Fig. 5: A graphical method explains the role of CNDD in reducing competitive exclusion and generating diversity.

a Without CNDD the species represented by the gray line is excluded because its break-even time (gray dot) is greater than \({t}_{i}\) With CNDD, \({{{\rm{\varepsilon }}}}_{i} < {{{\rm{\xi }}}}_{i}\) and \({t}_{i}\) shits to \({t^{\prime} }_{i}\) (blue line), allowing coexistence. b Simulations show that without CNDD \({{\rm{\varepsilon }}}\approx {{\rm{\xi }}}\) (red); with CNDD \({{\rm{\varepsilon }}} \, < \, {{\rm{\xi }}}\). Dashed lines represent Eq. (5) with \({r}_{i}=1/2\) and \(c=1.5\).