The Evolution of Sex

This has long been an interest of mine. It dates back to the old talk.origins days, prompted by a Creationist taunt with familiar tone – “I’d like to see someone explain the evolution of sex …” (with the implicit “hurr, hurr”). I articulated some thoughts, then was rounded on by the ‘mainstream’ community. I got a flavour of the world through Creationist eyes – an equally familiar tone: some very sharply expressed contempt and an invitation to f*** off back to high school and learn meiosis.

But, the more I thought about it, the more convinced I became that the ‘twofold cost’ picture traditionally presented, one that demanded an offsetting benefit of similar weight, was simply incorrect, however lofty the figures proposing it. The problem as expressed for a dioecious population (one with separate males and females: the ‘twofold cost of males’) or from the perspective of a locus on a genome (the ‘twofold cost of meiosis’) leads to the same result: an apparent halving of reproductive output for a female, or of survival odds for an allele. Yet since dioecy is quite rare, and ‘selfish alleles’ only exist when recombinant sex does, these cannot be taken as relevant to the origin of sex, and not all that relevant beyond it. The sensible perspective, it seems to me, is that of the haploid genome. From such a perspective, we are binary organisms – temporary unions of haploid genomes. It cannot be inherently more costly to unite then separate than simply to do nothing. The view that sex (as syngamy) should have existed for only a moment before being erased by permanent diploidy seems wrong. Meiosis is the brief return of the native organism – the haploid. Permanent diploidy is cancer: a trap.

It’s more complicated than that …

I have written the above essay summarising my views. It is a bit of a dry and technical read – few pictures, even fewer jokes! This venue is not particularly conducive to a sensible discussion of the subject. It may be of interest to no-one: too amateurish for the professionals, too technical for the interested layman. Almost none of it is really original thought, being more a synthesis than anything groundbreaking. Beyond the choice of perspective, there are only a couple of ideas I have not seen elsewhere (I might remain coy about which those are!).

I’d prefer comments to be held off until the paper has been read (a big ask; it’s 50 pages!) but I hope it doesn’t descend into yet another discussion about semantics, metaphysics, the evidence for common descent, or any other of the conversations we have all had on a few dozen other threads.

My own time defending this is limited – I’m off to the Pyrenees for 5 weeks on June 24th. But, if anyone is interested …

130 thoughts on “The Evolution of Sex”

  1. Allan Miller Post author

    John Harshman,

    Who considers males to be useless contrivances? What tendency?

    Corneel, who I was talking to, was arguing that males were a cost for a population. I was arguing against that. A role in dispersal does not save them – they don’t need saving – but there are extra dynamics provided by anisogamy, and dioecy (two separate issues), which cannot simply be ignored when considering ‘the cost of males’.

    There’s no need to rescue anyone here, but I merely point out that your most recent attempt at rescue doesn’t make a case for males. None of this helps advance any point about either the origin or the maintenance of sex.

    Why would you think talking about males was in any way a point about origins? Indeed, part of my main thrust is the error of exporting issues in the multicellular diploid world to the entirety of sex. And if you ask ‘who does that?’, it starts with Hamilton, Maynard Smith and Williams, among others, and continues in every paper that says sex has a twofold cost. It doesn’t. They know it doesn’t, because they discuss isogamy, but if the twofold cost of sex reduces to the twofold cost of males – itself artificial – then sex itself loses much of its mystery. The ‘massive twofold cost of sex’ repeatedly portrayed, as if it were an allele with a doubled selection coefficient, infests the literature.

    As I have said elsewhere, this idea of ‘maintenance’ is, I think, misguided. The implication is that sex can survive isogamy perfectly well, but as soon as dioecy comes along, sex becomes costly and needs ‘maintaining’ in some way. Implicit in this is an expectation that the Eukaryote tree should consist of isogamous sexuals and the secondarily asexual descendants of temporarily dioecious species, but for a still-cryptic benefit. I think that is false. Again, ‘who does that’? Anyone who thinks the twofold cost of males seems fatal for a dioecious population.

    Allan: Due to the need to find mates, some component of it [genetic impetus toward dispersal] must be in obligate species.

    John: It isn’t true either. True, some dispersal is necessary in an obligate outcrosser, if only the dispersal of sperm from one individual to an immediately adjacent one. But that isn’t what you were talking about: it was panmixis.

    Panmixis is an assumption of many models. Assuming it leads to the fact that, in models, genes are instantly mixed into the population. There is no recognition of the relationship of geometry to spread. This is not universally the case, but adding geometry renders models complex.

    In a panmictic model, you just take any two genotypes and mate them. You stir the population by that means, and in the model, you do so with maximum efficiency. In real populations, that stirring is actually performed more slowly, of course. But mating is still a vector in these populations. For the asexual component imagined in sex/asex populations, there is no vector of mating. Yet still one does the equivalent of stirring them into the population with maximal efficiency, if one uses a ‘one-population’ model. In reality, one of the vectors of stirring is absent for the asexual component.

    Perhaps you wrote off the cuff and have lost focus a bit?

