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Recruitment is calculated by summing random offspring-numbers entering thepopulation, where the number of summands (i.e. spawning population size) isalso a random process. A priori, it is not clear that individual reproductivevariability would have a significant impact on aggregate measures formonitoring populations. Usually these variations are averaged out in a largepopulation, and the aggregate output is merely influenced by population-wideenvironmental disturbances such as climate and fisheries. However, sucharguments break down if the distribution of the individual offspring numbers isheavy-tailed. In a world with power-law offspring-number distribution withexponent $1<\alpha<2$, the recruitment distribution has a putative power-lawregime in the tail with the same $\alpha$. The question is to what extentindividual reproductive variability can have a noticeable impact on therecruitment under environmentally driven population fluctuations. This questionis answered by considering the L\'evy-stable fluctuations as embedded in arandomly varying environment. I report fluctuation scaling and asymmetricfluctuations in recruitment of commercially exploited fish stocks throughoutthe North Atlantic. The linear scaling of recruitment standard deviation withrecruitment level implies that the individual reproductive variability isdominated by population fluctuations. The totally asymmetric (skewed to theright) character is a sign of idiosyncratic variation in reproductive success.

Broken symmetry of recruitment fluctuations in marine fishes: L\'evy-stable laws and beyond