Simulation
To quantitatively examine the behavior of the two components with
respect to variation in the SAD and total abundance, we carried out a
simulation study using the R package mobsim (May et al., 2018). We
simulated spatially explicit Poisson communities (i.e., species had
random spatial distributions) with different SADs and total abundances.
We assumed lognormal SADs for the simulated communities, and
parameterized them with different species pools (100, 200, 300, 400, 500
and 600 species) and total abundances (1000, 2000, 3000, 4000, 5000 and
6000 individuals) in a full-factorial design, using 20 replicates for
each factor combination. We then sampled each of the communities with a
constant quadrat size corresponding to 20 percent of the total area.
Following the approach outlined above, we calculated the SAD and
N-components for the samples and examined how they responded to the
simulation parameters (i.e. species pool and total abundance). Our
simulations show that the SAD component responded to changes in the
species pool but remained unaffected by total abundance (supplementary
figure S1). Conversely, the N component consistently responded to
changes in total abundance and was unaffected by changes in underlying
SAD (supplemental figure S2). The findings from these simulations are
consistent our theoretical expectations from the IBR curve, and the
conceptual example shown in figure 1.