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There two main mathematical models to describe the process of genetic drift are Moran model and Wright-Fisher model.

My questions concern the assumptions of these models, the existence of other models of genetic drift, explanation of the advantage/disadvantage of these models and the empirical results supporting one or another model.

  • What are the assumptions of each of these models?

    • stable population size?
    • iteroparous/semelparous
    • what about the probability density function of the fitness?
    • …?
  • What advantage/disadvantage do these models have? Or I should say, to which population do these various model applies?

  • What kind of biological population has been empirically shown to fit better one model rather than another one? What are the key experiments to test the validity of these models?

Please do not hesitate to post even if you answer only partially to the questions! Thank you!

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1 Answer 1

up vote 3 down vote accepted

This question has been around for a while, so I'll try to start with a partial answer.

The basic assumptions of the standard Wright-Fisher-Model are:

  • Constant population size $N$.
  • Discrete, non-overlapping generations.
  • Neutrality (e.g. all individuals are equally likely to reproduce)

I prefer looking at the model for haploid/chromosomes. If you bundle up chromosomes to polyploids, then you get the additional assumption of random mating, e.g. all pairs of individuals are equally likely to reproduce.

I might have missed something, but these assumptions should be sufficient to generate the Wright-Fisher-Dynamics: When we build a new generation, we have to fill $N$ spots again (follows from the first two assumptions). As each old individual is equally likely to reproduce (third assumption), e.g. to become parent of a new individual, we get the multinomial offspring distribution.

The main difference in the Moran model is that it assumes overlapping generations. Main assumptions here are:

  • Again constant population size.
  • Individuals reproduce at a constant rate.
  • Neutrality (however the Moran model can relatively easily be adapted to incorporate positive selection).

Every time an individual reproduces, another one instantly dies to maintain the constant population size.

Interestingly, the models have the same diffusion limit, e.g. they behave similarly for large populations (and identically for an 'infinitely large population'). If you trace the ancestry of a sample back in a large population, you will get close to Kingman's Coalescent under both models.

I think the two models exist more because of their distinct mathematical properties, than because one fits better to certain natural populations than the other. I'm not aware of any experiments that have shown how well they fit, maybe someone else can jump in here.

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