Skallagrim
Banned
EDIT: @Skallagrim I was also thinking of a Maya colonization during the Pre-Classic Collapse in the 2nd century AD but was unsure if Maya maritime technology was advanced enough to permit a large-scale migration from the Yucatan to Cuba. It would also allow more time for an even more extensive Maya presence and filtering of cultural ideas and technology to the other peoples in the region. Perhaps we would have Mesoamerican-tier kingdoms all over the Caribbean and Gulf Coast by the time that the Europeans come by.
The POD that @Jon the Numbat suggests seems perfect to me:
The cities that seem most poised to do this are Coba, Tulum, Xcaret, Xel-Ha, and Muyil; their strength lied in transport along the coast. Muyil in particular has been inhabited since late Preclassic times.
So how about a POD at Muyil that develops outrigger canoes in the late pre classic/early classic. They begin mostly like the canoes of old but their stability in rough waters is valued for trade along the Caribbean coast. Eventually the canoes are made longer and parts are weaved between to carry greater loads. Fisherman communities from the coastal cities are able to travel further in their trips and carry more of their catch back, reaching Cuba by 550 AD and solidifying the route to central America. The places where they visit most become outposts for resupply and grow into trading towns. Farming communities are established in these emerging towns and they become a new destination (or source) for Maya trade goods.
A POD that early allows for the trade network to be built up over time. And just as he says: while it will likely have effects on the factors that in OTL caused the collapse, it would probably not prevent it altogether. In fact... here's a thought: the increased trade and wealth could conceivably lead to a population boost at some point, which would in itself cause certain pressures. That might lead to an alternate situation, much like OTL's collapse, but with a more densely populated maya heartland. The dense population would be relevant for the issue raised by @Achaemenid Rome:
Maya settlements were characterized by low density urbanism, so it would be hard to create settler colonies elsewhere without an increase in density in the Yucatan creating population pressure.
An alt-collapse where population pressure is clearly more of a key factor would be a realistic impetus for suddenly increasing migration to the Caribbean islands in the eighth and ninth centuries.
At this point, as has been noted, the Maya did not yet have sails. On the other hand, they did impressively well with their oar-powered canoes in OTL, and so did the Taino. As you observed: the Taino originated from South America and managed to colonise most of the Caribbean within a few centuries. All this makes it very plausible for the “Maya migration” to eventually result in a Caribbean-spanning trade civilisation.
By the year 900, based on an earlier Maya presence and highly lucrative existing trade contacts, I would expect a well-established Maya presence on Cuba etc. – with all the cultural influence that would entail.
If, as @Jon the Numbat postulates, this “Carribean release valve” for excess population actually works to migitate the collapse to some extent, we are not so much looking at a migration an sich, and more at an organic expansion of Maya influence. And also, perhaps, a shift in the centre of power. Gradually, the Caribbean, rather than Yucatan, might become the centre of this culture’s power. Instead of the Carribean culture eventually (re)conquering Yucatan (as I initially described), we might see a situation where the more hybrid culture of the islands becomes ever more dominant, until the old homeland is just swept into its orbit entirely.
As the postclassical era dawns (albeit very different from the one of OTL!), we’d see this island culture gradually expanding, using outrigger canoes just as @Jon the Numbat describes. Island-hopping isn’t that difficult, and the Taino were already a rather nautical people who used their own canoes for island trade. Basically, you could see the Maya island culture expanding exactly in the opposite direction from the one the Taino did: tracing the Caribbean arc from Cuba to Trinidad. From there, they could go along the northern coast of South America.
(@Cuāuhtemōc, you noted that sails were used by South Americans. Would that include any South Americans along that coast? If so, that would be a handy way for the island Maya to pick up sail-making. If not, they could still either come into contact with sailing peoples via later expeditions along the South American coast, or they could eventually develop them independently, of course. But if anyone along thr northern coast of South America was using sails at the time, that would be a great boon, simply because it would vastly increase the load that Maya ships could carry, and would also make them less dependent on island-hopping for getting around the region.)
