> _how much_ do they regulate the carbon cycle?

"We estimate that rebuilding whale populations would remove 1.6×10^5 tons of carbon each year through sinking whale carcasses." [1]

"these changes are small relative to the total ocean carbon sink" [1]

The total ocean carbon sink is 10^9 tons of carbon each year [2]. So the changes in whale populations have had a 0.016% influence on the ocean carbon sink. So, not much.

But in the future when different geoengineering methods are suggested, maybe their impact in terms of tons of carbon per year could be compared to the size of this effect of stopping whaling altogether.

[1] http://journals.plos.org/plosone/article?id=10.1371/journal....

[2] https://en.wikipedia.org/wiki/Carbon_sink

I believe he is referencing the fact that "whale falls" (the ecosystem that subsists for decades on the corpse of a whale that died and sank in deep water) move the mass of the whale to the deep ocean, where it typically doesn't surface except on geologic time.

The obvious counter is that even at pre-human population levels the whales are an insignificant fraction of the shallow ocean biomass, and that artificial algea blooms over deep water could easily replace this carbon transfer in a sustainable way.

Perhaps more interesting is that the lack of whale falls has probably already driven to extinction many of the deep water species that prey on the drop sites. Those that are left are at risk. And at least until we can catalog the genetic diversity of these ecosystems, that could be a tremendous loss. There may be biological processes adapted there that are useful to us, in bio-engineering or medicine.