>>12239660>how many people... a large island is capable of supportingJust figure out how much arable land you have on your island. Rough rule of thumb I use in my world building is 1 to 4 people per acre of arable land, depending on the fertility, climate and technology. Obviously, you will need more land for livestock and in areas with poor fertility such as mountains, desert, etc. A desert region is not going to support as big a population as temperate or tropical lands. You need to subsistence farm over dozens of acres in the Alps, while the fertile Nile delta was once the breadbasket of Rome, producing tons per acre.
I would suggest about 10 to 20%% of your total land is going to be arable land, the rest is going to be plains, forests, orchards, marsh, mountains, towns, etc. You can still graze in many lands where can't plant crops, there is generally far more land suitable for grazing than for crops. To compare to real life, Japan is about 12% arable land, Madagascar is 6% arable and UK is 27% (bear in mind that different regions of the world have different climates and farm land can shrink due to urban sprawl and desertification, e.g. much of the Kanto plain is now under Tokyo).
You should also consider the history and culture of your land when figuring out population numbers. Fertile lands can be a victim of their own success, such as the urban sprawl mentioned above. Historically, fertile lands were hotly contested, with frequent raids from desperate neighbours (such as Scottish highlanders raiding the plains of northern England which resulted in much of the area being abandoned) and conquests (like the chaotic history of the fertile crescent). Were there any famines as a result of over-dependence on a single crop like the Irish potato famine, or bad administration like Holodomor or the Chinese famine, or was there a plague such as the Black Death? You also have to consider climate; weather, monsoons, droughts, etc.
Lots to think about, have fun!