Tuesday, February 28, 2012

Exam Question #7

Today is the day of the midterm test in my course on molecular evolution. Here's one of the possible question on the test. Almost every student should get full marks on this one.
Imagine that a new mutation gives rise to a beneficial allele with a selection coefficient of 0.1 (s = 0.1) . What is the normal fate of this allele in a population of 10,000 individuals? Explain your answer.
Sandwalk readers should try and put this selection coefficient into perspective. It's probably at the high end for new beneficial alleles. What this means is that most adaptive explanations need to postulate a significant benefit to each individual in order to make the probability of fixation come out to some reasonable number.

Exam Question #1
Exam Question #2
Exam Question #3
Exam Question #4
Exam Question #5
Exam Question #6


  1. I have been trying to make some sense of the results I have found, dp = spq^2 / (1-sq^2), which apparently should indicate the increase of the dominant allele by generation. Since the new allele is beneficial I take it that we might expect its frequency to increase over time so I take the probability of its survival as 1 and the of the preexisting allele as 1-0.1 - 0.9. Purely numerically, we expect the frequency of the beneficial allele to rise very slowly, since dp is approximately 10^-9 initially (given that p and q are 0.0001 and 0.9999). The preexisting allele would never quite die out as it is protected in the heterozygous pairing.

    But really with only 1 in 10,000 individuals carrying the beneficial allele, a dp of 10^9 means that likely only 1 individual will carry it in the next generation as well. Practically speaking it may never take hold; and the 1 individual with it may be hit by a bus in any case - that is an accident may remove the allele before it gets any chance in any case.

    Well that is my amateur analysis ... now I await the real story ...

  2. Assuming "normal fate" means "most probable fate", and assuming we are talking about a stable population in a species typical of, say, mammals (not, for example, salmon or oak trees) it is most likely, in the range of 80%? or so (off the top o my head) to get removed from the population due to genetic drift. (It would be nearly 100% if we are talking oak trees).

  3. Not factored into the question as posed is that if we stipulate that the beneficial new allele can arise, then that allele can arise more than once in the population. A fuller treatment of the population genetics would take into account the frequency with which the given allele arises with respect to time in the allele-negative fraction of the population, and the frequency with which the new allele decays due to mutation in the allele-positive fraction of the population.

  4. the dominant allele...The preexisting allele would never quite die out as it is protected in the heterozygous pairing.

    assumes facts not in evidence.

    1. Actually I just quoted that essentially from the analysis I found explaining the math, but it does seem to make sense that if the 2 alleles were present in some reasonable proportion each, then the weaker one would be difficult to remove as it would show up in the aA crosses (taking a and A as the alleles)

  5. Use Kimura's (1962) fixation probability formula. You will get a bit less than 0.2. So most beneficial mutants are lost. But still, the probability that a beneficial mutation survives is much greater than the probability that a neutral mutation survives, which here is 0.0002.

    1. Sorry, the probability a neutral mutation survives is actually 1/20,000 which is 0.00005.

      So the ratio of survival probabilities with/without selection is 0.1813/0.00005 which is 3,626, which is close to 4Ns which would be 4,000.

  6. This, or the equivalent with a new allele constantly arising in the population by mutation, is my favorite question to ask undergrads on their first exposure to popgen (playing with Joe Felsenstein's simulation software). Most people just say "it will get fixed" and even think they've set up the simulations wrong when it doesn't happen.

    (The probability of fixation is approximately 2s so the usual fate for such an allele is extinction)

  7. Assuming a randomly mating population of diploids, and using Kimura's formula number (10), we have:
    s = 0.1
    N = 10000
    p = (1 - exp(-2*s))/(1 - exp(-4*N*s))
    Which gives us 0.1813 as probability of fixation, or about 18%.
    So the normal (meaning here most probable) fate is that this mutation will disappear from the population.

  8. After Haldane, fixation probability is ~2s (ie 0.02 - 98% of the time, it will be lost).

    An interesting review of the background that would enable a fuller appreciation of the matter (probably beyond that expected in a molecular biology course?) - the answer does depend somewhat on the model you use.

    I do think this can be misleadingly interpreted, however, when deciding how much of evolution can be considered adaptive. The undoubted influence of drift renders loss of an individual allele likely. However, the fact that there is an environmental challenge with the potential to cause fitness differentials between accessible phenotypes does not disappear when a particular 'solution' disappears. The same allele, or a different allele or gene addressing the same challenge, can arise repeatedly. This counters the naive assumption for one allele that chance will swamp benefit - the LLN can be invoked even in smaller populations, because a whole succession of alleles converges on an overall positive result - an excess of fixation of s>0 over s<=0, even when the former is produced at somewhat lesser frequency than the latter. The population adapts, even with tiny s's for each individual allele.

    The same applies to the fixation of a deleterious allele. Evolution does not stop at that point. An opportunity remains - that it was relatively 'deleterious' in the first place means that there is an accessible opportunity for raising fitness for an allele that does better in the same circumstances than the present incumbent. The 'deleterious' allele is more likely to be knocked off its perch.

    This may not help, of course, when it comes to adaptive explanations.

    1. Oh, sodding hell! I misread your value for s. "Please read all questions carefully". Bong! F-.

  9. With essentially all mathematical population genetics belonging to the realm of spherical cows approximations, I am wondering how much of it has been tested experimentally? Not an easy thing to do, I realize.

