A Lattice Model for Population Biology
In statistical physics we study macroscopic properties of matter on the basis of constituent particles, and in theoretical population biology we study features of populations on the basis of behaviors of individuals or, more basically and generally, on the basis of properties of self-replicating entities such as genes or chromosomes. Let us refer to any object that we broadly regard as a unit of replication as a ‘replicon’, thereby extending the original meaning used by molecular geneticists. Each replicon has a definite genetic state and undergoes birth and death. Therefore, in addition to ‘attraction and repulsion’, interactions between replicons typically includes ‘attacking and helping’, which affects the birth and death of recipients. The particular mode of interaction depends on a replicon’s state. This state is inherited from its parent replicon, and we can therefore study what type of interaction is prevalent in a population by examining that population’s dynamics. This is simply the evolution of behavior by natural selection.
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