Extended Data Fig. 8. Properties of species leading to a high per capita population growth rate at low abundances.

The panels a) – d) show different quantities that determine the per capita population growth rate ${\tilde{\lambda }}_f\left(N_f\right)$ (eq. 11a, 13). a, the mean relative abundance N_f^*/J^*, which drives the risk factor ρ_f, averaged over all species of a given plot in dependence on latitude, b, same as a), but for the quantity ${(N_s/N_f^{*})}^{b_f+1}$ as it appears in eq. 2. c, same as a), but for the mean of the risk factor ${\rho }_f$ for niche differences (red) and no niche differences (black), d, same as a), but for the mean of the quantity k_fh/(k_ff –k_fh,). To outline the overall tendency in the data we fitted in panels a) a polynomial regression of order 2, and in panels b) and c) an exponential regression. For plot acronyms see Extended Data Fig. 2.