Fig. 9. Scaling of population growth rates in the BBS data set. (A) Distribution of population growth rates _slog[N(t+1)/N(t)] across all species in the data set. The growth rate _s is calculated by log transforming the ratio of species abundances in successive years. Abundances are taken as the total number of individuals of a particular species counted within each survey route. (After Keitt and Stanley, 1998.) (B) Probability density p(_s|N) of the growth rate _s for all bird species in the BBS database for different initial population size classes. The distribution represents all annual growth rates observed in the 31 year period 1966-1996. Data are shown for three different bins of initial sizes (circles, 10⁰<N(t)<10¹; squares, 10¹<N(t)<10^2.4; diamonds, 10^2.4<N(t)<,10^3.8). The solid lines are exponential fits to the empirical data close to the peak. (C) Scaled probability density p_scalp(_s|N) as a function of the scaled growth rate _{s scal}[_s-<_s>]/ for all species and years in the survey. The values were re-scaled using the measured values of <_s> and . Notice that all the data collapse upon the universal curve p_scal ^{(-|r scal|)}. (After Keitt et al., 2002.)