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Re: Alpha Male Breeding Success & population genetics


Doug Karpa-Wilson wrote a small ... and very nice ... treatise on genetics and crossing. 

Sample section: 

>>  The third offspring will also retain ½ A's genome, but 3/4 
>>  of that half are copies found in A1 and A2 as well, so the 
>>  part of A's genome that A3 preserves uniques amounts 
>>  only to 1/8 of A's genome. Total saved 7/8 of A's genome.    
>>  As you can see trying to keep a copy of every single on of 
>>  A's genes becomes very hard.

(1) I'd like to mention that this diversity in population genetics is very much a STATISTICAL effect, like flipping a coin. On AVERAGE, if you replicate the experiment many times, the second offspring will have a 50% overlap of genes from each parent with its first offspring sibling. However, in any individual trial, the possibilities range from 0 to 100%, with a standard bell-shaped  kind of curve. 

With large, freely inter-breeding populations, the randomness averages out so, so that (absent external influences such as "survival of the fittest" advantages to certain genes/combinations over others) the relative frequency of each flavor of a gene stays more or less constant.

However, with small, reproductively semi-isolated populations, the randomness of the genetic process at the individual level means that many of the flavors (that's NOT the technical term, of course) of each gene can be easily lost. In a sense, each flavor of each gene is playing Russian Roulette every round of the Reproduction Game, and once it "loses", it's permanently gone from that reproductive sub-population, unless/until it's re-introduced via individuals from the outside. 

At the fishroom (small isolated subpopulation) level, this is manifestly a biased game ... as a gene flavor, it you lose a round, you're gone "forever"; but if you win, you just get to play again (and face another risk of losing everything) . This can alternatively be written up as the "Economics of Casinos 101", namely the longer the sucker (gene flavor) plays, the greater the probability that he (it) loses everything. 

I'll try to write a little computer simulation to show the practical impact of this biasing effect on fish-room small samples.  Don't look for it until after the holidays, though. Anybody have any idea how many different genes a killifish might have? 2000? 5000? 10000? 

(2) This describes what happens at the offspring level. Due to culling biases, survival advantages in an aquarium environment, etc., the genetic diversity that you get "from a spawning" may not be what actually gets to that generation's reproductive age. And again, the impact of this is biased to the downside, you can lose "degrees of genetic diversity" from eggs to next generation eggs, but there's no offsetting way to gain any diversity points. (Barring the Fishroom Meister's intentional introduction of new stock, of course.)

(3) And it's not hard to envision the same effect happening in the wild. Take nothos as the near perfect example, good seasonal pond fish. There's 10,000 of them in a 2 acre pond. Along comes the 10,000-year flood, the original population is scattered over an area of 10*10 miles. Average density is therefore reduced to 100 per square mile. Their reproductive strategy, highly adapted to the seasonal pond life, prevents them from instantaneously flooring the procreation accelerator to take advantage of all this new territory/opportunity. Some encounter new predators or find themselves in environments they're not equipped to survive in, and thus perish prematurely ... this may or may not randomly effect the overall genetic diversity of the entire group. Dry season comes, the 10,000-yr flood waters finally run off or evaporate, and the remaining +/- 8000 fish find themselves in new mudholes. Say those are more or less evenly spaced at 10 mudholes per square mile, or 1000 mudholes in total. Average number of fish per mudhole, awaiting the next 10,000-yr flood to possibly bring in new blood .... eight.  Now we're talking fishrooms in the wild.  Given time, the randomly different subsets of the original gene pools found in each of these tiny mudhole populations has a good chance of becoming a identifiably different "location type," sub-species, or even species. (And, I suspect,  one of the tell-tale characteristics that this scenario really happens would be finding wild species that empirically have very low levels of genetic diversity ... suggesting that somewhere in the species/sub-species history, the gene pool went through a very restricted bottle-neck.) 

(Yes I know this is a simplistic example, the starting assumption that there's only one Garden of Eden pool of 10000 is unlikely, it doesn't work as well for species that can quickly breed to colonize new opportunities, you don't have anywhere near the same degree of reproductive isolation for river species, etc. Those are, however, IMO, largely issues of scale, degree and frequency, not concept.) 

$0.02 * 50% penalty for excessive length = $0.01. 

Doug Dame
Interlachen FL
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 * geology majors - we're trained to be accurate 
    within plus/minus 100 million years
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