Haven't played 1602 A.D. (American version) for long, but no matter on what island I plant cane fields or vines, even tobacco, the crops dry up and I get no production. I read a tip that the north islands produce cane but the south islands don't, but that makes no sense since warmer weather is needed for cane. Anyway, why are my cane fields drying up in the southern and central islands? Why can't my vineyards produce at least? Again, the vine fields are dried up.

I have the plantation buildings in the approximate center of a lot of fields in both cases, and I have at least one distillery for every two cane plantations.

I remember years ago I used to play 1404 or 1701 anno and had no problem supplying alcohol. Cane fields yielded well and there was a lot of rum left over to sell.

Can anyone help me with this?

Are you sure you pressed the eye icon with your ship when you were close to an island and seen that growth is 100% for the vines, tobacco etc.
If it's 50% it only grows partially and not on every field tile.
The eye icon that ships have is very important for knowing what kind of resources the island has, then use the mouse pointer on island to see how much growth it has for the needed fields.
Also if you get a message no rain or something like that they dry up for a short time i think.

This is the second time I am trying to respond to you. The earlier reply ran out of time being processed . I will try using the eye. I have been using it ijnfreqently and only when there are mountains, to look for ore.

By the way, do I have to establish small villages on other islands to plant and process crops and ore, or will a wharf, warehouse and market suffice?

Thanks a lot, I really appreciate your help.

You really don't need to establish small villages on other islands, to get access to more buildings it's more important to get more population on your main island. Anyway for plant likes tobacco and other you can decide to have only work buildings which will have the appropriate number of workers. Having housing buildings is useful on bigger islands as they bring taxes, and it's better to support your population by bringing them the needed materials and buildings. You can use the island for only planting or ore and bring it to your main island then with ships.
But if you decide to have some housing with it, it will maybe support more taxes since all these work buildings have a maintance cost. Market is also useful to have close facilities so they can get the materials faster. The buildings will suffice that you mentioned but a fishing hut will also be needed or something to at least feed your work only population.
Also am playing the german version since it sounds better.