As for later developments, I for one fully agree with this:
The Central American trade networks would also benefit from these developments on the Atlantic side. They could pick up sailing and metallurgy techniques from the south and western coast of Costa Rica, Panama, and Colombia. Settlements here and across into the Chibchan area utilized diches, causeways and terraces. The Diquis, Zenu, Tairona, Tierra Alta and an assortment of Panamanian and Colombian highland cultures could all contribute to the rise of a circum-Caribbean interaction sphere. A most interesting outcome would be the development of catamarans at Panama and Northern Colombia. The inspiration could come from the rafts made there and in Ecuador, combining the design with the outriggers to maximize the cargo load.
Especially combined with sails (if that’s in the cards), those catamarans could be a fun and plausible way to really give this trade empire an edge over everyone else in the region.
Of course, an island-based trade empire may very well not be an "empire" as we'd describe it, but rather a culturally and economically interlinked association of mostly autonomous city-states. In some cases, some of those city states might enjoy hegemony over lesser city-states, colonies, and inland chiefdoms (much like "princely states"). There might be a number of major cities that dominate the entire region and demand loyalty from all others in some form or another. Who knows? But I certainly don't expect it to be a rigidly hierarchical empire with one clear capital that calls all the shots.
Nor do I think it will be an example of a purely "Maya" cultural area. It will probably gradually change as more cultures are absorbed into its sphere. The exact culture, beyond the basic tenets, may vary from place to place, but a sense of fundamental common identity and mutual association could realistically be present. (Much like the Greek sense of a common Hellenic identity, even at times when various poleis were most opposed to each other.) Again, Jon is just right on target, as far as I can judge such things:
So we could have by the 1200s or 1300s a collection of thriving market centers across the Caribbean coast of Central America and the Antilles. The population is higher than OTL and the interior of the islands might be guarded by chiefdoms based around fortified cities and towns.
Politically the region is a mosaic of cities, confederations, towns, kingdoms and chiefdoms but there will certainly be cultural traits that bind them together, a Caribbean equivalent of the Southeastern Ceremonial Complex, that synthesizes all the interacting societies. Ceremonial pilgrimage sites, ball games, cults and recreational foods all shared across the sea lanes.
...and does that sound awesome, or what?
As others have noted, the trade-based origins (and lasting strengths) of such a culture would probably lend a more prominent role to the merchant class, and something of an evolution away from theocratic tendencies. This would serve to strengthen the culture, and broaden its various perspectives.
Another factor that would really help is (as has also been mentiond) more diversified and sustainable agriculture and/or aquaculture. The climates and soil types of the various islands and other regions that might potentially be settled can realistically be treated as the cause of a move away from slash and burn monoculture, and towards other alternatives. Ultimately, that would make the whole culture and trade network far less vulnerable to drought, climatological changes, and certain crop blights. (It may seem a bit over-the-top to focus on everything and anything that could potentially strengthen this culture, but once the Europeans show up, they’re just going to need every advantage they can get.)
As for the potential extent of this cultural sphere / trade network... given everything outlined so far, it’s not unrealistic to consider settlement of basically all Caribbean islands, Yucatan, various regions along the coast adjacent to Yuatan, and various colonies all along the Caribbean coast in North America, Mesoamerica and South America. Florida seems to have been in trade contct with the Caribbean anyway, slo that seems like a good candidate for relatively early (and perhaps therefore relatively dense settlement).
And any city-state at or near the the mouth of the Mississippi river is just poised to be a nexus for lucrative trade between our intrepid merchant culture and the Mississippian culture. (If you want to get really crazy — and by that I mean crazy awesome — you could have the interaction between these two cultural spheres / trade networks develop to such an extent that they really learn from each other. Particularly, if the Caribbean Maya culture indeed develops useful ideas on agricultural diversification etc., the Mississippians might adopt some of those ideas... which could then migitate the Mississippian decline of OTL. This would affect the ultimate fate of the native American peoples to an even greater extent, and I would gladly read such a TL.)
Well. That turned into an extended rant, didn't it? Sorry about that. Please take it as a sign of my great interest in this scenario and its many possible implications. Needless to say, if this ever gets turned into a timeline, you'll find an avid reader in me.