    I deal with points as they arise. People talk about males, I talk about males. People talk about haploids, I talk about haploids. Sex has wide-ranging consequences, and many complexities in specific organisms. Nonetheless, it is reducible to a very simple central dynamic, likewise its relationship to any asexual offshoots regardless of the detail of given organismal life histories. I haven’t lost focus on that at all.

  2. Allan Miller Post author

    Corneel,

    I believe that anisogamy developed in multicellular species, as the division of labour enabled the provisioning of the female gamete, right? It follows that all alleles contributing to anisogamy were benificial, as they increased the survival of the zygote by stacking it with resources. The constraint on male gametes to remain motile is what prevents the re-establishment of isogamy, and allows secondary asexuals to reap a substantial advantage, once they arise.

    Well, I think it worth looking at the ‘progressive’ argument again. If we imagine an increment of asymmetry (it could happen in hermaphrodites, but let’s say anisogamy and dioecy are simultaneous), is there a parallel increment of cost? If we go for a 49/51 split of provisioning, would we expect an asexual offshoot of the 51% group to replace the sexual version more frequently than if the split were 50/50? I don’t see it. Of course it’s not gamete asymmetry at all; it is the diploid organisms that produce them that offer the presumed threat, by producing more grandchildren – producers of the larger type produce only producers of the larger type.

    So, is it possible to put a figure on the investment asymmetry required for the cost to be twofold? It seems to me that it should either increase to that level in proportional increments, or it should appear suddenly. But it’s not obvious where it appears at all, except when you start here (in organisms most of which can’t even achieve the mutation).

  3. Allan Miller Post author

    Mung,

    phoodoo: Here we go again.

    Mung: Indeed. It was destined to happen! It is so ingrained that they don’t even know they are doing it.

    Ah, Stadtler and Waldorf, welcome.

    In no way am I saying that it was destined to happen. I think the planet could have remained cheerfully asexual forever. Obviously, something happened to give rise to the sexual clade we have today; that is what I am exploring. But I regard it as contingent, not destined at all.

  4. phoodoo

    Rumraket: and/or several of it’s intermediate stages must have been adaptive. And the challenge then is to identify in what way (under which circumstances) they could be adaptive.

    No, not SEVERAL of its intermediate stages Rumraket. If we use this philosophy, EVERY stage, EVERY mutation, must be accidentally advantageous, for not just this, but for EVERY thing we see in life. So your challenge is pretty huge, don’t be so modest.

    Hairy forearms, but hairless palms? Very useful for reproducing. Each step must have really been a huge advantage when it comes to reproducing. Any primate with hair on their palms would clearly be out-competed by their smoother cousins.

    Earlobes. You can’t imagine how useful those little droops of skin were in the hot savanna. What chance did the tight ears have? None obviously.

    And you know that little accidental mutation for an L ring in the bacterial flagellum? That was certainly fortuitous, because the old flagellum won’t work so good without it. And don’t even get me started about the P ring. What a good break!

  5. RumraketRumraket

    phoodoo: No, not SEVERAL of its intermediate stages Rumraket.If we use this philosophy

    What philosophy?

    EVERY stage, EVERY mutation, must be accidentally advantageous, for not just this, but for EVERY thing we see in life.

    I’m afraid that’s just not correct. We know of examples of traits that evolved requiring multiple mutations, but several of which were neutral, yet the resulting trait was adaptive.

    This idea that complex adaptive traits can evolve partially through several neutral intermediates was confirmed in the Avida experiment by Lenski et al. And as I said, we know of real-world examples such as chloroquine resistance in Malaria Falciparum.

    Hairy forearms, but hairless palms? Very useful for reproducing. Each step must have really been a huge advantage when it comes to reproducing.

    I think you’re not following the discussion here. This discussion is about the evolutionary origin of sexual reproduction, not the particular anatomical representations that take place by homo sapiens.

    When two gametes meet, there are no palms involved, hairy or otherwise.

    (By the way, our ancestors also had hairless palms as comparative anatomy reveals).

    bla bla bla … And you know that little accidental mutation for an L ring in the bacterial flagellum? That was certainly fortuitous, because the old flagellum won’t work so good without it.And don’t even get me started about the P ring.What a good break!

    Is there a point to this gibberish?

  6. Corneel

    Allan Miller: If we go for a 49/51 split of provisioning, would we expect an asexual offshoot of the 51% group to replace the sexual version more frequently than if the split were 50/50?

    I WAS in fact pondering your progressive argument. You asked where along the way the cost of males developed, and there it is. It is pretty hard to pinpoint where asexuality starts to pay of, but let’s assume dioecy and survival chances that are directly proportional to provisioning received by the parents. In that particular case, yes, as soon as an individual in the 51/49% group becomes asexual it will replace its sexual counterparts. The asexuals have a competitive edge since, although each asexual female is producing diploid offspring with just 51% of the resources that the sexual zygote has, there is a doubling in the potential number of diploid offspring in subsequent generations. Under our assumption this results in a slight surplus of asexuals every generation.

