  This paper studies the scaling properties of recruitment fluctuations in
randomly varying environments, for abundant marine species with extreme
reproductive behavior. Fisheries stock-recruitment data from the North Atlantic
display fluctuation scaling, a proportionality between the standard deviation
and the average recruitment among stocks. The proportionality covers over five
orders of magnitude in the range studied. A linear-scaling behavior can be a
sign of a universal distribution of the normalized data across stocks. In light
of this conjecture, it is demonstrated that the L\'evy-stable model offers a
better effective description of the recruitment distribution than the
log-normal model. Care is devoted to the problem of random sums of random
variables. Recruitment is calculated by summing random offspring numbers with
infinite variance, where the number of summands (i.e. spawning population size)
is also a random process with infinite variance.
