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Does natural selection tend to result in genes that maximize their longterm growth rate (growth of the number of copies of themselves), or in genes that simply maximize the expected number of copies of themselves in the next generation? Since replication is a chance process, these are not generally the same thing.
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Turns out this question has a simple, definite answer. Since gene replication is a branching process, the process either dies out or grows at the rate determined by expected number of offspring in the next generation. So in this case, there is no important distinction between maximizing number of copies in the next generation and maximizing the longterm growth rate of the number of copies of a gene. No need to invoke Kelly's strategy from gambling theory.
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