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Evenness drives consistent diversity effects in an intensive
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grassland system across 28 European sites
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L. Kirwan1, A. Lüscher2, M.T. Sebastià3, J.A. Finn4, R.P. Collins5, C. Porqueddu6, A.
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Helgadottir7, O.H. Baadshaug8, C. Brophy1, C. Coran9, S. Dalmannsdóttir7, I. Delgado10,
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A. Elgersma11, M. Fothergill5, B.E. Frankow-Lindberg12, P. Golinski13, P. Grieu14, A.M.
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Gustavsson15, M. Höglind16, O. Huguenin-Elie2, C. Iliadis17, M. Jørgensen18, Z.
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Kadziuliene19, T. Karyotis20, T. Lunnan21, M. Malengier22, S. Maltoni6, V. Meyer23, D.
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Nyfeler2, P. Nykanen-Kurki24, J. Parente25, H.J. Smit11, U. Thumm26, J. Connolly1
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Group, University College Dublin, Dublin 4, Ireland
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Switzerland
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Forest Technology Centre of Catalonia - University of Lleida, 25280 Solsona, Spain
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Teagasc Environment Research Centre, Johnstown Castle, Co. Wexford, Ireland
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IGER, Plas Gogerddan, Aberystwyth, SY23 3EB, Wales, UK
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CNR-ISPAAM, Via De Nicola, 07100 Sassari, Italy
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Agricultural University of Iceland, Keldnaholti, 112 Reykjavík, Iceland
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Dept. of Plant and Environmental Sciences, P.O. Box 5003, N-1432 Ås, Norway
UCD School of Mathematical Sciences, Ecological and Environmental Modelling
Swiss Federal Research Station for Agroecology and Agriculture, 8046 Zurich,
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The Netherlands
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Department of Crop Production Ecology, Box 7043, SE-750 07 Uppsala, Sweden
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Department of Grassland Sciences, Agricultural University of Poznan, Wojska
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Polskiego 38/42, 60-627 Poznan, Poland
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UMR ARCHE INRA-ENSAT, 31326 Castanet Tolosan, France.
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Department of Agricultural Research for Northern Sweden, Section of Crop Science,
SAASD, 33170 Pordenone, Italy
CITA-DGA, Av. Montañana 930, 50059 Zaragoza, Spain
Crop and Weed Ecology Group, Plant Sciences, Haarweg 333, 6709 RZ, Wageningen,
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Swedish University of Agricultural Sciences, Box 4097, SE-904 03 Umeå, Sweden
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Theophrastou Str, 41110 Larissa, Greece
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Norway
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Lithuania
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Str., 411 10 Larissa, Greece
The Norwegian Crop Res. Inst., Saerheim Research Center, N 4353 Klepp st., Norway
National Agricultural Research Foundation, Fodder Crops and Pasture Institute, 1
Bioforsk, Arctic Agriculture and Land Use Holt, P.O. Box. 6232, N-9292 Tromsø,
Lithuanian Institute of Agriculture, Dotnuvos Akademija, LT-58344, Kedainiai,
National Agricultural Research Foundation, Inst. for Soil Mapping, 1 Theophrastou
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Belgium
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DLF-Trifolium A/S, Højerupvej 31, DK 4660 Store Heddinge, Denmark
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MTT Agrifood Research Finland, Ecological Production, Karilantie 2A, FIN-50600
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Mikkeli, Finland
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ERSA, 34170 Gorizia, Italy
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University of Hohenheim, Institute for Crop Production and Grassland Research.
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D-70593 Stuttgart, Germany
Planteforsk Løken, N-2940 Heggenes, Norway
CLO - Gent, Department of Plant Genetics and Breeding, Caritasstraat 21, 9090 Melle,
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Correspondence: L Kirwan (Tel.: +353 1 7167103, Fax: +353 1 7161186, email:
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[email protected])
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Diversity effects in intensive grassland systems
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Summary
1. Ecological research suggests that increased crop diversity in species-poor
agronomic systems may improve their provision of ecosystem services. Such
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general predictions can have critical importance for worldwide food production
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and agricultural practice but are largely untested.
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2. We propose new methodology for the design and analysis of experiments to
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quantify diversity-function relationships. Our methodology can quantify the
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relative strength of interspecific interactions that contribute to a functional
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response, and can disentangle the separate contributions of species richness and
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relative abundance.
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3. Applying our methodology to data from a common experiment at 28 European
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sites, we show that the aboveground biomass of 4-species mixtures (two legumes
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and two grasses) in intensive grassland systems was consistently greater than that
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expected from monoculture performance and frequently exceeded the yield of the
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best monoculture. The additional performance of mixtures was driven by relative
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abundance more than species’ number.
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4. The combined analysis across geographical and temporal scales in our study
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provides a generality of interpretation of our results that would not have been
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possible from individual site analyses or experimentation at a single site.
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5. Our 4-species agricultural grassland communities have proved a simple yet
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relevant model system for experimentation and development of methodology in
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diversity-function research. Our study establishes that principles derived from
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biodiversity research in extensive, semi-natural grassland systems are applicable
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in intensively managed grasslands with agricultural plant species.
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Keywords
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Agricultural grassland, Ecosystem functioning, Evenness, Intensive grasslands,
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Interspecific interactions, Multi-site experiment, Relative abundance, Species identity,
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Simplex design, Transgressive overyielding.
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Introduction
As human activities cause widespread threats to biodiversity, investigation of the
potential effect of declining species diversity on ecosystem functions has emerged as an
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important scientific question (Costanza et al. 1997; Loreau et al. 2001; Hooper et al.
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2005). Investigations of the relationship between diversity and ecosystem functioning
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have mostly used extensively managed grassland communities as a model system, and
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generally demonstrate that biomass production is reduced when plant species diversity
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declines (Tilman et al. 1996; Hector et al. 1999; Tilman et al. 2001; Hooper & Dukes
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2004; Hooper et al. 2005; Roscher et al. 2005). Explanations of such patterns centre
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about hypotheses that more diverse communities better utilise available resources due to
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their greater occupation of niche space, and that they have a greater probability of
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containing positive interspecific interactions (Trenbath 1974; Harper 1977; Vandermeer
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1989; Hector et al. 1999). Selection effects (Huston 1997; Tilman et al. 1997; Loreau
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2000) can also contribute, and these different explanations need not be mutually
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exclusive (Loreau 2000; Hooper et al. 2005).
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Agronomic systems cover large land areas, perform important ecosystem functions
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such as biomass production and nutrient cycling and are often associated with the
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widespread use of monocultures and high input of nutrients. Despite being managed
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ecosystems, agro-ecosystems are similar to other ecosystems in having biogeochemical
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processes that are mediated by ecological characteristics of the constituent biological
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community (patterns of resource capture and utilization, and interspecific interactions)
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and provide a variety of ecosystem services. Intensive cropping systems with one, or
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sometimes two, plant species predominate, and diversity-function research suggests that
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increased crop diversity in species-poor agronomic systems could improve the provision
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of ecosystem services. The potential multiple benefits of diverse agronomic crops with
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more than two species could contribute to more sustainable agricultural systems by
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providing sufficient crop yield while minimising environmental impacts (Hooper et al.
