Figure 7. Stable fixed point of ${\displaystyle G}$ as a function of collective-level parameters.

Classification of the qualitative shape of the growth function and dependence on collective parameters B (bottleneck size) and T (growth phase duration). Considered here are particle traits that allow coexistence ($a_{01}<a_{11}$ and $a_{10}<a_{00}$, $r_0>r_1$, see Appendix 2—figure 3 for the other possible parameter regions). The black line represents the limit of the region of stability of the fixed point of G, separating the two qualitatively different scenarios illustrated in the inset (see Appendix 2, Proposition 4 for its analytic derivation): for short collective generations and small bottleneck size, the faster growing red type competitively excludes the blue type over multiple collective generations. In order for particle types to coexist over the long term, growth rate and the initial number of particles must both be large enough for density-dependent effects to manifest at the time that selection is applied.