    So where was the detrimental effect of males introduced when only benificial mutations can spread, you might ask. To see this, imagine that a mutation is introduced that decreases male gamete size, thereby increasing fertilisation success of any male diploid carrier in its competition with other males. The allele is beneficial, in that it increases the fitness of its bearer. But the competitive ability of the sexual population as a whole is decreased, since the resulting zygotes receive less provisioning, as the mutation spreads.

    The bottom line is that sexual reproduction introduces conflicts that reward strategies which are detrimental at the population level. That is why asexuals that can escape such conflicts may receive a substantial edge. In organisms where the male eventually contributes nothing in the way of resources or parental care, the cost has become twofold.

  7. RumraketRumraket

    phoodoo: The accidental materialist philosophy.

    Never heard of it. Presumably someone has told you that “the accidental materialist philosophy” requires that every step in the evolution of some complex function must be adaptive. If so, I don’t know of anyone who subscribes to this “philosophy”. I know I don’t.

  8. phoodoo

    Rumraket,

    Well, there are actually two schools of materialist thought.

    One is the Accidental Materialist Philosophy.

    The other is the Accidental Materialist Who Want to Hide the Word Accident When its Not Convenient Philosophy.

    I take it you are in the second.

  9. RumraketRumraket

    phoodoo: Well, there are actually two schools of materialist thought.

    One is the Accidental Materialist Philosophy.

    The other is the Accidental Materialist Who Want to Hide the Word Accident When its Not Convenient Philosophy.

    I take it you are in the second.

    No, I have no objections to the word accident. But I’m actually not a materialist. Metaphysical materialism is the position that everything which exists is made of material. I don’t know that this is the case, in fact I doubt that. So I’m not a materialist. As far as I’m aware, accidents do happen though.

    Rather, I was arguing against this fable you’ve convinced yourself of, that everything and every step of it must be adaptive for something to evolve.

  10. Allan Miller Post author

    Corneel,

    I WAS in fact pondering your progressive argument. You asked where along the way the cost of males developed, and there it is. It is pretty hard to pinpoint where asexuality starts to pay of, but let’s assume dioecy and survival chances that are directly proportional to provisioning received by the parents. In that particular case, yes, as soon as an individual in the 51/49% group becomes asexual it will replace its sexual counterparts.

    I think this is just an assertion. Try with a smaller increment still – 50.09% vs 49.91%. Are you really saying that, unless provisioning is identical, there is a twofold cost to remaining sexual? I doubt it.

    But taking it at face value, the competition is only realised when an asexual mutant arises. For the twofold cost argument, these are assumed available ad lib This is an unjustifiable assumption. If a population evolves to dioecy and anisogamy, there is almost certainly a role for the smaller gamete and its bearers. The two forms are tuned in the presence of each other. So, the assumption of universal replacement of sexuals is modified by that reality.

    There are further realities. The relative dynamics of sexual and asexual populations established during my ‘age of isogamy’ don’t disappear after multicellular forms have arrived and they start to differentiate into two genders.

    The fact that you can construct a very naive picture, flatten out all distinctions between the two genomes in terms of standing variation, anagenesis, ecology, complementary roles, availability of mutational pathway, genetic futures and then get replacement, is really neither here nor there. You are giving that as a will replace, not a may replace. Sure, in a well-stirred flat model with no role for males or their gametes, asexuality wins every time against dioecy. But exporting that to the real world doesn’t work. The model situation never occurs – or, if it does, we don’t get to hear about it, because both are extinct. We can still end up with the pattern we see without additional parameters, because the expectation of universal extinction is unjustified.

    There seems a strange loyalty to the twofold cost. I don’t know why. 4-5% of plants and 93% of animals are rendered ‘mysterious’ by it, at best. ‘Twill ever be thus, I fear, and people will forever sit in expectation of a hidden twofold benefit that is never gonna appear.

  11. dazzdazz

    phoodoo:
    Rumraket,

    Well, there are actually two schools of materialist thought.

    One is the Accidental Materialist Philosophy.

    The other is the Accidental Materialist Who Want to Hide the Word Accident When its Not Convenient Philosophy.

    I take it you are in the second.

    You’re fucking retarded

  12. RumraketRumraket

    Rumraket: And as I said, we know of real-world examples such as chloroquine resistance in Malaria Falciparum

    That should be Plasmodium Falciparum of course, not malaria. It causes malaria.

  13. phoodoo

    Rumraket: That should be Plasmodium Falciparum of course, not malaria. It causes malaria.

    This is just such a specious and uneducated argument. The mutations you are talking about knock out existing functions, they don’t make new ones. Just because it also makes you less susceptible to malaria, that is not evidence that beneficial mutations can add up to novel functions.

    Its like saying if someone got a mutation that made them lose their arms and legs, they are much less likely to step on a nail and get tetanus or get polio of the legs.

    Which although true, is not a useful argument for evolution whatsoever.

  14. Corneel

    Allan Miller: Are you really saying that, unless provisioning is identical, there is a twofold cost to remaining sexual?

    Goodness no, absolutely not. The twofold cost is only realised when the male party completely stops investing in its offspring, which rarely occurs. I was merely pointing out that there is, in fact, a cost building up in your “progressive” scenario, in the form of a loss of competitive ability of the sexual population.

