There is conjecture to the cause of the fate of Mayans. If it were over-population and drought, one can hardly blame the Mayans for changes in climate (in a localized area) and an increased birth rate.
I suspect birth control (outside of killing folks and just not doing it) was less of an option in their time than it is today?

In those times, I suspect population growth was mostly controlled by hunger, (predation, disease, and enemies. Producing their own food (and reducing relyance on wild species) and being good in battle likely lowered some of these variables.