How many pounds of beans are required to support a 10 pound eagle?

Question

Consider a food chain with beans as primary producers, mice as primary consumers, weasels as secondary consumers, and eagles as the top carnivores that eat the weasels.  Plants absorb about 1.2 % of the sunlight that strikes them, and about a third of that energy becomes incorporated in organic molecules that another organism might eat. These organic molecules constitute the biomass of the plant. Organisms at higher trophic levels are able to incorporate about 10 % of ingested biomass as biomass of their own. Thus a herbivore that eats 100 pounds of plant matter may gain 10 pounds in weight.

Answer 1

I've taught environmental science, and this question exemplifies the issues with the sloppy terminology commonly found in such course materials (since the school district I taught in wasn't sufficiently organized to decide on and provide a textbook, I wasn't particularly constrained by that!).

First, there's that word "support". Students need to be made aware, that courses generally only consider the immediate flow of mass and energy UP AN IDEAL FOOD PYRAMID; that is, every mature bean plant gets immediately eaten by a mouse, every mature mouse gets immediately eaten by a weasel, and every mature weasel gets immediately eaten by a growing eagle. What nonsense! If nature worked that way, there could never be any mature animals to maintain natural population levels by breeding (this is obviously not the case with such textbook writers, unfortunately!)

So, the caveats need to be added, 1) "assume perfect efficiency of operation of a food pyramid, according to the ideal values for energy and mass transfer that you have learned", 2) "assume 'support' means to grow to maturity only, according to the stated perfect efficiencies", and 3) assuming only the stated pyramid operates.

Higher-level students will realize that, depending on an actual particular food pyramid web and local conditions, "the results you obtain may vary" as they say; creatures die for various causes and do not become higher-trophic-level food, food energy may be diverted into other top predator species, and so on.

I've never seen data on actual vs. theoretical limited food webs, i.e for actual vs. theoretical transfer percents, though I'm sure such data could be calculated -- perhaps because real ecologists are busy considering real world food webs only?

Answer 2

There is no question here.  A lot of background but no question.  

1.2% of sunligt hits a plant.

1/3 of that energy goes into the beans

10% of the beans get to the mice

10% of the mice get to the weasle

And finally

10% of the weasels energy gets to the eagle

 

If I want to know how much of the sun's energy gets to the eagle through feeding, taking the above into account, I would say it is:

sun light * 0.012 * 0.333 = energy in beans

beans * 0.1 = energy in mice

mice * 0.1 = energy in weasels

weasels * 0.1 = energy in eagle.

 

So the result would be:

Sun light * 0.012 * 0.333 * 0.100 * 0.100 * 0.100 = energy supplied to eagle.

or

Sun light energy * 3.996 * 10^-6 = energy supplied to eagle.