Table 4 Model parameters and notation
Parameter | Interpretation | Values used |
|---|---|---|
\({R}_{in}\) | Nutrient influx per group per generation | \(5\, \mathrm{or}\, 50\) |
\(\delta\) | The fitness deficit suffered by A-type cells | \(0.98\, \mathrm{or}\, 1.00\) |
\({D}_{min}\) | The probability of death per cell per generation in an A-type population | \(0.05\) |
\({D}_{max}\) | The probability of death per cell per generation in an S-type population | \(0.30\) |
\({P}_{mut}\) | The probability of a “switch” mutation per cell per generation | \({10 }^{-6}\) |
\(\Delta g\) | Number of generations between sets of dispersal events | \(1, 25, 50, 100\) |
\(p\) | The proportion of cells drawn from a donor group for form a migration propagule | \(0.25\) |
\({N}_{A}={N}_{cap}(\pi =1)\) | The number of cells in an A-type group at birth–death equilibrium | \({R}_{in}{/D}_{min}\) |
\({N}_{S}={N}_{cap}(\pi =0)\) | The number of cells in an S-type group at birth–death equilibrium | \({R}_{in}{/D}_{max}\) |
Notation | Interpretation |
|---|---|
\({w}_{A}\left(\pi \right)\) | The fitness of an A-type cell in a population in which the proportion of A-type cells is \(\pi\) |
\({w}_{S}\left(\pi \right)\) | The fitness of an S-type cell in a population in which the proportion of A-type cells is \(\pi\) |
\(cR(\pi )\) | The proportion of nutrient influx \({R}_{in}\) consumed by the subpopulation of A-type cells within any population or group |
\({P}_{AS}\) | Probability that an A-type population will transition to an S-type population by selection following an A-to-S-type mutation in a single A-type cell |
\({P}_{SA}\) | Probability that an S-type population will transition to an A-type population by drift following an S-to-A-type mutation in a single S-type cell |
\({\pi }_{AS}\) | The expected proportion of A-type cells in a recipient S-type group after it has received a migration propagule from an A-type donor |
\({\pi }_{SA}\) | The expected proportion of A-type cells in a recipient A-type group after it has received a migration propagule from an S-type donor |
\({W}_{A}\) | The nominal fitness of an A-type group in a metapopulation with dispersal by migration |
\({W}_{S}\) | The nominal fitness of an S-type group in a metapopulation with dispersal by migration |
\({F}_{A}\) | The proportion of A-type groups in a metapopulation |
\({F}_{S}\) | The proportion of S-type groups in a metapopulation |