Fig 1.
Cell concentrations as a function of time in different runs of the lattice model.
Each run begins with randomly positioned P, N and S cells with a concentration of 0.05 each. For all examples r1 = 2, r2 = 2.5, b = 10 and the lattice size is 1024×1024. The other parameters differ. A) Sensitive cells win when c = 0.0011 and a = 30. B) Producers win when c = 0.0011 and a = 100. C) Non-producers win when c = 0.0002 and a = 90. D) The three cell types coexist when c = 0.001 and a = 150.
Fig 2.
Snapshot showing the spatial structure of the lattice in a case where the three cell types coexist.
The snapshot corresponds to the state of the system at time t = 4800 in Fig 1D. Parameters: c = 0.001; a = 150; b = 10; lattice size: L = 1024×1024.
Fig 3.
Majority outcomes of 100 runs of time 10,000 as a function of production rate a and production cost c.
Green–S only; red–P only; blue–N only; grey–S, P and N; yellow–S and P. Parameters: r1 = 2, r2 = 2.5, v = 1, b = 10, L = 1024x1024, δt = 0.01.
Fig 4.
Possible outcomes of 100 simulation trials for each value of production rate a.
Green–S only; red–P only; grey–S, P and N; yellow–S and P. Parameters: r1 = 2, r2 = 2.5, v = 1, b = 10, c = 0.001, δt = 0.01.
Fig 5.
Time averaged cell concentrations for the surviving cell types as a function of a.
Parameters as in Fig 4. P—red; N—blue; S—green.
Fig 6.
Possible outcomes of 100 simulation trials for each value of production rate a in the presence of mutation between P and N.
Green–S only; red–P only; grey–S, P and N; yellow–S and P. Parameters: r1 = 2, r2 = 2.5, v = 1, b = 10, c = 0.001, δt = 0.01, u = 10−4. This should be compared with Fig 4 for the case with no mutation. Results are much more predictable when mutation is present.
Fig 7.
Time averaged cell concentrations for the surviving cell types as a function of a in the presence of mutation between P and N.
Parameters as in Fig 6. P—red; N—blue; S—green.
Fig 8.
Time evolution of cell concentrations in a case where a low-rate producer replaces a non-producer.
There are three cell-types initially: P with a = 110 (red), N (blue), and S (green). At t = 6000, a low-rate producer with a = 50 (violet) is introduced. The low-rate producer replaces the non-producer and a new stable coexistence is established. Parameters: b = 10, c = 0.001, δt = 0.01, u = 10−4, lattice size: L = 1024x1024.
Fig 9.
Time averaged cell concentrations in simulations with mutations between producers of many different production rates.
Three sets of initial conditions are described in the text. These converge to similar distributions in the long-time limit. Simulations were run for 100,000 time units and an average was taken over the second half of the simulation. Parameters: b = 10, c = 0.001, δt = 0.01, u = 0.0001, lattice: L = 1024x1024. The equilibrium concentration of S in these runs is close to 0.32.
Fig 10.
Equilibrium concentrations of four cell types P (red), N (blue), S (green) and R (violet).
Mutations occur between P and N, and between S and R. Parameters: r1 = 2.0, r2 = 2.5, a = 110 b = 10, c = 0.001, δt = 0.01, u = 10−4, and lattice size: L = 1024x1024.