Study site and experimental setup

Our experiment was conducted at the La Hampa field station of the Spanish National Research Council (CSIC) in Seville, Spain (37°16′58.8″ N, 6°03′58.4″ W), 72 m above sea level. The climate is Mediterranean, with mild, wet winters and hot, dry summers. Soils are loamy with pH = 7.74, C/N = 8.70 and organic matter = 1.16% (0–10-cm depth). Precipitation totaled 532 mm during the experiment (September 2014–August 2015), similar to the 50-y average. We used ten common annual plants, which naturally co-occur at the study site, for the experiment. These species cover a wide phylogenetic and functional range and include members of six of the most abundant families in the Mediterranean grasslands of southern Spain (Table 1). Seeds were provided by a local supplier (Semillas silvestres S.L.) from populations located near to our study site. Our experiments were located within an 800 m2 area, which had been previously cleared of all vegetation and which was fenced to prevent mammal herbivory. Landscape fabric was placed between plots to prevent growth of weeds.

Theoretical background for quantifying niche and fitness differences

Here we summarize the approach developed in ref. 38 to quantify the stabilizing effect of niche differences and average fitness differences between any pair of species. Both these measures are derived from mathematical models that capture the dynamics of competing annual plant populations with a seed bank19,39. This approach has been used in the past to accurately predict competitive outcomes between annual plant species38. Population growth is described as:

$$frac{{N_{i,t ,+, 1}}}{{N_{i,t}}},=,left( {1,-,g_i} right)s_i,+,frac{{lambda _ig_i}}{{1,+,alpha _{ii}g_iN_{i,t},+,{mathrm{{Sigma}}}_{j = 1}^{mathrm{S}}alpha _{ij}g_jN_{j,t}}},$$


Where ({textstyle{{N_{i,t + 1}} over {N_{i,t}}}}) is the per capita population growth rate, and Ni,t is the number of individuals (seeds) of species i before germination in the fall of year t. Changes in per capita growth rates depend on the sum of two terms. The first describes the proportion of seeds that do not germinate (1 − gi) but survive in the seed soil bank (si). The second term describes how much the per germinant fecundity, in the absence of competition (λi), is reduced by the germinated density of conspecific (giNi,t) and various heterospecific (left( {{mathrm{{Sigma}}}_{j = 1}^{mathrm{S}}g_jN_{j,t}} right)) neighbors. These neighbor densities are modified by the interaction coefficients describing the per capita effect of species j on species i (αij) and species i on itself (αii).

Following earlier studies14,38, we define niche differences (1 − ρ) for this model of population dynamics between competing species as:

$$1,-,rho,=,1,-,sqrt {frac{{alpha _{ij}}}{{alpha _{jj}}}frac{{alpha _{ji}}}{{alpha _{ii}}}} .$$


The stabilizing niche differences reflect the degree to which intraspecific competition exceeds interspecific competition. 1 − ρ is 1 when individuals only compete with conspecifics (i.e., there is no interspecific competition) and it is 0 when individuals compete equally with conspecifics and heterospecifics (i.e., intra and interspecific competition are equal). Niche differences between plant species can arise for instance from differences in light harvesting strategies29,37,38,39, or in soil resource use and shared mutualisms40.

The average fitness differences between a pair of competitors is ({textstyle{{kappa _j} over {kappa _i}}})38, and its expression is the following:

$$frac{{kappa _j}}{{kappa _i}},=,frac{{eta _j,-,1}}{{eta _i,-,1}}sqrt {frac{{alpha _{ij}}}{{alpha _{ji}}}frac{{alpha _{ii}}}{{alpha _{jj}}}} .$$


The species with the higher value of ({textstyle{{kappa _j} over {kappa _i}}}) (either species i or species j) is the competitive dominant, and in the absence of niche differences excludes the inferior competitor. This expression shows that ({textstyle{{kappa _j} over {kappa _i}}}) combines two fitness components, the “demographic ratio” (left( {{textstyle{{eta _j – 1} over {eta _i – 1}}}} right)) and the “competitive response ratio” (left( {sqrt {{textstyle{{alpha _{ij}} over {alpha _{ji}}}}{textstyle{{alpha _{ii}} over {alpha _{jj}}}}} } right)). The demographic ratio is a density independent term and describes the degree to which species j has higher annual seed production, per seed lost from the seed bank due to death or germination, than species i

$$eta _j,=,frac{{lambda _jg_j}}{{1,-,left( {1,-,g_j} right)s_j}}.$$

The competitive response ratio is a density-dependent term, which describes the degree to which species i is more sensitive to both intra and interspecific competition than species j. Note that the same interaction coefficients defining niche differences are also involved in describing the competitive response ratio, although their arrangement is different. Because of this interdependence, a change in interaction coefficients (( {alpha _{ji}^prime s} )) simultaneously changes both stabilizing niche differences and average fitness differences21.

