Suggested reasons why many New World population centers seem to have been abandoned around 1300 CE include:

drought, failure of crops

http://www.rawstory.com/rs/2012/11/08/collapse-of-maya-civilization-tied-to-drought-study/

the indian ocean was largely spared large-scale warfare because

To understand the suggested reasons for the abandonment of many New World population centers around 1300 CE, we can examine historical evidence, archaeological findings, and theories proposed by researchers. Here are a few possible explanations for this phenomenon:

1. Environmental Factors: Changes in climate, including prolonged droughts or shifts in vegetation patterns, may have led to resource scarcity and agricultural difficulties, making it unsustainable for communities to continue living in certain areas.

To explore this possibility, you can search for scientific studies or research papers that analyze climate data during this period, examine pollen or sediment samples, or investigate archaeological sites for signs of environmental change.

2. Disease Outbreaks: Epidemics and the spread of infectious diseases could have devastated indigenous populations, leading to a decline in settlements. Diseases introduced by European explorers and colonizers, such as smallpox, measles, or influenza, were especially known to have devastating impacts on New World populations.

To delve deeper into this theory, you can look for historical accounts of diseases brought by Europeans, analyze population data, or refer to scholarly articles discussing the impact of epidemics on indigenous societies.

3. Warfare and Conflicts: Intertribal conflicts, territorial disputes, or invasions from other groups may have disrupted societies and forced people to abandon their settlements for safety reasons or due to displacement.

To investigate this possibility, you can consult historical sources, archaeological evidence of violence, or anthropological studies that examine cultural interactions and conflicts.

4. Socio-Political and Economic Factors: Internal social or political changes, economic transformations, or shifts in power dynamics could have played a role in population center abandonment. Factors such as changes in trade networks and patterns, political instability, or shifts in cultural practices may have influenced people to relocate.

To explore this perspective, you can study historical accounts, analyze trade routes and networks, examine changes in material culture, or look for anthropological studies that explore shifts in social dynamics.

It's important to note that no single explanation can fully account for the abandonment of New World population centers around 1300 CE. The reasons are likely complex and interconnected, and further research and evidence are necessary to form a comprehensive understanding of this phenomenon.