Final answer:
The split between strepsirrhines and haplorhines occurred during the Paleogene period, likely within the Oligocene epoch, approximately 34 to 22 million years ago, based on fossil evidence.
Step-by-step explanation:
The split between strepsirrhines and haplorhines is a significant event in primate evolution. Strepsirrhines include prosimians like lemurs and lorises, while haplorhines include tarsiers and simians such as monkeys, apes, and humans. The division between these two groups dates back to the Paleogene period, specifically within the Oligocene epoch, which began approximately 34 million years ago (MYA) and ended about 22 MYA. The earliest unambiguous haplorrhine fossils were discovered at the Fayum site in Egypt, placing the origin of the haplorhine lineage within this timeframe. Prior to the Oligocene, all four superorders of mammals, including primates, appear to have become distinct from one another between 85 and 105 MYA, indicating that the initial split between strepsirrhines and haplorhines could have occurred during this period.