I have found rather an interesting study by Choquenot and Bowman (1998) that applies a predator-prey model to the late Pleistocene extinction in Australia.
The two species predator prey model examines the population density and hunting efficiency of an aborigine population needed for overkill to have led to mass extinction. Now this model highlights some rather large flaws in the overkill hypothesis. Primarily, the model demonstrates the smaller megafauna would have been more readily killed over larger ones because they would have reproduced at a faster rate to satisfy meat demand. As we already know, this was not the pattern at the end of the Pleistocene, and in fact many smaller species survived. The Aborigine population densities and hunting efficiencies would have had to be unrealistically high to kill out the majority of large megafauna. The authors go on to highlight the fact there are few co-existing human and megafaunal remains found at archaeological sites and dating is very precarious. This is very true on both counts, meaning it is hard to prove solidly any theories in Australia. However, since archaeological evidence has been found on other continents, mainly North America where humans were known to have hunting megafaunal species, then why isn’t there in Australia?
A few more details about the mathematical model used in this study reveal the downfalls in the overkill hypothesis. The model showed that to exterminate all of the megafaunal species 500kg and more, the population of Aborigines would have had to be in excess of 0.07 aborigines per km and a rate of effective search of 100 ha per person per day, now that is a lot! 100 ha, blimey I would be knackered (slash dead) if I had to cover that every day!
Figure 1 shows that, as expected, the larger the species, the higher the aborigine population density and hunting efficiency needed.
Now another model that I think is worth mentioning is that designed by Mosimann and Martin (1975). They made the process of species reproduction spatially significant by having human populations colonise a certain geographical area only supporting unexploited megafauna. Once all of the megafaunal species are exterminated, the humans will move to new areas containing less exploited species. But because these species were indefensible to these human populations, soon the complete extinction of megafaunal species was inevitable. Hence the extermination of these species was dependent on the concentrated formation of a colonising human population, precipitating regional extinction. Wherever the human population density and per capita offtake exceeded the capacity of regional megafaunal populations to sustain breeding, extinction occurred. However, although this facilitates the overkill hypothesis, it is inaccurate to presume per capita offtake remains the same ignores the effect of declining prey and hence the need to hunt further afield. This means that fact that as the prey population declines as it is hunted; the proportion of prey removed thereafter is ignored, dramatically increasing chances of hunters to exterminate species. They also predict a high level of wasted meat and an exaggerated population growth among humans to make the demand as high as it would need to be to eliminate all the larger species.
So all in all, unrealistically high hunting efficiencies and even idealistically large Aborigine populations would have been needed to cause the mass extinction of megafaunal species in the late Pleistocene. To be honest, the figures given by this model prove how implausible the overkill hypothesis is. The archaeological evidence found to date in Australia doesn’t account for such large Aborigine populations and there is no way one individual could hunt over a 100ha area every day! The model by Mosimann and Martin (1975) proves the improbable parameters needed for the overkill hypothesis to apply and this in itself is proof that climate obviously had a key role to play in the mass extinction.