  We introduce the term net-proliferation in the context of fisheries and
establish relations between the proliferation and net-proliferation that are
economically and sustainably favored. The resulting square root laws are
analytically derived for species following the Beverton-Holt recurrence but, we
show, can also serve as reference points for other models. The practical
relevance of these analytically derived square root laws is tested on the the
Barramundi fishery in the Southern Gulf of Carpentaria, Australia. A
Beverton-Holt model, including stochasticity to account for model uncertainty,
is fitted to a time series of catch and abundance index for this fishery.
Simulations show, that despite the stochasticity, the population levels remain
sustainable under the square root law. The application, with its inherited
model uncertainty, sparks a risk sensitivity analysis regarding the probability
of populations falling below an unsustainable threshold. Characterization of
such sensitivity helps in the understanding of both dangers of overfishing and
potential remedies.
