In order to study the impact of fishing on a grouper population, we propose in this paper
to model the dynamics of a grouper population in a fishing territory by using structured
models. For that purpose, we have integrated the natural population growth, the fishing,
the competition for shelter and the dispersion. The dispersion was considered as a
consequence of the competition. First we prove, that the grouper stocks may be less
sensitive to the removal of large male individuals if female population are totally
protected. Second, we show that fishing does not disturb the demographic structure of the
population. Finally, we prove that female selective fisheries have the potential of
drastically reduce reproductive rates. We also prove that male fishing decreases
competition and then increases the total population number.