Measurements of the intensity and importance of competition
To quantify the competition intensity, we calculated the target response to competition for each target species using the natural-log transformed response ratio (ln RR) (Hedges et al. 1999):
\begin{equation} Competition\ intensity=ln\frac{\text{Biomass}_{\text{mixture}}}{\text{Biomass}_{\text{alone}}}\nonumber \\ \end{equation}
Where \(\text{Biomass}_{\text{mixture}}\) is the biomass of the target species (S. grandis or S. krylovii ) grown in mixture with a neighbor under the low (or high) soil nutrition treatment, and\(\text{Biomass}_{\text{alone}}\) is the average biomass of the target species (S. grandis or S. krylovii ) grown alone under the same soil nutrition treatment. The competition intensity is the degree to which competition contributes to the overall decrease in growth potential of an organism below its alone condition. Values of lnRR are symmetric around 0, so that a positive value indicates a positive effect (competition facilitation) of the treatment on the target species and a negative value indicates a negative effect (competition inhibition).
In addition, to quantify the importance of competition, we calculated the neighbor-effect importance with additive symmetry (NImpA ) as recommended by Díaz‐Sierra et al. (2016):
\begin{equation} \text{NImp}_{A}=2\frac{Biomass}{2\text{MaxBiomass}_{\text{alone}}-\text{Biomass}_{\text{alone}}+|Biomass|}\nonumber \\ \end{equation}
Where \(Biomass\) is calculated as\(\text{Biomass}_{\text{mixture}}-\text{Biomass}_{\text{alone}}\), indicating the total impact of neighbors, and it is positive for facilitation and negative for inhibition. \(|Biomass|\) is its absolute value, and \(\text{MaxBiomass}_{\text{alone}}\) is the maximum of the biomass grown alone under both soil nutrition conditions. The importance of competition is the relative contribution of the presence of a neighbor among all processes (i.e. soil nutrition) that affect the organism’s performances and population dynamics.
For each target species, we got its intensity and importance of competition within each soil nutrition condition (2) and neighbor (3) cross-treatment, respectively.