Price Equation
We used an ecological adaptation of the Price equation (Fox & Kerr 2012; Bannar-Martin et al. 2017) to partition overall richness and biomass changes into those associated with species losses, species gains, and persistent species between two samples in time in every plot (Figure 1). This equation quantifies additive differences between comparable units (e.g., plots). Here, this equates to additive species-level changes in aboveground biomass through time associated with specific changes in species composition. To quantify changes through time, we compared the composition of each plot in the year before fertilization (year 0, t0) to itself at every subsequent time-step (comparison, year n, tn) using the R package priceTools (Bannar-Martin et al. 2017) (Figure 1). We use this approach to quantify a cumulative rate of change in each plot across time.
We partitioned changes in species richness and biomass in each plot into five continuous response variables: 1) number of species lost (s.loss, species unique in baseline (t0) compared to same plot at another point in time (tn)), 2) number of species gained (s.gain, species unique in comparison plot (tn) compared to species in baseline (t0)), 3) biomass change associated with species loss (SL, biomass change associated with species loss, year 0), 4) biomass change associated with species gains (SG, biomass associated with species unique in comparison, year tn), and 5) the change in biomass associated with persistent species (PS, species shared between comparisons year t0 and year tn) (Figure 1). We compare control plots to themselves through time, and NPK plots to themselves through time to examine component changes under ambient conditions and under fertilization. These pairwise comparisons resulted in continuous response metrics for every year after year 0 (t0) that we hierarchically modelled as a function of time. This estimates a rate of change over time (i.e., slope) for each metric, allowing us to examine general temporal trends and make direct comparisons of site-level variability within and among treatments and sites. We focus on the estimated overall rates of change (slope parameters) for each metric component in our results and discussion.