With niche differences stabilizing coexistence and average fitness differences promoting competitive exclusion, the condition for coexistence (mutual invasibility) is expressed as14,38:

$$rho,<,frac{{kappa _j}}{{kappa _i}},<,frac{1}{rho }.$$


This condition shows that species with large differences in fitness need to also have high niche differences to coexist. In contrast, species with similar fitness can coexist even with small niche differences. As a consequence, the mutual invasibility criterion allows us to quantify the degree to which a pair of species can stably coexist. Species pairs whose niche differences are much larger than the minimum required to overcome the fitness differences between them will be more stable than species pairs whose niche differences are close to the minimum. Species pairs whose niche differences are smaller than the minimum needed to overcome fitness differences will be unstable. We used this condition to relate the degree of stability to productivity (see below “Analyses” section).

Field parameterization of population models under two contrasting climatic conditions

We conducted a field experiment to parameterize these models with estimates of species germination fractions, seed survival in the soil and per germinant fecundities in the absence of neighbors. We also estimated all pairwise interaction coefficients between the species by growing each species in competition with itself and with all other species, in experimental plant communities in which we manipulated competitor density and identity, following previous experimental designs18. Specifically, we established 180 rectangular plots (0.65 m × 0.5 m) in September 2014 prior to the major autumn rains. We randomly assigned each of 80 plots to be sown with one of the ten species at a density of 2, 4, 8, or 16 g m−2 of viable seed, giving two replicates per density and per species. Each plot was divided into 20 subplots (a four row by five column array) with a buffer of 2 cm along the edge of the plot. At the center of each subplot, we sowed five viable seeds of one of the ten species, and germinants were thinned to a single individual per subplot. With this experimental design, we estimated each species’ germination fraction (gi) by counting the number of germinants and dividing by the total number of seeds originally sown in each plot. We also measured viable seed production on two focal individuals per species and plot, when they were competing with different numbers of neighbors of the same species, and with each of the other nine species (Nj) within a radius of 7.5 cm. We additionally established ten plots that had the same array but did not include any density treatment in order to measure viable seed production of focal individuals of the ten species in the absence of competition. Information from plots both with and without density treatments were combined to estimate per germinant seed production in the absence of neighbors (λi) and the interaction coefficients (αij) according to the function18.

$$F_i,=,frac{{lambda _i}}{{1,+,mathop {sum}nolimits_j {alpha _{ij}N_{j,t}} }}.$$


To fit this function, we used a maximum likelihood approach (optim method = L-BFGS-B with log-norm error structure) to ensure that λi ≥ 1 because negative germinant fecundities are not biologically meaningful. However, pairwise interaction coefficients (αij) were not bounded to any specific range. This procedure allows us to estimate the strength of both competitive and facilitative interactions between pairs of species. For each target species i, we fit a separate model jointly evaluating its response to individuals of all other species and itself. This approach fits a single per germinant fecundity in the absence of competition, λi for each species i. With this modeling approach, we found that competitive interactions were prevalent in our system. All pairwise interactions were positive (i.e., competition) under the control climate, and only two pairwise interactions were negative (i.e., facilitation), but close to zero, under the drought treatment. Although facilitation can be a source of complementarity15, we did not consider it in our further analyses because it was so rare.

Finally, to obtain the seed bank survival (si), we followed the method detailed in38, burying five replicates of 100 seeds each on the surrounding area from September 2014 to August 2015 and determining their viability as described in ref. 7. Finally, we repeated the same experiment with the remaining 90 plots, sowing seeds on 10th December 2014 to simulate a drier climate. We selected this type of treatment because annual species germination only occurs after major autumn rains and, in Mediterranean ecosystems, delays in the start of the rainy season strongly affect annual plant population dynamics41. This delay of 64 days resulted in changes in daylight, temperature, and rainfall between treatments. However, most notably, it produced a 38.7% reduction in precipitation (from 532 in the first experiment to 326 mm for this second experiment).

A biodiversity-functioning experiment with multiple functions

We conducted a biodiversity-functioning experiment to simultaneously estimate complementarity and selection effects for three different functions: biomass production, litter decomposition, and changes in soil nutrient content. We established 104 circular plots (0.75 m2) in the same area and at the same times as the competition experiment. We randomly assigned each plot to be a monoculture or a mixture of 3, 5, 7, 9, and 10 species. All plots were sown at a total seed density of 15 g m−2, and seed mass was evenly divided between the species in mixtures. To create the mixtures, we randomly assembled six different communities of three species, four communities of five species, three communities of seven species, and two communities of nine species. These communities, as well as the ten monocultures and the one 10 species mixture, were all replicated twice within each climatic condition (i.e., climate control and drought). We visually assessed the biomass of each plot biweekly, and collected aboveground biomass when it was maximal in each plot. We defined the peak of biomass as the first date when a majority of species were senescent. At this time, all species had produced flowers. Biomass was separated by species, air dried for 2 weeks, then oven dried at 60 °C during 3 days and weighed (g).

