Tuesday, March 11, 2014

What did Joe Felsenstein say about sex?

Today we talked about the evolution of sex. The take-home message is that sex is one of the most difficult problems in biology. We really don't know why sex evolved and why it's so important in eukaryotes.

The evolution of recombination is part of the discussion. It's not necessarily the same as the evolution of sex but many of the explanations for the evolutionary origin of sex invoke homologous recombination.

When I asked my students to explain the evolution of sex they mostly came up with arguments about why it is advantageous to generate genetic diversity in a population. Some of this diversity requires recombination to create new combinations of alleles on the same chromosome. The problem with this argument is that for every new combination produced, an old one will be restored. As John Maynard-Smith pointed out in 1968, when genes/alleles are in linkage equilibrium then recombination does not result in a change in allele frequencies (i.e. evolution).

This led Joe Felsenstein to write the following in 1988.
It is worth noting that Maynard Smith's argument invalidates the earliest genetic argument for the evolution of recombination, that advanced by East (1918). That argument is also the one commonly found in textbooks, which tend to be a bit out of date (in this case, by over 50 years). East argued that recombination creates new genotypes. So it does. An AB/ab parent will have among its gametes not only the two types that formed it, AB and ab, but also Ab and aB if there is recombination between the two loci. But if the population is in linkage equilibrium, then somewhere else an Ab/aB parent will be undergoing recombination, which will remove Ab and aB gametes and replace them by AB and ab. These two processes will exactly cancel each other if the two types of double heterozygote, coupling (AB/ab) and repulsion (Ab/aB) are equally frequent. This will happen precisely when the population is in linkage equilibrium. In that case no new genotypes arise by recombination.


We have that anomalous situation that a detailed population genetic analysis analysis reveals not only that the standard explanation for the evolution of recombination will not work, but also that there is a good evolutionary reason for believing that modifiers will be selected to eliminate recombination.
Is it true that what students are being taught is wrong? What did Joe Felsenstein really mean?

Felsenstein, J. (1988) "Sex and the evolution of recombination." in The Evolution of Sex: An Examination of Current Ideas. R.E. Michod and B.R. Levin eds. 74-86. [PDF]


  1. Is it true that what students are being taught is wrong? What did Joe Felsenstein really mean?

    I was describing a theory that is often heard, particularly in rather shallow descriptions in undergraduate textbooks. The author vaguely remembers hearing this "explanation" and includes a version of it.

    More serious discussions will not use this theory, but will invoke the Fisher-Muller or the Sturtevant-Mather theories, or theories that are not based on evolutionary advantages but on the occurrence recombination as a side effect of types of DNA repair mechanism.

    Whether this flawed explanation is as widely taught as I said is an interesting issue. I would hope that in the 25 years since my article was published, it has started fading away.

    The 1988 article is a good starting point (I would modestly say) for a wider reading on the various theories. I would still say that it is not true that we have no theories, but rather that we have too many, and no easy way to tell which of these scenarios is most important.

  2. Sorry but I do not understand this argument at all. There are two possible scenarios:

    1. No sex. In this case, there will be Ab and aB in the population but no ab nor AB.

    2. Sex. In this case, ab and AB can also arise through recombination.

    Yes, in #2 they can also revert but that is completely besides the point; the point is simply that there is now a possibility to get ab and AB, which you wouldn't get under asexual reproduction, or at least not nearly as quickly because then you would have to wait for more mutations. I know you don't like adaptationism, but if AB is a big advantage over the three other combinations then sex massively speeds up the acquisition of this advantage.

    Joe Felsenstein's argument as presented above seems to assume that sex with all its advantages already exists, and then looks at what happens to the alleles in a population in linkage equilibrium, comparing between two different moments in time. But to understand what sex is good for, the real comparison must be between that population and an asexual one, right?

    But I know that JF is much more qualified at this than I am; what am I missing?

    1. Good to remember that if there's a round of selection, then recombination will have a higher probability of recombining successful alleles from different loci.

