susu.exp wrote:

Allan Miller wrote:The distinction was made explicit in an article I read (and I am now kicking myself for not making more careful notes, such as who and where!) in which the author noted the technical difference between the two, and it struck a chord vis a vis sex. It's a common enough distinction, particularly in ecology, and I don't think it is helpful to simply insist 'a population is any set of individuals' - it obscures the very distinction that I am attempting to draw.

The question is whether that distinction is useful in evaluting the models we are discussing. Neither the Moran Model nor the Fisher-Wright model assumes sexual reproduction. Hence when you use these population genetics models, your population isn´t defined by interbreeding.

But this is precisely what I'm driving at - if the models don't consider breeding system relevant, other than as the source of segregation/recombination, or haploid/diploid, then they aren't much use for evaluating traversal of the breeding-system boundary, whatever other merits they may have. While I have no idea what cutting-edge pop-gen thinking is on sex, I do know that use of an erroneous kind of population-based thinking on the matter is rife, leading directly to errors of the "Twofold Cost" kind, and hence a large part of the ongoing "sex is a mystery" paradigm. The fact that a population behaves differently, both ecologically and genetically, when it is sexual seems a significant fact to me.

susu.exp wrote:

Allan Miller wrote:I am using the terms in a specific sense, as defined above, yes. There is a real and natural dynamic that sex applies to a population (and which has no equivalent in a community). Obligate sexual individuals must find mates. That very fact effects much of the mixing that lies at the heart of the simple 'panmictic' population models. There are other sources of mixing of course - the 'random walks' that individuals perform as they wander about during the course of their lives - but ultimately sex coheres the population and draws its boundaries.

I agree, though it´s worth noting where these dynamics come in. They do alter Ne, a clonal community - as CP noted - has half the effective population size as a panmictic sexual population with the same number of individuals.

If their behaviour was equivalent, then yes – this compounds the genetic stasis provided by lack of recombination. Essentially, asexuals lack both recombination and segregation, and it is the latter that causes the sexual population to take twice as long to fix the average mutation. Any chromosome in the sexual diploid has a segregating homologue, and this creates twice as many loci for a mutation to be resampled into vs the asexual. In the asexual, even if genetically diploid, each chromosome is ever chained to its homologue, so it behaves as an evolutionary haploid. But this is only relevant for secondary asexuality IMO.

I view the sexual cycle as starting with haploid fusion – attempts to start it with the diploid raise major problems of simultaneity. An early eukaryote (a very early eukaryote) with a truly haploid genome (possibly just a single chromosome and no recombination) joined forces with another, creating a diploid, which ejected the haploids at some future point (this is not a million miles from how sex operates now). The number of cellular individuals in this case is not particularly relevant. The question is all about how this process benefits haploid genomes. The population size of the putative free-living haploid is N. This can create a maximum of N/2 diploids directly (of course these may then perform diploid mitosis, though this may be simply unavailable in the early stages – they may have to return to haploidy simply to increase).

A free-living haploid would take 2N generations to be fixed. If all N of these haploids fused to make sexual diploids (pop size N/2), full coalescence would take 4N/2 = 2N generations – so sex does not lead to increased variation there. Which is a bit of a paradox. In order to get the extra N/2 individuals, you’d have to allow one additional mitosis per individual in the sexual line. Which is not comparing like with like – the sexuals then have twice as much genetic material to replicate. Now, when we look at secondary asexuality – suppression of meiosis, say - the books have been balanced by duplication of the haploid genome. N sexuals and N secondary asexuals are equivalent. (Of course, sexuals can reduce variation substantially eg by inbreeding, unbalancing the sex ratio or gene conversion).

susu.exp wrote:

Allan Miller wrote:But with recombination, the sample is a mosaic of the parental rows. Iteration of this slicing through the generations creates an independence of motion - the genome is subdivided into 'columns', and a gene can fill its column independently of what is going on upstream and downstream (along the row). This is the arena in which I visualise the metaphor of selective pressure operating. An allele that confers a selective advantage is likely to 'flow' more strongly into the rows in which it is absent, thanks to its effect on fitness. Recombinant sex draws the structure of this spreadsheet - sex itself influences the total number of rows any one such array contains, recombination the boundaries of the columns.

