Population, finite evolving

When the system is prepared in the higher of the coupled electronic states, the electronic population typically decays on a time scale of several fs, followed by transient partial recuiTences which evolve into more or less erratic fluctuations around a finite long-time limit. Examples of this type of behavior will be discussed in Section 3. The calculations have revealed that the electronic population decay is intimately related to the multi-mode nature of the problem. The strong coupling between the nuclear degrees of freedom affects not only electronic, but also nuclear observables, such as the expectation values of the position and momentum operators of the various modes ... 

They represent the mean, variance, skew, and curtosis of the fitness distribution. To give an intuitive picture, the first two cumulants roughly capture the infinite population size limit of the model. The higher cumulants, skew and curtosis, are important to describe the dynamics of a finite population where, e.g., selection causes the fitness distribution to quickly become skewed and thus deviate from a Gaussian. An evolving population can, at each time step, be approximated by a set of these variables. Its dynamics can then be viewed in terms of the evolution of the cumulants. In the following, the dynamics of an evolving population will... 

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