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2005). Such general predictions can have critical importance for worldwide food
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production and agricultural practice but are largely untested due to the rarity of multi-
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species agronomic experiments (Vandermeer 1989; Federer 1999; Gibson et al. 1999). In
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addition, experimental designs have ignored or confounded important components of
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diversity i.e. relative abundance, species richness and species identity (Connolly et al.
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2001; Schmid 2002). However, whether ecological principles from diversity-function
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research in extensive semi-natural grassland communities (Hector et al. 1999; Tilman et
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al. 2001; Hooper et al. 2005) translate to intensively managed grasslands (Tilman 1999)
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requires investigation.
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Diversity-function studies have generally manipulated the number (richness) or
composition of species or functional groups in the community. However, relative
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abundance is also expected to be an important determinant of diversity-function
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relationships (Nijs & Roy 2000; Wilsey & Potvin 2000; Hooper et al. 2005). To date, the
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relative abundance of species has been almost universally used as a passive descriptor of
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a community (Smith & Wilson 1996; Stirling & Wilsey 2001; Mulder et al. 2004) but has
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rarely been investigated as an active determinant of ecosystem function (Schmid 2002).
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The few results from experimental manipulations of relative abundance are ambiguous,
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sometimes indicating an effect (Wilsey & Potvin 2000; Smith 2004) and sometimes not
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(Wilsey & Polley 2004) on selected ecosystem functions. Where the effect of diversity
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depends on interspecific interactions among species in a community (Trenbath 1974;
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Harper 1977; Loreau 2000), the total contribution of interspecific interaction to a
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functional response depends on the expression of individual interspecific interactions and
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their number. The number of interactions depends on species richness of the community
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while the expression of a particular interaction depends on the strength of the interaction
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and the relative abundance of the species involved. In a multi-species community, one
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would not expect a large expression of interaction for two species that can interact
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strongly but for which one or both have a very low relative abundance. The net effect of
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interactions may lead to overyielding (or underyielding), where the performance in
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mixture exceeds that expected from performance in monocultures and interactions may
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be so strong as to lead to transgressive overyielding (Trenbath 1974), where mixture
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performance exceeds that of the highest-yielding monoculture. To assess the contribution
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of interspecific interaction to ecosystem function requires the experimental manipulation
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of species relative abundance.
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We manipulated relative abundance to investigate the contribution of interspecific
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interaction to diversity–function relationships in an experiment using 4-species plant
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mixtures, repeated at 28 sites in Europe. We developed novel methods of design and
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analysis to address issues in diversity-function research. We address the following
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questions and discuss how our methods contribute to resolving issues in diversity-
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function research.
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1.
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into the sum of identity effects, and the effects of interspecific interaction?
2.
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Can functional responses in mixed-species communities be decomposed
Is there evidence of overyielding or transgressive overyielding in our 4species communities?
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Are diversity effects consistent across large spatial scales?
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Materials and Methods
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EXPERIMENT DESIGN.
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A common experiment of 30 plots was established at 28 sites in 17 countries in Europe
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(see Fig. 1 and Table S1 in Supplementary Material) in 2002 or 2003, giving 840 plots in
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total. At each site two legume and two grass species were sown. One of the grass and one
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of the legume species was fast- and the other was slow-establishing. Five species-groups
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were used: North European (NE), Mid European (ME), Dry Mediterranean (DM), Moist
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Mediterranean (MM) (Table 1) and a fifth group (Other) consisted of three sites, each
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with its own species (Table S1). We used a simplex design (Cornell 2002; Ramseier et al.
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2005) to define four monocultures and 11 mixtures of the four species (Fig. 2(a)). The 11
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mixtures consisted of four mixtures dominated in turn by each species (sown proportions
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of 70% of dominant and 10% of each other species), six mixtures dominated in turn by
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pairs of species (40% of each of two species and 10% of the other two) and the centroid
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community (25% of each species). The monocultures and mixtures were sown at two
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levels of overall sown abundance (Connolly et al. 2001) (low being 60% of high).
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A common protocol was established for plot management. Experimental
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communities were randomly assigned to plots and managed by cutting (2 to 5 cuts per
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annum as appropriate to local conditions). Annual application of nitrogen fertiliser ranged
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from 0 to 200 kg ha-1. Minimum plot size was 2 m x 3 m. For estimation of yield (total
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annual aboveground biomass including unsown species) a subplot (3 m2) was cut to a
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height of 5 cm at each harvest. See Table S1 for other site information and management
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details.
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DIVERSITY MODEL
We propose a diversity model for the analysis of yield that includes the effects of
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species identity, interactions based on species relative abundance and overall sown
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abundance. We define the diversity effect (D) as the difference between mixture
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performance and that expected from proportional combination of monocultures (Polley et
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al. 2003; Spehn et al. 2005). D is zero for a monoculture and must be close to zero for a
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community that is almost a monoculture. We first define a simple model based on a
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measure of sown community evenness that captures the effect of all pairwise interactions;
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this generalises naturally to a wide range of models that describe alternative patterns of
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interspecific interaction.
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Evenness is a measure of the distribution of the relative abundance of species in a
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community. Where there are up to s species in a community and Pi is the sown relative
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abundance of the ith species, we define the sown evenness (E) of the community as
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E
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s species are equally represented (Fig. 2). Since D and E are zero for monocultures the
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relationship between D and E must intercept the origin. Overall sown abundance (M) was
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coded -1 and 1 for low and high, respectively, with a mean of zero for the design.
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Applying the evenness formula to the species proportions in our experimental design
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gives sown evenness values of 0, 0.64, 0.88 and 1 (Fig. 2(a)). We related yield (y) to
2s s
 Pi Pj , which lies between 0 for monocultures and 1 for a community in which all
s  1 i j
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species’ sown relative abundance, total sown community abundance and evenness. The
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basic model for yield at a site was
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y    i Pi  M  E   .
s
[1]
i 1
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where βi is the expected monoculture performance of the ith species (Pi=1) at mean sown
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total abundance and reflects species identity, α is the effect of sown overall abundance, δ
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is the linear effect of evenness and ε is normally distributed with zero mean and constant
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variance. As the performance expected solely from monocultures is
s
  P  M , the
i i
i 1
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diversity effect in model [1] is D= δE. For this model the diversity effect changes linearly
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with evenness and its maximum is δ when E=1. From the definition of evenness all
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pairwise interactions among species in this model have the same coefficient ( 
2s
).
s 1
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GENERALISATIONS OF DIVERSITY MODEL
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The diversity effect in model [1] generalises to a rich class of alternative models
based on alternative assumptions about the strength of pairwise species interactions.
s
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Pairwise interactions may all be different, leading to a term
2s
 P P s  1 where δ
ij i
j
ij
i j
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captures the strength of interaction between species i and j. There may be clear patterns
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among the δij reflecting the traits of the species in the mixture (e.g. a functional group
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model that has a common coefficient for all pairwise interactions between species from
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different functional groups). Interactions may also involve more than two species or more
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complex functions (e.g. quadratic) in E. Many of these alternative models are hierarchical
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(Dobson 2002) to model [1] or to the model with separate coefficients for each
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interaction, which leads to straightforward statistical tests to select the most appropriate
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model. This modelling approach requires an experimental design that allows estimation
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of all the coefficients, those of likely alternative models, and the facility to test between
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them.
