Asymmetric competition, ontogenetic growth and size inequality drive the difference in productivity between two-strata and one-stratum forest stands

Size inequality has been considered a key feature of plant population structure with impacts on ecosystem functions. In forest ecosystems, studies examining the relationship between tree size inequality and stand productivity have produced mixed outcomes. These studies found positive, neutral or negative relationships and discussed how this could be influenced by competition for light between trees (e.g. light interception efficiency), but far less attention has been paid to the role played by tree ontogenetic growth. In this article, we present a simple mathematical model that predicts the basal area growth of a two-strata stand as a function of tree basal areas and asymmetric competition. Comparing the growth of this stand to the growth of a spatially homogeneous one-stratum stand and a spatially heterogeneous one-stratum stand, we show that higher growth of the two-strata stand is achieved for concave shape, increasing functions of ontogenetic growth and for low intensities of absolute size-asymmetric competition. We also demonstrate that the difference in growth between the two-strata stand and the one-stratum stands depends on tree size inequality, mean tree basal area and total basal area in the two-strata stand. We finally found that the relationships between tree size inequality and productivity can vary from positive to negative and even non-monotonous. However, we highlight that negative relationships may be more frequent. As a conclusion, our results indicate that ontogenetic growth can have a major impact on the form and the magnitude of the size inequality–productivity relationship.