    1. Well, if you get the conditions set up just right, so that the population is of constant size, the selection coefficient is constant at 0.1, and so on ... well then you might as well computer-simulate instead. Which has been done and fits the mathematical theory extremely well.

  10. It will depend on the degree of dominance, if the census size of the population (N) remains stable, and the effective size of the population (Ne). If degree of dominance (h) is less than 1, than the probability of fixation (p) is p = 2*h*s*(Ne/N), where s is the selective advantage. If Ne = N, then it is 2*h*s. In cases of complete dominance, h = 1, (and where also Ne = N), then you recover Haldane's result of 2*s. Haldane's result is only an approximation and works when s is much less than 1 and much greater than 0.25*Ne. Kimura showed that multiplying the approximation by Ne/N makes it less restrictive. Including a term of N makes sense as the mutation can arise in anyone, but the Ne term helps "modulate" the dynamics of its fate in the face of its selective advantage. The Ne/N term can also be used when populations fluctuate.

  11. Epigenomics?
    5. Natural Selection is a trait of organisms, life?
    No. Natural selection is ubiquitous for ALL mass formats, all spin arrays. It derives from the expansion of the universe. All mass formats, regardless of size and type, from black holes to the smallest particles, strive to increase their constrained energy in attempt to postpone their own reconversion to energy, to the energy that fuels cosmic expansion.
    6. Life is an enigma?
    Life is just another type of mass array, a self-replicating mass array. Earth life is a replicating RNAs mass. It has always been and still is an RNA world. ALL Earth’s organisms are evolved RNAs, evolved for maintaining-enhancing Earth’s biosphere, for prolonging RNAs survival.
    7. Cells are Earth-life’s primal organisms?
    NO. Earth’s life day one was the day on which RNA began replicating. RNAs, genes, are ORGANISMS. And so are their evolved templates, (RNA and DNA) genomes, ORGANISMS, as evidenced by life’s chirality and by life’s sleep.
    8. Circadian Schmircadian sleep origin?
    Sleep is inherent for life via the RNAs, the primal Earth ORGANISMS originated and originally active only under direct sunlight, in their pre-biometabolism genesis era.
    9. Epigenetics are heritable gene functions changes not involving changes in DNA sequence?
    The “heritable or enduring changes” are epiDNAtics, not epigenetics. Alternative splicing is not epigenetics, even if/when not involving alteration of the DNA sequence. Earth life is an RNA world.
    10.Genetics drive biology and culture modifications?
    NO. It is culture that modifies genetics, not genetics that modifies culture. Culture modifies genetics simply via the evolutionary natural selection process of the RNA ORGANISMS. Likewise many natural genetic changes are due to aging and/or circumstantial effects on the genes and/or genomes ORGANISMS, similar to aging and/or evolutionary processes in monocell communities or in multicelled organisms.
    Dov Henis (Comments From 22nd Century)
    Seed of Human-Chimp Genomes Diversity

  12. New Era For Science Including Genomics ???

    From: Dov Henis
    Sent: Friday, April 13, 2012 10:43 PM
    To: genome biologists
    Subject: A new era for science including genomics ??? Please examine carefully…

    Yesterday, SN , after many years of refusing my similar postings, SN posted my following statement-comment:

    Biorhythms Schmiorythms
    Circadian Schmircadian sleep origin?

    Life sleeps because RNAs genesized, evolved from inanimate nucleotides into self-replicating nucleotides, organisms, of course long before metabolism evolved. They were then active ONLY during sunlight hours. Thus sleep is inherent for RNAs, even though, being ORGANISMS, they later adapted to when/extent sleep times are feasible just as we adapt to jetlag or night work time.

    Dov Henis (comments from 22nd century)
    Apr. 12, 2012 at 9:10am

    From: Dov Henis
    Sent: Saturday, April 14, 2012 9:05 AM
    To: genome biologists
    Subject: FW: A new era for science including genomics ??? Please examine carefully…

    Unbelievable?! Here’s another one…

    From: Dov Henis
    Sent: Sunday, April 08, 2012 9:06 PM
    To: ‘editors@sciencenews.org’
    Subject: On Pavlov and genes…

    Fatty Diet Leads To Fat-Loving Brain Cells

    Learn from Pavlov:
    Fatty diet lead to fat-loving RNA-nucleotides genes, Earthlife base primal ORGANISMS.

    Dov Henis (comments from 22nd century)


    Since the above two statements are basis for the following statement, may it also soon pass the SN “peer review”… ?!

    USA Science? Re-Comprehend Origins And Essence

    • Higgs Particle? Dark Energy/Matter? Epigenetics? All YOK!
    • Earth-life is just another, self-replicating, mass format.
    • All mass formats follow natural selection, i.e. intake of energy or their energy taken in by other mass formats.
    • Evolution Is The Quantum Mechanics Of Natural Selection.
    • Quantum mechanics are mechanisms, possible or probable or actual mechanisms of natural selection.
    • Life’s Evolution is the quantum mechanics of biology.
    • Every evolution, of all disciplines, is the quantum mechanics of the discipline’s natural selection.

    Update Concepts-Comprehension…
    Earth life genesis from aromaticity-H bonding
    Universe-Energy-Mass-Life Compilation
    Seed of human-chimp genome diversity


    Dov Henis (comments from 22nd century)