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Monocultures differ significantly in their ability to colonize the C. elegans intestine
To investigate community assembly in the gut of C. elegans, we fed germ-free synchronized adult worms with different bacterial species, in monoculture or in mixture, over 4 days in a well-mixed rich liquid medium (Methods, Fig. S1A). The majority of worms survived the 4-day period of feeding and colonization, after which we allowed live worms to feed briefly on heat-killed E. coli OP50 to remove transient colonizers [35, 45]. We then cleaned the surface of the worms with consecutive washes, and measured the intestinal bacterial densities by grinding batches of worms, plating, and counting colony forming units (CFU, Fig. S1B) with distinct morphologies [46]. The supernatant of each sample was plated to verify that CFU counts came from the worm digestions instead of the background media (Methods). This protocol allowed us to construct and quantify simple microbiotas in C. elegans.
We began by feeding C. elegans in monoculture to quantify the ability of a range of bacterial species to colonize and grow in the worm intestine. As a starting point, we first utilized an immunocompromised C. elegans mutant (AU37) and a set of eleven non-native bacterial species (Fig. 1B), representing the phyla Firmicutes (gram-positive) and Proteobacteria (gram-negative). We found that all bacterial species colonize (i.e., accumulate with or without active growth) the C. elegans intestine, with mean population sizes (Figs. 1C, S1C) ranging from 200 CFU per worm in the case of B. cereus, up to 20,000 CFU/worm in the case of S. marcescens. Our three Firmicutes reach low population sizes in the worm gut and low carrying capacities in the liquid media (Fig. S1E), but the carrying capacities in the liquid media do not explain the variation in monoculture colonization (Fig. S1F, G). These results indicate that different non-native bacterial species have a wide range of abilities to colonize the C. elegans intestine in monoculture.
Composition of two-species microbiotas are influenced by competitive and hierarchical bacterial interspecies interactions
To assess the compositional trends of the C. elegans microbiota, we constructed the simplest intestinal communities in this worm by feeding it with all possible two-species mixtures from the same eleven non-native bacteria as before (55 pairs, Figs. 2A, S2A). We fed worms with both bacteria present at similar concentrations (~107 CFU/mL, Methods) to normalize the rate of ingestion. We found that a majority (41 out of 55, ~75%) of pairs displayed coexistence, with both species present above the detection limit of 2%, whereas the remainder (14 out of 55, ~25%) led to competitive exclusion of a species (Figs. 2B, S2B). These results show that bacteria with no prior conditioning for the C. elegans gut commonly reach coexistence in two-species microbiotas.
Fig. 2: Monoculture colonization of the worm intestine often fails to predict composition of two-species microbiotas.

A LEFT panels: Fractional abundances of 55 co-culture experiments in C. elegans intestine (AU37); error bars are the s.e.m. of 2–8 biological replicates (Fig. S2). Bacterial species are ordered from left to right by their mean fraction across all co-cultures. RIGHT panels: Null expectation for the fractional abundances based on a noninteracting model where each bacterial species reaches its population size in monoculture; error bars are the s.e.m. from bootstrapping over the monoculture data. * and ** represent a statistically significant difference between the two panels at p values of 0.05 and 0.01, respectively (Welch’s T test). B Coexistence of two species is more common than competitive exclusion in the worm intestine. C Low yields in two species microbiotas—relative to monocultures—are indicative of competitive interactions (Fig. S2); error bars on X-axis are the s.e.m. and on Y-axis the s.e.m. from bootstrapping over monoculture and pairwise data simultaneously. D Competitive ability, defined as the mean fractional abundance in co-culture experiments, relates to monoculture population size, but there are significant deviations; error bars on Y-axis are the propagated error from the s.e.m. of the co-culture experiments.

Full size image

The interactions between bacterial species in a microbiota can be classified as positive, negative, or neutral based on the yields of the bacteria relative to their monoculture population sizes. To classify the interactions in our two-species microbiotas, we calculated the relative yield of species “i” with species “j”, RYi|j, as its population size in co-culture, Ni|j, divided by its population size in monoculture, Ni (RYi|j = Ni|j/Ni, see Methods for detailed implementation). We found that most species cannot reach their monoculture population size in co-culture experiments, RY  More

