This led me into a sidetrack looking at sunrise/sunset and day length charts and I have learned that my first 12 hour daylight day will be March 18th. That's fun.
Cayenne/red pepper flake CAN have something to do with it, if the birds are already lacking Vitamin A. It won't make them lay more eggs than they normally would IF they are normally getting all the vitamins they need.
Daylight is the huge aspect, though.
I do pick up some red pepper flake when the big jars are on sale for $1 in the bin at the farm store and try to remember to give them some. They like it, doesn't hurt. I do want to get some Nutri-Drench at some point though, especially if I'm going to breed in the winter next year.
I really don't know what causes lack of Vitamin A, whether it goes old in the feed, or whether some birds just simply need more of it, or if more is needed at a given time of year, etc. I wouldn't necessarily blame the feed.