    Allan Miller: But taking it at face value, the competition is only realised when an asexual mutant arises.

    True, as long as no asexuals arise, everything is fine.

    Allan Miller: If a population evolves to dioecy and anisogamy, there is almost certainly a role for the smaller gamete and its bearers.

    Yes, but that role will always be in the service of those gametes and its bearers, which may not necessarily benefit the bearers of the large gametes or the population as a whole.

    Allan Miller: The relative dynamics of sexual and asexual populations established during my ‘age of isogamy’ don’t disappear after multicellular forms have arrived and they start to differentiate into two genders.

    I think they do, because the differentiation of distinct genders introduces opportunities for sexual conflict which could not exist before.

    Allan Miller: The fact that you can construct a very naive picture, […] and then get replacement, is really neither here nor there.

    Yes, I am guilty of ignoring all the factors you mentioned. Things may indeed play out very differently when these are taken into account. But I do note that these are all long-term benefits.

    Allan Miller: There seems a strange loyalty to the twofold cost. I don’t know why. 4-5% of plants and 93% of animals are rendered ‘mysterious’ by it, at best.

    Nonsense, I gladly concede that there is no twofold cost of males. But sex is costly and its perceived benefits are long-term, so that deserves some explaining. And everybody likes a good puzzle, right?

  15. John HarshmanJohn Harshman

    Allan Miller:
    John Harshman,

    Corneel, who I was talking to, was arguing that males were a cost for a population.

    There’s a big difference between “has a cost” and “is a useless contrivance”. You’re coming across, to me at least, as dodging around and creating a cloud of straw men.

    As I have said elsewhere, this idea of ‘maintenance’ is, I think, misguided. The implication is that sex can survive isogamy perfectly well, but as soon as dioecy comes along, sex becomes costly and needs ‘maintaining’ in some way.

    Doesn’t the existence of facultatively asexual populations, like most aphids, argue that sex is indeed costly, and that sometimes the costs outweigh the benefits? And doesn’t every bodily function and organ have a cost? Things tend to be lost if not needed. Cave fish lose eyes, endoparasites lose digestive tracts, etc. Why is sex different?

    Panmixis is an assumption of many models. Assuming it leads to the fact that, in models, genes are instantly mixed into the population. There is no recognition of the relationship of geometry to spread. This is not universally the case, but adding geometry renders models complex.

    So what? Why is any of that relevant here? Why is any of your subsequent discussion of “stirrring”, whatever that may mean, relevant?

  16. RumraketRumraket

    phoodoo: This is just such a specious and uneducated argument.The mutations you are talking about knock out existing functions, they don’t make new ones.Just because it also makes you less susceptible to malaria, that is not evidence that beneficial mutations can add up to novel functions.

    Its like saying if someone got a mutation that made them lose their arms and legs, they are much less likely to step on a nail and get tetanus or get polio of the legs.

    Which although true, is not a useful argument for evolution whatsoever.

    Phoodoo, Im talking about resistance to chloroquine, a drug used as an antbiotic against plasmodium. Not about sickle cell anemia. Do try to keep up. Read for comprehension.

  17. phoodoo

    phoodoo:
    Rumraket,

    Well, there are actually two schools of materialist thought.

    One is the Accidental Materialist Philosophy.

    The other is the Accidental Materialist Who Want to Hide the Word Accident When its Not Convenient Philosophy.

    I take it you are in the second.

    dazz: You’re fucking retarded

    It must be beneficial!

  18. Allan Miller Post author

    Corneel,

    Goodness no, absolutely not. The twofold cost is only realised when the male party completely stops investing in its offspring, which rarely occurs. I was merely pointing out that there is, in fact, a cost building up in your “progressive” scenario, in the form of a loss of competitive ability of the sexual population.

    Hmmm. Just don’t see that as a cost at all. The ‘loss of competitive ability’ comes as a consequence of a 2-step process: buildup of a ‘major’ and ‘minor’ contributor in the population, mutation of the ‘major’ to asexuality. But elimination of the major/minor is still not a given, so I don’t see why this would lead us to say ‘sex costs’ – especially given all the other things I keep mentioning! I think it’s basically mistaking a ‘dodge’ for an adaptation …

    Allan Miller: If a population evolves to dioecy and anisogamy, there is almost certainly a role for the smaller gamete and its bearers.

    Corneel: Yes, but that role will always be in the service of those gametes and its bearers, which may not necessarily benefit the bearers of the large gametes or the population as a whole.

    The bearers of the large gametes and the bearers of the small gametes are just packages – ‘vehicles’, in Dawkins’s terms. A gene in a sperm will become a gene in an egg, and vice versa. That supports a stable symmetry. I think looking at things from the ‘male’ and the ‘female’, diploid point of view leads to error. They are just genes. If a detrimental gene arises in this system, it selects for antagonists within the same system, not abandonment. And the mutation to asexuality probably never happens in a way that leaves everything else unaffected. We are talking of multicellular organisms with extensive adaptations towards gamete production, in both sexes – possibly extensively tuned to each other during a period of hermaphrodity. The simplistic notion of consequence-free ‘turning off meiosis’ is less likely to be available in the very organisms ‘twofold cost’ needs it to happen in, because of the complementarity of the system prior to that point, and the tuning of the female not just to ‘offspring’ production, but to males and their gametes. We also need to consider development and life history. On the face of it, it seems mechanistically harder to evolve asexuality in animals than plants.

