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Models of evolution. (English) Zbl 0531.92015
Summary: Different ways in which evolution can be modelled will be reviewed. Two asexual models - ’Muller’s ratchet’ and a model due to M. Eigen and P. Schuster [The hypercycle. Springer (1979)] - both lead to the conclusion that the accuracy of replication must reach a limiting value, but the details are different. In classic population genetics models, difficulties arise if fitnesses depend on interactions with others.
Two approaches - ’trait group’ methods, and game theory - are discussed. If the interacting individuals are relatives, there is again a choice between the exact ’neighbour-modulated fitness’ approach and the more intuitive ’inclusive fitness’ method. A more drastic change in the nature of the model arises if the units of the evolving system are not individual organisms, but either genes or species. There are conceptual difficulties which must be clarified before species selection can be analysed mathematically.

92D15 Problems related to evolution
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