If I may expand DEMurray's comment on trees a bit...
After reading a fair number of academic guesstimates, I've developed a short set of 'rules of thumb' for forests coverage.
Rule 1. If there were no people, forest coverage is immense. Trees tend to win over grass if the climate supports both.
Rule 2. For civilized but not industrial civilization there's a simple relationship between deforestation and population density, excluding the bottom 15% extremes. At 50 people per square km mi, forests are reduced by 50%. At around 85 pop/kmmi^2 forest coverage has been reduced to ~15%. At this point a severe change in slope happens, and the curve runs from here through ~12% coverage for 160 pop/kmmi^2 to the extreme point of ~7% for 200 pop/kmmi^2.
I want to accent that very last point. For pre-industrial age (ie before about 1800 in US and western Europe) it sort of looks like there's a cap on population density of 200 people per square kilometer mile. It's basically a Malthusian breakpoint. Even with that there's about 7% of forested land that's just too inaccessible for use, too marginal for farming, or whatever, and it remains untouched or replanted.
It looks like a depopulation event causes reforestation. From what we can tell, the depopulation of the world in the mid to late 14th century was accompanied by an increase in forest coverage. Sure it was "new growth" forest, but it was reforestation nonetheless.
The above is a general guidance. As an example that emphasizes DEMurray's point, Scotland pretty much deforested itself despite remaining under 60 pop/kmmi^2, and despite heavy use of peat for heat. My theory is that it was because so much of the land was marginal for farming; that it took more acreage to feed a population and so more land needed cleared, but I'm just guessing from available estimates.
Post-industrial, by the way, appears to maintain a pretty constant 6 to 9% forestation rate regardless of average density. Food production gets more efficient per acre, and population growth increases local densities instead of spreading.
edited to correct units of measure. deleted km and replaced with mi.
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