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With new observational facilities becoming available soon, discovering and characterising supernovae from the first stars will open up alternative observational windows to the end of the cosmic dark ages. Based on a semi-analytical merger tree model of early star formation we constrain Population III supernova rates. We find that our method reproduces the Population III supernova rates of large-scale cosmological simulations very well. Our computationally efficient model allows us to survey a large parameter space and to explore a wide range of different scenarios for Population III star formation. Our calculations show that observations of the first supernovae can be used to differentiate between cold and warm dark matter models and to constrain the corresponding particle mass of the latter. Our predictions can also be used to optimize survey strategies with the goal to maximize supernova detection rates.