  We numerically show that the Lattice Lotka-Volterra model, when realized on a
square lattice support, gives rise to a {\it finite} production, per unit time,
of the nonextensive entropy $S_q= \frac{1- \sum_ip_i^q}{q-1}$ $(S_1=-\sum_i p_i
\ln p_i)$. This finiteness only occurs for $q=0.5$ for the $d=2$ growth mode
(growing droplet), and for $q=0$ for the $d=1$ one (growing stripe). This
strong evidence of nonextensivity is consistent with the spontaneous emergence
of local domains of identical particles with fractal boundaries and competing
interactions. Such direct evidence is for the first time exhibited for a
many-body system which, at the mean field level, is conservative.
