Response to Comments on ‘‘On the Regulation of Populations

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. W e analyzed the relation between the size of a population and its rate of growth, in 1780 time series of mam-mals, birds, fish, and insects (1). Nonlinear regression was used to fit a discrete version of the theta-logistic equation (see Eq. 2 below). The parameter q takes values less than 1, equal to 1, or greater than 1, depending on whether the relation is concave, linear, or convex viewed from above. We reported that the relation is concave in 78 % of species and that there i