Highly fecund natural populations characterized by high early mortality abound, yet our knowledge of such population's recruitment dynamics is rudimentary at best. This knowledge gap has implications for our understanding of genetic variation, population connectivity, local adaptation, and resilience of highly fecund populations. The concept of sweepstakes reproductive success, which posits huge variance in individual reproductive output, is key to understanding recruitment dynamics, the distribution of individual reproductive and recruitment success. However, it is unknown whether highly fecund organisms reproduce by sweepstakes and if they do, the relative roles of neutral and selective sweepstakes. Here we use coalescent-based statistical analysis of genomic population data and show that selective sweepstakes are a strong candidate for explaining recruitment dynamics in the highly fecund Atlantic cod. The sweepstakes result from recurrent and pervasive selective sweeps of new variation generated by mutation. We show that the Kingman coalescent and the Xi-Beta coalescent (modelling random sweepstakes), including complex demography and background selection, are inadequate explanations. Our results show that sweepstakes reproduction processes and multiple-merger coalescent models are relevant and necessary for understanding genetic diversity in highly fecund natural populations. Our findings have fundamental implications for understanding the recruitment variation of fish stocks and general evolutionary genomics of high fecundity.