For a unimodal growth function f having its maximum at a critical state x_c, the interval bounding the population size asymptotically is usually presented as being equal to [f²(x_c), f(x_c)]. This interval however does not represent the maximum range within which the population size can vary, even asymptotically. The actual invariant interval containing the population size is equal to: [min(x*, f²(x_c)), f(x_c)], where x* denotes the non-zero fixed point, assumed to be unique, of the iteration of f.