When a disturbance regime or any other pattern of spatial or temporal
environmental variation changes, it takes time for populations to
reach their new stationary distributions, and during this time, the
competitive landscape is also in flux. This transition period between
one stationary distribution and another can be especially important
for plants and other sessile organisms, whose population dynamics are
especially sensitive to spatial structure. How long do these
transient dynamics last? How quickly can a community adjust to a
change in environmental variation? As a first step toward
understanding community responses to altered variational regimes, I
investigate the convergence of an annual-perennial plant system to its
stationary spatiotemporal distribution following a change in the
pattern of environmental variation. I calculate the convergence rate
(a.k.a. resilience) using a perturbative approach that assumes
environmental variation is small and explain when the calculation is
and is not sensitive to violating that assumption.
Results/Conclusions
I find that to good approximation, convergence is the sum of two
separate processes: global convergence and local convergence. The
global convergence process describes how the total or spatially
averaged populations reach their new levels. This is the process that
governs whether a change in environmental variation will lead to
extinction. The local convergence process describes how the
populations rearrange themselves into their new pattern of high and
low density areas, relative to the current means. This is the process
that governs how a change in environmental variation will affect
crowding or spatial segregation. Both processes are important in
describing how an individual's competitive environment changes
following a change in environmental variation. Global and local
convergence may occur on different time scales and either one may be
slower. While the slower process governs the populations' convergence
at later times, the faster process may dominate initially if it starts
further from its attractor than the slower process. In such a case,
the population converges to its new distribution quickly at first and
then slow down. That is, if the faster convergence process initially
dominates, a system may initially appear to be more resilient than it
would be under other circumstances.
