Statistical analysis
The main goal of this experiment was to estimate the contributions of
species sorting, ecological drift, and initial state to community
change. Overall variation in final species composition among communities
can be broken into these three components, whose contributions to
variation can be partitioned using an Anova framework (Travisano et al.
1995, Bell 2013). If Yij is the final frequency of the
focal species in community type i and replicate j, then its deviation
from that species’ mean initial frequency, Yinitial, can
be partitioned into three additive components representing the three
sources of variation:
Yij - Yinitial = (Yij -
Yi) + (Yi - Y) + (Y -
Yinitial)
where Yi is the mean final frequency of the focal
species in community type i, and Y is the grand mean final frequency of
the focal species across all community types and replicates. For n
community types (communities with different initial species composition)
each replicated m times, the total variation attributable to sorting,
drift and initial state can be calculated as follows:
- nm S (Y - Yinitial)2, the shift in
grand mean representing an overall convergence to an equilibrium
composition (sorting),
- m S (Yi - Y)2, the variance among
community types around the grand mean representing the influence of a
community’s initial state, and
- S S (Yij - Yi)2, the
variance among replicates of same community type representing neutral
variation (drift).
Such a partition was done for each species at the end of the experiment
to estimate the overall contributions of sorting, drift and initial
state, as well as for each intermediate census to assess how the
contributions changed over time.
We calculated a normalized value of the change in relative abundance of
each species at each census in each mesocosm as the difference between
the relative abundance of that species in the current and immediately
preceding census, divided by its relative abundance in the preceding
census. For each species, we used the regression of this normalized
change in relative abundance on its preceding relative abundance to
determine whether species dynamics were frequency-dependent. We used the
X-intercept (at which change in relative abundance is zero) as an
estimate of the equilibrium abundance of that species in a stable
community.