William Morse wrote:
> "EKurtz99"  wrote in
> news:cp7f4i$7q9$1{at}darwin.ediacara.org: 
> 
> 
>>>>"EKurtz" (NoJunk{at}ForgetIt.com) writes:
>>>>
>>>>>Consider the case of a sexual species into which a parthenogenic
>>>>>female is introduced by mutation. Assuming that she and her
>>>>>immediate offspring survive, and that the population size is
>>>>>constant, her offspring will effectively displace the sexual type
>>>>>in a few dozen generations.
>>
>>Catherine Woodgold wrote
>>
>>>>Even if the parthenogenetic individuals average only 1.5
>>>>fertile offspring each, they will tend to take over the whole
>>>>population.  The sexual ones could be declining while
>>>>averaging 1.8 offspring each, while the parthenogenetic ones
>>>>grow exponentially at 1.5 offspring each.  So number of
>>>>fertile offspring is not a very useful definition of
"fitness".
>>>
>>"William Morse"  wrote
>>
>>>But what if (as is normally the case for most organisms) the average 
>>>number
>>>of offspring (before predation and disease) is on the order of
>>>hundreds to thousands? In this case the parthenogenetic individuals
>>>have very little advantage in terms of having more offspring - they
>>>invest less energy per offspring but that investment is not
>>>particularly large - while their offspring suffer higher rates of
>>>predation and especially disease. 
>>
>>Why is this? Assuming populaton size to be constant, a single
>>parthenogentic type will, after predation etc have taken their toll,
>>produce 2 p-type offspring, whereas 2 sexual types, M&F, are required
>>to generate 2 offspring s-types. As Catherine Woodgold states, this
>>will lead to an exponential increase of the population size of
>>p-types, with corresponding decline and ultimately elimination of the
>>s-type. 
> 
> 
> This is quite true if there is no difference in fitness between p-types 
> and s-types. My point was that if there is a huge die-off of offspring in 
> any case, a very small edge in survival of s-types will eliminate the p-
> type advantage of more offspring. 

That depends on the relative magnitudes.  The number of offspring after 
the dieoff is the proportional to the product of the number before and 
the probability of surviving.  So, the s-type will be fitter if the 
ratio of s-survial to p-survival is larger than the ratio of the numbers 
of s-offspring to p-offspring.

Of course what one should expect based
> on this logic is that parthenogenesis would be more common in organisms 
> that have relatively few offspring, and AFAIK this is not the case.I 
> suspect this may have something to do with parental investment, but I 
> would appreciate any insights.
> 
A problem with parthenogenesis is that it is more difficult to produce 
variation (hence the Red Queen ideas about the evolution of sex).  I 
have an idea that this is less of a problem for species that produce a 
lot of offspring, because producing more offspring means that you're 
more likely to get a variant.  I'm not sure whether this works in 
practice - one day I should look at this seriously.
> 
>  
> 
>>I would guess that this effect will take place, though more slowly, if
>>only a fraction of the eggs in the "p-type" female are clones, the
>>rest requiring normal fertilization. However, to prove the point would
>>involve some mathematical modelling, which would upset some of the sbe
>>regulars no end. 
> 
> 
> I don't know if we need to actually resort to such desperate measures as 
> mathematical modelling :-) Facultative parthenogenesis is apparently 
> fairly widespread (based on a quick google search), and a look at the 
> conditions under which this occurs should shed some light on the 
> tradeoffs between sexual reproduction and parthenogenesis. I might even 
> pursue the subject further when I get a significant chunk of spare time - 
> which based on my current workload should be in 2006 :-(
> 
Nick Barton went as far as doing some mathematical modelling a couple of 
years ago:

  Title: Selection for recombination in small populations
Author(s): Otto SP, Barton NH
Source: EVOLUTION 55 (10): 1921-1931 OCT 2001

Abstract: The reasons that sex and recombination are so widespread 
remain elusive. One popular hypothesis is that sex and recombination 
promote adaptation to a changing environment. The strongest evidence 
that increased recombination may evolve because recombination promotes 
adaptation comes from artificially selected populations. Recombination 
rates have been found to increase as a correlated response to selection 
on traits unrelated to recombination in several artificial selection 
experiments and in a comparison of domesticated and nondomesticated 
mammals. There are, however, several alternative explanations for the 
increase in recombination in such populations, including two different 
evolutionary explanations. The first is that the form of selection is 
epistatic, generating linkage disequilibria among selected loci, which 
can indirectly favor modifier alleles that increase recombination. The 
second is that random genetic drift in selected populations tends to 
generate disequilibria such that beneficial alleles are often found in 
different individuals; modifier alleles that increase recombination can 
bring together such favorable alleles and thus may be found in 
individuals with greater fitness. In this paper, we compare the 
evolutionary forces acting on recombination in finite populations 
subject to strong selection, To our surprise, we found that drift 
accounted for the majority of selection for increased recombination 
observed in simulations of small to moderately large populations, 
suggesting that, unless selected populations are large, epistasis plays 
a secondary role in the evolution of recombination.


Bob

-- 
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax:  +358-9-191 51400
WWW:  http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org
---
ž RIMEGate(tm)/RGXPost V1.14 at BBSWORLD * Info{at}bbsworld.com

---
 * RIMEGate(tm)V10.2į’* RelayNet(tm) NNTP Gateway * MoonDog BBS
 * RgateImp.MoonDog.BBS at 12/10/04 9:34:01 PM