    Allan Miller: The relative dynamics of sexual and asexual populations established during my ‘age of isogamy’ don’t disappear after multicellular forms have arrived and they start to differentiate into two genders.

    Corneel: I think they do, because the differentiation of distinct genders introduces opportunities for sexual conflict which could not exist before.

    That does not appear to select for abandonment of meiosis, more than balanced genetic strategies in the reducing population.

    Allan Miller: The fact that you can construct a very naive picture, […] and then get replacement, is really neither here nor there.

    Corneel: Yes, I am guilty of ignoring all the factors you mentioned. Things may indeed play out very differently when these are taken into account. But I do note that these are all long-term benefits.

    No – the sexual form typically already has variation, before the asexual arrives. Tenure must be worth something. And it has a genetic system that enables it to deal more effectively with competitors and the wider ecology through locus-level selection. These things are already in the sexual population when the asexual arises. It has to defeat the sexual by repeat runs of the same genome, and avoid being made extinct by other exterior and interior challenges. It will not have a better allele at any locus than those already in the population, and may well have many worse.

    Allan Miller: There seems a strange loyalty to the twofold cost. I don’t know why. 4-5% of plants and 93% of animals are rendered ‘mysterious’ by it, at best.

    Corneel: Nonsense, I gladly concede that there is no twofold cost of males.

    Great! That’s all the twofold stuff out the way then! My work here is done 😉

    But sex is costly and its perceived benefits are long-term, so that deserves some explaining. And everybody likes a good puzzle, right?

    Yep, one I have been wrestling with for some time. But I do think the answer is available – nothing more is needed, especially when one stops thinking of it as if it were a simple locus with a doubled selection coefficient. That has been my mission – maybe what John might call a ‘strawman’, but I see that approach everywhere I look, textbooks onwards.

    When one considers the world into which a secondary asexual is thrust, it should be clear that its success is not a given, but the reasons are not half as easily articulated as the advantage it is presumed, naively, to have.

  19. Allan Miller Post author

    John Harshman,

    There’s a big difference between “has a cost” and “is a useless contrivance”. You’re coming across, to me at least, as dodging around and creating a cloud of straw men.

    Just the way I paraphrased Corneel; an ironic turn of phrase. I know you frequently take exception to the way I express myself. I’ll try and do better.

    Doesn’t the existence of facultatively asexual populations, like most aphids, argue that sex is indeed costly, and that sometimes the costs outweigh the benefits?

    Not directly, no. The succession of diploid bodies is a strategy (yes, yes, teleology … let it pass) used by genes in a sexual organism – the aphid – in a very similar manner to the way we generate a succession of diploid mitoses in the germ line, or a diploid succession in a unicellular organism. I doubt there is any organism that does not do numerous mitoses in between meioses. Aphid bodies do not cohere the way our cells do, but essentially parthenogenesis is being used by that sexual organism as part of its life history. Sex isn’t costing it; it still does it.

    Of course the aphid is a short step away from permanent parthenogenesis. But it’s still a sexual organism until then. Haploids are released by aphids far more frequently than they are by us, one could observe.

    And doesn’t every bodily function and organ have a cost? Things tend to be lost if not needed. Cave fish lose eyes, endoparasites lose digestive tracts, etc. Why is sex different?

    It can be hard to say whether a given loss is due to cost or drift in the absence of positive selection. But in all cases, loss of alleles within a sexual system is a fairly simple matter. The sexual system diffuses those alleles out of the population independent of all other loci. Other alleles fix.

    But for loss of sex to happen, the entire genome has to be replaced, not merely a small segment of it. It’s not just ‘the bit that does sex’. The asexual has to completely replace the sexual. This is not reducible to a simple contest between alleles; I think the analogy fails.

    Me: Panmixis is an assumption of many models. Assuming it leads to the fact that, in models, genes are instantly mixed into the population. There is no recognition of the relationship of geometry to spread. This is not universally the case, but adding geometry renders models complex.

    John: So what? Why is any of that relevant here? Why is any of your subsequent discussion of “stirrring”, whatever that may mean, relevant?

    Sorry, I don’t quite know how to make the point a different way, because I don’t know what you aren’t getting. I’m criticising simple models, which incorrectly treat asexuals as being subject to the exact same forces as sexuals, leading to an overestimation of the likelihood of extinction of the one by the other.

  20. Corneel

    Allan Miller: Hmmm. Just don’t see that as a cost at all.

    The sexual population is not realising the maximal attainable growth rate, because males often will not or can not fully invest in their offspring. That is a cost.

    Allan Miller: I think looking at things from the ‘male’ and the ‘female’, diploid point of view leads to error. They are just genes.

    Didn’t realise you were such a Dawkins fan. The gene eye’s view can be instructive in some cases. But all genes that are spending quality time with each other inside an organism (or a gamete) need to cooporate in the genome, be it haploid or diploid.

