Background/Question/Methods In a heterogeneous environment, short-range seed dispersal can
strongly promote coexistence by causing species to become spatially
segregated. However, selection acts to maximize the fitness of each
species individually, not to maximize the likelihood of coexistence.
If the mean seed dispersal distance of two species is allowed to
co-evolve, does this promote or discourage coexistence?  That is, will
each species have a faster or slower growth rate from low density in
the presence of its competitor?  I have investigated this question
using a model of competing annual and perennial plants in a
stochastically fluctuating environment that is positively
auto-correlated in space and time. To calculate fitness/long-run
growth rate, I use an analytic approximation which assumes
small-amplitude environmental variation. I then use adaptive dynamics
to calculate the optimal mean dispersal distance for each species when
growing alone and when growing in the presence of its competitor
(dispersal co-evolution). Finally, I compare each species' growth
rate from low density when it and its competitor disperse their
co-evolved distances to when they disperse their monoculture-evolved
distances. (For simplicity, I only consider parameter regimes in
which there is a stable monomorphism.)

Results/Conclusions I find that if the annual and perennial prefer different environmental
conditions, so that short-range dispersal produces spatial
segregation, then co-evolution shortens both species' dispersal and
promotes species coexistence. (I.e., both species have a higher
growth rate from low density in the presence of their competitor when
the two disperse their co-evolved distances instead of their
monoculture-evolved distances.)  If the two species prefer identical
environmental conditions, then the annual (the inferior competitor)
disperses farther than it would in monoculture, while the perennial
disperses slightly shorter. This allows the annual to reduce the
competition imposed by the perennial at the expense of reducing its
association with favorable habitat. For very short-range spatial
correlation in environmental conditions, these changes in annual and
perennial dispersal increase the perennial's low-density growth rate
at the expense of the annual's low-density growth rate. In most
cases, however, co-evolution promotes coexistence.