In the GoT book and/or HBO canon, are the giants now below a minimum viable population?

Question

In the books, I recall some small, unspecified number of giants escaping South. In the HBO series, Wun Wun is the only giant we see escaping from Hardhome and passing through the wall (and wow does he look tired and existentially unhappy). Book canon seems to be that giants were made extinct South of the wall long ago, and I do not recall the HBO series addressing that.

Is there enough canon material to determine whether the giants are now below a minimum viable population in the books, the HBO series, or both?

Answer 1

TL;DR: No, we do not currently have enough information in either the books or the HBO series to determine if the Giants have a minimum viable population. They seem at the line, though.

Most of what we know about the Giants comes from the books, although even then information is sparse. There are no mentions of their actual number and very few insights into their culture or breeding habits. The consensus among the wildlings is that the race is dying, which may be accurate. But let's speculate given what we DO know...

Let's Speculate!

Much of what we know comes from Chapter 15 of "A Storm of Swords", from Jon Snow's POV:

Jon took the horse in hand and held him still, so he could count the giants emerging from the blowing snow and pale mists that swirled along the Milkwater. He was well beyond fifty when Tormund said something and he lost the count. There must be hundreds. No matter how many went past, they just seemed to keep coming.

Later, as Ygritte and the other wildlings sing the song "Last of the Giants", the following conversation takes place:

There were tears on Ygritte’s cheeks when the song ended. “Why are you weeping?” Jon asked. “It was only a song. There are hundreds of giants, I’ve just seen them.” “Oh, hundreds,” she said furiously. “You know nothing, Jon Snow. You - JON!”

Assuming a generous estimate of 800 individuals, it could be difficult to maintain a viable population, even with individuals cross-breeding. This estimate places them right around the line, with 500-1000 being the MVP for most species we know of.

According to the wildling general Tormund Giantsbane, at least a dozen giants were killed during the Battle of Castle Black:

"You fought us hard here." Tormund turned his garron back toward the wildling camp. "You and your brothers. I give you that. Two hundred dead, and a dozen giants. Mag himself went in that gate o' yours and never did come out."

To make an accurate assessment of the remaining giant population, we would need to have not only more information regarding the actual number of available giants, but also their normal breeding & migration patterns. Given what little we currently know, however, we are probably right to assume that giants as a race will soon be extinct without careful population management.