  Using game theory we provide mathematical proof that if a species of
asexually reproducing microbes does not possess maximum variability in
competitive abilities amongst its individual organisms, then that species is
vulnerable to replacement by competitors. Furthermore, we prove that such
maximally variable species are neutral towards each other in competition for
limited resources; they coexist. Our proof is constructive: given one species
which does not possess maximum variability, we construct a species with the
same (or lower) mean competitive ability which can invade, in the sense that
its expected value in competition is positive whereas the expected value of the
non-maximally variable species is negative. Our results point towards the
mechanistic underpinnings for the frequent observations that (1) microbes are
characterized by large intra-specific variability and that (2) the number of
extant microbe species is very large.
