How is the opening quote from movie Apocalypto related to the movie?

Well, I believe that this is attributed to many of the great civilizations decaying from within that contributed to the eventual fall of said civilization. There is a lot of evidence that the Maya empire was near the brink of collapse before the Spanish came (due to famine, overpopulation in specific cities, fighting among social classes, etc.). You can see many of these factors throughout the movie, not to mention the actual "harvesting" of people used for sacrifices that many "Spiritual Leaders" thought could help out these situations.

Hmmm well civilization wouldn't define the tribe that was the one that Jaguar Paw lived in, but rather the conquering Mayans with temples, sacrifices, forced slavery, and sport killings. In other words there were two sides of the natives shown in the movie, the hunter gatherer types and the city state civilization type. One was altruistic, family, mythological, and headed by elders and shamans. The other was hierarchical, agricultural, and headed by "anointed ones (kings,emperors etc..) and religious priests (the ones at the top of the temple cutting out hearts).

So in essence it is a reflection of the of the primordial and the "civilized". One is large scale and the other a small scale. So the quote is relevant to the city, which is a reflection of what the Spaniards eventually did themselves, just on a higher and sophisticated scale.

I always interpreted the quote referring to the Maya themselves, the great civilization. Since the Maya had already decayed when the Spaniards arrived - most of their cities abandoned -, the quotes fits more to the Aztecs or Incas, which were actually conquered from without by the Spaniards. The small tribe in the movie, which village is destroyed, is definetely not a great civilization.

We also know that the Aztec and Inca had large internal problems. I don't think it's a victim blaming quote. Just because a great civilization is weak from the inside, does not give you the right to destroy it from the outside. I like the quote, even though it does not always fit to all cases of history.

It's starts off with a primitive tribe that have nevertheless created some pretty nifty boobytraps. They think they're pretty evolved yet they single out one tribe member and pester him. It's nothing inhumane but it's not right, societywise. Low civilisation with minor problems. This tribe gets overtaken by a civilisation that is much more evolved than the primitive tribe could fathom when they thought they were the top of the evolutionary hierarchy. This much bigger civilisation is already more obviously flawed. The movie ends with the conquistadores arriving. The highly evolved natives are about to find out they're not at the top of the pyramid either. I feel the quote is a warning to the viewer: We like to think of ourself as the most evolved civilisation yet it seems to be falling apart. Aliens are coming soon.

I have studied Mayan culture for ten years. Lack of a strong single unit, the arrival of the Spaniards, and disease all played there part to the Maya demise. It is my opinion that the main reason for the collapse of the Mayan Empire was the scarce amount of water during the final decades. This was caused by their excavation of trees to build temples. No trees less rainfall. No rainfall no survival. Ironically in the movie a tree is chopped down and nearly falls on them before the arrival to the Mayan temple. Unfortunately, this happened way too often in that area in this civilization.

In my opinion it means that internal strife and lack of cohesion is the reason why empires are lost. Chanakya said" The reason for the loss of an empire are always from inside". It surely applies to India which was conquered by the British and the Soviet Union whose own internal dissensions were the reasons of their downfall.

It is a way to basically blame the Maya for what the Spanish later did to them when they invaded and destroyed all the native populations. It is a victim blaming quote.

Oh, and the Maya did not harvest people to sacrifice. That was the Aztecs, and it wasn't on that large of a scale.