**Frederick R. Adler, and Julio Mosquera. 2000. Is space necessary?
Interference competition and limits to biodiversity. Ecology 81:3226-3232.**

Suppose the coalition includes all species between *m*=0 and *m*=*z*_{max}.
For stability, we require that

for
. Differentiating with respect to *m*gives that 2*s
p*(*m*)=1 or
for
. Therefore,
.

Next,
where the integral is taken over all members of the coalition,
because *f*(*m*)=0 on this set. However,

where is the mean of *m*. The interaction
terms cancel because losses by the species with strategy *z* are gains
by the species with strategy *m* (as can be shown by changing the order
of integration in the second term).

We can then solve for
. With the additional relation
for a uniform distribution, we
find
. This coalition will be stable to invasion because any species
with
*m* > *z*_{max} has no competitive advantage over
*z*_{max} itself, but at the cost of higher mortality. In
terms of the invasion function *f*,
*f*(*m*) < *f*(*z*_{max}) = 0.