Table 2 Model parameters.
From: The evolution of biogeochemical recycling by persistence-based selection
Model parameter | Default value and units | Qualitative impact on results |
|---|---|---|
\(K\) | Carrying capacity (maximum number of individuals of either species), \(K=10000\) | Dictates maximum size of a population in the absence of limitation by the level of environmental substance |
\({G}_{q,{jPR}}\) | Reproductive growth rate (genotype \(j\), species \(q\)), per unit environmental substance \(R\) assimilated | Controls the time a population takes to reach equilibrium size and composition |
\({f}_{{conv}}\) | Conversion efficiency between assimilation of environmental substance \(R\) and production of offspring by parent individuals \({f}_{{conv}}=0.5\) unless otherwise stated | Impacts the number of biological individuals a given environmental substance pool can support |
\({G}_{0}\) | Baseline growth rate (offspring individuals produced per parent individual, per time-step) \({G}_{0}=5\) | Impacts rate at which population reaches equilibrium size and composition |
\({R}_{{assimMAX}}\) | Maximum quantity of environmental substance that can be assimilated by a single individual during a single time-step \({R}_{{assimMAX}}=3\) | Dictates rate of net population growth |
\({\kappa }_{{prod}}\) | Relative decrease in reproductive growth rate associated with the producer phenotype compared to the non-producer phenotype. Default value \({\kappa }_{{prod}}=0.1\) | Dictates range of boundary conditions over which the producer can coexist with the non-producer |
\({p}_{k\to j}\) | Probability of a mutant offspring from another genotype being the \(j\)th genotype, \({p}_{k\to j}=\frac{1}{{j}_{{total}}-1}=0.5\). | Ensures unbiased mutation |
\({\mu }_{0}\) | Baseline mutation probability per offspring produced. Default value \({\mu }_{0}=0.01\). | Sustains genotypic diversity delaying displacement of producers by non-producers for a given set of boundary conditions |
\({\delta }_{0}\) | Death probability due to “random” factors unconnected with environmental substance levels, per individual per generation. Default value \({\delta }_{0}=0.1\). | Thins the population, ensures starvation is not the only cause of death |
\({{\varphi }_{0}}_{{R}_{q}}\) | Baseline net abiotic influx of environmental substances \({R}_{1}\) and \({R}_{2}\), units of substance per time step. Default value \({\varphi }_{0}=10\) for both substances. | Dictates net equilibrium population size, if this number is below carrying capacity |
\({R}_{q,{NET}0}\) | Scaling factor representing sensitivity of abiotic removal flux to existing size of environmental substance pool, corresponding to baseline abiotic steady state residence time \({R}_{q,{NET}0}=\frac{{R}_{q,{NET}(t)}}{{{\varphi }_{0}}_{{R}_{q}}}\) Default value \({R}_{q,{NET}0}=100\) | Inversely related to the time an environmental substance pool will take to become exhausted in the absence of abiotic influx or biotic production |
\({f}_{{conv},{PROD}}\) | Efficiency with which individuals with the producer phenotype convert the environmental substance that they assimilate to the by-product substance that they emit. Default assumption \({f}_{{conv},{PROD}}=\left(1-{f}_{conv}\right)\cdot ({1-f}_{{loss},{prod}})\) | Dictates the net efficiency with which producers generate one environmental substance from the other, thus impacts net population size during shut-off intervals |
\({f}_{{loss},{prod}}\) | Fraction of growth-by-product environmental substance lost during production flux \({f}_{{loss},{prod}}=0.4\) | As \({f}_{{conv},{PROD}}\) |
\({f}_{{symmetry}}\) | Symmetry breaking parameter applicable in a subset of runs, causing a difference in physiological efficiency between the two distinct producer genotypes, implemented as: \({f}_{{conv},{PROD},{S}_{1}}=\left(1-{f}_{{conv}}\right)\cdot ({1-f}_{{loss},{prod}})\) \({f}_{{conv},{PROD},{S}_{2}}=\left(1-{f}_{{conv}}\right)\cdot ({1-f}_{{loss},{prod}})\cdot {f}_{{symmetry}}\) Default value \({f}_{{symmetry}}=1\) | Deviation from 1 causes net production in one species to exceed that of the other, meaning, increasing the rate of incremental population decline when abiotic influx is switched off. |
\({{R}_{q,{BIOAVAILABLE}}}_{{crit}}\) | Bio-available environmental substance level at which the plastic genotype switches phenotype (producer above, non-producer below) \({{R}_{X,{BIOAVAILABLE}}}_{{crit}}=1\) | When non-zero ensures that plastic genotype can contribute to an existing recycling loop, but not sustain it in the absence of the producer genotype |