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DISENTANGLING SPECIES RICHNESS AND RELATIVE ABUNDANCE
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The diversity effect includes the effects of both species richness and relative
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abundance. The contribution of species richness to the diversity effect can be discerned
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by comparing mean or maximum diversity effects at different levels of richness. The
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effect of variation in relative abundance can be isolated by exploring the diversity effect
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in communities that have the same level of richness but vary in relative abundance.
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In model [1], the diversity effect, D = δE, is maximum when E=1, which is only achieved
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at the s-species centroid (Fig. 2). For lower levels of species richness (t), the maximum
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diversity effect is reached at the t-species centroids, (where Pi=1/t for t of the species and
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0 for the other species, Fig. 2(b)) and is δE where E  2s
t
1

s 1 t
i j
2
 (t  1)s /(( s  1)t ) . The
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maximum diversity effects for 2, 3 and 4 species are 0.67δ, 0.89δ and δ (Fig. 2).
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Comparing these D values gives the effect of changing species richness. Changing
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relative abundance within any level of richness (t) may also change the value of E (Fig.
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2(b)) and hence the diversity effect. D varies from nearly 0 for t-species communities that
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are almost a monoculture to the maximum for a t-species centroid.
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STATISTICAL ANALYSIS.
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Individual Site Analyses
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We fitted model [1] to yield in the first complete year following establishment
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using multiple regression. Alternative models were fitted and tested against model [1].
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These included a model with separate coefficients for each pairwise interaction,
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functional group models for grass-legume and fast-slow establishing species, a model
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with both functional groupings and a model with a quadratic evenness term. Three-
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species interactions among the relative abundances of the species were also tested. We
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fitted model [1] to yield from the second year for 17 of the sites.
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Combined Analysis
For the combined analysis of yield across sites we used a random-coefficients
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approach (Verbeke & Molenberghs 2000) to fit model [1] and also tested for the
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interaction between all model terms and species-group. We only included the three
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species-groups ME, NE and MM in this analysis and omitted the DM species-group as its
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yields were very much lower. We assumed that model coefficients for species identity,
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sown abundance and evenness were random across sites within species-group. In this
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combined analysis, the average value of each model coefficient is effectively tested
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against the variation in the coefficient across sites. A wide range of alternative models
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allowing for different assumptions about pairwise species interactions were tested against
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model [1] (Table S2). We used the structure for the variance-covariance matrix of the
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random coefficients shown in Appendix S1. Maximum likelihood (Littell et al. 2006) was
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used to fit and test between models and residual maximum likelihood (Littell et al. 2006)
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to test between random effect structures and to provide estimates of the variance-
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covariance matrix (Appendix S1).
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Transgressive Overyielding
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Within each species-group, we used a permutation method (Appendix S2, Table
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S3) to test for transgressive overyielding, comparing the mean yields across sites of each
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of the 11 mixtures with the mean yields across sites of each of the 4 monocultures.
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Results
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INDIVIDUAL SITE ANALYSES
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Our data showed consistent positive effects of increasing plant evenness. Almost all
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analyses of individual sites showed a positive diversity effect that was linearly related to
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evenness, significantly so in 25 of 28 sites in the first year (Table 2). Analysis of second
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year data at 17 sites using model [1] again showed at all sites, which were significant at
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16 of them (Table 2). Model [1] usually best explained yield at individual sites.
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Generalisations of model [1] were also fitted to yield for the individual sites for the first
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year: more complex relationships better explained yield in several sites, either a quadratic
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effect of evenness (7 sites), and/or a grass-legume functional group effect (1 site). There
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was some evidence of interaction involving three species (4 sites).
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COMBINED ANALYSIS
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In the combined analysis across sites the diversity effect differed between species-
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groups. D was positively linearly related to evenness for NE (P=0.006, 5 sites) and MM
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(but not significantly, P=0.160, 3 sites) and the maximum diversity effect was 2.26 and
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1.38 t ha-1 respectively at E=1 (Table 3). For ME (15 sites), the relationship between the
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diversity effect and evenness was quadratic ( D  E  1E 2 ). The estimated maximum
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diversity effect for ME was 3.09 t ha-1 (P<0.001) at E=0.97 (Fig. 3). For ME the effect on
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yield in multi-species agronomic mixtures seemed not so sensitive to modest changes
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across higher evenness levels (Table 3, Fig. 3), although to intercept the origin the
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diversity effect must decrease at lower evenness levels. There was a significant difference
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among identity effects (i) for each of the three species-groups, indicating that estimated
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performance in monoculture differed among species (Table 3).
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Across sites, the annual use of nitrogen (N) fertiliser ranged between 0 and 200 kg
ha-1 (Table S1). High N application was not incompatible with producing diversity
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effects, which were significant for sites (n=6) with annual N application > 150kg ha-1
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(Table 2, Table S2). To check the robustness of the models based on sown evenness, we
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fitted the models in Table 3 using established evenness at harvest 1 and obtained similar
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coefficient estimates (Table S5).
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TRANSGRESSIVE OVERYIELDING
For ME, NE and DM (Fig. 4, Table S3) virtually all the mean yields of mixtures
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exceeded the mean yield of the highest-yielding monoculture, providing very strong
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evidence for transgressive overyielding. Estimates of average transgressive overyielding
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of 15%, 12% and 16% for ME, NE and DM respectively were computed by comparing
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the average mixture yield with the highest yielding monoculture; but the true
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overyielding effects are likely to be even larger (Appendix S2). Each of the Other sites
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demonstrated transgressive overyielding (P<0.05) but the MM species-group did not.
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Discussion
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Models of the diversity effect that are based on our evenness index assume that the
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effect of diversity is due to pairwise interspecific interactions, all of which are equally
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strong. However, a model based on evenness may not best describe the diversity effect in
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other communities. Species may not interact equally, i.e. the strength of interspecific
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interaction may differ; patterns of interaction may be associated with particular species
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traits (Hooper & Vitousek 1997; Hooper & Dukes 2004) or may involve more than two
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species. Our experimental and analytical approach quantifies the strengths of different
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interspecific interactions in multi-species systems and permits discrimination among
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alternative descriptions.
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In our combined analysis we found no evidence for a more complex diversity effect
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than one based on evenness, despite some evidence for alternatives at individual sites.
