our lot are just ramping up their laying with the new chicks from last year starting to lay now. Its very early, more than a month earlier than last year.
We've gone from ticking over with only 3 layers to knowing I have at least 7 that are laying at the moment. That number is only going to increase. I have at least another 3 newbies (chicks from last year) that will start laying soon, very soon. One of their number laid her first egg yesterday and being at a total loss as to what to do or where to lay, and not being in the 'non-free range' run, decided to come and lay on the backdoor step, literally. She is the bottom of the pecking order and always the first to jump down off her perch and say hello to me at night. She knows she'll get some goodies from my pocket (I walk around with seed or black sunflower seeds in my pockets all the time). Then there remains 3 more from whom I may get eggs. Hopefully my old girl won't even try laying eggs this year. She has a calcium issue and always has had which makes her egg laying a problem and a life threatening issue but an implant to stop her laying was going to cost me AUD $300! She might be my oldest and longest had girl at 6 years old (I've had her for her 4th winter now), but $300 is pushing it a touch and she would need one every 6 months.
Anyhow, it will be the same with chickens on your island as well... they will start their laying without the need for artificial light and the likes before very long. then comes the glut and the price drop.... mind you mine are free so its hard to get cheaper.