Our recent research has found that we are systematically underestimating the true value of marine protected areas (MPAs) to fisheries.

An important function of MPAs is to protect both representative and unique ecological communities, but scientists have long hoped they can play another role: contributing to the replenishment and maintenance of exploited fish stocks.

Wild fisheries are under intense pressure and landings of fish catches have flattened out despite an ever-increasing fishing effort. The most effective kind of MPAs are areas we set aside as ‘no take’ zones, where removal of animals and plants is banned. Fish populations within these areas can grow with limited human interference and potentially ‘spill-over’ to replenish fished stocks outside of MPAs. Despite the potential benefit, anglers remain sceptical that any spill-over will offset the loss of fishing grounds and the role of MPAs in fisheries remains contentious.

When we calculate how much a protected area contributes to a fishery, we work out the average length of both fished and unfished populations. Fish inside MPAs are bigger, on average, than those outside and so will produce more offspring than their smaller relatives outside MPAs. Generally, fisheries scientists relate the size of the fish to the reproductive output, whereby one unit increase in size equates to one unit increase in egg production.  They estimate how many juveniles will ‘spill-over’ and enter the fishing grounds.

It turns out there are a number of problems with the way the spill-over effect is currently calculated. Length is generally the measure of fish size recorded in a survey, but focusing on length risks underestimating the differences in reproduction inside and outside of MPAs.  Length and mass do not change at the same rate, so a 28% increase in fish length results in a 109% increase in mass. It can seem counter-intuitive that increasing fish length by around one quarter more than doubles the mass because the human brain tends to struggle when thinking about non-linear relationships.

This is compounded when we consider another non-linear relationship; fish mass and reproductive output. Our research team from the Centre for Geometric Biology and collaborator Ross Robertson from the Smithsonian Tropical Research Institute, recently found that bigger fish produce disproportionately more eggs than smaller fish in all fish species they looked at. This research made us realise that we need to be focused on protecting the biggest fish in a fishery.

And that is not all. In 1906, Danish mathematician Johan Jensen described the ‘fallacy of the average’, now known as Jensen’s inequality. Jensen pointed out that when relationships are non-linear we can’t assume that the average performance is equal to the performance under average conditions.

In our example, Jensen’s inequality means we further under-estimate reproductive output from inside the MPA. This is because fish size relates to reproductive output in a non-linear way so the reproductive output at average size is not the same as the average reproductive output. The inequality is greater inside the MPA where fish sizes are bigger and so this makes a further contribution to our under-estimate of reproductive output.

When we take Jensen’s inequality into account, and add it to the underestimates relating to the non-linear relationships already discussed, we find that there is a 175% increase in reproductive output for fish inside MPAs compared to those outside.

While this translates to a much smaller ‘spill-over’ effect, (more like a 12% increase in tonnes of caught fish per year for the coral trout fishery when MPAs are included in the management of the fishery), it is still a substantial increase in yield.

MPAs represent an essential tool for protecting larger fish, and the research team hope that a more accurate accounting of the value of MPAs will increase support for their use by a wide variety of stakeholders, including anglers themselves.

This research is published in the journal Frontiers in Ecology and the Environment.