Fig 1.
A: The life cycle of Dictyostelium discoideum (after [28]). B: The simplified life cycle of a generalized aggregative multicellular organism, modelled in this paper. 1. Under normal circumstances cells are free living. 2. During starvation, cells secrete attractive molecules and form aggregates. 3. From the aggregates, fruiting bodies form. In this period there are two cell types: stalk and spore cells. Only spore cells will survive this period, stalk cells die. 4. The spores (or propagules) disperse to the new habitat and cells colonize it. We note that although in reality, cells only aggregate during propagule formation, in our model cooperators constitutively express the adhesive molecules thus can aggregate any time.
Fig 2.
Possible reproduction mechanisms considered for the population when a new habitat is colonized.
During selection for colonization (transfer), cells are either selected randomly (B, C, D) or based on strongest aggregate (E, F). After transfer to the new habitat, the population either retains its original structure (D, F) or is dispersed (B, E). For more details, see text. The labels A-F are used consistently in all figures.
Fig 3.
Relative frequency change of cell types over multiple colonization events depending on propagation mechanism (rows) and size-dependent selection (i.e. predation; columns).
Each subplot shows the result of 140 independent simulations (coloured lines) with mean (dashed) and ± standard deviation enveloped in grey. The y axis shows the ratio of cooperators. Bars on the right of each subplot show the average outcomes categorized into five categories (see legend) by the terminal percentage of cooperators (for more details, see Figs E, F in S1 Text). There is no real coexistence: simulations converge either to a monomorphic cooperator or defector population. If there is no size dependent selection (left column), cooperators can only survive under aggregation-based dispersion (E left) or, with a small probability, under aggregation-based propagule formation (F left). Aggregation-based dispersion is indifferent to size-dependent selection (E right), however, cooperators now can survive with high probability in case of no colonization (A right) or aggregation-based propagule formation (F right). The parameters of these plots are as in Table 1.
Table 1.
The symbols, parameters and their values used throughout the paper.
Parameters defined separately for cooperators and defectors are denoted with a C or D in subscript, respectively.
Fig 4.
Terminal cooperator ratio depending on association propbability AC (x axis), dissociation probability (DC, y axis), propagation mechanism (rows) and size-dependent selection (s, columns; e.g. predation).
Each pixel on the heatmap represents the mean of terminal cooperator ratio of 7 independent simulations. The white asterisk denotes the parameters of the first experiment (Fig 3). When size-dependent selection was not in effect (A, left column), only defectors survive in case of no colonization, and the introduction of selection (e.g. predation stress) clearly benefits cooperators with reasonable association rates (A, right column). Random dispersal (B left) shows a slight benefit for cooperators due to decreased competition at the new habitat, but only for high association rate and even higher dissociation rates. In case of random refuge and fragmentation (C, D), size-dependent selection barely has any effect. Aggregation-based dispersion (E) always benefits cooperators, regardless of predation stress or even association/dissociation rates. Aggregation-based propagation is beneficial when there is no predation stress (F left) but is even more advantageous when predation is introduced (F right). For more details and explanation, see text; for the time-evolution of independent simulations for selected (AC, D) pairs, see Fig I in S1 Text; for a detailed examination of differences in division at certain (AC, D) pairs, see Fig J in S1 Text. Parameters are as in Table 1, except for aggregation-based fragmentation, where T = 150 000 000.
Fig 5.
The effect of size-dependent selection (predation) on aggregation-based propagule formation.
Top row: terminal cooperator ratio, depending on various association (AC, x axis) and dissociation probabilities (D, y axis); bottom row: temporal dynamics of independent simulations at AC = 0.95, D = 0.3 (indicated by the white crosshair in the top row). First column (s = 7) corresponds to weakest, last column (s = 3) to strongest predation, cf. Eq 1. The middle case s = 5 is the same as in Fig 4F, right panel. Defectors suffer more from predation, because they are less associated, hence as the predation stress increases, the area where they win reduces considerably. As predation decreases, defectors do not suffer from predation load, and cooperators lose their advantage, especially when the association rate is larger than the dissociation rate (AC>D). If predation is effectively removed (s>7, also Fig 4F, left panel), cooperators can still survive at AC<D. For more details, see text and Figs E, F in S1 Text.
Fig 6.
Possible representative states of the simulated population of cooperators (blue) and defectors (red) on lattice.
Teal arrows indicate population dynamics, green arrows subpopulation transfer to new habitat. Simulation starts from a random state with low cell count (1). Approximately 4% of the available space is occupied by cells. Cells consume resources, grow in numbers and spread on the lattice (2). After resource is depleted, a propagule is formed, possibly containing both types, and colonizes a new habitat (3) where it starts to spread (4). There are three possibilities: neither type outcompetes the other (5), cooperators outcompete defectors (6), and defectors outcompete cooperators (9). In mixed populations (5), three propagule types can emerge and colonize new habitats: mixed (3), cooperator-only (7) and defector-only (8). Uniform defector populations (9) cannot form propagules and colonize new habitats–without constant resource inflow, the population is doomed. All-cooperator populations (7) can successfully form fruiting bodies and colonize new habitats for eternity, whenever resources are exhausted (6), but without mutation, cheaters will never reappear, and simulation can be terminated.
Fig 7.
Dynamical changes in the population composition.
A: Cell, food and association matrices represent the population at every timestep. Cell matrix row: blue represents cooperators, red defectors, empty cells are white). Food matrix row: orange represents available resource amount, white denotes resource-poor cells. Association matrix row: the brighter a cell is, the more associated neighbours it has (from 0 to 8). B: Temporal dynamics of the population composition. Abrupt abundance drops indicate successive colonization events of new habitats after propagule formation. Note, that in the second colonization, only cooperators were transferred, and defectors were lost.