Output variables

The most important output variables are the coevolution coefficients (\(coevo_H\), \(coevo_P\)), which measure the trend in the distribution of a population among its types.

\[\begin{equation} \tag{Eq. 17} coevo_H[t]=\frac{\sum_{i=1}^{n_H}pop_{H_i}[t] * (types_{H_i} - 1))}{n_H - 1} * 2 - 1 \end{equation}\]

\[\begin{equation} \tag{Eq. 18} coevo_P[t]=\frac{\sum_{i=1}^{n_P}pop_{P_i}[t] * (types_{P_i} - 1))}{n_P - 1} * 2 - 1 \end{equation}\]

The dependency coefficients (\(depend_H\), \(depend_P\)) express the direction and intensity of the selective pressure caused by the other population. It is calculated as the slope coefficient of a linear model of the fitness scores (\(fitness_A[t]\)) using the type indexes (\(types_A\)) as an independent variable.

Positive values of both these coefficients reflect the tendency of a population towards the most mutualistic types (effective coevolution), while negative values indicate an inclination towards the non-mutualistic type due to a low selective pressure exerted by the mutualistic relationship.

We recorded the time step at the end of simulations (\(time_{end}\)), obtaining a measure of the overall duration of the process. Whenever applicable, we register the duration of change towards more mutualistic types in both populations (\(timing_H, timing_P\)). We consider change to be effective when the respective coevolution coefficient is greater than 0.5 (coevolution_threshold, in the implementation in R), meaning that at least half of the population is concentrated on the higher quarter of the type spectrum.

Variables (output only)

R notation	Math notation	Description
coevolution_coefficient_humans, coevolution_coefficient_plants	\(coevo_{H},\,coevo_{P}\)	Coevolution coefficients. A coefficient representing the distribution of the proportion of a population per type (\(pop_{A_1}\) to \(pop_{A_n}\)) weighted by type index (\(1\) to \(n\)). Each indicates if and how much the population distribution has been modified by the coevolutionary process. Their values range between -1, the entire population is of type \(1\), and 1, the entire population is of type \(n\).
dependency_coefficient_humans, dependency_coefficient_plants	\(depend_{H},\,depend_{P}\)	Dependency coefficients. The slope of the linear model of the fitness score per type (\(fitness_{A_1}\) to \(fitness_{A_n}\)) using type index (\(1\) to \(n\)). Indicate if and how much the overall fitness score of a population is dependent on the other population.
timing_humans, timing_plants	\(timing_{H},\,timing_{P}\)	Iterations past until coevolution successfully changes the proportions of population per type; generally, when \(pop_{A_1}\gg pop_{A_n}\) or, more specifically, \(coevo_A>coevo_{\theta}\).
time_end	\(t_{end}\)	Iterations past until the end state (stationary point)