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We used a dataset from a grassland diversity experiment at Zürich-Reckenholz, Switzerland, in the Atlantic central climatic zone of Europe. The data contain measurements on many functions from 78 plots that comprised monocultures and mixtures sown at a wide range of species relative abundances, set up at three levels of N fertiliser application and maintained for 3 years following establishment, which is a typical time in grassland-crop rotations.
Monocultures and mixtures were sown following a simplex design64. Four perennial species, known to be key forage species in ruminant production, were selected based on the factorial combination of their functional traits related to temporal establishment (fast-establishing vs. temporally persistent), and N acquisition (non-fixing for grasses, N2-fixing for legumes). The species were Lolium perenne L. cultivar (cv.) Lacerta (fast-establishing grass), Dactylis glomerata L. cv. Accord (temporally persistent grass), Trifolium pratense L. cv. Merviot (fast-establishing legume), and Trifolium repens L. cv. Milo (temporally persistent legume). The type of stands were: monocultures (100% of one species), binary mixtures (50% of each of two species), an equi-proportional mixture (25% of each of the four species), dominant mixtures (70% of the dominant species, 10% of each of the other three), and co-dominant mixtures (40% of each of two species, 10% of each of the other two; see Supplementary Table S1). All types of stands were sown at two levels of overall sown density, with the high level being the recommended seed weight (100%) under conditions typical of Switzerland, and the low level being 60%.
The experiment was sown in August 2002 on plots of 3 m × 6 m and was maintained from 2003 (year 1) to 2005 (year 3). The plots were fertilised with N fertiliser (as NH4NO3) at rates following a geometric series: 50, 150, or 450 kg N ha−1 yr−1 (N50, N150, and N450, respectively), split into five equal applications. In early spring, all plots received phosphorus and potassium in amounts expected to be non-limiting for intensively managed grasslands on fertile soils in Switzerland. At the N150 treatment, all types of monocultures and mixtures were established, whereas the N50 and N450 treatments only included the monocultures, the equi-proportional mixture, and the dominant mixtures. The 78 plots were arranged in a fully randomised design. Consult Nyfeler et al.37 for full details of the experimental design, establishment, and maintenance.
Ten functions were measured representing (i) forage production: aboveground biomass yield, standard deviation of yield, temporal stability, weed biomass; (ii) N cycling: symbiotic N2 fixation, N efficiency, NO3 in soil solution; and (iii) forage quality: crude protein content, organic matter digestibility, metabolisable energy content (Table 1). To date, detailed analyses from the experiment have been published on two functions, namely biomass yield37 and symbiotic N2 fixation33.
Measurement of functions
Aboveground biomass yield and weed biomass
All plots were harvested five times annually at 5 cm above ground surface. Aboveground biomass yield at each harvest was determined by drying a representative subsample to constant weight (65° C for 48 h), and this data was summed to give total annual biomass yield. Biomass proportions of the four sown and pooled unsown species (weeds) were measured by manually separating samples from permanent sub-plots (0.8 m × 0.3 m), which was done at the first, third, and fifth harvest of each year. These data allowed for calculation of weed biomass per ha and year.
Standard deviation and stability of yield
Year-to-year standard deviation of yield (SDyield) was calculated from the annual yields of the three experimental years, and stability was defined as the ratio of averaged annual yields to year-to-year SDyield (following Lehman and Tilman65). To measure yield variation within each year, seasonal SDyield was calculated from the five annual harvests, and seasonal stability was defined as the ratio of total annual yield to seasonal SDyield. We purposely use both SDyield and stability as both measures are essential to evaluate yield variation66.
Symbiotic N 2fixation
Symbiotic N2 fixation (Nsym) was determined by the isotope dilution method67. Double-labelled 15N-enriched 15NH415NO3 was applied on a permanently defined, central part of each plot (1.4 m × 1.5 m). Plant samples were analysed for 15N and 14N abundance by gas isotope ratio mass spectrometry and by thermal conductometry. Nsym in the sward, as calculated here, comprises legume N derived from the atmosphere (Ndfa) plus N derived from apparent Ndfa transfer to the grass (Ntrans). See Supplementary Appendix S1 and Nyfeler et al.33 for full details of measurements and calculations.
N efficiency
N efficiency was defined as the ratio of total N yield to the amount of applied fertiliser N and therefore measures the total N output of the system in relation to the fertiliser N input. Total N yield was calculated by first multiplying N content from biomass samples with their total dry mass to give the N yield per harvest. Annual total N yield was then computed as the sum of all harvests.
NO 3in soil solution (NO3)
Porous cup tension lysimeters were installed to extract soil water from a depth of 60 cm below ground surface. In 2-week intervals from October 2004 to April 2006, a suction of 80 kPa was applied 1 day prior to sampling, and concentrations of nitrate–N (NO3-N) were determined by spectrophotometry. We note that NO3 data were only available for years 2 and 3. See Supplementary Appendix S1 for details of the measurements.
Crude protein content 
Crude protein content (CP) in stand biomass was calculated from the N content in biomass samples, multiplied by 6.25. The justification for the multiplicative factor is given by the fact that all biological proteins contain on average 16% N68.
Organic matter digestibility
Organic matter digestibility (OM digestibility) was determined from biomass samples of the second and fourth harvest following the two-stage in vitro fermentation process with rumen liquor and acidic pepsin solution according to Tilley and Terry69; see Supplementary Appendix S1 for details. Information on OM digestibility was only available for years 2 and 3 of the study.
Metabolisable energy content
Metabolisable energy content (ME) of stand biomass was calculated based on OM digestibility and CP following a reference manual of Agroscope70; see Supplementary Appendix S1 for calculation. Due to the connection with the measurement OM digestibility, ME data were only available for years 2 and 3.
Data for each function were computed at the plot level for each of three experimental years (the three exceptions as noted). For analyses across years, data was averaged across available years, except SDyield and stability (see above).
Data analyses
We applied the multivariate modelling framework13 to estimate simultaneously species identity and diversity effects of the ten functions along with effects of N fertilisation. To allow direct comparisons of the model terms, all functions’ data were standardised to a common scale by dividing them by their maximum value (at a single year) over the 3-year experiment and N fertilisation treatments. This scaling allowed for a direct comparison of results among years. Note that the multivariate approach is a generalisation of the univariate diversity interaction model61, and we refer to Supplementary Appendix S1 for a summary to the univariate regression.
In the following, we generally refer to the analysis of data averaged across experimental years, and all equations model the response at a single plot (plot subscripts are omitted). A preliminary regression equation was specified for the kth function (k = 1–10) with:

$${y}_{k}={alpha }_{k}mathrm{DENS}+sum_{f=1}^{3}sum_{i=1}^{4}{beta }_{ifk}{P}_{i}times {mathrm{N}_mathrm{Treat}}_{f}+sum_{begin{array}{c}i,j=1\ i More