MIGRATE: Maximum-likelihood estimation of migration rates and effective population numbers


Beerli, P. and J. Felsenstein (1999). “Maximum-likelihood estimation of migration rates and effective population numbers in two populations using a coalescent approach.” Genetics 152: 763-773. 

Beerli, P. and J. Felsenstein (2001). “Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach.” Proceedings of the National Academy of Sciences of the United States of America 98(8): 4563-4568.

Beerli, P. (2004). “Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations.” Molecular Ecology 13(4): 827-836.

Beerli and Felsenstein (Beerli and Felsenstein, 1999) developed maximum-likelihood and coalescent theory based method to estimate migration rate and effective population size.  The likelihood parameter Θ= [Θ1, Θ2, М1, М2], where Θ is 4Neμ and Μ is m/μ, are calculated by exploring genealogical trees, including topology of branch length and migration scenarios.  Rather than exploring all possible genealogical trees, parameters are calculated focusing the trees with high likelihood using Markov chain Monte Carlo approach.  After each chain, parameters are recalculated and the likelihood is reevaluated.  To obtain more accurate estimate, this process is repeated for many times.

In 2001, Beerli and Felsenstein (Beerli and Felsenstein, 2001) developed a program called MIGRATE.  MIGRATE use n-Island model (n is number of subpopulations) and estimates asymmetrical migration rates (Μ) between demes and effective population size of demes (Θ) for more than three sampled populations at same time.  Multiplying Μ and Θ gives Nem.  Because gene flow influence within-population genetic diversity and MIGRATE estimates Θ accounting for gene flow (Ray et al., 2003), MIGRATE should provide more accurate estimates of effective population size than traditional methods (See also here).

Unfortunately, human populations usually violate the important assumptions to estimate parameters, so the interpretation of the data has to be treated with cautions.  First, MIGRATE assumes that there is no unsampled population exchanging genes with sampled populations.  Beerli (Beerli, 2004) examined the effects of unsampled populations on these methods.  He found that migration rate, Μ=m/μ, is not seriously affected, but effective population size is upwardly biased and Nem tends to be overestimated.  Beerli suggests that more accurate estimation can be obtained by running the program with many populations at the same time.  However, human populations tend to interact with many different populations and many of them are not sampled. 

Second, MIGRATE assumes that population size and migration rate did not change over time.  However, many human populations experienced demographic expansion or bottleneck in the past.  Development of better transportation technologies, recent state expansion, European contact, globalization, and industrialization increased movement of people over time.

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3 thoughts on “MIGRATE: Maximum-likelihood estimation of migration rates and effective population numbers

  1. Several users of MIGRATE worry about the assumptions MIGRATE makes (ad then keep using methods that have very similar assumptions built in). Often the estimates are usable even when assumptions are violated. I have investigated a little what happens when two populations have diverged very recently (surely a common situation with human populations). With recent divergences the migration rates estimated by MIGRATE are biased upwards, but even under scenarios where we encounter such biases it is often still possible to evaluate migration directions consistently. I strongly suggest that researchers should test more often whether the data actually supports the structured model used, in particular whether the sample locations are differentiated enough to make the various claims commonly found in the literature, with MIGRATE we made recently considerable inroads to compare different population models correctly, for example to test whether the sampled locations belong to a single panmictic population or whether they are structured.

    I suggest to look at the following resources:
    (1) A recent blog I wrote about divergence and violation (click through to blogs MIGRATE website http://popgen.sc.fsu.edu or here http://tinyurl.com/migdivblog
    (2) A paper about comparison of models: Beerli and Palczewski 2010 Genetics
    http://www.genetics.org/cgi/content/abstract/185/1/313
    and a tutorial on the model comparison can be found here:
    http://tinyurl.com/bayesfactors

    • Thank you, Peter. I believe that MIGRATE is a useful analytical method, even for human populations. Now, I understand that recently diverged populations, especially populations that located closely, can have larger migration rate than they should. As you mentioned, examining if samples come from locations within a randomly mating population is important especially for human populations. However, I believe that, in their publications, each investigator have to address how the violation of the assumptions might have affected the results of analyses.

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