The evidence is very suggestive. Very shortly after the arrival of humans into Australia, which as this paper indicates, has been increasingly narrowed to around 50,000 years ago, the enormous diprodont wombats, giant short-faced kangaroos, marsupial lions, and megalania a 20 foot lizard all become extinct. Again, the arrival of the Clovis culture in North America, coincides with the disappearence of mammoths, mastodons, native horses, giant beavers, and short-faced bears. These extinctions occur in regional pulses at different times that seem to match with local arrival of human populations, not like the Cretaceous-Paleogene extinction of the dinosaurs, which was global in nature.
From the Proceedings of the National Academy of Sciences of the U.S.A.:
Megafauna biomass tradeoff as a driver of Quaternary and future extinctions
1. Anthony D. Barnosky*
Extinction intensity varied by continent, with Australia, South America, and North America hard-hit, losing 88% (14 extinct, 2 surviving), 83% (48 globally extinct, 2 extinct on the continent, 10 surviving), and 72% (28 globally extinct, 6 extinct on the continent, 13 surviving), respectively, of their megafauna mammal genera. Eurasia lost only 35% of its genera (4 globally extinct, 5 extinct on the continent, 17 surviving). Africa was little affected, with only 21% loss (7 globally extinct, 3 extinct on the continent, 38 surviving), including at least three Holocene extinctions.
Humans evolved in Africa, and hominins have been interacting there with megafauna longer than anywhere else. Insofar as they are dated, there is no correlation between human arrival or climate change for the few African extinctions. In general, extinctions in Australia intensified within a few thousand years of human arrival ¡Ö50 kyr B.P. but did not correspond with unusual climate change. Extinctions in northern Eurasia corresponded in time with the first arrival and population expansions of H. sapiens, but both pulses also were concentrated in a time of dramatic climate change, the first pulse at the cooling into the Late Glacial Maximum (LGM) and the second pulse at the rapid fluctuation of YD cooling followed by Holocene warming (2, 4). Other species of Homo had been interacting with the megafauna for at least 400,000 years without significant extinctions before H. sapiens arrived. In Alaska and the Yukon, the first pulse of extinctions corresponded with LGM cooling but in the absence of significant human presence; the second pulse coincided with humans crossing the Bering Land Bridge and with the YD and Holocene climatic events. In central North America, extinction was sudden and fast, coinciding with the first entry of Clovis hunters, the YD¨CHolocene climatic transition, and the purported comet explosion. In South America, humans were already present by 14.6 kyr B.P., megafauna did not start going extinct until Holocene warming commenced some 11 kyr B.P., and species of ground-sloths, saber cats, glyptodonts, and horses have seemingly reliable radiocarbon dates as young as 8 kyr B.P. (21). Link: <http://www.pnas.org/content/105/suppl.1/11543.full>
Online book dealing with the issue: <http://www.megafauna.com/>