Currently Reading

Karen M. Page and Martin A. Nowak, “Unifying Evolutionary Dynamics.” Journal of Theoretical Biology 219 (2002): 93–98 (PDF). Abstract:

Darwinian evolution is based on three fundamental principles, reproduction, mutation and selection, which describe how populations change over time and how new forms evolve out of old ones. There are numerous mathematical descriptions of the resulting evolutionary dynamics. In this paper, we show that apparently very different formulations are part of a single unified framework. At the center of this framework is the equivalence between the replicator–mutator equation and the Price equation. From these equations, we obtain as special cases adaptive dynamics, evolutionary game dynamics, the Lotka-Volterra equation of ecology and the quasispecies equation of molecular evolution.

Page and Nowak disavow interest in explicitly spatial models, although they do incorporate frequency-dependent selection by writing the fitness of strategy [tex]i[/tex] as a function of the population distribution:

[tex]f_i(\vec{x}) = f_i(x_1, x_2, \ldots, x_n),[/tex]

where [tex]x_i[/tex] denotes the frequency of strategy [tex]i[/tex].

2 thoughts on “Currently Reading”

  1. Interestingly, like both Price and Fisher before him, Nowak apparently harbors religious beliefs though he doesn’t make a big deal about it.

    Here’s hoping that Nowak doesn’t go off the deep end like Price did!

  2. One of the advantages of a mathematical paper is that, even if Nowak starts prancing around Harvard Square wearing a traffic cone on his head, proclaiming “Yes, I am the Pope!” and blessing random passers-by, the content will remain as valid and interesting as it ever was.

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