Field experiment
In the third year of our field experiment, we tested the individual and
interactive effects of nitrogen and phosphorus addition on biomass
production and plant species richness by performing ANOVA. We used
generalized linear models with normal error distributions for both
variables.
To quantify plant growth, we fitted a four-parameter logistic growth
model to species biomass data through time using a non-linear
mixed-effects regression model with equation 1 and 2 yielding 109 values
of \(\text{RGR}_{t}\) between day 146 and 254.
To assess whether early differences in growth rate between species
predict short-term competitive dominance in real-world ecosystem, we
related the relative difference in abundance at harvest and daily
relative differences in growth rates between day 146 and 254 for each
combination of pairs of species in a treatment combination using
equation 3 and 4 respectively, thus generating 109 regressions, one for
each day between day 146 and 254 during the growing season in 2013.
Because of the lack of a randomised blocked design, we fitted separate
models for each treatment and compared the estimates informally.
Calculations of \(\text{RGR}_{t}\) in the field study are based on
species growing in mixtures (in the common garden experiment these were
based on species growing in monocultures). In this case, \(K\), the
asymptotic mass in mixture, is a direct measure of competitive ability.
Hence we would expect competitive dominants to have high \(K\) values
and therefore high \(\text{RGR}_{t}\). We thus run a simple additional
analysis in which we calculated RGR as\(\log\left(\frac{B1}{B0}\right)/t\) where \(B0\) and \(B1\) are the
first and second measurements of biomass and \(t\) the time between. We
then related relative difference in abundance at harvest to relative
differences in growth rates for each combination of pairs of species in
a treatment combination using equation 3 and 4 respectively.
We assessed the relationship between the relative abundance in mixture
and daily relative differences in growth rates using generalized linear
models with a normal error distribution. The relative abundance in
mixture was the response variable and relative differences in growth
rates, nutrient treatments and their interaction were the explanatory
variables. A positive relationship would indicate that species with a
higher RGR at time \(t\) have greater competitive ability and
aboveground biomass at harvest.
We assessed whether early differences in species growth rate predict
short-term competitive exclusion in the nutrient addition treatment
using generalized linear models with a
quasibinomial
error distribution. A species was considered lost when it was present in
a plot in 2011 and absent from that plot in 2013. We related the
likelihood of a species to be lost after three years of nutrient
addition to daily RGR values for that species, thus
generating 109 regressions, one for each day between day 146 and 254
during the growing season in 2013. The likelihood of a species being
lost was the response variable, and RGR values, nutrient treatments and
their interaction were the explanatory variables. A negative
relationship would indicate that species with a higher RGR at
time \(t\) have greater competitive ability and exclude species with
lower\(\ \text{RGR}\). For each regression, we extracted the slope and
95% CI as well as the percentage of variance explained
(R2 value).