The concept of overyielding originated in plant sciences in the 1950s and 1960s and was widely used in the following decades to assess whether mixtures of plants performed better than expected when compared with monocultures. Overyielding has re-emerged in the last few years as an important method in the analysis of biodiversity experiments (Hector, 1998; Loreau, 1998; Loreau et al., 2001, 2002; Hooper et al., 2005) and other new research areas (Bernasconi et al., 2003). Biodiversity experiments manipulate community diversity (while holding other factors constant) to investigate impacts on ecosystem functioning. Previously, use of the overyielding concept has been limited mainly to the analysis of community ecology experiments on species interactions and in agricultural research, particularly intercropping. However, there has been relatively little work that assesses the overyielding concept in the context of community ecology theory. Loreau (2004) used the classical Lotka–Volterra competition model to investigate overyielding and functional redundancy of species in the context of theory on the stable coexistence of species (Fig. 1). In this issue, Beckage & Gross (pp. 140–148) also use Lotka–Volterra competition models to assess the frequency and degree of overyielding of theoretical communities.
Overyielding and relative yields
The concept of overyielding is based on the measures of relative yield and relative yield total. These measures were devised and pioneered in Wageningen during the 1950s and 1960s by De Wit (1960). The measures were devised for the analysis of traditional experiments in plant ecology (Harper, 1977) and agriculture (Vandermeer, 1989) where species were grown in monocultures and mixtures. The relative yield of a species is simply its yield in mixture compared with that in monoculture where the null expectation is the monoculture yield times the starting proportion in mixture (e.g. in a two-species mixture where species were planted or seeded at equal density the expected yield of each species is 50% of its monoculture value). The relative yield of a species is a measure of its performance under conditions of intra- and interspecific interactions relative to when only experiencing intraspecific interactions. An important additional consideration is the density under which species start growing. Biodiversity experiments have tended to use a substitutive approach where total density is held constant and in a two-species mixture plants of another species are substituted for half of the conspecifics of the monoculture. In biodiversity experiments, the monocultures provide the obvious null expectation as the situation with no effective biodiversity (at least at the species level and above). However, substitutive designs alter both diversity and individual species densities at the same time. Additive designs preserve monoculture density while adding plants from other species; a common application is in investigating the effects of weeds on crop yields. Density and diversity can be independently manipulated in a response surface approach which varies the density of both species as orthogonal design variables.
Relative yields tell you about individual species responses but not about the performance of the whole community. The relative yield total (RYT) is simply the sum of the individual relative yields. The null expectation is a value of one, as increases in the relative yields of some species are exactly compensated by declines in others. In a simple resource competition framework, RYT = 1 is consistent with a zero-sum game where a fixed amount of resource is divided up amongst species. RYT > 1 indicates increases in the relative yield of some species which are not exactly compensated for by declines in the relative yields of others. This could occur for various reasons, including resource partitioning in which species’ resource requirements do not exactly overlap and a mixture of species can therefore exploit resources more completely than any species alone. However, other processes could also produce RYT > 1, including facilitation where one species benefits another. RYT > 1 could also occur as a result of more indirect processes, such as reduced incidence or severity of pests or pathogens in mixtures relative to monocultures.
Mixtures of species are said to overyield when RYT > 1 (De Wit, 1960; Harper, 1977; Vandermeer, 1989). However, RYT > 1 does not mean that the mixture of species will necessarily outperform the monocultures of all of the constituent species. Whether this occurs or not depends on the balance between the yield-enhancing effects that cause RYT > 1 and the dilution effect caused by substituting individuals of the species with the best performing monoculture with those from species with lower-yielding monocultures. When the yield-enhancing effects outweigh the monoculture-dilution effect such that the mixture outproduces the highest yielding monoculture, a mixture is said to show ‘transitive overyielding’ (Harper, 1977; Vandermeer, 1989, but see Hector et al., 2002).
An additive partitioning of biodiversity effects
Relative yield totals have proved very useful but they have a number of limitations. The RYT gives an indication (subject to caveats like those above) of collective community performance (resource partitioning, etc.). However, it gives no collective indication of how abundant species are in mixture and how this relates to their monoculture performance. From an analytical perspective, the scaling of the RYT to a null value of one has the disadvantage that it imposes the asymmetry of a floor at zero but an open ceiling. The additive partitioning method (Loreau & Hector, 2001) extended the relative yield approach to define an overall net effect and to partition this into two additive components: a complementarity effect and a selection effect. The ‘net biodiversity effect’ (for a community formed from species started at equal densities) is simply the difference between the observed yield of the mixture and the average of the monoculture yields. The complementarity effect is based on changes in relative yields (or rather differences in observed relative yields vs their null expectation values) and is linearly related to RYT but scaled to a value of zero (so as to avoid the asymmetry mentioned above and for the convenience that anova and related methods usually automatically test vs a null value of zero). Complementarity effect values > 0 are consistent with resource partitioning, facilitation and related effects as described above, while values < 0 indicate interference competition. The other half of the partition is a covariance term which was inspired by the Price equation from evolutionary genetics (although the additive partitioning method and Price equation are not equivalent). The selection effect measures the covariance between a species trait (e.g. monoculture biomass) and its performance in mixture. In this scenario, positive selection effect values indicate dominance of communities by species with greater than average monoculture biomass and negative values indicate the converse.
A tripartite extension of the additive partition
One limitation of the additive partition is that it assumes, as do relative yields, that complementarity is distributed equally across species. This means that it may underestimate total complementarity, some of which falls under the selection effect (Petchy, 2003). Recently, Fox (2005) has extended the partition by adding a further split. The new extension removes the trait-dependent complementarity from the selection effect, leaving a pure dominance effect that quantifies changes in relative abundance resulting from pure resource competition. Interpreting the new trait-dependent complementarity effect is a little less straightforward, but Fox (2005) provides some possible biological interpretations. One simple application would be to view the new term simply as a correction factor. A new total complementarity effect could be defined as the sum of trait-dependent and trait-independent terms from the tripartite partition (the latter being the complementarity effect from the original partition). The dominance effect from the tripartite partition quantifies shifts in relative abundance resulting from pure resource competition, and the selection effect from the two-way partition quantifies shifts in relative abundance resulting from resource competition and all other species interactions.
As Beckage & Gross point out, there is some debate about how best to define transitive overyielding in biodiversity experiments. The situation in an agricultural setting is relatively clear: for a farmer the question is whether a mixture can overyield the most productive monoculture. However, in a nonagricultural setting the choice is less clear, because, in principle, every monoculture provides a potential benchmark for comparison (Hector et al., 2002). When would it not make sense to select the species that is highest yielding in monoculture as the benchmark? One situation occurs when the species that is highest yielding in monoculture is not highly abundant in mixture. Abundance is often taken as being inversely related to extinction risk (small populations are usually more likely to become extinct) so that a species that is not highly abundant in the original community may be one of the species that is lost. In this case, it would make no sense to take this species as a benchmark, no matter how high yielding it is in monoculture, since it is not present in the later depauperate community (Hector et al., 2002).
Overyielding and species coexistence: future perspectives
The new theoretical analysis by Beckage & Gross produces results largely in accord with Loreau (2004): a striking parallel between the conditions necessary for stable coexistence and those that generate overyielding. However, transitive overyielding will only occur under certain conditions, and situations are possible in which diversity and ecosystem functioning are not positively linked (Mouquet et al., 2002; Loreau, 2004). Further exploration of the conditions necessary for both overyielding and coexistence in different theoretical frameworks will provide a solid basis for the interpretation of biodiversity experiments and help to put the experimental results into the broader framework of community ecology.