Evolutionary dynamics and diversity in populations

Abstract

The dynamics of populations is rich, taking into account that both, the individual's actions and the population's fitness are coupled. The way in which an individual chooses a strategy depends off course on the interaction with other individuals and the relation between selection and mutation within the population. The present model considers individuals with {\it memory}. This memory is represented by a device where information of past actions is stored as bits in a 1D Ising chain. The selection of a new individual action depends on the individual's memory. If the selection of a strategy does not improve the individual's fitness, a new individual with different memory size replaces it. Both, actions and memory are observables that characterize the population. They can change in time, and both depend on the fitness of the population. This model allows the implementation of {\it learning} parameters as well as an {\it external information source}, acting as an {\it external field} which drives individuals to select one preferred action. In particular we show that the {\it diversity} of the population, measured as a {\it Shannon's diversity index} (equivalent to a neg-entropy), is not only related to the {\it energy consumption and size} of the system, but is also related to the way in which the individuals are influenced by the {\it external field}.