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The commercial egg laying chickens were developed much the same way the broilers were developed. The commercial poultry producers, sometimes working through university programs funded by commercial money and sometimes internally, used selective breeding and detailed study of genetics to develop the commercial egg layers. They decided what traits they wanted and paid genetics experts to help them develop chickens with those traits. Research is still going on.
It was not just a case of selecting your best egg layers and breeding them. They wanted chickens that lay a Grade A Large egg practically every day, have small body weight so more of what they eat goes to egg production rather than maintaining a large body, handles confinement well, does not often go broody, is sexable at hatch, and who knows what else. They paid to hatch a lot of chicks and raise them so they could select what they wanted. It was science, years of hard work, and a lot of money, not luck. Leghorns played a major part, but other breeds were brought in to add specific traits.
Tyson is headquartered here in Northwest Arkansas and has donated enough money to the University of Arkaksas Poultry Science department that the U of A has one of the top three poultry science departments in the country. The poultry science building is named after a Tyson since their donated money help pay for it and helps maintain it. Tyson influences what projects graduate students work on to earn their advanced degrees so they can hire people specifically trained in what they want them trained in. I see it as a win-win. It is not all through the universities, but they play a major part.