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The models presented in Tables 2 and 3 assume that all pairwise interactions between
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species contribute equally to the diversity effect; thus, the positive interaction between
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two grass species or two legume species was as strong as that between a grass and a
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legume. There is considerable evidence for positive interactions between grasses and
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legumes (Vandermeer 1989; Hector et al. 1999; Spehn et al. 2005). The mechanism for a
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mixing effect among grass or legume species is less clear but synergistic effects can
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occur in mixtures without legumes (Trenbath 1974; van Ruijven & Berendse 2003;
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Hooper & Dukes 2004). If these grass-grass and legume-legume effects in our study are
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due to temporal partitioning between fast- and slow-establishing species (Ofori & Stern
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1987; Chesson 2002) it is somewhat surprising that the strength of interaction between
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species that share both functional group differences (e.g. slow grass x fast legume) does
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not show an even greater positive effect (Table S2). To provide mechanistic explanations
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of observed responses and model terms will require information on the contribution of
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individual species to total yields and temporal dynamics.
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The net effect of the pairwise interactions underlie the magnitude of the observed
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diversity effect in the present study. A positive diversity effect implies overyielding; but
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does it lead to transgressive overyielding? Our analyses show that these agricultural
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grassland mixtures demonstrated transgressive overyielding, and that this was a general
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effect, occurring in three species-groups (Fig. 4) and the Other sites and accounted for 25
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out of 28 sites. The magnitude and generality of transgressive overyielding observed in
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our study strongly suggests that modest increases in agronomic species diversity can
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contribute to agricultural production in intensive grassland systems.
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This study suggests that to obtain the practical benefit of the diversity effect in
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intensively managed agricultural grasslands, sowing rates and adaptive management can
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be used to maintain evenness above levels suggested by Fig. 3. Results for ME indicate
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that this range of evenness may be quite broad for this species-group (Fig. 3). Of
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course, yield is one of several important functional responses that are of practical
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relevance in agronomic systems. Mixtures contained much lower proportions and
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biomass of unsown species than monocultures for all species-groups (Table 4),
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suggesting reduced invasibility of mixtures. (As our yield analysis includes unsown
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species, the diversity effect would be even greater if analysed in terms of sown species
2
only.) Other important functional responses will include the nutritional quality of the
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produced yield as well as the seasonal and multi-annual stability of yield production.
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Given that the diversity effect in these agricultural mixtures was related to evenness, the
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temporal persistence of the species in mixtures (to realise the diversity effect) is a
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significant issue, as are the effects of vegetation dynamics and abiotic factors in affecting
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persistence.
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Our methodology can be used to quantitatively disentangle the separate
contributions of species richness and relative abundance to the diversity effect. In the
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broadest sense, the contribution of species richness to the diversity effect can be
11
discerned by comparing mean or maximum diversity effects at different levels of
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richness. At each level of richness the community with the maximum diversity effect will
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depend on the relative strength of interspecific interactions and may not occur at
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maximum evenness. The effect of variation in relative abundance can be isolated by
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exploring the diversity effect in communities that have the same level of richness but
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vary in relative abundance. This broad approach simplifies greatly when the diversity
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effect is a function of evenness (E) only. The relative effect of changing richness and
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evenness can be calculated from model [1] or the quadratic model in evenness. For model
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[1], increasing richness from 2 to 4 species increased maximum diversity effects from
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0.67δ to δ. Within each level of richness, the effect of varying relative abundance ranges
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from 0 to 0.67 for 2 species and 0 to  for 4-species mixtures. For the quadratic model
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fitted for ME sites, the effect of changing species richness was weak; the maximum
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estimated diversity effect for 2 and 3 species was only 9.6% and 0.6% lower,
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1
respectively, than that of the 4-species community. By comparison, changing relative
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abundance had a far greater effect within 2- and 3-species mixtures. For 2 species the
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range of diversity effects associated with different patterns of relative abundance ranged
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from 0% to 90.4% of the maximum diversity effect achievable for 4 species. For 3
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species the range was 0% to 99.4%. In both models the effect of changing relative
6
abundance for a given level of richness was greater than the effect of changing richness
7
(except from a monoculture to 2 species). The responses to richness in the quadratic
8
model for ME sites suggests saturation (Hooper et al. 2005) of the diversity effect at 4
9
species while model [1] suggests diminishing diversity benefits from increasing richness.
10
Designs based on the simplex allow us to estimate interaction effects, to
11
discriminate between a range of possible models and to describe the diversity effect over
12
the widest range of relative abundance and species richness. This includes models in
13
which the relative strengths of interspecific interactions differ and for which the
14
maximum diversity effects will generally not occur at maximum evenness. A classic
15
design includes all monocultures and only the centroids (mixtures in which all species are
16
equally represented) for randomly selected subsets of species richness (from 2 to s) from
17
a pool of s species. This design cannot explore the diversity effect for communities with
18
patterns of relative abundance not at the centroids. Experimental multi-species plant
19
communities have been questioned for having an unusually high degree of evenness,
20
whereas real communities typically have a few dominant species and several rare species
21
(Huston 1997; Wilsey & Polley 2004). Designs based on the simplex offer a method for
22
testing the importance of this issue. The diversity effect in the ME sites did not vary very
23
much across the range of evenness in our design so, in retrospect, the classic design
19
1
would have estimated the diversity effect quite well. However, it would not have been
2
possible to check this finding against alternatives. Our approach also avoids the
3
difficulties associated with replacement and additive series designs (Connolly et al.
4
2001).
5
Multi-site experiments increase statistical power to detect general relationships that
6
may not be obvious from individual site analyses. Three of the individual site analyses
7
did not show significant diversity effects (Table 2) and 12 sites provided evidence of a
8
more complex diversity effect than model [1]. The combined analysis identifies effects
9
that are generally consistent, despite variation across individual sites. This analysis
10
generalizes interpretation (Verbeke & Molenberghs 2000); the average diversity effect
11
coefficient(s) is the most reliable predictor of the magnitude of the diversity effect at any
12
location in the absence of additional location-specific information. The formulation of
13
general predictions from diversity-function research for large areas of agronomic or
14
natural systems therefore requires experiments to be conducted across multiple sites
15
(Hector et al. 1999). Experiments with perennial species should be conducted over
16
several years to check the persistence or evolution of effects (Hooper et al. 2005; Tilman
17
et al. 2006); our currently available data (Table 2) highlight the persistence of the effect
18
of diversity over at least two years.
19
In our study, the yield of 4-species mixtures exceeded that expected from
20
monoculture performances and frequently exceeded that of the most productive
21
monoculture. This diversity effect was consistent across a wide geographical scale,
22
adding generality to our finding. Our methodology partitions functional responses into
20
1
the sum of the effects of species identity and the effects of interspecific interactions. The
2
data were best described by a model in which all interactions contributed equally to the
3
diversity effect, and a simple model based on the evenness of the community captured all
4
interspecific interactions. Our methodology allows for discrimination among alternative
5
descriptions of species interactions, which may be more complex than those found here
6
and may more directly reflect species’ traits. We demonstrate that even a modest increase
7
in the diversity of intensive grassland systems can produce diversity benefits leading to
8
transgressive overyielding. Moreover, our methodology contributes to resolving issues in
9
diversity-function research and is relevant for both agronomic and ecological
10
investigations of diversity-function relationships.
