The answer is really fascinating.

Many of the native tribes of North America used one variation or another of this farming method. We mostly know this system as the "Three Sisters", a term based in Iroquois legend. They believed that each plant inhabited the spirit of one of three sisters sent by the Great Spirit to help humans, and each being said to be inseparable from her sisters.

While that paints a pretty picture, the reasons as to why the three were said to be inseparable is based real world applications. The three plants thrive when planted together, more so than they would if planted alone.

The corn grows straight and has a solid stalk, meaning that it provides the beans a natural pole on which to climb. Beans, other than providing something else to eat, provide the corn stalk with a stronger root system. Making the probability that it could blow over in the wind far rarer. Beans also work their magic on the plot of land, beans have a tendency to fix nitrogen around their root system. Which means they provide nitrogen to all of the plants growing on the plot. Finally we come to the squash, it provides crawling leaves, meaning it serves in two respects. It improves soil humidity by shielding the dirt from the sun but it also has a deterrent effect on weeds. Which means that with squash growing, you don't have to contend with weeds stealing nutrients from the soil. Squash stems also discourage some pests, they have small stout hairs running all over their stems meaning that aphids and stinkbugs sometimes have issues feeding.

But the trio has other benefits, nutritionally, as you pointed out, they complement each other quite well. Corn provides sugars, beans provide protein and squash can provide fat from its seeds and more calories and vitamins from its flesh.

So, to answer your question, native americans used the trio for hundreds, even thousands, of years because it's an efficient nutritional and planting system.

This combination is Mesoamerican. http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1039&context=nebanthro

Though squash is probably the oldest, the different species were selected for over thousands of years through foraging and then likely selected for their different properties (abundance, resilience, adaptability, nutrition, stability, etc.).

Their ecological synergy might have been easily notable or discovered through trial and error. Either way, once crops become well established and their benefits become visible they generally spread through trade to those cultures which are open to their cultivation.

They have ancient roots, as it were, and didn't get the globalization treatment until somewhat recently by comparison.

hi! you may be interested in these posts

• How common among Native North/Central/South Americans was the so-called "Three Sisters" diet?

• How exactly did the "Three Sisters" agriculture system work in indigenous America? Has it been replicated by modern farmers and/or researchers?

• When did maize farming reach the part of north America where Maryland now is?

• why did maize farming agriculture take so long to spread north?

• What is the current historical understanding of how Native Americans developed corn (maize)?