  3. You are assuming that the population can only reach linkage equilibrium if there is recombination. But mutation can do it too.

    Once one is in LE, recombination does not create variability, because it does not change either the gene frequencies or the haplotype frequencies.

    In many cases where this argument is invoked

    1. OK – Now I am humbled…

      Earlier today, I learn my treatment of the RNA World in my classroom was woefully inadequate…

      … and now I discover that I am probably making a similar hash of genetics and Hardy Weinberg!

      So a strict reading of Maynard Smith generates a vexing pilpul that recombination does not result in a change in allele frequency.

      Uhmm… of course not. Why should recombination generate any change in allele frequency? Recombination only shuffles pre-existing alleles at the frequency that recombination finds them (as it were).

      For linkage disequilibrium in populations to occur something else must also occur:

      Eg. Selection on multilocus genotypes.
      Eg. Genetic drift
      Eg. Population mixing

      This seems too obvious! Am I getting something wrong again?

      That said – I have to disagree with one statement of yours: “… recombination does not create variability”

      I am scratching my head on that one.

      Of course it does. Recombination does indeed create new versions of allele combinations that otherwise could not exist with complete linkage.

      I teach my students that without crossing over, each human can produce 2^23 different gametes.

      That said - The number of crossovers during meiosis in humans is slightly more than two per chromosome meaning that any human can produce 4 * 2^23 gametes theoretically possible different gametes per meiotic division.

      The mutation rate required to generate that magnitude of gamete diversity would be lethal.

      Given that diversity is grist for Natural Selection’s mill, and phenotypic diversity is generated from genotyptic diversity; again, I remain at a loss to see what we are really debating here.

    2. See my comments about what causes linkage disequilibrium, far below in the thread.

  4. (woops, ignore sentence fragment starting with "In many cases ...")

  5. Still, is it not true that sex massively speeds up the occurrence of AB (and potentially massively speeds up the spread of a gene through the population)? The former is how I understand and always have understood the argument that sex "generate[s] genetic diversity in a population", and I do not understand how your argument dispatches that.

    "Once it is in LE" the relevant events have already taken place. Maybe I am just too obtuse, but it feels as if you were arguing that building houses does not make sense because assuming they are already built we already have shelter.

    1. Suppose we have a population which is all ab, and alleles A and B are occurring by mutation, and have higher fitness. Suppose that the relative fitness of Ab (compared to ab) is (1+s), and similarly for aB. And suppose that these two loci have independent effects on fitness, so that the fitness of AB is the square of (1+s). (I guess I'm talking about a haploid population, for simplicity.

      In an infinitely large population you can then show that the frequencies of A and of B will rise, but that they will always be in linkage equilibrium.

      In this model there is no effect of recombination in creating variability or speeding the spread of the favorable alleles. And yet the naïve theory that I decried does suggest that there would be some such effect,

    2. Our comments have crossed mid-way. I see; you are assuming that the effects are independent. What I was taught is that the point of sex is to get the combinations where fitness(AB) > fitness(any other combination).

    3. @ Joe - my apologies...

      I too just cross-posted. In future I will check for activity before posting.

      I think I understand where you are coming from, but you hypothetical is a red herring nu?

      Why assume an infinite population?

      Meanwhile, cannot selection on multilocus genotypes, genetic drift and population mixing generate your linkage disequilibrium; but occuring only after recombination first took place?

    4. @ Joe

      OK - one last kick at the can:

      Muller’s ratchet: the accumulation of deleterious alleles places SMALL asexually reproducing populations at a disadvantage compared to sexually reproducing populations.


    5. @Tom Mueller

      Infinite populations are used a lot in theoretical population genetics. They allow us to see what happens without genetic drift.

      I am not sure what your point is about Muller's Ratchet in relation to this discussion.