    Allan Miller:
    Me: But I do note that these are all long-term benefits.
    Allan: No – the sexual form typically already has variation, before the asexual arrives. Tenure must be worth something. And it has a genetic system that enables it to deal more effectively with competitors and the wider ecology through locus-level selection.

    Yes- variation in itself is not beneficial, but comes in handy during adaptation. It is a long-term future benefit. Same goes for evolving (locus-level selection) to deal with competitors and ecological changes.

    BTW. Are you be packing already?

  21. Allan Miller Post author

    Allan Miller,

    Sorry, I don’t quite know how to make the point a different way, because I don’t know what you aren’t getting. I’m criticising simple models, which incorrectly treat asexuals as being subject to the exact same forces as sexuals, leading to an overestimation of the likelihood of extinction of the one by the other.

    OK, I’ve had a sleep and I’ll have a go at explaining this more thoroughly.

    On the naive ‘twofold cost’, we are led to believe that sexuality and asexuality can just be treated as alleles with a twofold difference in selection coefficient. There are many problems with this; the effect of range geometry on expectations is but one.

    Such a differential in coefficient would be more than enough to fix an allele within a genetic sexual population, so such a fate is felt equally certain for a mixed sexual/asexual ‘population’. However, this expectation confuses genetic and ecological populations. In a sexual, the genetic population is the ecological population. But this is not the case in a sexual/asexual competition.

    In the first, you can ignore geometry. But in the other, when we expect physical replacement of the entire species, you can’t.

    Implicitly, if one represents a population by means of an equation or a simple ‘Monte Carlo’ simulation, one is simply ignoring the effect of geometry and range on allele spread. One places all individuals an equal distance apart, and every single individual is an immediate neighbour of every other. You can justify this simplification within sex because the geometric progress of gene flow around the genetic population can be ignored. If an allele becomes fixed, it has managed to get itself, through the vector of matings and other dispersal mechanisms, into every individual in the future population. Sex ‘stirs’ this process; I don’t think that’s an unreasonable way to express it. It provides the vector of gene flow, in several ways, one of which is gamete motility (in certain species), another of which is physical mating (in others).

    But if one wants to imagine wholesale replacement of the sexual by the asexual, this model is invalid. The asexual has to take over from a single point and spread. If there is no sex, it lacks the very vector that allowed us to put the population into a ‘dimensionless’ range, in the sexual case.

    Imagine an asexual in single copy on the edge of a range. Since it is not sexual, it is not confined to spread in one direction only. The organisms to one side exert no ‘pull’. Therefore, only a part of its exponential expansion poses any threat to the sexual. If you just throw it into the same ‘dimensionless’ model as used within sex, you do the equivalent of taking all the asexuals that are outside the sexual’s range and throwing them back inside it, then giving the whole a good old shake. Within the parent range, asexuals are prevented from interfering with their own progress by being cast to the four corners of the sexual range. So, one is gaming the picture in favour of the asexuals in an unrealistic manner by ignoring geometry. Of course asexuality wins!

    One is basically confusing genetic and ecological populations, and applying the same model to both.

  22. Allan Miller Post author

    Corneel,

    The sexual population is not realising the maximal attainable growth rate, because males often will not or can not fully invest in their offspring. That is a cost.

    Still hmmmm … I’m a bit ‘anti-cost’ in general I’m afraid. There is far to much else going on that feeds back on the assumption that ‘maximum attainable growth rate’ is what it’s all about. If a mutation doubles fecundity after a population has achieved some kind of balance with its ecology, I don’t see that as necessarily a good thing – a benefit. It’s always zero sum – the maximum attainable growth rate in a steady state population for example is 1 diploid (or two haploids) per diploid. The species can temporarily go ballistic for non-adaptive reasons – the asexual doubling is not a response to environmental pressures – but gets pegged back by the same limit as the sexual was under.

    Allan Miller: I think looking at things from the ‘male’ and the ‘female’, diploid point of view leads to error. They are just genes.

    Corneel: Didn’t realise you were such a Dawkins fan. The gene eye’s view can be instructive in some cases.

    ‘Fan’ would be overstating it. I think he over-eggs his own pudding, seeing conflict where it does not necessarily belong. It leads to gene-centrists being as puzzled over sex as ‘diplocentrists’. But the point about which element actually benefits is a good one (he’s only taking Williams’s stance of course. He didn’t invent gene centrism). This is why I am making a case for the humble haploid as the ‘beneficiary’ of the sexual transaction. The haploid is an evolutionary allele, just as happy in a sperm as an egg.

    Gene centrism does not translate to only taking the perspective of the smallest possible unit of selection. Larger haplotypes have interests too, even if sliced by crossover. Meanwhile the ‘diplotype’ is not even a thing!

    But all genes that are spending quality time with each other inside an organism (or a gamete) need to cooporate in the genome, be it haploid or diploid.

    They do, but a gene that has an effect in one gender is simply silent in the other. It just has a bimodal component to its overall selection coefficient. The fact that a neighbour may be an antagonist in the opposite gender is not visible to it. This is not an intragenomic competition like ‘drive’.

