Effects of migration on populations

[Patrick Foley]

Paul,

If indeed, the mating in Mexico is panmictic for the Eastern Monarchs, then humans
shuffling genes within that region will have no long term effect. There we are agreed.
Are butterfly breeders careful not to ship across the continent? Or are we only concerned
here with shipments from Maine to Minnesota. In which case we are wasting the time of
everyone from other states and countries.

I do not understand what mathematical models you need. There are plenty of mathematical
models of migration in Crow and Kimura 1970 and in Maruyama 1977. Ask Bruce about them. I
think he will agree with me about the long term homogenizing effect of even small amounts
of migration on neutral allele frequencies in populations. Strongly selected allele
frequencies may however remain strongly differentiated, but many to most phylogenetic
studies appear to be on nearly neutral alleles.

Patrick Foley
patfoley at csus.edu

Paul Cherubini wrote:

> Pat wrote:
>
> > The contribution of this year's releases to the target gene pool will presumably
> > continue to influence next year's population. And so on. If the location-unique
> > alleles are presently selectively neutral (this is not to say neutral forever),
> > they will on average then build up in the target population to the point where they
> > would be noticeable. In fact until the source and target populations are
> > homogeneous (for _neutral_ alleles only!). The cumulative homogenizing effects of
> > even a small amount of migration on otherwise separated populations is astonishing.
> > Some models require only one migrant per generation to bring about long-term
> > homogeneity (Crow and Kimura 1970, p 269, Maruyama 1977 ch 11).
>
> Pat, I guess I should have made clear that I was interested in a
> reasonable MATHEMATICAL model that demonstrates the validity of Dr.
> Karen Oberhauser's concerns; i.e. that a modest amount of human assisted
> shipping of Maine monarchs to Minnesota (or vice versa) in late summer
> has a slight chance of disrupting the genetic structure of the recipient
> monarch population and could make it difficult for a researcher to study that
> structure.
>
> Bruce Walsh explained the value of mathematical modeling last year:
> "The concern about [interstate] transfers have never been stated in terms of
> explicit models with parameters and assumptions that we can examine/debate.
> Clearly, I'm sure some of my numbers may be too high or too low, but we can
> examine the consequences of those changes to see if they have a real impact.
> In other works, we can do hypothesis testing."
>
> Pat, since I don't have a math based model from you at the moment to
> examine and debate, I would like to ask you to expand on your statement
> "The contribution of this year's releases to the target gene pool will presumably
>  continue to influence next year's population. And so on."  What I don't
> understand is how can Maine to Minnesota and vice versa transfers possibly
> influence next year's genetic structure in those states given
> what we already know about monarch population genetics:
>
> 1. The same authors (Eanes & Koehn 1978) that found monarchs become
> slightly genetically differentiated (based on electrophoretic markers)
> in late summer in the northern states from (presumably)
> either local adaptation or non-adaptive genetic drift, also found the
> fall migratory population has the same gene frequencies throughout the
> area from the Rockies to the Atlantic coast.  "Western" monarchs were
> not analyzed at the time of this 1978 study, but a subsequent
> electrophoretic study has found they have the same gene frequencies as well.
>
> 2. At the overwintering sites in Mexico, "the mating is random
> and the population can be characterized as panmictic" (O.R.Taylor, 2001)
>
> 3. In the spring, "Males move north in good numbers along with
> the ovipositing females. Mating occurs en route and females reaching
> the end of their life have usually mated more than four times"
> (O.R.Taylor, 2001)
>
> Best regards,
>
> Paul Cherubini
>
>
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