  The cyclic Lotka-Volterra model in a $D$-dimensional regular lattice is
considered. Its ``nucleus growth'' mode is analyzed under the scope of Tsallis'
entropies $S_q=(1-\sum_i p_i^q)/(q-1)$, $q\in \mathbb{R}$. It is shown both
numerically and by means of analytical considerations that a linear increase of
entropy with time, meaning finite asymptotic entropy rate, is achieved for the
entropic index $q_c=1-1/D$. Although the lattice exhibits fractal patterns
along its evolution, the characteristic value of $q$ can be interpreted in
terms of very simple features of the dynamics.
