  We analyze the fluctuation of the number of individuals when two competing
species, beginning with a few initial individuals, are submitted to a logistic
growth. We show that when the total number of individuals reaches the carrying
capacity, the number of each species is subject to giant fluctuations (variance
$\sim$ mean 2) if the two species have similar growth rate. We show that the
deterministic logistic equation can be used only when the growth rates are
significantly different, otherwise such growth has to be investigated by
stochastic processes tools. These results generalize to a wide class of growth
law.
