This is over North and South America and I have seen estimates that disease wiped out over 80% of the native population. Some areas lost well over 95% of the population others much less so. But, disease tends to spread more rapidly though more densely populated areas, so it’s effect is going to be concentrated on farming communities. And those areas where early europeans spent most of their time aka South America.
Still, it's hard to estimate what percentage of those people where farmers, but based on current results from slash and burn agriculture in South America sustained clearing of 10+ acres per person would not be unreasonable considering the crops and methods used during that period. Also, even non farmers are going to start a fair amount of forest fires simply by cooking food. So over all their numbers seem far more credible than you might expect.
What's being described is not slash and burn agriculture in the way it's practiced now, or "deforestation", but a regular seasonal burn-off of prairie or savanna. It prevented trees from taking hold in very wide areas. The book 1491 has good pointers in its bibliography to reputable sources about pre-Columbian grassland burns.
We're talking about the Amazon basin, much of which was probably farmland prior to European influence. According to the archeological record, that region may have grown enough food to support millions of people. That's a lot of land, which then converted into dense rainforest.
Still, it's hard to estimate what percentage of those people where farmers, but based on current results from slash and burn agriculture in South America sustained clearing of 10+ acres per person would not be unreasonable considering the crops and methods used during that period. Also, even non farmers are going to start a fair amount of forest fires simply by cooking food. So over all their numbers seem far more credible than you might expect.