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.