6 Responses to “Rabbit Massage”

1. nobody Says:
   May 30th, 2008 at 3:53 pm

   Hmm. Are you trying to reignite the Artificial or Natural debate?!

   

Comment by nobody — May 30, 2008 @ 3:53 pm

2. Salvador T. Cordova Says:
   May 31st, 2008 at 5:08 pm

   Open thread. YAY!

   I point to two discussions by myself and Joe Felsenstein.

   I wrote the thread: Darwin's Ruin.

   To my surprise, Dr. Joe Felsenstein (probably one of the world's top population geneticists) offered his reply in:

   Darwin's Gain

   Some of the terms used in the two discussions might not pass the TelicThoughts spam filter, so discussions might have to deliberately mis-spell words in order to pass the spam filter…..

   I think the discussions and analysis will be on-going with refinements by parties on both sides….

   I think it is important to say, independent of ID or creation science, some of the ideas discussed can lead to empirically testable conclusions, thus the ideas will fall within the realm of empirical science…..

   For the record, creationism or ID do not necessarily have to be true if my critique of Darwinian evolution is theoretically and empirically correct. There is always the chance another yet-to-be-discovered mechanism for evolution in the past was in operation….

   My essay is basically a simplification of the fine work of Dr. John Sanford of Cornell and Walter ReMine…

Comment by Salvador T. Cordova — May 31, 2008 @ 5:08 pm

3. Raevmo Says:
   May 31st, 2008 at 6:59 pm

   Darwin's Ruin, my a**.

   The probability to become fixed for an allele with selective advantage s, having initial frequency p in a diploid population of size N, is approximately given by

   P_fix = (1-exp(-2Nsp))/(1-exp(-2Ns))

   As derived by Kimura a long time ago.

   Example: N=10^6, p=0.001

   s=0.00001 => P_fix=0.020
   s=0.0001 => P_fix=0.181
   s=0.001 => P_fix=0.865
   s=0.01 => P_fix=1.000

   Compare this with a neutral allele (s=0), which has P_fix=p=0.001. A deleterious allele (negative s) has practically no chance to get fixed.

   Rule of thumb: when Nsp>5, fixation is practically guaranteed.

Comment by Raevmo — May 31, 2008 @ 6:59 pm

4. olegt Says:
   June 1st, 2008 at 3:46 pm

   Hi Raevmo,

   Sal is talking specifically about an allele that has just arisen by mutation, which means that there is a single instance of it in the population and thus the frequency p=1/N. The product Nsp=s is small compared to 1 in the case of a slight advantage. Then, in a large population (N much larger than 1/s), it will be fixed with probability s, which is small compared to 1.

   This is indeed a well known fact (as was pointed out by Joe Felsenstein at Panda's Thumb) and Sal's tilting at windmills with his argument. There is nothing wrong with that: we all are learning and it's okay to dwell on a well-known example to understand it.

   But Sal doesn't seem to appreciate what this simple model tells us, namely that selection works. If one looks at the case of a slightly deleterious allele (s is small and negative), it has no chance of surviving in a large population: its probability of getting fixed is now |s| exp(−N|s|), suppressed by an exponentially small factor relative to the case of an advantageous allele with the same |s|. For the numbers he used (|s| on the order of 0.01) a large population means "more than a few hundred." In such a case advantageous mutations occasionally filter through and propagate throughout the entire population, while deleterious ones are filtered out completely.

   Of course, when the bias is small compared to 1/N selection won't work. If |s|=10^{−6}, as in Sal's latest response at panda's Thumb, then advantageous and deleterious mutations will fare equally well in a population of N=10^6.

Comment by olegt — June 1, 2008 @ 3:46 pm

5. Salvador T. Cordova Says:
   June 2nd, 2008 at 7:21 pm

   Raevmo wrote:

   A deleterious allele (negative s) has practically no chance to get fixed.

   Then how does mutational meltdown happen? It seems that it is empirically demonstrated that the bad doesn't get weeded out of a population in all cases.

   The size of the population is important as well as how well the population is stirred. So I think that claim is overly optimistic.

   Of course you could argue, the population dies, therefore the bad is weeded out, but then this still means the bad doesn't get weeded out of a population….you solve the problem of the bad not being fixed by killing the entire population. The bottom line is that inevitable progress is not guaranteed as Darwin mistakenly supposed.

   N=10^6, p=0.001

   For the reader's benefit, please explain how you get an initial frequency of p=0.001 for one mutant appearing with an N of 10^6

   Also regarding selection s, is it possible to have a genome of 4 giga base pairs and a selection s=.01 for all base pairs? If not, what is your estimate of the average s for a given number traits under selection?

   If we have M traits under selection, what is the average selection value for s(k), that is s1, s2….sM? Is this a tractable problem?

Comment by Salvador T. Cordova — June 2, 2008 @ 7:21 pm

6. Salvador T. Cordova Says:
   June 5th, 2008 at 3:47 pm

   Also regarding selection s, is it possible to have a genome of 4 giga base pairs and a selection s=.01 for all base pairs? If not, what is your estimate of the average s for a given number traits under selection?

   If we have M traits under selection, what is the average selection value for s(k), that is s1, s2"¦.sM? Is this a tractable problem?

   The question I posed was not a trick question, but one I've been trying to get a little more closure on.

   If -1 less than s less than 0,

   then it appears that numerous traits can have s = -1, such that

   s1 + s2 + s3 … sN greater than 1 for all traits with s = -1

   however, for 0 less than s less than 1 the converse appears untrue

   s1 + s2 + s3….sN less than 1 for all s, where 0 less than s less than 1

   Sanford alludes to this on page 77 of Genetic Entropy

   for a population such as our own, the maximal number of mutations which could be selected simultaneously is approximately 700. Kimura (1983, p.30) alludes to the same problem, and although he does not show his calculations he states that only 138 sites can undergo selection simultaneously

   Sanford sketch out his calculations in terms of cost of selection using terms like c and C, not s. There might be a relationship between s anc c and C, but it was not clear to me.

   Briefly, in appendix 2 from Sanford's book:

   Total selective cost (C) to a population is that fraction ofthe population that is not allowed to reproduce — in order to achieve all selection. On the simplest level, we will assume that the fraction of the population which is slected against is C, and produces zero offspring. So the remainder (1-C) is that part of the population which is selected for….

   Cost per trait (c) is that part of the population which is eliminated to affect a specific trait (or nucleotide)

   It seems the benefit of using C and c instead of s, is that appears more amenable to experimental verification. The Cost concept was made famous by Haldane in his 1957 paper on the cost of natural selection. Haldane also argued the s-values must necessarily be weak for mutiple traits…..

   What I don't know is that if we have say N traits, is the maximum average positive s generally limited to 1/N? If so, then this poses severe restrictions on natural selection:

   1. the selection must be weak for each trait in general

   2. only a limited number of traits are subject to positive selection, say 700 out of 4 giga base pairs in humans

   3. because of considerations from gambler's ruin, what little are subject to natural selection, are eliminated anyway due to random selection

   Sanford's conclusion is that natural selection is ineffective at shaping the genome and biology in a positive way. Kimura was more reserved, arguing that natural selection did not account for the majority of molecular evoution. Nei postuatles that not only is selection a non-factor in the majority of molecular evolution, but everything else about biology. He argues the appearance of design is an artifact of our post-dictive perceptions and our tendency to project our concepts onto objects….

   For example, we use the word "hydrophobic", the molecule isn't necessarily afraid, it is just a projection….

   Mike Gene's design matrix deals with the issue of projection versus identifying something of real significance…

Comment by Salvador T. Cordova — June 5, 2008 @ 3:47 pm