11
12
Acknowledgements
13
We wish to thank Tom Bolger, David Gibson, Kristina Stinson, Paul Struik and Brian
14
Wilsey for very helpful comments. Many colleagues, too numerous to list, have assisted
15
with this work. We were supported by the EU Commission through COST Action 852.
16
LK was supported by the Irish Environmental Protection Agency.
17
18
19
20
21
1
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26
1
SUPPLEMENTARY MATERIAL
2
The following supplementary material is available for this article:
3
4
Appendix S1 Covariance structure for the random coefficients for the final model across
5
sites.
6
Appendix S2 Transgressive Overyielding Permutation Test.
7
Table S1 Information on sites.
8
Table S2 Model Selection in the Combined Analysis of yield across sites.
9
Table S3 Data and Permutation Test for Transgressive Overyielding.
10
Table S4 Combined Analysis using established proportions.
11
12
This material is available as part of the online article from:
13
http://www.blackwell-synergy.com/…
14
15
Please note: Blackwell Publishing is not responsible for the content or functionality of
16
any supplementary materials supplied by the authors. Any queries (other than missing
17
material) should be directed to the corresponding author for the article.
18
19
27
1
Tables
2
Table 1: Composition of species-groups in the different geographical areas ME, NE, MM
3
and DM.
Species Functional Mid European
group
(ME)
1
2
3
4
GrassFast
GrassSlow
LegumeFast
LegumeSlow
Number
of sites
Northern
European
(NE)
Lolium perenne Phleum
pratense
Dactylis
Poa pratensis
glomerata
Trifolium
Trifolium
pratense
pratense
Trifolium
Trifolium
repens
repens
15
5
Moist
Mediterranean
(MM)
Lolium perenne
Dry
Mediterranean
(DM)
Lolium rigidum
Dactylis
glomerata
Trifolium
pratense
Medicago sativa
Dactylis
glomerata
Medicago
polymorpha
Medicago
sativa
2
3
4
Five species-groups were used: North European (NE), Mid European (ME), Dry Mediterranean (DM),
5
Moist Mediterranean (MM) (Table 1) and a fifth group (Other) consisted of three sites, each with its own
6
species (see Table S1).
7
8
9
28
1
Table 2: Estimates of the coefficient of evenness () in model [1] for 28 sites in year 1
2
and 17 sites in year 2 (coefficients in bold indicate significance at < 5%). This estimates
3
the maximum diversity effect in mixtures in tonnes ha-1. Also shown for each site for year
4
1 are species-group, mean mixture yield, and mean monoculture yield (mono). Multiple
5
sites for a country are distinguished by letters in parentheses.
Country
Species- Mean
group
mixture
yield
(t ha-1)
Germany
Ireland
Lithuania (a)
Lithuania (b)
Lithuania (c)
Netherlands
Norway (a)
Norway (b)
Poland
Spain (a)
Sweden (a)
Sweden (b)
Switzerland
Wales (a)
Wales (b)
Iceland (a)
Iceland (b)
Norway (c)
Norway (d)
Sweden (c)
France
Greece
Italy (a)
Italy (b)
Spain (b)
Belgium
Denmark
Finland
ME
ME
ME
ME
ME
ME
ME
ME
ME
ME
ME
ME
ME
ME
ME
NE
NE
NE
NE
NE
MM
MM
MM
DM
DM
Other
Other
Other
17.6
16.6
5.7
10.6
11
11.5
13.7
11.7
8.5
8.5
10.7
10.6
15.5
10.4
10.5
5.4
2.3
11.3
10.2
9.1
9.5
3.3
9.3
3.3
2.5
16.1
13.6
9.3
Mean Coefficient of evenness
mono ˆ  s.e.
yield
(t ha-1)
(t ha-1) Year 1
Year 2
4.84 ± 0.835
13.6
3.75 ± 0.515
1.51
13.6
1.84
5.5
0.34 ± 0.545
2.44 ± 0.681
8.7
2.17 ± 0.464
9.1
3.03 ± 1.127
5.44
9.1
6.85 ± 0.602
4.08
7.8
2.13 ± 0.36
3.44
9.9
1.77 ± 0.489
2.66
6.7
6.8
2.01 ± 1.217
5.75 ± 0.548
6.00
5.6
2.17
3.72
8.8
± 0.662
5.64 ± 0.689
7.46
10.4
4.37 ± 0.583
2.21
6.7
4.68 ± 0.655
4.05
6.8
1.13 ± 0.533
4.3
0.49
1.16 ± 0.262
1.25
1.3
4.18 ± 0.481
7.1
2.4 ± 0.465
2.04
8.1
2.38
7.2
± 0.32
8.1
1.71 ± 1.002
0.92 ± 0.222
2.5
1.5 ± 0.712
8
1.62 ± 0.217
0.91
1.9
1.7 ± 0.263
3.57
1
5.18 ± 0.577
9.14
11.6
4.57 ± 0.488
9.7
2.65 ± 0.355
7
±
±
0.641
0.543
±
±
±
±
1.375
0.402
0.579
0.610
±
±
±
±
±
±
±
0.512
0.496
0.573
0.674
0.729
0.293
0.239
±
0.334
±
±
±
0.428
0.684
0.789
6
7
8
29
1
Table 3. Estimates of the coefficients in the diversity model for three species-groups
2
from the combined analysis of yield across sites. For the linear model D = δE and for the
3
quadratic model D  E  1E 2 .
Coefficient
Speciesestimate Standard
group
Coefficient (t ha-1)
Error
ME
1
7.92
0.752
8.47
0.753
2
9.93
0.861
3
7.50
0.861
4
0.27
0.145

6.41
0.814

1
-3.32
0.782
Approx
DF*
22
23
25
25
20
216
548
Approx t
10.53
11.24
11.53
8.71
1.89
7.88
-4.25
P>t
<.001
<.001
<.001
<.001
0.073
<.001
<.001
NE
1
2
3
4


6.42
4.74
6.92
4.72
0.19
2.26
1.302
1.302
1.496
1.491
0.252
0.734
22
22
26
25
20
20
4.94
3.64
4.63
3.16
0.74
3.08
<.001
0.001
<.001
0.004
0.469
0.006
MM
1
2
3
4


5.13
4.24
8.06
7.43
0.08
1.38
1.680
1.680
1.924
1.924
0.323
0.945
22
22
25
25
20
20
3.05
2.52
4.19
3.86
0.25
1.46
0.006
0.019
<.001
0.001
0.805
0.160
4
5
* The approximate degrees of freedom (DF) are based on the Kenward-Roger
6
approximation (Kenward & Roger, 1997) and used in approximate t tests for
7
coefficients.
