We consider a competitive reaction diffusion model of two species in a
bounded domain which are identical in all aspects except for their
birth rates which differ by a function $g$. Under fairly weak
hypothesis, the semitrivial solutions always exist. Our analysis
provides a description of the stability of these solutions as a
function of the diffusion rate $\mu$ and the difference between
the
birth rates $g$. In the case in which the magnitude of $g$
is small we provide a fairly complete characterization of the
stability in terms of the zeros of a single function. In particular,
we are able to show that for any fixed number $n$, one can choose
the
difference function $g$ from an open set of possibilities in such a
way that the stability of the semitrivial solutions changes at least
$n$ times as the diffusion $\mu$ is varied over $(0,\infty)$.
This
result allows us to make conclusions concerning the existence
of
coexistent states. Furthermore, we show that under these hypothesis,
coexistent states are unique if they exist.
The biological implication is that there is a delicate balance
between resource utilization and dispersal rates which can have a
dramatic impact with regards to extinction. Furthermore, we show that
there is no optimal form of resource utilization. To be more precise,
given a fixed diffusion rate and a particular spatially dependent
utilization of resources which are expressed in terms of the
birth
rate, there always exists a birth rate which on average is the same
but differs pointwise which allows the corresponding species
to
invade.