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The technical comments by Getz and Lloyd-Smith, Ross, and Doncaster focus on specific aspects of our analysis and estimation and do not demonstrate any results opposing our key conclusion-that, contrary to what was previously believed, the relation between a population's growth rate (pgr) and its density is generally concave.

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Wagner and Graf (2010) derive a population evolution equation for an ensemble of convective plumes, an analogue with the Lotka–Volterra equation, from the energy equations for convective plumes provided by Arakawa and Schubert (1974). Although their proposal is interesting, as the present note shows, there are some problems with their derivation.

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