8
30
1
Table 4: The effect of diversity on unsown species biomass and proportion.
2
The average biomass of unsown species (tonnes ha-1), also expressed as a percentage of
3
yield, for monocultures and mixtures for each of four species-groups. The average
4
biomass was calculated over all sites in each species-group. For the calculation of the
5
average percentage, the average biomass from unsown species was calculated for each of
6
the communities across all sites within the species-group and an average percentage
7
computed for each community. These percentages were then averaged for monoculture
8
and mixed communities.
Speciesgroup
ME
NE
MM
DM
Monoculture
t ha-1
%
1.28
15.2
0.86
18.0
1.38
17.7
0.38
22.1
Mixture
t ha-1
0.61
0.29
0.95
0.32
%
5.3
4.3
10.1
10.0
9
10
31
1
Figures
2
Figure 1: Location of European sites.
3
The 28 sites are displayed according to the geographic species-groups. The red sites are
4
Mid-European (ME), the green are Northern-European (NE), the blue are Moist-
5
Mediterranean (MM), the orange are the Dry-Mediterranean (DM) and the pink are the
6
sites that used their own site-specific species (Other)
7
8
32
1
Figure 2: Graphical representation of (a) the 4-species simplex design and (b) the
2
relationship between sown evenness (E) and richness in the simplex.
3
(a) Each point in the tetrahedron represents a community with its position determined by
4
its sown relative abundance pattern, (P1, P2, P3, P4). Communities vary in sown evenness,
5
with the most even community at the centroid, where all s species are equally
6
represented. The communities at the vertices are the most uneven, containing 100% of a
7
species (e.g. (1, 0, 0, 0) represents a monoculture of species 1). The 15 experimental
8
communities in our design consisted of four monocultures (red points, e.g. a), four
9
mixtures dominated in turn by each species (blue points, e.g. b), six mixtures dominated
10
in turn by pairs of species (green points, e.g. c) and the centroid community (black point,
11
d). The sown evenness of the communities in the design varied from 0 through 0.64 and
12
0.88 to 1. The full design repeated this simplex at two levels of overall sown abundance.
13
(b) Species evenness-richness relationships within the simplex. The four vertices contain
14
100% of each species in turn and so have species richness (R) of 1 and evenness of 0 (e.g.
15
a). Where there are t species, E varies from nearly 0 to the maximum for that level of
16
richness, where the t species are equally represented. The six lines joining the vertices
17
contain all possible communities with species richness of 2 (e.g. the red line depicts all
18
two-species communities containing species 1 and 4 and point b shows a community with
19
maximum two-species evenness). The four faces contain all communities with species
20
richness 3 (e.g. the green shaded face depicts all three-species communities containing
21
species 2, 3 and 4 and point c shows a community with maximum three-species
22
evenness). In the interior of the tetrahedron, all communities contain all four species
23
(with evenness maximum at point d).
33
1
Figure 2(a)
2
3
Figure 2(b)
4
34
1
Figure 3: Average diversity effects (♦ for ME and □ for NE) and predicted diversity
3
effects ( for ME and --- for NE) for four levels of evenness. Average diversity effects
4
for the 11 mixed communities for each species-group were computed as the mean yield
5
for the community in the species-group minus the weighted average of the monoculture
6
yields, weighted by the sown species proportions in the community.
Diversity effect (t ha -1)
2
4
3
2
1
0
0.0
0.5
1.0
Evenness
7
8
35
1
Figure 4: Evidence for transgressive overyielding. For each species-group we show the
2
mean yield averaged over sites for 11 mixtures communities () and 4 monocultures ().
3
Details of the test of significance used are given in Appendix S2.
4
P < 0.01
14
P < 0.01
NS
P < 0.01
MM
DM
Average Yield (t ha-1)
12
10
8
6
4
2
0
0
ME
NE
8
5
6
7
36
1
Supplementary Material
2
3
Appendix S1: Covariance structure for the random coefficients for the final model across
sites.
4
In a random coefficient model with random coefficients for P1 to P4, M and E the form of
5
the variance-covariance matrix among these random variables must be specified.
6
Theoretically one can assume a completely unstructured variance-covariance matrix with
7
a distinct variance for each random variable and a distinct covariance between each pair
8
of random variables. For six random variables this gives 6 variances and 15 covariances
9
to be estimated. We could not achieve convergence of the process with such a large
10
number of parameters to estimate. Instead we used the following structure with 12
11
distinct parameters, assuming that the variances and covariances were indifferent to
12
species within grasses and also within legumes. Among the identity effects (Pi’s),
13
different values were used for the random coefficients for the grasses (2G) and legumes
14
(2L). There was a term for covariance between the identity coefficients for grasses (GG)
15
and legumes (GL) and between a grass and a legume (GL). The covariance between
16
either of the grass species (and either of the legume species) and M or either of the grass
17
species (and either of the legume species) and E was assumed to be the same.
P1
2G
P2
GG 2G
P3
GL
P4
GL GL LL
M
GM GM LM LM 2M
E
GE GE LE
LE
ME 2E
P1
P4
M
GL 2L
P2
P3
2L
E
18
19
37
1
The estimates of the random coefficients are as follows:
P1
2.84
P2
2.63
2.84
P3
0.11
0.11
5.17
P4
0.11
0.11
3.27
5.17
M
-0.13 -0.13 0.03
0.03
5.22
E
-0.06 -0.06 3.18
3.18
0.02
2.27
P1
P4
M
E
P2
P3
2
3
An E2 coefficient was not included in the final random model. A test (restricted to the ME
4
species-group) of the 5 terms (variance of E2 and covariance between it and the other
5
coefficients) indicated that they were not needed (P=0.146).
6
7
8
38
1
2
Appendix S2: Transgressive overyielding permutation test
3
Transgressive overyielding is estimated by the difference between the yield of a mixture
4
and that of the highest-yielding monoculture. Even if there is no difference between
5
species and no mixture effect, the expected difference between the yield of a mixture and
6
the highest yielding of a number of monocultures will be negative. This is a statistical
7
artifact caused by comparing one value sampled from a random distribution of yields
8
with the best of a number of other values drawn from the same distribution. Thus, this
9
test of trangressive overyielding is biased against the mixtures. Some bias against the
10
mixture will also occur even when there are true differences between monocultures. This
11
difficulty is also inherent in the following permutation test for transgressive overyielding.
12
It is based on observing for each species-group the number of the 11 mixtures in which
13
total aboveground yield exceeds that of the highest of the 4 monoculture yields. We then
14
check whether this number is extreme by comparison with what we might expect just by
15
selecting 11 values from the 15 yields at random and comparing them with the best of the
16
remaining 4. It is a two-sided test as the mixtures could be better than the best
17
monoculture or worse than the worst (underyielding); we cannot prejudge the direction in
18
advance. This is a conservative test for the reason of bias explained above i.e. the true P
19
value associated with the observed data is even lower than that delivered by the test.
