Framework assumptions.

<p>A) After food consumption, the time until the arrival of a new pulse of nutrients is a stochastic variable that follows an exponential distribution of mean value <i>λ</i>_T (not normalized for clarity). B) Spore viability decreases linearly with division rate, which is assumed to correlate negatively with cell size. C) Survivorship curves for starving non-aggregated cells with different division rates, <i>c</i>. The curves show the probability of being alive at a time <i>t</i> after starvation, which correlates negatively with the division rate. For D)–G) we used the survival curve corresponding to <i>c</i> = 0.15. D, F) Discrete aggregation mechanism. Genotypes are determined by the fraction of the population, <i>α</i>, that aggregates. The rest, a fraction 1 – <i>α</i>, remains solitary. The population partitioning takes place instantaneously after food consumption. E, G) Continuous aggregation mechanism. Genotypes are determined by the rate at which cells aggregate, <i>γ</i>. The fraction of the population that aggregates depends both on the aggregation rate, γ, and on the length of the starvation period. D, E) Fraction of the population at the beginning of the starvation period that has turned into aggregators at time <i>t</i> after starvation. F, G) Fraction of the initial population that remains as solitary cells at time <i>t</i> after starvation. Aggregated cells also die at a very small rate, δ, but this effect is imperceptible at short times scales. Other parameters are specified in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005246#pcbi.1005246.s002" target="_blank">S1 Table</a>.</p

Summary of the model and results.

<p>Summary of the model and results.</p

Correlations between overall chimeric success and non-social life history traits.

<p>Each one of the 31 winning genotypes obtained in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005246#pcbi.1005246.g002" target="_blank">Fig 2B</a> is mixed in pairs with the rest of the genotypes and the fraction of spores is counted following a growth phase and the subsequent starvation onset. The chimeric success is obtained as the mean value of this fraction of spores averaged over all the possible pair mixes as defined in Eq (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005246#pcbi.1005246.e010" target="_blank">5</a>) of the main text. From left to right: chimeric success versus division rate (A, E, I), aggregator to non-aggregator ratio (B, F, J), average number of aggregators (C, G, K) and average number of non-aggregators (D, H, L). From top to bottom: low cell:resource initial density (10³ cells and R₀ = 10⁸), intermediate cell:resource initial density (10⁷ cells and R₀ = 10⁸) and high cell:resource initial density (10¹⁰ cells and R₀ = 10⁸).</p

Winning genotypes in deterministic and stochastic environments.

<p>In both panels blue squares represent the aggregator to non-aggregator ratio and red circles represent the division rate; dashed lines are interpolations. Simulations are initialized with a number of genotypes that compete for a pulse of resources through several growth-starvation cycles. Long realizations show that only one strain (which we call the winner) is able to survive in the stationary state in a given environment. For computational feasibility, the winner is determined as the most abundant genotype at <i>t =</i> 10⁸, when a few genotypes still survive. A) Deterministic environments, simulations are initialized with 4141 genotypes (101 values of <i>α</i> and 41 values of <i>c</i>). B) Stochastic environments. Results averaged over 20 independent simulation runs initialized with 44772 genotypes (1092 values of <i>α</i> and 41 values of <i>c</i>). Parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005246#pcbi.1005246.s002" target="_blank">S1 Table</a>.</p

Correlations between non-social traits.

<p>A clonal growth period for each one of the 31 winning genotypes obtained in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005246#pcbi.1005246.g002" target="_blank">Fig 2B</a> is integrated to evaluate correlations between the non-social traits included in the model at the onset of starvation. A) The total population is constant for all genotypes. Number of aggregators versus B) the aggregator to non-aggregator ratio, <i>α</i>; C) division rate, <i>c</i>. Number of non-aggregators versus D) the number of aggregators; E) the aggregator to non-aggregator ratio; F) the division rate.</p

Relative chimeric success in pairwise mixes.

