Figure 2. Evolutionary dynamics of collectives and particles.

A population of ${\displaystyle D}$ = 1000 D collectives was allowed to evolve for ${\displaystyle M}$ = 10,000 generations under the stochastic birth-death model described in the main text (see Appendix 1 for details on the algorithm used for the numerical simulations). Initially, each collective was composed of $B=15$ particles of two types: red ($r_0=6,a_0^{\text{intra}}=0.8/K,a_0^{\text{inter}}=0.15/K,c_0=\text{red}$) and blue ($r_1=4,a_1^{\text{intra}}=0.3/K,a_1^{\text{inter}}=0.15/K,c_1=\text{blue}$), with ${\displaystyle K}$ = 1500. The proportions at generation 0 were randomly drawn from a uniform distribution. At the beginning of every successive collective generation, each offspring collective was seeded with founding particles sampled from its parent. Particles were then grown for a duration of ${\displaystyle T}$ = 1. When the adult stage was attained, 200 collectives ($\rho =20\%$) were extinguished, allowing opportunity for extant collectives to reproduce. Collectives were marked for extinction either uniformly at random (neutral regime, panels A, C, E, as well as Appendix 1—figures 1A and 4A), or based on departure of the adult colour from the optimal purple colour ($\widehat{\varphi }=0.5$) (selective regime, panels B, D, F, as well as Appendix 1—figures 1B and 4B). Panels A and B, respectively, show how the distribution of the collective phenotype changes in the absence and presence of selection on collective colour. The first 30 collective generations (before the grey line) are magnified in order to make apparent early rapid changes. In the absence of collective-level selection purple collectives are lost in fewer than 10 generations leaving only red collectives (A) whereas purple collectives are maintained in the selective regime (B). Panels C-F illustrate time-resolved variation in the distribution of underlying particle traits. A diversity of traits is maintained in the population because every lineage harbours two sets of traits for every colour (see Appendix 1). Selection for purple-coloured collectives drives evolutionary increase in particle growth rate (D) compared to the neutral regime (C). In the neutral regime, inter-colour evolution of competition traits is driven by drift (E), whereas with collective-level selection density-dependent interaction rates between particles of different colours rapidly achieve evolutionarily stable values, with one colour loosing its density-dependence on the other (F).