Growth rates on conditioned soil (ri,j) were derived
from plant biomass on PSF plots (input data) in 2017 and/or 2018
(Kulmatiski et al. 2011). ‘Neutral’ growth rates (νi)
were set to be growth rates on ‘home’, ‘away’, or across all PSF plots.
Growth rates were calculated from final biomass on different soil types.
For example for Pi,j, ri,t =
(Pi,j/P0)1/T-1, where
T=52 time steps, P0 = g m-2.
Two models (equation 1 or 2), three sources of input data (2017 only,
2018 only, or 2017 then 2018), and three ‘neutral’ growth rates (home,
away, all plots) produced 18 Null and 18 PSF model simulations. Carrying
capacities were defined as the mean ± two standard deviations of total
plant biomass (Κ) in diversity-productivity plots or plant species
biomass (κ) across all PSF plots. Models were run for three 52-time step
iterations (t). To simulate harvest, each 53rd time step, plant biomass
was set to 1 % of Pi,t. Simulations were performed in R
(R Core Development Team, 2015).
Dissecting Mechanisms Driving the Diversity-Productivity
Relationship
We estimated the net biodiversity effect based on calculations proposed
by Loreau & Hector (2001), which estimate the yield increase ΔY of a
plant community compared to the combined performance of plant species in
monocultures. We further used equations to partition the net
biodiversity effect (ΔY) into selection and complementarity effects
(Loreau & Hector, 2001).
Statistics
To describe species richness effects, we fit random intercept (linear
mixed) and linear mixed models in R (R Core Development Team, 2015)
using lme4 (Schielzeth & Forstmeier, 2009; Bates et al, 2015; Schmid et
al., 2017). Due to low establishment in 2015, we analyzed species
biomass data by plot and year (i.e., the sum of spring and fall harvests
as g dry mass m-2) for 2016 and 2017. Analyses
followed those of Roscher et al. (2008) on the pre-existing diversity
productivity experiment. The maximum likelihood method was used to find
the ‘best’ random model among random intercepts such as species
composition (com), year and their interaction (Roscher, Schumacher,
Weisser et al., 2007; Roscher et al., 2008). The effects of block (soil
gradient; Huston & McBride, 2002; Weisser et al., 2017) and the
interaction of block and Year (block:Year) were included as random
intercepts for the pre-existing experiment, but not for the current
experiment which was located in one area. From these random intercept
models with no fixed effects, we extracted fixed effects of interest
(Schmid et al., 2017). The contrast of monoculture and polyculture (MP)
and the linear contrast of species richness (SR) were fixed effects
(MP+SR). When analyzing mechanisms of the diversity-productivity
relationship (selection and complementarity), the model was fit without
the contrast of mono- and polycultures. Mixed models were fit with the
maximum likelihood method to derive statistical significance of fixed
effects from likelihood ratio tests (Χ 2;
Roscher et al., 2016). To avoid pseudoreplication, replicate plots were
averaged prior to analyses so that the diversity productivity dataset
had 300 samples (100 species compositions x three years). To compare
species richness effects between experiments and simulations, a second
random intercept model was used with the fixed effects model:
data+SR+data:SR and random intercept model: com+com:Year where data is
the data source (i.e., observed, PSF, or Null model predictions).