During the Pleistocene and the early Holocene, most of the terrestrial megafauna became extinct. It was a deep global-scale event. The extinction was notably more selective for large-bodied animals than any other extinction interval in the last 65 million years. Multiple explanatory hypotheses have been proposed for this event: climatic change, over hunting, habitat alteration, and the introduction of a new disease. Traditionally, the focus of research and debate has been on the Eurasian and North American extinctions. In North America, two mammalian orders (Perissodactyla, Proboscidea) were eliminated completely. At the species level, the extinction was total for mammals larger than 1000 kg and greater than 50% for size classes between 1000 and 32 kg. Early observations confirm that extinctions could be severe even in relatively climatically stable regions where the vegetation changed little. In South America the event was more severe, with the loss of 50 megafaunal genera. Three orders of mammals disappeared (Notoungulata, Proboscidea, Litopterna), as did all megafaunal xenarthrans and at the species level, the extinction was total for mammals larger than 320 kg (Koch and Barnosky, 2006).

“Descuartizando un gliptodonte. Escenas de
la vida del hombre primitivo” (Quartering a
glyptodont. Scenes from the life of primitive man). Painting by Luis de Servi, Museo de la Plata.
Before the Great American Biotic Interchange, about 3 million years ago, the largest mammals in South America were mainly endemic notoungulates, litopterns and xenarthrans. But, during the interchange, many other megamammals and large mammals arrived to South America. The late Pleistocene in this region is first characterized by a rapid cooling. During the Pleistocene-Holocene transition pollen sequences suggest a change to sub-humid climatic conditions. In addition to rapid climate change, the extinctions are seen as the result of habitat loss, reduced carrying capacity for herbivores, resource fragmentation or disturbances in the co-evolutionary equilibrium between plants, herbivores, and carnivores. The death event of the gomphothere population in Águas de Araxá (Brazil) about 55,000 years ago, is probably an example of individuals that were suffering with the climate changes during the Late Pleistocene.
Paleontological and archaeological data indicate that extinctions seem more common after the human arrival and during the rapid climate change between 11.200 and 13.500 years. This pattern suggests that a synergy of human impacts and rapid climate change—analogous to what is happening today — may enhance extinction probability (Prado et al., 2015).
References:
J.L. Prado et al. (2015). “Megafauna extinction in South America: A new chronology for the Argentine Pampas.” Palaeogeography, Palaeoclimatology, Palaeoecology 425: 41–49
Alroy, John. (2001). “A Multispecies Overkill Simulation of the End-Pleistocene Megafaunal Mass Extinction.” Science 292:1893-1896
Koch PL, Barnosky AD (2006) Late Quaternary extinctions: State of the debate. Annu Rev Ecol Evol Syst 37:215–250.
Prescott GW, Williams DR, Balmford A, Green RE, Manica A. (2012) Quantitative global analysis of the role of climate and people in explaining late Quaternary megafaunal extinctions. Proc. Natl Acad. Sci. USA 109,4527–4531
Barnosky AD, Lindsey EL.(2010) Timing of Quaternary megafaunal extinction in South America in relation to human arrival and climate change