Results
In the absence of animals, simple producer communities show positive diversity-productivity relationships across all levels of resource-use dissimilarity (RUD; Fig. 2a, overall average relationship shown by black line). The shape of the diversity-productivity relationship depends on the level of RUD and can be exponential (high RUD), sigmoidal (intermediate RUD), or saturating (low RUD) on a log2-scale of horizontal diversity (Fig. 2a, colored lines). Only for the special case in which all producers exploit the same resource compartments (i.e., RUD = 0, Fig. 2a), the relationship is neutral
At maximum producer species richness, all resources were accessible in all RUD scenarios, effectively maximizing yields regardless of RUD (Fig. 2a&b). On the contrary, the access to resources in monocultures directly depends on RUD: without RUD, all monocultures have access to all resource compartments, whereas, under the highest RUD, each monoculture can only utilize one-sixteenth of the total resource pool (i.e., one resource compartment). Consequently, monoculture yields (Fig. 2a, log2 yields at producer richness of zero) and thus expected yields YE (Fig. 2b, red dots) decreased linearly with increasing RUD. As a result, net diversity effects at maximum producer richness increased linearly with RUD, starting at zero net diversity effects when RUD = 0 (Fig. 2c). Since net diversity effects almost exclusively partition into complementarity effects with selection effects only playing a minor role (Fig. S1-3), RUD exhibits the behavior expected from resource-use complementarity. In comparison, the realized complementarity of the resources used by the producer community (i.e., Hexp) did not change linearly along the RUD gradient (Fig. 4b, Fig. S4).
Communities initialized with intermediate levels of producer richness (i.e., 2, 4, or 8 producer species) all failed to maximize yields at high levels of RUD (Fig. 2a&b), which led to reduced net diversity effects (Fig. 2c). For example, at maximum RUD, where species are never functionally redundant as they all access species-specific resource compartments, the loss of species directly lowers the resource availability and thus the primary production of the producer community. With decreasing horizontal diversity, net diversity effects became lower over more extensive parts of the RUD gradient. As the number of species necessary to fully utilize all resource compartments increases with RUD, losing species has the most severe effects at higher levels of RUD. Even though the resource availability might decrease, more species could coexist with increasing RUD (Fig. 4a, Fig. S5). The value of RUD at which net diversity effects were maximized shifted from its maximum in 16-species mixtures towards intermediate values in 2-species mixtures. Consequently, the power of RUD to explain the strength of net diversity effects depends on the completeness of the species pool. Regardless, as long as species differed in their access to resource compartments (i.e., RUD > 0), net diversity effects were consistently positive (Fig. 2c).
Introducing multi-trophic interactions and increasing animal richness increased net diversity effects on primary productivity (Fig. 3a, Fig. S1). For multi-trophic interactions to increase horizontal diversity effects, reductions in primary production due to animals feeding on producer species had to be larger in monocultures than in mixtures. A decrease in productivity of some producer species, which was apparent in monocultures and thus expected yields (Fig. 3e, Fig. S6), could be compensated in mixtures by competing producer species that shared resource compartments. Independent from animal richness, this maximized productivity in mixtures in most cases (Fig. 3d, Fig. S6) while also allowing more producer species to coexist (Fig. 4a, Fig. S5). Because the degree to which multi-trophic interactions could reduce monoculture productivity and thus expected yields does depend on how many resource compartments were accessible, increasing RUD reduced the potential of animals to alter horizontal diversity effects. This bottom-up control led to weaker effects of increasing animal richness and reduced variability of net diversity effects when increasing RUD (Fig. 3a, Fig. S1). When resource-use was not overlapping (i.e., RUD = 1), all producer species had access to independent resource compartments. Without animals, this led to maximum net diversity effects (Fig. 2c). In scenarios with animals, primary productivity losses due to consumption could not be compensated by other producer species. As a result, we found weak negative effects of multi-trophic interactions compared to no-animal scenarios in that specific case (Fig. S1). A loss of producer richness expanded the range of RUD in which producers could be limited to use distinct resource compartments, which makes multi-trophic interactions more likely to affect net diversity effects negatively.
With increasing animal richness, we found that complementarity effects increased from low levels in scenarios without animals to values that could be several times higher. The positive impact of animal richness on complementarity effects was exceptionally high in scenarios with low RUD (Fig. 3b, Fig. S2). A reduced producer richness can weaken these positive effects. Similar to scenarios without animals, the loss of producer species shifts the level of RUD at which net diversity effects maximize from high to medium values (Fig. S1). Further, the introduction of animals created both positive and negative selection effects. Neutral selection effects occurred in producer communities without animals. With increasing animal richness, we found that selection effects first increased (positive selection effects at low animal richness) and then decreased (negative selection effects at high animal richness). When RUD was high, selection effects were mostly neutral or negative (Fig. 3c, Fig. S3).
Complementarity and selection effects describe a gradual switch between two ways by which animals increase diversity effects: First, the positive selection effects found predominantly at lower animal richness indicate that more productive species in monoculture, i.e., species that experienced a lower feeding pressure, were on average also more productive in mixtures (Fig. 3c, Fig. S3). Second, negative selection effects found at high animal richness indicate that less productive monoculture species benefit more when growing in mixtures (Fig. 3c, Fig. S3). Because complementarity effects increase more than selection effects decrease, we found an overall increase of net diversity effects with increasing animal richness (Fig. 3a, Fig. S1). Without animals, selection and complementarity effects were entirely determined by RUD. Only when adding multi-trophic interactions, selection and complementarity effects directly responded to producer coexistence rather than RUD (Fig. S7-8). This effect was less apparent for net diversity effects (Fig. S9). Thus, increasing animal richness caused higher realized producer species richness (Fig. 4a, Fig. S5) and consequently higher realized complementarity in resource-use (i.e., Hexp; Fig. 4b, Fig. S4). In multi-trophic communities, producer species of low body-mass were less likely to survive as their productivity was reduced more due to herbivorous feeding. In simple producer communities, producer species survival and productivity were mostly independent of body-mass (Fig. S10, Fig. S11). Hence, the patterns in selection effects with increasing animal richness (Fig. 3c, Fig. S3) can be partially attributed to systematic shifts in the producer communities’ body-mass structure. Interestingly, we found that the survival of animal species was roughly constant at 80% across gradients of animal and producer richness (Fig. S12).