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Thanks for all answers. I find it fascinating.
I do know that a lot of African safari parks do two types of safaris, one for those who use a camera to take shots, the other who use rifles and never the two shall meet. It stands to reason that a safari is of limited size and animals will breed, leaving a surplus and safari parks can't exist without a profit.
If a very wealthy person waves hundreds of thousands of pounds at a poacher for horn and/or tusk, he is going to get it - the fact that it is illegal simply pushes the price up and so greater is the temptation to the poacher.
Maybe farming is the answer but I have no idea how it would work. I know there are crocodile farms that produce crocodile skin for the eastern and western markets but crocodile meat is readily available in the western world, including the UK, so it is farmed not just for skin.
I can't imagine how it would work for elephants and rhinos.