  6. Another way of putting it is that in the quotation above the existence of heterozygous parents is already assumed, so either sex must already have taken place or the asexuals were implausibly lucky. The real argument for sex creating genetic diversity, at least as I was taught, is this:

    Assume you have two populations, one sexual, the other asexual. It starts with all individuals ab/ab. Then somewhere in each of the two populations one individual acquires Ab/ab, and another elsewhere acquires aB/ab, through mutation. What you "want" is AB because that gives you a kick-ass new metabolic pathway producing a new type of resin that makes you resistant to your most destructive herbivore.

    (Guess it shows I am working on plants; I cannot as easily come up with a scenario for animals.)

    Here are the questions:

    In which of the two populations will we get the novel combination AB more quickly?

    Assuming that the specific mutations producing A and B are rare, what is the likelihood that the asexual population will have gone extinct (perhaps even through competition with the sexual one) before the second necessary mutation occurs in one of the asexual aB/aB, aB/ab, Ab/ab or Ab/Ab plants?

    1. This comment has been removed by the author.

    2. @Alex SL

      There is a chance that allele B comes into the population in an individual that carries allele a, but also a small chance that it comes into the population in an individual that already carries A. Yes, this is a small chance, but we have to average over what happens in the two cases (weighted appropriately).

      If we assume a finite population, then we have already started to discuss Fisher's (1930) and Muller's (1932) scenarios. Not the "it produces variability" scenario of E. M. East (1918), which says nothing about finiteness of the population, and which is supposed to work in an infinite population. Which it doesn't.

    3. If we are trying to understand what sex is for we have to be realistic; the probability that AB arises from recombination given sex is high if A and B are already out there, but the probability that it independently arises through mutation from aB or Ab is much, much, much lower.

      I do not have a relevant paper here at the moment but am fairly sure I have heard of people doing simulation experiments on those lines.

    4. The relevant papers are cited in my 1988 paper, which is linked to here. One is my 1974 paper in Genetics, which is freely downloadable on line from the journal.

    5. should add that yes, there have been simulations. My simulation, published in 1974, is the first one (and Shozo Yokoyama and I did more in our 1976 paper). Both papers are free at www.genetics.org

  7. I don't really understand the issue here but I'll take a shot at it. If A is a more beneficial allele than a and b is better than B or there is some beneficial interaction between them, then recombination allows them to be selected together, rather than at the expense of each other

    1. ... if b has occurred in the population in different individuals than A has. (Note -- in this exchange b, not B is the favored allele).

      However if b is in the same haploid genome as A, then the effect of recombination is to disrupt the spread of the superior haplotype Ab. So we need to properly average over these cases. In an infinite population, b will occur among A-bearing genomes just frequently enough to have recombination make no difference, on average.

  8. Some of this diversity requires recombination to create new combinations of alleles on the same chromosome. The problem with this argument is that for every new combination produced, an old one will be restored.

    But the problem here seems to be that you don't take selection into account. Selection can eliminate those ""bad" recombinants, while the good ones potentiate the adaptations available that can deal with whatever selection pressure. Experiments on directed evolution using recombinant PCR evolves new activities orders of magnitude faster than random mutation and selection without recombination. Same is true for genetic algorithms that allow for recombination. They produce results much faster than genetic algorithms that don't have recombination. I truly don't see the problem with this "argument." (It's not an argument, but a hypothesis, and it has succeeded at least under those two conditions: experimental evolution and computer algorithms.)

    1. I did so take account of selection. So there. If A and B are favored, and their combination AB has fitness the square of (1+s), then we can work out the equations with mutation, selection, and recombination. If we start in linkage equilibrium we stay in it, as A and B increase in frequency (and AB with them).

      John Maynard Smith kept track of all this when he first pointed out the vacuity of East's argument in his 1971 paper in Journal of Theoretical Biology "What use is sex?".

    2. I meant Larry. But now I realize that the point was about increasing variability. which I agree it might not.

      But with selection rounds, I am still perplexed that recombination works so well in experimental evolution and genetic algorithms. Why then posit that it should not work in the realities of evolution in nature? That I don't get at all. Is it really that most people think that selection coefficients are always so low that advantageous alleles never increase in frequency and then that recombination therefore has little change of recombining them?

