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.