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Author Topic:   Fixation Of Alleles And The Red Queen's Race
Dr Adequate
Member (Idle past 284 days)
Posts: 16113
Joined: 07-20-2006


Message 1 of 3 (363875)
11-15-2006 9:09 AM


Suppose we have a species with two alleles, A and B, of some gene; and that it is succeptible to some form of parasite (virus, bacterium, or what have you) which also has a gene with two alleles, which we shall also call A and B; such that the "A" form of the parasite is more effective at infecting the "A" form of the host species; and the "B" virus more effective at infecting "B" hosts.
I have sometimes seen it suggested that such a situation would lead to an equilibrium, in both host and parasite, between the two sorts of allele. This is very far from the truth.
It is, of course, true that such a situation has a point of equilibrium, but this is unstable. However close to equilibrium we start, the allele frequency of any of the alleles (host or parasite, A or B) when plotted against time, describes a curve which tends from having a shallow and sinusoidal shape (if we start reasonably close to equilibrium) to a "square curve" the amplitude of which tends to the maximum possible value --- that is, as time goes on, the peaks of the graph of allele frequencies tend to 100%, the troughs to 0%.
The graph below was produced by taking natural selection to be completely deterministic and the population to be continuous rather than discrete: this makes the effect most clear visually.
In any real, finite population, then, one allele will eventually be fixed in the gene pool of the host species, and one will be fixed in the gene pool of the parasite. The winner of this leg of the Red Queen's Race will, of course, be the species that achieves fixation second.
Simulations show that this applies also in cases where the host (as is usual in nature) has two copies of each gene, and one of the alleles is taken to be recessive.
As we have some geneticists on this forum, perhaps they could tell me if this is a new observation or old hat. In any case, I found it interesting and I hope someone else does.
Edited by AdminJar, : fix image width

AdminNosy
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Posts: 4754
From: Vancouver, BC, Canada
Joined: 11-11-2003


Message 2 of 3 (363908)
11-15-2006 11:11 AM


Thread copied to the Fixation Of Alleles And The Red Queen's Race thread in the Biological Evolution forum, this copy of the thread has been closed.

AdminJar
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Message 3 of 3 (363911)
11-15-2006 11:13 AM


Thread moved here from the Proposed New Topics forum.

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