A natural pool with the proper filtration system should require no use of outside chemicals. Sometimes, you may want to use natural bacterial or mineral adjusters to maintain the health of your swimming pool. However, the vast majority of filtration will be done within your regeneration zone.
Don't add plant foods, fertilizers, pesticides, or fungicides to your pool! These will seriously harm the plants in your regeneration zone, and may make them unable to naturally filter your pool.