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Is there any comprehensive reference on (or introduction to) how people have tried to model non-independent random variables? I already know about mixing processes, which express in various ways according to various coefficients how "future" events depend on "past" events, but that's about it...

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'Non-independent' is a bit vague; there are many causes and models for dependence (clustered data, hierarchical/multilevel models, time series, ...). Could you be a bit more specific on your area of interest? – onestop Nov 30 '10 at 10:31
Yes, I'm mostly interested in dependencies between organisms. More specifically, a virus that would have evolved over time by means of mutations would lead to several different strains, which are all related in some way because they were derived from the same sequence. – Anthony Labarre Nov 30 '10 at 12:20
The mutations are still random and independent. It's the selection process that is not random and introduces dependencies (although which selection process is acting could be random). Or maybe you have more complex selection processes in mind where the specific proportion of genotypes can act as a selector as well, which would be an explicit dependence? – Raskolnikov Nov 30 '10 at 14:44
No, what you describe seems to fit the situation, but an idea of what has been used so far to model that selection could still be helpful. – Anthony Labarre Nov 30 '10 at 15:17
What do you know about the computational side of phylogenetic trees? There's a whole mathematical field flourishing around that type of problems. I'm no expert, but I know of a few papers using that approach. I'll try to dig them up and post them as a reply. – Raskolnikov Nov 30 '10 at 15:51

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OK, I think in what exists now, what comes closest to what you are looking for is the coalescent theory. Quoting from wikipedia:

In genetics, coalescent theory is a retrospective model of population genetics. It employs a sample of individuals from a population to trace all alleles of a gene shared by all members of the population to a single ancestral copy, known as the most recent common ancestor (MRCA; sometimes also termed the coancestor to emphasize the coalescent relationship[1]). The inheritance relationships between alleles are typically represented as a gene genealogy, similar in form to a phylogenetic tree. This gene genealogy is also known as the coalescent; understanding the statistical properties of the coalescent under different assumptions forms the basis of coalescent theory. The coalescent runs models of genetic drift backward in time to investigate the genealogy of antecedents.[2] In the most simple case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure. Advances in coalescent theory, however, allow extension to the basic coalescent, and can include recombination, selection, and virtually any arbitrarily complex evolutionary or demographic model in population genetic analysis. The mathematical theory of the coalescent was originally developed in the early 1980s by John Kingman[3].

The citations list of the wikipedia article mentions a primer on coalescence, looks like a good place to start.

This paper gives a review of coalescence and natural selection.

This paper gives a relatively lowbrow example of how coalescence theory is used in the case of neutral selection. This can help you get the feeling for the ideas. It also contains references to seminal papers in the field.

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