In addition, we conducted biweekly surveys of leaf senescence within species to estimate when to put litter bags in the soil. During these surveys, we collected senesced leaves to fill litter bags, which were placed in the ground at the peak of leaf senescence. We defined the peak of leaf senescence as the date when the number of individuals with clear senescence symptoms (several leaves dropped from the individuals) outnumbered those without. These litter bags initially contained between 0.35 and 1.5 g of leaf litter material from a single species, which was collected from individuals of the same plot where we placed the bags. We therefore avoided pooling litter from different plots to ensure that litter quality and litter decomposition rates are driven by the specific species traits and competitive, soil, and microenvironmental conditions of each plot. We separated litter bags for each of the species included in the plot. This might underestimate litter mixing effects but the alternative, a single litter bag with mixed litter, would not have allowed us to distinguish the identity of decomposed litter and therefore to estimate decomposition rates at the species level. After 3 months, litter bags were harvested, carefully brushed clean, dried at 60 °C during 3 days, and weighed to calculate the percentage of litter mass loss.

We assessed soil nutrient dynamics as changes in C, N, P, and K, Ca, Mg cations right before (September 2014) and after the experiment (September 2015), in the first 10 cm of soil. This corresponds to the soil depth influenced by annual plant vegetation in Mediterranean ecosystems and contains 95% of the total community root biomass42. For chemical analyses, soils were dried in the lab at 30 °C until constant weight, and sieved (2 mm) to eliminate stones and large roots. Soils were analyzed for total organic C (%) (Walkley-Black method43), total organic N (%) (Kjeldahl method44), available P (mg/kg) (Olsen method)45, and exchange cations (mg/kg) (Ca2+, Mg2+, K+, extracted with 1 M ammonium acetate and determined by atomic absorption).


We first explored the relationships between species diversity and biomass production, litter decomposition and soil nutrient contents at the end of the experiment. We tested for linear and nonlinear saturating relationships for the three types of functions using diversity interaction models20.

Then, we tested for correlations between complementarity/selection effects and niche/fitness differences, under the two climatic conditions and for the three functions considered. Because niche and fitness differences are defined as pairwise measures, we could not use the standard additive partitioning approach to calculate them10 and instead we used diversity interaction models20 to calculate measures analogous to complementarity which can be estimated for each pair of species and measures analogous to selection effects, which can be derived for each individual species. Although diversity interaction models were not originally built to estimate selection and complementarity effects, we reinterpret them as providing measures that relate to selection and complementarity conceptually and empirically. Species selection effects were estimated as the main effect of each species on each function and large values therefore indicate species that provide high levels of function when they dominate communities. This is analogous to the selection effect, which is high and positive when functioning in mixtures is dominated by species with high monoculture functioning. Complementarity effects occur when species on average increase their functioning in mixture compared to monoculture and therefore when functioning in mixtures is delivered by multiple species. Complementarity effects therefore occur when species compete less strongly with each other and perform better in mixtures than monocultures because for instance they partition resource use or they dilute each other’s specialist enemies. We therefore consider the pairwise interactions between species from the diversity interaction model to indicate complementarity between them. In order to convert selection effects to a pairwise measure we calculated the ratio between “selection effects” (intercepts from diversity interaction model) for pairs of species. We used the ratio rather than a difference because fitness differences are also defined as a ratio between species fitnesses (see Eq. 3). We then checked whether our measures of selection and complementarity effects derived from the diversity interaction models20 correlated with the original effects produced by the additive partition of Loreau and Hector10. In order to do this, we summed the individual (selection), or pairwise (complementarity) values from the diversity interaction models across all species in each community. These values correlated reasonably well with the values from the additive partitioning (r-values ranging between 0.487 and 0.769; Supplementary Fig. 2).

We used Mantel tests, and the Benjamini and Hochberg correction for multiple comparisons, to test for significant correlations between coexistence (niche and fitness differences, Eqs. 2, 3) and biodiversity-functioning mechanisms (complementarity and selection effects). In addition to analyzing the overall fitness differences we also split them into their two components, the demographic ratio and the response to competition ratio, and correlated each component with complementarity and selection effects. The same Mantel test procedure was also used to test for the correlation between the stability of species pairs (difference between the observed niche difference and the minimum niche difference needed to allow coexistence) and the degree of function predicted for that pair. We used our diversity interaction models to estimate the degree of functioning predicted for each species pair. Finally, we analyzed whether niche differences need to exceed fitness differences to maximize function or whether large niche differences alone are sufficient to lead to high ecosystem function. We derived a metric that combines the effect of both determinants of competitive interactions following Eq. 4, we computed for each species pair its excess of niche differences, i.e., the extent to which niche differences exceed those necessary for stable coexistence. The metric was derived as the observed niche differences minus the niche differences needed to offset the observed average fitness differences between the species. A more positive excess of niche differences means that the species pair can coexist more stably whereas a more negative value indicates the opposite. We then determined whether niche differences alone, or the excess of niche differences, correlated better with predicted functioning for the species pair by comparing the correlation coefficients between the two measures of niche differences and ecosystem functioning using package “cocor” version 1.1-346. All analyses were conducted in R Version. 3.5.347.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.


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