Do insects farm?

Yes. Here is a photo of an 'aphid' farm. And who is the farmer? The big ant on the left. Even in our climate you can find this symbiotic relationship going on between these 2. The ants protect the aphids from other insect predators. In exchange they eat the 'honeydew' produced by the aphids.
A nice name for aphid poop. Aphids will typically be found in the topmost growth as they prefer the softer new plant tissue. When you notice them, destroy! They will multiply quickly in hot weather and can disfigure you plants. Around here, I have mostly noticed them on zinnia, but you can find them on a variety of plants. Their color can range from green to grey to black to the reddish color in this photo.