Though I never breed as many as BDLvr, I have grown silkworms in the past and its easy. The hard part is making sure they are not in a too humid environment and make sure they are pretty sterile. Bacterial infestations or mold kill the worms off fast.
I can't breed them in my apartment in the summer because it gets too humid most days...even with AC on. But other than that, I don't have problems keeping them in the winter..but I haven't bred them as I really don't have many lizards to feed them to.
Basically to breed them, temperatures around 70-75F is fine. A little warmer and they do grow faster but I find they die easier too. Too cold and they won't grow at all...and temps below 65F they probably die, or go dormant. I never had them that cold so not sure.
Best way to start is buy a 100 large silkworms (or medium), let them eat all the chow they want (feed once a day enough so its all gone in a few hours) I just keep them on egg grate (they pupate nicely in the little 'cups' which can be easily cut from the tray) Once I have cocoons, I gently remove them from the others and put them in a container in a dry ventilated area (pretty much just a sweaterbox or shoebox sized container with the lid off. If you don't have anything to get into the container (ie kids, animals etc), leave the lid off..If you have something that can get into it, cut a hole in the lid (large) and cover with screen (typical window screen)
Roughly 10-20 days later the cocoons will hatch and you get about half inch to 2/3" long brown moths. They look remarkably like tent caterpillar moths.... But years of farming has rendered them flightless..they can lap their wings fast but won't fly. THe females tend to be larger than the males..and often enough they will find eachother without any help from you. Once you have a mating pair (they stay joined for about 20 or so hours), I put them into a small sandwich sized container lined with wax paper (others just use small sandwich sized paper bags). Once the male detaches, take him out and pair him off with another female (if still alive) if you have one available, or just feed him to your bearded dragon.
The female will soon lay eggs after the male detaches. She lays several hundred eggs give or take, then dies. Feed her to your dragon, its a nice treat. Wait till the eggs turn dark (kind of purple) then you can either leave them out at same temperatures as the worms, or refrigerate for up to a year. When you need to hatch some, take out roughly how many eggs you need and at the temperatures above, they should hatch in about 8-12 days. You will have tiny black worms...feed finely shredded silkworm chow. Keep them as clean as possible (pretty much impossible at this size.) I just add more grated chow, letting the worms move from the old dry stuff to the fresh stuff...till they are about an inch long and I can feel confident of moving them to a clean setup without squishing the. Wash hands before handling them, just plain soap and water...cleansers like Puril or Zoo-med's Wipe Out may very well kill the worms.
The use of silkworm chow I think it is about half a pound of powder can grow 100 silkworms to 2".
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PHLdyPayne