20
21
The two-sided permutation test is based on the number of mixture means that exceed (or
22
are less than) the largest (smallest) of the four monoculture means. Let Z = {Z(1), Z(2), ... ,
23
Z(15)} be an ordered random vector; let S = {Z(i), Z(j), Z(k), Z(m)} be any subset of Z with
24
i,j,k,m  1,...,15 and i<j<k<m; let T be the other eleven elements of Z. For each unique S
25
(there are 1365), we observe the number of elements in T greater than Z(m) (say n1) and
26
less than Z(i) (say n2) and record the absolute difference between these two values as
39
1
d=|n1-n2|. The value of d ranges from 0 to 11 and the number of times each difference
2
from 0 to 11 occurs for all possible S and T is recorded. The most extreme difference is
3
11, which occurs when either all 11 elements of T are higher than Z(m) and none are less
4
than Z(i) (i.e. i=1, j=2, k=3 and m=4) or when all 11 elements of T are lower than Z(m)
5
and none exceed Z(i) (i.e. i=12, j=13, k=14 and m=15). Since a difference of 11 can only
6
occur in two situations, its probability is 0.0015 = 2/1365. The following cumulative
7
probability distribution is based on the proportion of cases giving a value of d greater
8
than or equal to the value of d in column 1:
d
11
10
9
8
7
6
5
4
3
2
1
0
# times out of 1365
that d occurs at
random
2
6
14
26
44
68
100
140
190
250
322
203
Cumulative
Probability
0.0015
0.0059
0.0161
0.0352
0.0674
0.1172
0.1905
0.2930
0.4322
0.6154
0.8513
1.0000
9
10
To apply this test we set Z to be the ordered set of averages for each of the 15
11
communities, S to be the ordered set of averages of each of the monoculture communities
12
and T to be the set of averages of each of the mixture communities.
13
40
1
Table S1: Information on sites. Multiple sites for a country are distinguished by letters in parentheses.
Country
Site**
Latitude
Longitude
Altitude
(m.a.s.l.)
SpeciesMean
N Fertiliser Harvests Size of
group* yield of all (kg ha-1 per
per
plots (m2)
plots
annum)
annum
(t ha-1)
Annual
rainfall
(mm)
Annual
temp (oC)
Germany
Renningen
48o46'N
9o11'E
460
ME
16.5
150
4
18.0
693
8.2
Ireland
Wexford
52o16'N
6o30'W
54
ME
15.8
150
5
16.0
1033
10.1
Lithuania (a) Dotnuva
55o24'N
23o50'E
71
ME
5.6
120
3
47.5
650
6.1
Lithuania (b) Dotnuva
55o24'N
23o50'E
71
ME
10.1
120
3
6.5
650
6.1
Lithuania (c) Dotnuva
55o24'N
23o50'E
71
ME
10.5
120
3
24.0
650
6.1
Netherlands
Wageningen
51o58'N
5o40'E
Norway (a)
Saerheim
58o46'N
5o39'E
7
ME
10.9
0
5
6.0
760
9.6
90
ME
12.1
0
3
12.0
1180
7.1
Norway (b)
Ås
59o40'N
10o51'E
95
ME
11.3
135
3
12.0
785
5.3
Poland
Brody
52o26'N
16o18'E
94.2
ME
8.0
120
4
9.0
587
8.0
Spain (a)
Gosol
42o13'N
1o39'E
1410
ME
8.0
40
3
8.75
948
7.9
Sweden (a)
Svalöv
56o55'N
13o07'E
55
ME
9.3
0
3
8.8
700
7.7
Sweden (b)
Svalöv
56o55'N
13o07'E
55
ME
10.1
0
3
8.8
700
7.7
Switzerland
47o26'N
8o32'E
491
ME
14.1
150
5
18.0
1031
9.4
Wales (a)
ZurichReckenholz***
Aberystwyth
52o26'N
4o01'W
30
ME
9.4
90
4
6.0
1038
9.7
Wales (b)
Bronydd Mawr
51o57'N
3o37'W
323
ME
9.5
90
4
6.0
1500
8.2
Iceland (a)
Korpa
64o09'N
21o45'W
35
NE
5.1
40
2
6.0
900
4.5
2
41
1
Table S1 Cont.
Country
Site
Latitude
Longitude
Altitude
(m.a.sl.)
Speciesgroup
Mean
Yield
(t ha-1)
Annual
rainfall
(mm)
Annual
temp (oC)
Iceland (b)
Korpa
64o09'N
21o45'W
35
NE
2.1
80
2
10.0
900
4.5
Norway (c)
Tromsø
69o40'N
18o56'E
15
NE
10.3
60
2
21.0
1031
3.1
Norway (d)
Løken
61o07'N
9o04'E
435
NE
9.6
80
2
10.5
576
1.6
Sweden (c)
Öjebyn (Piteå)
65o19'N
21o24'E
5
NE
8.6
60
2
19.0
539
2.1
France
43o05'N
1o43'E
162
Greece
Auzeville
Tolosane
Larissa-IKF***
MM
9.1
120
3
6.0
680
13.0
39o07'N
22o05'E
80
MM
3.1
0
4
4.7
451
15.7
Italy (a)
Fiume Veneto
45o55'N
12o43'E
19
MM
9.0
150
5
24.0
1260
12.0
Italy (b)
Ottava
40o44'N
8o32'E
80
DM
3.0
85
4
9.0
547
16.2
Zaragoza***
41o44'N
2o53'E
Spain (b)
225
DM
2.1
61
2
9.0
409
14.3
Belgium
Merelbeke
50o59'N
3o49E
11
Other
14.9
150
4
8.4
780
9.9
Denmark
Store
Heddinge
Mikkeli****
55o20'N
12o22'E
10
Other
12.5
200
3
12.0
603
8.5
61o40'N
27o13'E
107
Other
7.6
60
3
16.0
643
3.1
Finland
2
3
4
5
6
7
8
9
N Fertiliser Number
Size of
(kg ha-1 per
of
plots (m2)
annum) harvests
* There were three sites in the species group ‘Other’. They did not use one of the standard species groups and each used species that
were specific to that site. Belgium: Lolium perenne, Phleum pratense, Trifolium pratense and Trifolium repen. Denmark: (50%
Lolium perenne, 50% hybrid Lolium x boucheanum Kunth), Dactylis glomerata, Trifolium pratense and Trifolium repens. Finland:
Phleum pratense, Lolium arundinaceum, Trifolium pratense and Trifolium repens.
**Studied soils are located in a wide range of bio climatic regions and derived from different parent material (alluvial deposits, sand
dunes, lacustrine materials, volcanic formations). Basic soil properties greatly differ. Most soils are acidic and they have a light soil
42
1
2
3
4
5
6
7
8
texture. Increased CaCO3 was observed mainly in soils of South Europe (i.e. Spain, Italy). The content in soil organic carbon (C) and
distribution of organic N varied and can be attributed either to soil genesis factors or to human activities that affect biomass
production (e.g. irrigation, fertilization, crop history and land use). The C/N ratio in the soils ranged from 7.93 to 21.08 indicating
different degrees of decomposition of soil organic matter. The value of base saturation in the acidic sandy soils was low.
