Bias of migration rate estimates caused by population bottleneck?

[Paul]

Hi Peter and Group,

What is the expected bias on migration rate estimates (Nm) when all
populations show evidence of a bottleneck? Should I expect more bias
in magnitudes, or in the extent/direction of asymmetry of immigration
and emigration?

I have 4 population and want to estimate asymmetric gene flow rates
among them using 8 microsatellite loci. Each population shows
evidence of a bottleneck and thus violates the assumption of constant
population size. I am particularly interested in knowing if migration
is higher in one direction compared to the other for one pair of
populations, and in general I am interested in knowing which pair has
the highest overall migration rate.

Thanks for your help!

Paul

[Peter]

Paul

a cartoon version, but I hope you guess what a less drastic scenario
could do:
a recent bottleneck will purge the rare alleles and the most common
allele(s) will remain, if the populations share the common alleles
then
the estimates of the migration rates will be biased upwards whereas
the sizes are biased downwards. If rare alleles remain then the
direction
will be most likely little affected if you have multiple loci, with a
single locus by change all rare alleles on one population are erased
but not in the other,
this will result in changes in direction. If the bottleneck is less
drastic then the directionality will be easy to detect.

I often read about bottlenecks, and I think you should qualify what
exactly do you mean, if you talk about a relative reduction of
population size, say of 50% and the
effective sizes were >10000 before the incident then you will not see
any (or not much) evidence of the genetic bottleneck, if the
populations were reduced to 100 or less then
the above scenario may hold. I would think that in most cases it is
rather difficult to measure the bottlenecks with confidence people
report.

Peter

[Paul]

Hi Peter,

Thanks for your very helpful reply.

I used several analyses to determine whether or not there was a
bottleneck. First, I used the ratio of allelic richness to allele
size range (M) of Garza & Williamson (2001), and found strong support
for a bottleneck (M = 0.19 to 0.33). I also used Bottleneck to test
for heterozygosity excess, but did not find evidence for a
bottleneck. Finally, I used IMa to estimate pairwise divergence,
gene flow, and effective sizes of populations. IMa suggested smaller
modern effective population sizes than ancestral sizes. In one case I
am particularly interested in, the modern populations were about 10%
and 1.5% the size of the ancestor (if I convert parameter estimates to
demographic units using an approximate mutation rate, this equates
roughly to an ancestral population size of 100,000 that diverged into
populations of about 10,000 and 1,500).

Originally, I was thinking of just using the gene flow estimates from
the IMa analysis, but I have read (Strasburg & Rieseberg 2010) that
they can be severely biased when other interbreeding populations are
ignored, as in our pairwise approach, so I did not trust them.
Migrate-n permits multiple populations, but the assumption of constant
population size may be violated in our data.

Thanks for any further insight.

Paul

[Peter Beerli]

Paul,

- I have written some notes on migrate and very recent divergences (http://popgen.sc.fsu.edu/Migrate/Blog/Blog.html)
- if you are interested in directionality, migrate will often work OK despite recent diverngece, but the migration rates will be inflated.
- Garza and Williamson is a method using the cartoon version I described in the earlier post, I guess that it assumes no structure _and_ perfect stepping stone or brownian motion mutation model.
- Heterozygosity excess signatures decays very quickly, I guess if you would know the population sizes than one could see this over a longer time period.
- IMa may work just fine for you, although I have not seen many studies that point to bottlenecks [this only reflects my ignorance not IM].
- You could use lamarc and coestimate immigration/size/exponential growth or shrinkage
- You could use migrate's skyline plots
- Strasburg and Rieseberg: it was interesting to see that concerning unknown populations Beerli (2004) "Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations" and Slatkin (2004) "Seeing ghosts: the effect of unsampled populations on migration rates estimated for sampled populations" got missed in that paper.

Peter

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[AVIK RAY]

Peter,
just gone through your blog about recent splits, but ."....With very recent population splits MIGRATE-N will fail to give accurate migration rates, but the divergence time needs to be very recent.."...how recent you suggest? however, (if understood correctly) from the tables it appears that it is not at all affected by recent splits! or may be wrong!

AVIK

[Peter Beerli]

I have seen dataset where directionality could be easily deducted with migrate with "known" split of the population of <100 generation [and no direct migration], but depending on the data this may lead to large biases.

I believe that for most problems that involve glaciation etc migrate will do ok, because commonly the populations under investigations are not huge. If you want to be cautious compare with IM when you have recent divergences but

if there is some migration after divergence migrate will work OK.

The estimates of  M do not always include the true simulated value of M with recent splits, but if the migration is high then the divergence does not affect results tremendously.

Peter

[Paul]

Thanks for the additional info. So, it sounds like in my case,
Migrate may reasonably determine relative magnitudes or directionality
of migration, which is my main interest. I am also looking into
Lamarc, but the run time seems very long in my preliminary attempts.

paul