). Overyielding will have a stabilizing effect (reduced CV) when diversity increases the ratio of the mean relative to the standard deviation. Spatial CVs were also calculated for the biomass of individual species, functional groups and the experimental communities they composed. However, as there was no effect of diversity on spatial variability and as there is a clear danger that we could publish a false-negative result due to the reduction of spatial heterogeneity at our field sites during establishment we present the results only shortly in the Appendix A.

Analysis

Since our design includes fixed and random effects we used mixed-effects analysis using the lme function from the nlme package (Pinheiro and Bates 2000) for R 2.10.1 (R Development Core Team 2009). Readers not familiar with mixed-effects models can think of them as a maximum likelihood-based form of ANOVA that is the recommended approach for analysis of mixed-model designs that include fixed and random effects (Bolker et al. 2008). Mixed-effects models use restricted maximum likelihood (REML) to estimate regression intercepts and slopes or treatment means (generally: 'intercepts') for fixed-effect explanatory variables (e.g., treatments) and to predict the variability (variance components) of slopes or intercepts for random effects (e.g., sites and blocks). Following the BIODEPTH experimental design and our a priori hypotheses, our analysis treats diversity (sown species richness) and organizational level (individual species, functional group or aggregate community) as fixed effects, reporting their point estimates with 95% confidence intervals. Sites were treated as random effects, allowing both the intercepts and slopes of the regression slopes versus diversity to vary with location and year as required. Species compositions were also treated as a random effect (nested within sites). The fixed-effect component of our models therefore examined the effects of diversity, level and their interaction. For the random-effect component of our models we followed a model building strategy (Pinheiro and Bates 2000) that uses likelihood ratio tests of models with and without a given random effect to determine which show significant levels of variation and are required in the model. The likelihood ratio test is based on the change in deviance (≈ sums of squares) due to the removal of the random effect that is omitted from the reduced model. The change in deviance approximately follows a χ2 distribution with the appropriate degrees of freedom and the test tends to be conservative (Pinheiro and Bates 2000). Variance components for the random effects are reported as standard deviations (that is the square root of the variance component) to be on the same scale as the original measurements. To calculate the evenness between experimental and reference plots we used the reciprocal Simpson’s index divided by the number of species by plot (Magurran 2003) by replacing number of species with biomass of species per plot. All intervals are 95% confidence intervals unless otherwise stated.

Acknowledgments

We are grateful to Charles Godfray for the logistical support that enabled us to complete this database.

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