    Yes- variation in itself is not beneficial, but comes in handy during adaptation. It is a long-term future benefit. Same goes for evolving (locus-level selection) to deal with competitors and ecological changes.

    Yes – my point in taking the ‘progressive’ approach is that all these things arise for non-adaptive reasons during elaboration of the initial haploid-diploid cycle. You get them for free during the ‘age of isogamy’. One does not need to invoke them to provide a ‘benefit’ to sex at the individual level.

    A frequent objection is that twofold cost or equivalent is immediate, so there is no time for sex to get the population/ecology effects. But that assumes a multicellular organism that has evolved anisogamy and then sex! That’s not really a sensible starting point; you don’t get either multicellularity or anisogamy without sex.

    BTW. Are you be packing already?

    Only got to pack a rucksack! Away Saturday! 🙂

  23. Corneel

    Allan,

    Some thoughts on your geometry argument: Ecological models of interspecies competition, which seem perfectly valid approximations of the sexual-asexual situation here, usually don’t have any spatial information either. The competitors are simply assumed to compete for the same ecological niche. These models typically assume that the niche and any resources within it are limited, which seems reasonable to me. No evolution occurs in these models either, unless explicitely introduced.

    Yes, all models are simplifications but I don’t see any objections in your post that do not equally apply to competition models in ecology. But perhaps you are not impressed with ecological modelling, if even a doubling of fecundity doesn’t strike you as a benefit?

  24. Allan Miller Post author

    Corneel,

    OK – not hugely au fait with ecological modelling. Simplifications are not completely invalid; I’m just pointing out that this is another reason to roll back one’s expectations that asexuals ‘always win’.

    It may be more appropriate when both populations have the same genetic system – dunno! Certainly I could perceive situations where the ‘single-population’ approach would lose traction. If the populations do not remain coextensive, they each spill out into regions the other does not occupy; competition occurs only in the overlap. One might do the modelling equivalent of beating them back into range with dog and stick, but one would need to recognise that this is what is happening, and not over-extend conclusions.

    But perhaps you are not impressed with ecological modelling, if even a doubling of fecundity doesn’t strike you as a benefit?

    It must surely depend? If it leads to a scorched earth, then surely not. If the increase in fecundity relates to a type that is making more efficient use of resources, and the population grows through adaptation, then yeah, that’s a benefit. But I don’t see asexual fecundity (ignoring aphids) as any kind of ‘adaptation’.

  25. John HarshmanJohn Harshman

    Allan Miller: Imagine an asexual in single copy on the edge of a range. Since it is not sexual, it is not confined to spread in one direction only. The organisms to one side exert no ‘pull’. Therefore, only a part of its exponential expansion poses any threat to the sexual. If you just throw it into the same ‘dimensionless’ model as used within sex, you do the equivalent of taking all the asexuals that are outside the sexual’s range and throwing them back inside it, then giving the whole a good old shake. Within the parent range, asexuals are prevented from interfering with their own progress by being cast to the four corners of the sexual range. So, one is gaming the picture in favour of the asexuals in an unrealistic manner by ignoring geometry. Of course asexuality wins!

    I’m afraid you are so caught up in your conclusion that you are grasping at straws to maintain it. Why does the species range have edges? Presumably there is some barrier to dispersal, which ought to act equally on sexual and asexual individuals. Or if there isn’t a barrier, sexual and asexual individuals should disperse equally, and the range will expand. There seems in fact no difference except that it takes only one asexual to expand the range rather than two for sexuals.

    And again:

    Allan Miller: It’s always zero sum – the maximum attainable growth rate in a steady state population for example is 1 diploid (or two haploids) per diploid.

    That’s the average growth rate. But what matters here is the differential growth rates of different genotype fractions. If individuals are otherwise identical but asexuals reproduce at a greater rate than sexuals, whatever maintains the constant population size, even random death, will result in the asexual population replacing the sexual population.

    You also seem, in various comments, to be supposing that selection operates for the good of the species. An adaptation that results in “scorched earth” as you put it will still become fixed if it gives advantages over other individuals in the population, even if that results in the reduction of total population size in the end.

  26. Allan Miller Post author

    John Harshman,

    I’m afraid you are so caught up in your conclusion that you are grasping at straws to maintain it. Why does the species range have edges?

    It occupies a physical space. How can it not have edges? There is bound to be a point beyond which there are no individuals of that species.

    I am not saying there is a physical barrier to dispersal – on the contrary, I couldn’t have an illustration where the asexual arises at the edge of the population and then expands in all directions from there if that was what I was saying. I was illustrating the potential to mislead of a model in which both sexual and asexual are continually mixed into the one population in order to compete.

    [eta – and to head off the ‘gotcha’, I am not saying that asexuals always arise at the edge either …]

    Allan Miller: It’s always zero sum – the maximum attainable growth rate in a steady state population for example is 1 diploid (or two haploids) per diploid.