<p>The winning genotypes from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005246#pcbi.1005246.g002" target="_blank">Fig 2B</a> are mixed in pairs and their relative number of spores measured after a single growth-starvation cycle. Genotypes are ordered according to the environment where they evolved in, with 0 corresponding to the fastest-recovery environment (i.e. <i>λ</i>_<i>T</i> = 10 hours) and 30 corresponding to the slowest-recovery one (i.e. <i>λ</i>_<i>T</i> = 10⁴ hours). To define chimeric success, we refer to one of the genotypes in the mix as reference genotype (x-axis) and to the other as mixed (genotype). Mixes in which the reference genotype produces more spores than its mixed partner are represented by red squares, whereas blue squares represent mixes in which the mixed genotype produces more spores. Mixes in which both genotypes produce the same amount of spores are represented by gray squares. A ranking of the genotypes according to their chimeric success is determined using the number of pair mixes in which a given genotype produces more spores than its partners; this depends on the initial amoebae relative to resource density. A) Low initial cell:resource density: 10³ cells and <i>R</i>₀ = 10⁸ resources, B) Intermediate initial cell: resource density: 10⁷ cells and <i>R</i>₀ = 10⁸ resources, C) High initial cell:resource density: 10¹⁰ cells and <i>R</i>₀ = 10⁸ resources.</p

The evolution of different phenotypes shown by an evolutionary tree.

<p>The phenotypes that are associated with the three most-abundant genotypes that were present at the end of the simulation () are called phenotype 1, 2 and 3, each belonging to a distinct ecotype. The phenotypes that are projected on the evolutionary tree correspond to the ancestral and evolved genotypes at respectively time step 0, 100.000, 300.000, 400.000, 500.000 and 550.000 (from the left to the right). Each phenotype is shown by a small graph that shows the behavior of a cell for different environmental conditions: <i>red</i> area is sporulation; <i>green</i> area is signal production; and <i>blue</i> area is no differentiation. For the parameter settings see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002818#pcbi-1002818-g005" target="_blank">figure 5</a>.</p

Selection pressures that act on the three most abundant phenotypes.

<p>The direction of an arrow shows how the phenotype frequencies change over time. The length of an arrow indicates the speed of this change and hence the strength of selection. The <i>red</i> dot shows to the phenotype frequencies at equilibrium (i.e. the population state in which all phenotypes have exactly the same fitness). The frequency changes are determined from the onset of the current nutritional cycle to that of the next nutritional cycle. The calculations therefore include both cellular-level and colony-level selection. For the parameter settings see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002818#pcbi-1002818-g005" target="_blank">figure 5</a>.</p

Evolution of signal production under various levels of signal costs and colony bottleneck sizes.

<p>The plots show the amount of signal that is present in a population of cells that evolved for 550.000 time steps for different values of (plot A) and (plot B). The grey area shows the standard deviation. For every parameter setting, 50 independent runs were studied. ‘Signal’ gives the average amount of signal that is present in the environment per time step and colony. is the reduced chance of having cell division. Thus, is equal to a 2% lower chance of having cell division. Notice that the maximum chance of having cell division is 10% (). is the number of individuals that initiate a colony and hence the bottleneck size. For plot A we assumed that and for plot B we assume that . Thus, the runs of plot B at are performed under the same parameter settings as those of plot A at . The relatively large standard deviation in plot B can be explained by the co-existence of multiple communicative strategies, of which some produce signal, while others do not. Since the abundances of these strategies change over time, the amount of signal that is being present differs strongly between the runs. Furthermore, in some runs cell-to-cell communication does not evolve (e.g. at high values of ). The other parameter settings are the following: , , , , , , , , , , , , , , and .</p

Agreement of simulations with analytic results.

<p>We test our simulation procedure against the analytic results of the set model of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000615#pcbi.1000615-Tarnita1" target="_blank">[40]</a>. Parameters used are and . or is the number of sets an individual is in, is the strategy mutation, and is the set mutation. We run simulations for generations. We use a low strategy mutation in (A) and a high strategy mutation in (B).</p