Do brown leghorns lay as many eggs as white leghorns? I heard they do, but I'm not sure if it is true. ( I ordered brown ones and that's why I am wondering)

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Thank you! That is still a good amount of eggs from brown leghorns though. I'll be happy with that.http://www.mypetchicken.com/chicken-breeds/Leghorn-Non-White-B66.aspx
According to this link no they don't. At least not any more.
I think that the reason is that the brown leghorn has fallen victim to the show ring. When showing poultry, egg laying doesn't matter, if it did every egg farm would be stocked with silkies or other fancy breeds. Therefor the breeders of brown leghorns do not select the best layers to go in their brood pens. I would expect todays' brown leghorns to average 250 to 275 eggs a year under ideal condition compared to 300 to 325 eggs per year for commercial white leghorn strains, or crosses also under ideal conditions.
Both brown and white leghorn hens just sip chicken feed while the dual purpose brown egg breeds wolf down chicken feed like there is no tomorrow. Figure as much as 50% more feed for up to 15% fewer eggs with a dual purpose breed.
A brown leghorn may well be a good choice if you are free ranging and are worried about hawks because regardless of color, a dead hen lays few eggs. To me the reason that the white leghorn took off and the brown, buff, and black leghorn did not is because the visual carcass quality at retail is better for white chickens than for dark colored ones.
The commercial white leghorns are a cross between two or more white leghorn strains in order to maximize health and vigor, all of which is needed for egg production.