    3. Read my 1988 review. The naïve theory doesn't work, but the Fisher/Muller or Sturtevant/Mather scenarios, which do involve linkage disequilibrium, can work.

      (In answer to Tom Mueller far upthread, linkage disequilibrium can arise by genetic drift, my migration, or by natural selection in which loci interact.)

    4. @ Joe

      I met John Maynard Smith personally and remember him discussing this very question with my wife and my wife’s supervisor many many years ago in my wife’s supervisor’s kitchen… the details are long lost in the mists of time.

      I do remember something along the lines that clonal expansion is efficient at generating large numbers quickly, a useful trait in situations of intense competition but sex is useful when “circumstances change”… That is as much as I can remember.

      Let’s see if I can take it from there…

      Why is sex beneficial? The most likely advantage of sex is that it increases a parent’s chances of producing offspring that can survive.

      Sex must be beneficial for small populations subject to Genetic Drift allowing them to escape Muller’s ratchet?

      i.e. In a small population subject to genetic drift - the burden of accumulating deleterious mutations may eventually cause some populations to go extinct (bad luck of the draw due to drift, as it were).

      Sexual reproduction short-cuts Muller’s ratchet. E.g. two individuals each with one copy of some deleterious mutation will produce offspring that are free of either mutation 25% of the time.

      ITMT I am about to teach Taxonomy and I am reminded that so-called “primitive” organisms (forgive me – you know I mean “basal” for “primitive”) employ asexual reproduction in constant environments as their default setting and sexual reproduction kicks in under scenarios of environmental stress.

      In other words; if environment changes, not only may offspring be poorly adapted but ALL offspring will be poorly adapted because they are identical.

      Zygospores are quiescent resting bodies awaiting environmental conditions to return to "normal" ...

      or alternatively...

      ...allow recombination resulting in novel variable offspring, some of which can to adapt to the “new normal”.

      I can imagine zygospores as some evolutionary quiescent exaptation that eventually gave rise to sexual reproduction… the exaptation possibly being DNA repair.

      Why is sex beneficial? Parent’s chances of producing offspring that can survive competition are greatly enhanced, remembering that each generation produces far more progeny than can possibly survive.

      Again, this appears too easy… what am I getting wrong?

    5. You have raised many of the arguments that people have raised for evolution of "sex" (recombination with outcrossing). These scenarios are among those that are proposed to embody the two great classes of models: the Fisher/Muller and the Sturtevant/Mather.

  9. God created male and female in order to increase life after its kind. The essence of sex is the segregated operastions of the two sexes.
    So its not why is there sex but why is there such segregated sexual traits in a type of creature.
    Remember nothing evolved. Nature does not have a mind of its own.

    1. Did you know that earthworms and snails blatantly violate God's decree about the sexes being in separate individuals? They are evil.

    2. Did you know that earthworms and snails blatantly violate God's decree about the sexes being in separate individuals? They are evil.

      And fish. That's why I cook them. Serves them well.

    3. Joe Felsenstein
      The segregation of sexual traits into male and female dominates nature and especially large nature. the few exceptions, I understand its few, can be dismissed as adaptations in a post fall world.
      Indeed moth worms and snails must breed alone in order to reproduce quickly which is a order from God. Thats why worms/snails are so numerous despite being slow moving creatures.
      the purpose of sex and sexual identity, except in people, is simply reproduction.
      A creator had a idea that reproduction is best served by segregated sexual traits in a creature type and so male/female.
      No evidence at all it evolved. Its just guessing.

    4. I didn't notice anyone mentioning moths. But earthworms, and snails don't "breed alone". They defy that order of God and sinfully engage in bisexual sex with other bisexual sinners. They do not self-fertilize, having at least that much respect for Divine Law. So yes, I guess the Fall is the only possible explanation for their evil behavior.

    5. Thats why worms/snails are so numerous despite being slow moving creatures.

      Robert's world is so wonderfully Ptolemaic.

  10. I wonder if the whole debate over the evolution of sex isn't misguided because purely asexual organisms really don't exist. It's a continuum, given that the diversity benefits from sex can also be achieved through other methods such as competence and viral infection.

