Fig 1.
The Metabolically Coupled Replicator System concept.
Metabolic replicators (I1, I2 and I3) provide catalytic support (dashed arrows) to a common metabolism (M), which produces monomers (dotted arrows) for replicators to replicate (circular arrows). In this case, system size is A = 3 (number of catalytic activities needed for the metabolism). Parasites (P) use monomers supplied by metabolism in their replication, but they do not contribute to monomer production.
Fig 2.
Simplified flow diagram of a single site update.
Fig 3.
Neighbourhood types used in the simulations.
(A) The von Neumann type neighbourhoods of the focal cell (red cross): black cells–the classical von Neumann neighbourhood with 5 cells; dark grey and black– 13 cells; light grey, dark grey and black– 29 cells. (B). The Moore type neighbourhoods of the focal cell (red cross): black– 3x3 neighbourhood with 9 cells; dark grey and black– 5x5 neighbourhood with 25 cells; light grey, dark grey and black– 7x7 neighbourhood with 49 cells.
Fig 4.
The types of replicators in the two dimensional space of enzymatic activities.
Coloured regions represent parts of the phenotypic trait-space which replicators are permitted to occupy by the trade-off constraints. The concave orange line represents a strong trade-off, while the convex blue line stands for a weak trade-off between enzymatic activities A and B. Specialists (replicators in the green areas) have only one significant enzymatic activity; generalists (red area) feature both activities. Replicators of very weak or no catalytic activity are parasites (black area). While the generalist-specialists continuum is gradual, we distinguish them by artificial boundaries defined by a threshold value m = 0.01 (represented by black lines).
Fig 5.
Trade-off surfaces with two enzyme activities.
The surfaces delimit the section of the trait space that replicators can occupy in case of A = 2. The surfaces are calculated by Eqs 6 and 7; all replicators take trait values from below the trade-off surfaces shown. The axes are the two enzymatic activities (E1 and E2) and replicability (k). Catalytic (activity/activity) trade-off differs in columns (left: strong, middle: neutral, right: weak) and activity/replicability trade-off differs in rows similarly (bottom: strong, middle: neutral, top: weak).
Table 1.
Parameters of the model.
Fig 6.
Time plots of the coexistence of different promiscuity patterns at different parameter settings.
b, kmax and D are specified on the top and right sides of the panels, other parameters: A = 3, Nmet = 5, g = 1.0. The colour code of replicators: orange - parasites, red–E1, green–E2, blue–E3, yellow–E1/E2, purple–E1/E3, turquoise–E2/E3 and black–E1/E2/E3.
Fig 7.
The effect of changes in key parameters of the system after 50 000 generations.
This figure contains the results for simulations with D = 0 (left panels) and with D = 5 (right panels). The replication/catalytic activity trade-off parameter was g = 1 in every case. System size (number of enzymatic activity types in the system) is A = 3 (top) and A = 5 (bottom). Maximum replication rate (kmax) and the size of the metabolic neighbourhood (see Fig 3) change from left to right. Square colour (within columns) represents the average of the relative (compared to system size) number of enzymatic activities per replicator after 50 000 generation (Eq 8), scaled from yellow (specialism) to red (generalism), represented by the index of overall catalytic promiscuity G (see Eq 8) within the whole replicator population. White squares indicate system extinction. White circles within coloured squares represent the whole replicator community, the black circles in them show the proportion of parasites (radii representing proportions). Each square / dot is calculated as the mean of at least 5 parallel simulations with the same parameter setting but different random number generator seeds.
Fig 8.
Promiscuity patterns of coexistence.
The distribution of replicators under the trade-off surface of enzymatic activities after 50 000 generations at A = 3 and g = 1. Axes are scales of the three different enzymatic activities. Size and colour of dots represent the frequency of replicator groups with a certain enzymatic activity pattern. (A) a system dominated by specialists (b = 1.1, D = 5, kmax = 2.0, Nmet = 5), (B) a system dominated by two-activity generalists (b = 1.5, D = 5, kmax = 2.5, Nmet = 5), (C) a system dominated by three-activity generalists (b = 1.6, D = 0, kmax = 2.0, Nmet = 5). On (D) a two-activity generalist type and its complementary specialist dominate the system (b = 1.4, D = 5, kmax = 2.0, Nmet = 5).
Fig 9.
The effect of activity/replicability trade-off (g).
This figure contains the results for simulations with D = 0 (left panels) and with D = 5 (right panels). The system size (number of enzymatic activity types in the system) is A = 3 and maximum replication rate is kmax = 4.0 in all these simulations. Rows differ in metabolic neighbourhood sizes (top-down: Nmet = 5 (vonNeumann), Nmet = 9 (Moore), Nmet = 25 (5x5)). In the basic figures, the activity/replicability trade-off (g) gets weaker from left to right and the catalytic trade-off gets weaker from bottom to top. Square colour (within columns) represents the average relative (compared to system size) number of enzymatic activities per grid site after 50 000 generation (Eq 8), scaled from yellow (specialism) to red (generalism), that is calculated by the index of overall catalytic promiscuity G (see Eq 8) within the whole replicator population. White squares indicate system extinction. White circles within coloured squares represent the whole replicator community, the black circles in them show the proportions of parasites to the total number of replicators (radii representing proportions). Each square / dot is calculated as the mean of at least 5 parallel simulations with the same parameter setting but different random number generator seeds.