designed carefully, these can give fishers a long-term stake in the health of the
fishery.
Figure 12: When fishing managers tried to control fish harvests by limiting the number of fishing
boats, fishers responded by increasing the size and capacity of their boats. Mathematics can be
used to predict the impact of fishing regulations in advance and avoid such unintended
consequences. Credit: Skagman
That careful design requires mathematics. Agent-based mathematicalmodels represent each individual fish and each individual fisher in a computer
model and can play out the consequences of strategies before implementation,
avoiding a continuation of the costly trial-and-error approach that dominated early
attempts at regulation.
Mathematicians are also working to develop models that will help predictthe fish populations from year to year. “Age-structured models” can determine
the age at which a caught fish will have the least impact on the population as a
whole. By adjusting the size of the mesh of their nets, fishers can ensure that
they won’t catch younger fish – and if the quotas are designed well, fishers will
support such rules even if it reduces their catch in the short run. But so far, these
models only work well in fish whose populations aren’t subject to large changes
from outside forces – and there aren’t very many of those. Most fish are strongly
impacted by ocean circulation, which changes based on weather patterns from
year to year in ways that aren’t predictable. Predicting fish populations precisely
is impossible given this variability, but a mathematical challenge that could be