How much land area do my land-based animals (herbivores) need for food?

Question

I'm trying to work out the kinks of an ecosystem on a planet that is rather similar to Earth, but with some species of animal (both carnivores and herbivores) we aren't familiar with in our world. The particular species I'm working with right now are purely land-based creatures.

I've been able to use for example What is the maximum size of a flying creature? and What efficiencies make a realistic food chain? to come up with reasonable amounts of food needed for each step in the food chain. (In my case, I started with the apex predators and am working my way down the food chain.) I'm also looking to real-world Earth species for inspiration. This is the easy part.

However, the numbers that come out of that is an amount of biomass. Borrowing from the accepted answer to the latter question to illustrate this:

The 2.5 tonnes of mountain goats will, by the 10% rule, need 25 tonnes of plants to support them; the lemmings will need about 5.5 tonnes, and the songbirds will need about 1 tonne of fruits and seeds. Treating the 2 tonnes of insect biomass as roughly 100% herbivores means they'll need 20 tonnes of plants to support them (and everything that depends on them), for a total plant biomass of around 50 tonnes. (This figure does not generally include things like tree trunks, which are not easily consumed by herbivores.)

This leaves me with my problem. Just how much is (for example) 50 tons of the easily digestable plant biomass, in terms of land area?

The answer to that will obviously depend on the specific biome, and have a large fudging factor depending on the local environment. I'm hoping for an answer that gives some kind of conversion figure (like, pulling out of thin air, "approximately one ton per square kilometer") at least for each of tundra, northern latitude forest, mediterranean forest, and jungle. Because I'm shooting for reasonable rather than an absolute truth, something that is within half an order of magnitude or so is probably good enough.

Note that this is science-based, not hard-science, but bonus points for citations.

Answer 1

Much depends upon the specific animal in question, the fertility of the land, the weather, the regional climate, and other parameters.

Lower Bounds

However, in the US Midwest, using modern agricultural techniques, in a typical year, and using high intensity farming, hobby farm enthusiasts estimate that it takes 1 acre of farm to support each person for a year.

Carrying capacity ($C_{Human}=\frac{kg}{km^2}$)
Estimated human population ($P_{human}= 1$)
Average Individual human mass ($M_{human}=100 kg$)
Area of Cultivation ($A_{\text{Farm}} = 1 Acre = 0.004 km^2$)

$$C_{Human} = \frac{P_{Human} \times M_{Human}}{A_{\text{Farm}}} \rightarrow \frac{1 \times 100 kg}{0.004 km^2}=24,710 \frac{kg}{km^2}$$

Real Life Example

A real life estimate for natural carrying capacity could be derived from the bison population of the American plains prior to major European settlements.

Multiply by the population of bison by their average weight and then divide by the area of that region.

Carrying capacity ($C_{Bison}=\frac{kg}{km^2}$)
Estimated Bison peak population ($P_{bison}= 60,000,000$)
Average Individual Bison mass ($M_{bison}=700 kg$)
Area of Great Plains ($A_{\text{Great Plains}} =1,300,000 km^2$)

$$C_{Animal} = \frac{P_{bison} \times M_{bison}}{A_{\text{Great Plains}}} \rightarrow \frac{60,000,000 \times 700 kg}{1,300,000 km^2}=32,307 \frac{kg}{km^2}$$

Conclusion

These results are close enough to be mutually supportive. For North America Midwest and Great Plains regions, a carrying capacity of $25,000\frac{kg}{km^2}$ to $35,000 \frac{kg}{km^2}$ seems quite reasonable.

Answer 2

I'd like to preface this by saying: You really can find anything on the Internet.

Apparently the United Nations Food and Agriculture Organization (FAO) does routine studies on world biomass. From this report (page 41), they state that the world's forests have an average of about 149 tonnes per hectare, with tropical forests reaching above 200 tonnes per hectare. "Above-ground woody biomass" was estimated for the assessment, defined as "The above ground mass of the woody part (stem, bark, branches, twigs) of trees, alive or dead, shrubs and bushes, excluding stumps and roots, foliage, flowers and seeds" (source). Of course, not all of that is may be easily digestible (depends on species), but that seems a good place to start from.

At the moment, I can't find any data for other biomes. I'll keep looking and edit this for any more information I find.

Answer 3

Since you seem to have a value for tons biomass/ton goats. I'll work with goats values.

Raising Goats (1 acre is about 4,047 m²)

Poor ground may support 2-4 goats per acre while better pasture may be able to support 6-8 goats per acre.

Mountain Goats

Mountain goats continue to grow through their fourth year achieving average weights of 125 to 155 pounds for females and 135 to 180 pounds for males.

From these values I'm taking 15 average goats to the tonne.

On poor pasture (they're mountain goats) you're going to need about 4-8 acres per tonne of goats or 1.66acres/tonne biomass. Lots of rounding involved, I have no delusions of accuracy. I'll leave it as an exercise to the reader to convert the units into something sensible.

This would be the value for poor ground. It's reasonable to double it for more fertile areas. Though it's generally said that you need an acre per horse on good grazing. Goats are a special case, they'll eat anything.

You could also just measure the place in Cow's Grass

In Ireland, before the 19th Century, a "cow's grass" was a measurement used by farmers to indicate the size of their fields. A cow's grass was equal to the amount of land that could produce enough grass to support a cow.

Now of course diet is a key factor in this. It's not about biomass per unit area, it's about useful biomass per unit area.

If you are adding goats to cattle, you can add 1-2 goats per head of cattle. Goats will eat the weeds cattle dislike, thus improving the grazing for the cattle. [source]