 From this, the population-level evolutionary dynamics can be derived elegantly: the instantaneous rate of change for the proportion of the population following strategy \(S_i\) simply equals the total rate at which players following other strategies switch to \(S_i\), minus the total rate at which current followers of \(S_i\) switch to some other strategy. Substituting an individual learning rule into the following equation schema, and then solving the resulting system of equations, gives the population-level dynamics.