    John: That’s the average growth rate. But what matters here is the differential growth rates of different genotype fractions. If individuals are otherwise identical but asexuals reproduce at a greater rate than sexuals, whatever maintains the constant population size, even random death, will result in the asexual population replacing the sexual population.

    Yes of course. In a simple model, where there is no other distinction between the species than the number of grandchildren accruing, and vigorous mixing within, asexuality wins. I have never disputed this point.

    You also seem, in various comments, to be supposing that selection operates for the good of the species.

    No. Species, like individuals, are temporary states in a longer continuum. Fundamentally, eukaryotes are sexual because their ancestors were, and it is a mode that is resistant to invasion, simplistic intuitions on twofold cost notwithstanding.

    An adaptation that results in “scorched earth” as you put it will still become fixed if it gives advantages over other individuals in the population, even if that results in the reduction of total population size in the end.

    Corneel was talking of population level benefit – maximising the output of the species, which sex somehow gets in the way of. You are talking of substitution within, a somewhat different issue. I have never doubted that asexual doubling has the capacity to replace an asexual population.

    You are illustrating exactly the kind of thinking I try to critique. I argue, in my essay, that taking a simplistic view of the two modes leads to assumptions that are not sustainable when one examines their dynamics in detail from a justifiable starting point in asexual haploidy – rather than taking modern organisms out of their current context and creating contests which are significantly weighted in the diploid asexuals’ favour. You seem determined to stick with the simplistic – notions I have never disputed – in order to dismantle an argument you haven’t actually read.

    There is no doubt that there are circumstances in which an asexual offshoot can replace its sexual ancestor. Not disputed. The principal issue is the extent to which we should regard that as problematic for the existence of sex, or of dioecious species. Treating sex/asex as if it were a simple adaptive allele in one population is not, IMO, a very useful approach.

  27. Allan Miller Post author

    Here’s an illustration to try and widen thinking out from single populations. One could consider a sexual clade with a single founder species. We artificially imagine that anagenesis is constant, speciation of sexual populations occurs at a constant interval, and there is a constant probability p(reversion) of an asexual arising in a given time in a given lineage.

    When reversion occurs, there is a probability p(replacement) that the parent population will be extinguished by it. For any instance, p(replacement) will diminish as anagenesis progresses, because there is no reason to suppose that the two will track each other eternally as close competitors.

    We also have two probabilities p(sexualextinction) and p(asexualextinction) of a lineage due to factors unrelated to the contests between them.

    It would not be too difficult to build this as a model. But even without doing so, it should be clear that all we need to do is provide sufficiently low values for p(reversion) or p(replacement), and/or make p(sexualextinction) lower than p(asexualextinction), to end up with a final clade that has a proportion of sexual to asexual members that we might, if all we thought of was ‘sex is costly’, consider surprising and in need of special explanation.

    There is no need to talk of ‘good of the species’, nor is there any need to talk of sex/asex as an adaptation. A lot of these arguments have been about p(replacement), which extreme 2fold cost thinking would put at 1. It’s nowhere near, but even if it were, we’d see sex if p(reversion) were sufficiently low, or the competition-independent extinction differential significant.

  28. John HarshmanJohn Harshman

    Allan Miller: I’m afraid you are so caught up in your conclusion that you are grasping at straws to maintain it. Why does the species range have edges?

    It occupies a physical space. How can it not have edges? There is bound to be a point beyond which there are no individuals of that species.

    I am not saying there is a physical barrier to dispersal – on the contrary, I couldn’t have an illustration where the asexual arises at the edge of the population and then expands in all directions from there if that was what I was saying. I was illustrating the potential to mislead of a model in which both sexual and asexual are continually mixed into the one population in order to compete.

    You answered a rhetorical question, which you really should have noticed was rhetorical, and ignored the rest. Species ranges do have edges, and those edges are generally barriers to dispersal. That is, species tend to occupy all the contiguous favorable habitat. Exceptions are generally transient, such as range expansions due to climate change. The more important point is that asexuals do not differ from sexuals in their ability to expand into new habitat, so you are creating a difference where there is none. Sexuals and asexuals at the edge of the population will have equal tendencies to disperse outside the habitat and so be lost to the population.

    Allan Miller: Yes of course. In a simple model, where there is no other distinction between the species than the number of grandchildren accruing, and vigorous mixing within, asexuality wins. I have never disputed this point.

    It doesn’t seem that way. And you keep bringing up differences that don’t exist in order to justify yourself.

    Allan Miller: Fundamentally, eukaryotes are sexual because their ancestors were, and it is a mode that is resistant to invasion, simplistic intuitions on twofold cost notwithstanding.

    I suggest that one reason it’s resistant to invasion is that there are benefits that often outweigh the cost (which, as Corneel pointed out, can vary continuously from 1-fold (i.e. none) to 2-fold). This is quite different from claiming that the cost doesn’t exist.

    Allan Miller: You seem determined to stick with the simplistic – notions I have never disputed – in order to dismantle an argument you haven’t actually read.

    I apologize for not reading your paper. I’m actually ashamed. But your arguments here do not encourage me.

    I see you have replaced your “good of the species” language with a bit of species selection (lower speciation rates or greater extinction rates). Better.

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