Final answer:
The extinct order of mammals related to primates known as proto-primates includes Plesiadapis, which lived in the Cenozoic era and resembled modern squirrels and tree shrews. They went extinct by the end of the Eocene epoch and are a separate group from the megafauna that disappeared during the Pleistocene Extinction.
Step-by-step explanation:
The extinct order of mammals closely related to the primates or considered as their precursors is referred to as proto-primates. These mammals resembled modern squirrels and tree shrews in size and appearance and are known from fragmented fossil evidence mostly from North Africa. An example of a proto-primate is Plesiadapis, which had certain features in common with true primates and was found in North America and Europe during the Cenozoic era, becoming extinct by the end of the Eocene epoch.
It's important to acknowledge that during the Pleistocene Extinction, a variety of megafauna became extinct in North America and Eurasia after the last glaciation period, including woolly mammoths, mastodons, and saber-toothed cats. However, this extinction is more recent and not directly related to the proto-primates, which disappeared much earlier.
The first true primates are thought to have appeared about 55 million years ago, and these early primates evolved into several main groups, including prosimians and anthropoids, with prosimians resembling modern lemurs and similar species.