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).