Spatial distribution of microbial biomass and respiration
(H1)
To test the effects of distance to the closest tree and depth on the
soil microbial biomass and respiration, we used linear mixed-effects
models and normal distribution assumptions that included plot as a
random effect, and distance and depth as fixed effects. The model was
fitted on monospecific pairs and was used to predict the soil microbial
properties over a distance to the closest tree from 0 to 90 cm and a
depth from 0 to 10 cm (Suppl. S2).
Belowground overyielding between heterospecific tree pairs
(H2) Belowground overyielding of soil microbial biomass and respiration was
calculated as the difference between observed soil microbial properties
between a heterospecific pair and what would be expected based on the
weighted means of the monospecific pairs for a given position between
the trees (overyielding (position = i, depth = j) =
observed (i, j) – ((expectedL.
formosana (i, j) + expected S.
saponaria (i, j)) / 2)), where ”i ” is the
position between the trees and ”j ” is the depth. Positive results
indicate soil microbial properties in mixed pairs are overyielding
(i.e., producing more biomass or respiration than expected based on
monospecific pairs), and negative results indicate soil microbial
properties in mixed pairs are underyielding (i.e., producing less
biomass or respiration than expected based on monospecific pairs). The
expected values were predicted from the model fits from H1.
We used belowground overyielding as a response variable to test for the
effect of the heterospecific pair on the aggregated soil samples, as
well as for the effect of depth using a linear mixed-effects model with
plot as random effect and pair as fixed effect.
To determine differences between soil depths, we used a Tukey HSD test
based on an analysis of variance (ANOVA type 1).
Spatial distribution of belowground overyielding (H3)
To test the effects of distance to the tree species and depth on the
belowground overyielding of soil microbial biomass and respiration, we
used linear mixed-effects models, which included plot as a random effect
and distance in centimeters from the trees and depth as fixed effects
(Suppl. S2). We fixed the positions of the trees to L. formosanabeing tree 1 and S. saponaria being tree 2 in a mixed pair. Like
this, the positioning of the trees was fixed within the data and could
be analysed in terms of a spatial gradient.
All linear mixed-effect models were fitted, using the ”lmer” function of
the R package lme4 (Bates et al. 2015). To define the
quality of the model fits of all used linear mixed-effects models, the
”check_model” function of the R package performance (Lüdecke et
al. 2021) was used to investigate various model assumptions, such as
normality of residuals, normality of random effects, linear
relationship, homogeneity of variance, and multicollinearity (Briggs and
Cheek 1986).