The chicxulub asteroid impact caused climate change, and the climate change caused a mass extinction. But many land-based animal groups survived, crocodillians, lizards, snakes, turtles, frogs, salamanders, birds, and mammals, including primate ancestors.
How would a radiation-based mass extinction event affect current animal groups? Specifically, what would be the apex predators and/or herbivorous "apex species" (term for "animals/organisms with no [significant] natural predators" that encompasses herbivores) that survive?
Assumptions, limitations, details, etc:
The scenario is akin to nuclear world war 3, all sides throwing all the nuke they have, etc.
Assume exactly enough radiation is released in to the atmosphere to kill all humans through radiation related effects, but no more. Higher radiation concentrations are allowed in directly attacked areas, but even the most remote human populations are still killed by absolute minimum lethal doses.
Assume nuclear winter is negligible. This is about radiation-induced, not climate-change-induced, extinction.
Sea life and plant life can be disregarded (unless it directly affects a population of land-based animals that would otherwise survive), stick with land-based animals.
To summarize and reword the main question, for clarity: At this level of global radiation, many species would die off due to radiation poisoning many more would survive the radiation itself but their prey would not, so they would also die off. Food chains/webs would be massively disrupted. Which apex species(singular) or apex species(plural) would end up at the "top" of whatever food chains/webs were left after things stabilized?(because they can both survive the radiation, as well as have a food source that also survives the radiation)
EDIT: I used the term "Stabilized" to mean just that the "apex species" can live long enough to reproduce for 1-3 generations, depending on the length of their reproductive cycles. And the radiation itself is no longer having any significant effect on food chains and food webs. I'm not talking about geological or evolutionary time-scales.
EDIT 2: The "spirit" of the question is meant to be about animals with higher radiation tolerances than humans, either due to biological differences or (as pointed out in an answer) lifestyle differences. Not about just how difficult it might be to wipe out every last human on the planet with radiation alone (after all, that wouldn't leave anyone left for the story...). So the radiation levels involved should be considered to be lethal to unprotected human populations. Not necessarily those that made it to shelters that don't suffer direct nuclear strikes.