Parameters and variables
Figure 0.2: The HPC model (Forrester diagram)
| R notation | Math notation | Description |
|---|---|---|
initial_population_humans, initial_population_plants |
\(ini_{H},\,ini_{P}\) | initial populations of humans and plants |
number_types_humans, number_types_plants |
\(n_{H},\,n_{P}\) | number of types of humans and plants. The number of phenotypic variants of each population that relate to human-plant coevolution. Types are arbitrarily ordered from type \(1\) (less mutualistic) to type \(n\) (more mutualistic). |
undirected_variation_humans, undirected_variation_plants |
\(v_{H},\,v_{P}\) | level of undirected variation in humans and plants. For any value greater than zero, these parameters regulate how even is the distribution of a population among its types. |
intrinsic_growth_rate_humans, intrinsic_growth_rate_plants |
\(r_{H},\,r_{P}\) | intrinsic growth rates for human and plant populations. The maximum rate at which a population grows when there are no external constraints. |
utility_per_capita_type_n_plants_to_humans |
\(\bar{U}_{P_{n}H}\) | utility per capita of type \(n\) plants to humans |
utility_per_capita_type_1_plants_to_humans |
\(\bar{U}_{P_{1}H}\) | utility per capita of type \(1\) plants to humans |
utility_per_capita_type_n_humans_to_plants |
\(\bar{U}_{H_{n}P}\) | utility per capita of type \(n\) humans to plants |
utility_per_capita_type_1_humans_to_plants |
\(\bar{U}_{H_{1}P}\) | utility per capita of type \(1\) humans to plants |
utility_other_to_type_n_plants |
\(U_{bP_{n}}\) | utility of other resources to type \(n\) plants or the baseline carrying capacity for plants of type \(n\); i.e. that independent of humans. |
utility_other_to_type_1_plants |
\(U_{bP_{1}}\) | utility of other resources to type \(1\) plants or the baseline carrying capacity for plants of type \(1\); i.e. that independent of humans. (non-anthropic space) |
utility_other_to_type_n_humans |
\(U_{bH_{n}}\) | utility of other resources to type \(n\) humans or the baseline carrying capacity for humans of type \(n\), i.e. that independent of plants. |
utility_other_to_type_1_humans |
\(U_{bH_{1}}\) | utility of other resources to type \(1\) humans or the baseline carrying capacity for humans of type \(1\); i.e. that independent of plants. |
max_area |
\(MaxArea\) | Maximum number of plant population units fitting the contiguous area available. It is used as the maximum carrying capacity for plants. |
| Simulation flow control | ||
max_iterations |
\(time_{max}\) | maximum number of iterations allowed before halting a simulation run. |
reltol_exponential |
\(\epsilon\) | base 10 negative exponential controlling how small population change must be to halt a simulation run. |
coevolution_threshold |
\(coevo_{\theta}\) | value between -1 and 1 to which to compare coevolution coefficients and decide if qualitative shift in type proportions has happened, so timing can be registered (see “Table: Variables (output only)” below). |
| R notation | Math notation | Description |
|---|---|---|
humans, plants |
\(H[t],\,P[t]\) | Human and plant populations at time \(t\). Population units are abstract, arbitrarily defined units that can express individuals, working hours, households, etc. (humans), and sprouts, certain amount of biomass, soil surface, etc. (plants) |
carrying_capacity_humans, carrying_capacity_plants |
\(K_{H}[t],\,K_{P}[t]\) | Carrying capacity to human and plant populations or maximum population at time \(t\), expressed in population units |
utility_humans_to_plants, utility_plants_to_humans |
\(U_{HP}[t],\,U_{PH}[t]\) | Utility of one population to the other or the total contribution of a population to the carrying capacity of the other population at time \(t\), expressed in population units |
utility_other_to_humans, utility_other_to_plants |
\(U_{bH}[t],\,U_{bP}[t]\) | Utility of other resources to a population at time \(t\), expressed in population units (baseline carrying capacity) |
type_indexes_humans, type_indexes_plants |
\(types_{H},\,types_{P}\) | Population types, arbitrarily ordered from \(1\) to \(n\) (vector or array). |
type_proportions_humans, type_proportions_plants |
\(pop_{H_{i}}[t],\,pop_{P_{i}}[t]\) | Proportion of a population belonging to each type at time \(t\) (vector or array). |
type_utility_per_capita_humans_to_plants, type_utility_per_capita_plants_to_humans |
\(\bar{U}_{H_{i}P},\,\bar{U}_{P_{i}H}\) | Utility per capita of type \(i\) individuals of one population to the other (vector or array). |
type_utility_other_to_humans, type_utility_other_to_plants |
\(U_{bH_{i}},\,U_{bP_{i}}\) | Utility of other resources to type \(i\) individuals of a population (vector or array). |
type_fitness_humans, type_fitness_plants |
\(fitness_{H_{i}}[t]\), \(fitness_{P_{i}}[t]\) | Fitness score of type \(i\) individuals of a population at time \(t\) (vector or array). |
population_change_humans, population_change_plants |
\(\Delta H[t],\,\Delta P[t]\) | Population change (delta) at time \(t\) in respect to time \(t -1\) (vector or array). |