Whether in the context of patchy disturbance, resource pulses, or
other, more subtle forms of environmental variation,
variation-mediated coexistence has attracted ecologists' interest for
years.  Under what circumstances is environmental variation likely to
have a large influence on species coexistence and under what
circumstances can we likely ignore variation?  Environmental
variation's capacity to promote or suppress species coexistence
depends on its spatial and temporal scales and on the life history
traits of the species involved.  I have investigated when and how
environmental variation becomes important using a model of competing
annual plants with a seedbank in a stochastic environment that is
correlated in space and time.  I find that at least for this model,
spatiotemporal variation and spatial variation influence coexistence
more than temporal variation and that environmental variation promotes
coexistence most strongly when variation is correlated over larger
spatial and temporal scales (``reddened noise'').  Variation has the
most influence on species coexistence when both species have
long-range within-species competition, short-range between-species
competition, and short-lived seeds that disperse over short distances.
These traits cause the numerically dominant species to accumulate in
favorable areas and allow the low-density species to become
concentrated in areas with little competition, although possibly with
less favorable habitat.  Species thus coexist in a regional sense but
are locally segregated.  These traits are most effective for variation
at large spatial and temporal scales, the scales that dominate in
reddened noise, but even white (uncorrelated) variation influences
coexistence most when species have these life history traits.