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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 16 of 17 (394089)
04-09-2007 3:42 PM
Reply to: Message 14 by Allopatrik
04-09-2007 10:25 AM


Re: Code Walkthrough
v[n] := (v[o]*h[o] + v[o]*cv*(1-h[o])) /
(v[o]*h[o] + v[o]*cv*(1-h[o]) + (1-v[o])*cv*h[o] + (1-v[o])*(1-h[o]));
Hokay.
Let's say for convenience that x = (v[o]*h[o] + v[o]*cv*(1-h[o]))
and
y = (1-v[o])*cv*h[o] + (1-v[o])*(1-h[o])
Then we can write the formula as v[n] := x / (x + y)
v is the proportion of A type viruses, h is the proportion of A type hosts. We assume that the virus does not select its host type but ends up in either A or B at random.
So the proportion of A type viruses that that wind up in an A type host is h, and the proportion that wind up in a B type host is 1 - h.
cv represents the fitness of an A virus in a B host relative to the fitness of an A virus in an A host.
y is just the same calculation but for the B virus, the proportion of which is given by 1 - v.
The reason we divde by x + y is that we want v to express a proportion of the population.
---
Does that make sense?

This message is a reply to:
 Message 14 by Allopatrik, posted 04-09-2007 10:25 AM Allopatrik has replied

Replies to this message:
 Message 17 by Allopatrik, posted 04-09-2007 6:00 PM Dr Adequate has not replied

  
Allopatrik
Member (Idle past 6187 days)
Posts: 59
Joined: 02-07-2007


Message 17 of 17 (394119)
04-09-2007 6:00 PM
Reply to: Message 16 by Dr Adequate
04-09-2007 3:42 PM


Re: Code Walkthrough
quote:
Does that make sense?
Yes, thanks. I don't see anything that could give us a clue as to why that particular pattern develops, so I did some digging, and found this interesting paper:
Nuismer SL and Otto SP (2005) Host-Parasite Interactions and the Evolution of Gene Expression. PLoS Biol3(7): 1283-1288.
It has an intriguing figure (fig 2), which I cannot link to (it's too large), but it seems to show a similar pattern under certain circumstances. Here's the link to the paper:
http://biology.plosjournals.org/perlserv/?request=get-doc...
There is an ecologist at UC Santa Cruz that writes about coevolution and does host-parasite modeling by the name of JN Thompson. You might want to discuss your model with him--maybe he can give a lucid explanation for the results you are getting. Here's a link to his lab page:
http://bio.research.ucsc.edu/people/thompson/Index.htm
A
Edited by Allopatrik, : No reason given.

Natural Selection is not Evolution-- R.A. Fisher

This message is a reply to:
 Message 16 by Dr Adequate, posted 04-09-2007 3:42 PM Dr Adequate has not replied

  
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