The paper investigates an age-structured infinite-horizon optimal control model of
harvesting a biological resource, interpreted as fish. Time and age are considered as
continuum variables. The main result shows that in case of selective fishing, where only
fish of prescribed sizes is harvested, it may be advantageous in the log run to implement
a periodic fishing effort, rather than constant (the latter suggested by single-fish
models that disregard the age-heterogeneity). Thus taking into account the age-structure
of the fish may qualitatively change the theoretically optimal fishing mode. This result
is obtained by developing a technique for reliable numerical verification of second order
necessary optimality conditions for the considered problem. This technique could be useful
for other optimal control problems of periodic age-structured systems.