***Sites Greece-Larissa-IKF and Spain-Zaragoza weeded throughout and Switzerland weeded for the first two harvests in the
establishment year.
**** Barley was used on all plots as a nurse crop at establishment and harvested in the establishment year.
9
43
1
Table S2: Model selection in the combined analysis of yield across sites
2
Table S2 presents a number of random coefficient models fitted by maximum likelihood using SAS Proc Mixed. The models are
3
constructed so that additional hypotheses to be tested are introduced as additional coefficients in a set of hierarchical models. Tests of
4
these hypotheses are carried out by comparing the fit (measured by –2Log Likelihood (-2LL)) of models with and without the extra
5
coefficients representing the hypothesis of interest. The difference is asymptotically chi-squared with degrees of freedom equal to the
6
number of parameters being tested. Shown below are the models fitted, the comparison of coefficients/hypothesis being tested, the
7
degrees of freedom of the tests and the test statistics (the difference in –2LL) and the P value associated with the tests. SG is a factor
8
representing the different species-groups (ME, NE and MM). All the models presented below are crossed with SG. The definitions of
9
the factors and variables included in models, and associated with hypotheses to be tested, are:
10
N is the amount of Nitrogen applied (kg ha-1)
11
M is a factor indicating high and low levels of sown abundance.
12
BGL and BFS indicate a common pairwise interaction effect between species from different functional groups (BGS = grass x legume
13
and BFS = fast x slow)
14
WGL and WFS indicate a common pairwise interactions between species of the same functional group (WGL = grass-grass and
15
legume-legume interactions and WFS = slow-slow and fast-fast interactions).
44
1
2
‘Both’ indicates a common interaction coefficient between species that differ in both functional groups (i.e. slow grass x fast legume
3
and fast grass x slow legume).
4
Model A is the most basic model. For each species-group it includes only the sown composition (proportion of each species) and
5
overall sown abundance. It does not include any diversity effect. Model B introduces the E diversity coefficient for each species-
6
group. Models C-F are generalizations of model B that test for the inclusion of coefficients representing specific functional groupings;
7
Grass-Legume (C), Fast-Slow (D) and Both (E), and also unique coefficients for each pairwise interaction (F). Models G and H
8
include non-linear terms in evenness. Model I includes three species interactions. Models J and K include interactions between the
9
diversity terms and overall sown abundance. Model L includes a linear effect of nitrogen. Models M and N include interactions
10
between nitrogen and the diversity effects. Model O checks if the nitrogen effect changes with composition.
11
12
13
45
1
Table S2: Model selection tests for the combined analysis over sites.
Model #
A
Fixed Model by Species-group
P1+P2+P3+P4+M
Comparison
Terms Tested
Change #
Parameters*
-2LL
2583
P-Value
B
Model A+E
BvA
E
3
2546.4
< 0.001
C
Model A+BGL+WGL
CvB
Grass-Legume
3
2542
0.221
D
Model A+BFS+WFS
DvB
3
2545.6
0.849
E
Model A+BGL+BFS+Both
EvB
6
2541.3
0.531
15
2531.8
0.481
GvB
Fast-Slow
Both functional
groups
6 separate pairwise
interactions
E2
3
2525.5
< 0.001
Model
Model A+E+E2 +three-species
interactions
HvG
E3
3
2524.4
0.777
IvG
Three-species
interactions
12
2516.8
0.728
Model A+E+E*M+E2
JvG
E*M
3
2525.4
0.992
6
2523.2
0.890
F
G
H
I
J
Model A+P1P2+ P1P3+P1P4+P2P3+
P2P4+P3P4
Model A+E+E2
A+E+E2+E3
A+E+E2+E*M+E2*M
K
Model
L
Model A+E+E2+N
M
Model A+E+E2+N+N*E
N
O
Model
A+E+E2+N+N*E+
N*E2
Model
A+E+E2+N*P1+N*P2+N*P3+N*P4
FvB
KvG
E*M
E2*M
LvG
N
3
2514.9
0.014
MvL
N*E
3
2517.5
0.457
NvL
N*E+N*E2
6
2513.8
0.999
OvL
N*Pi
12
2508.7
0.906
2
3
* Models are fitted without an intercept due to unit constraint on the species relative abundances and so the model fits a separate parameter for
4
This is then a test of whether the three coefficients are equal and also a test of whether they are different from zero.
each species-group, e.g. the E*SG term will fit a separate E coefficient for each of the three species-groups.
46
1
Table S3: Data and permutation test for transgressive overyielding.
2
3
4
Mean yields (t ha-1) for 15 experimental communities averaged across sown abundance
levels and sites for each of the four species-groups. Community type is specified as either
Monoculture (Mono) or Mixture (Mix).
Sown proportions of
Species
1
2
3
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0.25
0.25
0.25
0.25
0.7
0.1
0.1
0.1
0.1
0.7
0.1
0.1
0.1
0.1
0.7
0.1
0.1
0.1
0.1
0.7
0.4
0.4
0.1
0.1
0.4
0.1
0.4
0.1
0.4
0.1
0.1
0.4
0.1
0.4
0.4
0.1
0.1
0.4
0.1
0.4
0.1
0.1
0.4
0.4
Community
Mono
Mono
Mono
Mono
Mix
Mix
Mix
Mix
Mix
Mix
Mix
Mix
Mix
Mix
Mix
Average mixture yield as % of best mono
yield
Value of d in permutation test
P value
Mean yields (t ha-1) of
Species-group
ME
NE
MM
DM
8.2
6.7
5.4
2.5
8.7
4.5
3.8
0.4
10.0
6.8
7.9
1.6
7.4
4.4
7.7
1.4
11.6
8.0
7.2
3.3
10.8
7.6
6.5
3.5
11.2
6.9
6.9
2.4
12.2
8.0
8.4
3.1
11.0
7.4
7.3
2.7
11.2
7.4
6.4
2.7
12.1
8.0
7.7
2.9
11.4
7.8
7.1
3.1
12.2
8.1
7.3
2.9
11.5
7.5
7.4
2.6
11.8
7.2
8.9
2.9
115
112
93
116
11
11
2
10
0.0015 0.0015 0.6154 0.0059
5
6
47
1
Table S4: Combined Analysis using established proportions.
2
3
Estimates of the evenness coefficients in the diversity effect from the combined analysis
based on calculating evenness from the established species proportions at harvest 1.
4
Estimates of coefficients (t ha-1)
Species-group
 (P value)
ME
6.70 (<0.001)
NE
1.67 (0.054)
MM
1.45 (0.199)
1 (P value)
-4.46 (<0.001)
5
6
7
48