That does not make sense. If the radiation culled the weakest, then it would also affect the stronger individuals. Essentially, radiation would make the stronger weak and make the weak too unhealthy to survive.
More importantly, 'strong' and 'weak' only have meaning relative to a particular evolutionary niche. Adding massive radiation changes the niche so that strong means 'able to survive massive doses of radiation' and 'weak' means 'not'. There is no reason to assume this definition of 'strong' correlates with 'strong' outside a highly irradiated zone.