About being gradual, I think what you want is a system that doesn't involve sheep multiplying out of all control like a nanobot plague. Try this:
Trigger 1 (looping)
Condition Objects in Area: 2 sheep in the pen
Condition Timer: 5
Effect Change Variable: Increase Variable by 1.
Trigger 2 is the same but applies when there are 4 sheep in the pen rather than 2.
Trigger 3 is the same but applies when there are 6 sheep in the pen.
Trigger 4 is the same but for 8 sheep.
Trigger 5 (looping)
Condition Variable Value: 10
Effect Change Variable: Reduce Variable by 10
Effect Create Object: Sheep in a corner of the pen.
Effect Task Object: Moves newly created sheep.
Of course, you can adjust the numbers to taste and you can make your AoK sheep-breeding simulator arbitrarily more complex.
You can't use variables quite so easily if you are not using DE. However, you can do the same thing in earlier versions of the game by using a resource stockpile that is not being used for anything else (stone for an AI that doesn't gather or build anything, for example).
[This message has been edited by Julius999 (edited 05-24-2020 @ 09:16 AM).]