    1. > purely asexual organisms really don't exist

      I think you need an odd definition of purely asexual to argue that there are none whatsoever. And even if there are a few grey areas, we can still easily classify most organisms into a group where sex is pretty much obligate (how many asexually reproducing humans are there?) and one where clonal reproduction is the norm and sex happens only as a freak accident (many apomictic plants).

    2. The point is does it really matter from the standpoint of evolution that a variant got into a lineage through traditional sexual means or through a virus or just sucking up DNA?

    3. Yes, because beneficial variants will compete with each other if they arise in different genetic backgrounds (linkage disequilibrium). Sexual reproduction will remedy this situation more rapidly than competence and viral infection can.

  11. @Joe Felsenstein

    Another naive thought, unbacked by math. If recombination of alleles was so advantageous, would not a scenario of no effective linkage be the most beneficial situation? An organism with 20,000 chromosomes (which did happen at least once in Oxytricha trifallax), or all genes spaced 50 cM apart. If this was so advantageous, why have have these extremes not become more common?

    My impression is that "recombination" always confuses people. General allele mixing by any means versus intro genetics, meiotic-type chromosomal segment swapping, (which is actually more rare than people seem to think, and is, in the case of Drosophila, confined to only one sex).

    1. The mechanisms for the evolution of recombination (with outcrossing), which is what we are calling "sex", give an advantage to a little but of recombination, but that advantage decreases as one adds more recombination.

      At the same time, there are counteracting forces of natural selection against recombination when it breaks up disequilibrium of favorably interacting genes. So one can imagine a balance between these forces and an optimum level of recombination, far short of no effective linkage.

  12. I think a lot of confusion stems from regarding sex and recombination as near-synonyms, and the sex/asex boundary as mechanistically symmetrical and its traversal adaptive.

    1. In the Yokoyama and Felsenstein 1976 paper we simulated a case where a population had (initially) 50% asexual individuals, and 50% sexuals who could cross with each other. The simulation showed that the sexuals fixed more often than the asexuals. So that was a case where the boundary was traversible -- simply by change of frequency of the two types.

      (I should add that the case did not have Maynard Smith's phenomenon of the "cost of sex", so it avoided that serious issue).

    2. I don't think that is quite what I would call a 'traversible boundary'! Grey squirrels are eliminating red in the UK, but one would not suggest that a boundary is being traversed.

      The boundary I had in mind is that whereby a sexual lineage gives rise to an asexual one, or vice versa. Traversal in the two directions is mechanistically distinct, and not symmetrical in most relevant parameters. Starting from a homogeneous equilibrium ignores this (in simpler models).

    3. I may have misunderstood what 'crosses' with what. But it rather illustrates my point. I'm not sure why syngamy and reduction don't count as 'sex', but recombination is seen as diagnostic. It seems wholly the wrong way round to me.

    4. There have been theories that concentrated on syngamy and reduction to explain outcrossing. Those effects would then not explain recombination.

    5. Mmm. I was not so much trying to explain any element but to get things the 'right way out'. I perceive a further confusion now because of the two senses in which 'cross' could be taken - 'crossover' or simply getting two diploids to make another.

      Without syngamy/reduction, you don't get an opportunity to do recombination, nor much out of it. It puzzles me why the consequences of those elements seem so secondary - to the point where people exclude them from their definition of sex. We don't need to be slaves to definition, of course. But cyclic haploidy/diploidy with two different diploids providing each gamete seems to be a sufficient 'minimal' definition of outcrossing sex, without going near recombination. In early evolution, this may be all there was.

      Of course despite that context, very few modern mitoses do without 1-chiasma-per-chromosome. This does argue for a substantial cytological role. It's not just Poisson-distributed across the genome (nor even the chromosome) for example. On the other hand, in the few achiasmate meioses that do occur species make sure that crossover does occur in the other sex, so it's probably not just about cytology.

