  Recruitment is calculated by summing random offspring-numbers entering the
population, where the number of summands (i.e. spawning population size) is
also a random process. A priori, it is not clear that individual reproductive
variability would have a significant impact on aggregate measures for
monitoring populations. Usually these variations are averaged out in a large
population, and the aggregate output is merely influenced by population-wide
environmental disturbances such as climate and fisheries. However, such
arguments break down if the distribution of the individual offspring numbers is
heavy-tailed. In a world with power-law offspring-number distribution with
exponent $1<\alpha<2$, the recruitment distribution has a putative power-law
regime in the tail with the same $\alpha$. The question is to what extent
individual reproductive variability can have a noticeable impact on the
recruitment under environmentally driven population fluctuations. This question
is answered by considering the L\'evy-stable fluctuations as embedded in a
randomly varying environment. I report fluctuation scaling and asymmetric
fluctuations in recruitment of commercially exploited fish stocks throughout
the North Atlantic. The linear scaling of recruitment standard deviation with
recruitment level implies that the individual reproductive variability is
dominated by population fluctuations. The totally asymmetric (skewed to the
right) character is a sign of idiosyncratic variation in reproductive success.
