I don't have enough room to separate mine and have never had any problems. They are part of the same plant family and are subject to attack from the same bugs and diseases. Some recommend not growing plants in this family (tomato, pepper, potato, eggplant) in the same spot as any of the others for at least 3 years. I don't have that kind of room especially because I grow so many tomatoes, peppers and potatoes compared to everything else. For me this falls under the "don't sweat the small stuff" umbrella.
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