    6. @Joe Felsenstein
      You wrote: "In the Yokoyama and Felsenstein 1976 paper we simulated a case where a population had (initially) 50% asexual individuals, and 50% sexuals who could cross with each other. The simulation showed that the sexuals fixed more often than the asexuals. So that was a case where the boundary was traversible -- simply by change of frequency of the two types.

      (I should add that the case did not have Maynard Smith's phenomenon of the "cost of sex", so it avoided that serious issue)."

      As I understood that paper, you considered a recombination modifier locus that switches recombination between homologous chromosomes (due to crossing-over) on or off depending on genotype.

      Let's take the simpler case, where the allele for crossing-over is recessive, a, and only the genotype aa will have recombination between homologous chromosomes due to crossing over.

      Unless I'm seriously mistaken, the genotypes Aa and AA should still have the recombination due to segregation of homologous chromosomes during meiosis and subsequent gamete fusion.

      For me, that are not asexual genotypes but sexual genotypes lacking crossing-over and the additional recombination that comes with it.

      That's also, why your disclaimer in parentheses is necessary. IMHO you did not pit asexual mutants against sexuals but two extreme recombination modifier alleles against each other.

      Did I overlook something?

    7. As it happens, Joachim Dagg also sent me a personal email with the same content. I have answered him: in brief the simulation had only one cromosome pair, so independent segregation of chromosomes would not bring about recombnation in the no-crossing-over case. It was thus a fair simulation of recombination versus no recombiation. PS: the 1976 Y&F paper can be read free at the Genetics web site (www.genetics.org), as is their policy with papers older than a few years/

    8. @Joachim For me, that are not asexual genotypes but sexual genotypes lacking crossing-over and the additional recombination that comes with it.

      This chimes with the point I've been making. To explain sex, one first needs to explain cyclic syngamy and reduction. Recombination could be the reason for that cycle, though I rather doubt it, and I am puzzled by the general insistence that homologous recombination is what sex is, rather than something it has, with a near-universal role in the cytological control of segregation. The fact that there is reciprocal exchange in 50% of DSB's is not necessarily the 'desired' result of crossover. It's a mechanical link which provides tension as the bivalents are teased apart by opposing spindles. Crossover and non-crossover resolution products are inevitable given the essential blindness of the process as to which upstream strand 'belongs' to which downstream one. There is no fundamental reason for a gene to 'care' which partners it ends up with.

    9. @Alan: There are cases like Drosophila where there is no crossing-over in males. So crossing-over is not inevitable. Furthermore most organisms go to a great deal of trouble to outcross. That is difficult and expensive. Wouldn't they be a lot better off just producing diploid eggs by mitosis?

      As for what "is sex", I have always preferred to talk of the evolution of recombination. Saying you are going to explain "sex" implies to the reader that you are discussing why the sexes are different, and they are likely to be very disappointed when they discover what you are really discussing. It is a good way to sell books, though.

    10. Right, thanks again, Joe. As my question here did not show up for some hours, I thought this discussion was over and sent you the e-mail. Therefore the - er - crossover (overlap:-).

    11. OK – again I must be missing something!

      I always understood that Bacteria often display the linkage equilibrium (for all intents and purposes) of sexual populations.

      For example:

      What am I missing?

  13. Why would Joe Frankenstein write about sex..? He has no idea, and nobody else has an idea... Why doesn't he write about the real sex, the wild one.... oh yeah... that one ..ummmmmm what's wrong with Joe? He no like siks...?

  14. As John Maynard-Smith pointed out in 1968, when genes/alleles are in linkage disequilibrium then recombination does not result in a change in allele frequencies (i.e. evolution).

    Shouldn't that be linkage equilibrium?

    1. Joe - the quote was from Larry's piece. No need to apolgise!

  15. @Larry
    There's a typo in:
    "As John Maynard-Smith pointed out in 1968, when genes/alleles are in linkage disequilibrium then recombination does not result in a change in allele frequencies (i.e. evolution)."

    Must be: "... linkage equilibrium..."

    1. Fixed it. Sorry for leaving the error up for so long.