This visualisation would represent the asexual community as a set of separate spreadsheets, each of which contains one individual - one row and one column, ie a single cell in the spreadsheet, by happy coincidence (though obviously we also have multicellular asexuals and single-celled sexuals).

Yes, but this merely is a special case of linkage. In sexual organisms genes on the same chromosome only get inherited independently if crossing over occurs. Rarer than two genes on different chromosomes. And genes that are closer to each other on the same chromosome get co-inherted more easily than genes far apart.

Recombination is a yin-yang process, with multi-level effects. Genomically, it simultaneously sunders linkages and creates them (rendering the other old saw about recombination load something of an oddity - to offer as detrimental the very process that enables creation of co-adapted gene complexes in the first place.). The simplest kind of recombination is simply possessing more than one chromosome. Because there is no labelling of chromosomes going into the zygote, there is no 'memory' pulling them out in meiosis, and they recombine with a precise 50% chance. Subchromosomal recombination is a neat way of creating many 'mini-chromosomes'. Again, interestingly, it happens with an exact 50/50 impartiality, though as you say physical linkage means that the fate of any two linked genes is constrained by distance. Half of all DSB's resolve to give the same chromosomal arrangement as they started with, because there is nothing to favour either of the two possible resolutions of the Holliday junction. Snip it one way, and you get a little bit of gene conversion. But snip it the other, and you get a whole-segment swap with resounding consequences.

What recombination enables (among other things) is the engagement of the whole population in the (passive) search for novelty. Therefore, in my 'spreadsheet' model, a mutation in any row can progress along its column by insertion into the future population within the same sheet. Beneficial change, wherever it arises, can be 'passed around' the population. Multiple solutions to the same problem can be integrated, as well as parallel solutions to separate problems. And of course in the process a pool of variation is built up within the sheet, by both selection and drift. Meanwhile, asexual individuals, lacking any means of integrating change other than by serial genome substitution, and fighting even amongst themselves (eg clonal interference), are forever alone.

The sexual population is a particular evolutionary unit, and this is thanks to both recombination and the constraint of mating. The asexual 'population' is a rather repetitive bunch of individuals, out of which evolution can emerge, but with significant differences in dynamic that are not always reflected in the models.

Allan Miller wrote:But this is precisely what I'm driving at - if the models don't consider breeding system relevant, other than as the source of segregation/recombination, or haploid/diploid, then they aren't much use for evaluating traversal of the breeding-system boundary, whatever other merits they may have.

Well, we´ve got our basic models, which we then can expand into multigene models, etc. The main merit of these basic models is their universality and expandability. They have the same job as fundamental formulae in physics, which you then apply boundary conditions, innitial conditions and parameters to, if you want to look at a particular question. Because they are so general they will of course be of use to look at the breeding-system boundary, but they alone are insufiicient - there´s additional modeling to be done there. Because these models are both well supported by the evidence and make a lot of sense (if you start with the assumptions that the number of offspring an organism leaves is a random variable and define the properties of alleles in the usual fashion, you can derive them from that), problems with the literature on the evolution of sex would very likely arise not from these models, but from the additional components.

Allan Miller wrote:Recombination is a yin-yang process, with multi-level effects. Genomically, it simultaneously sunders linkages and creates them (rendering the other old saw about recombination load something of an oddity - to offer as detrimental the very process that enables creation of co-adapted gene complexes in the first place.).

Well, there´s something of a smearing out of selection coefficients if you have recombination. Assume two advantageous alleles A and B arise in one asexual organism. Then the linkage means that the benefits do compound. In a sexual population with recombination even with A and B arising in one individual you will more likely see Ab and Ba type organisms in the next generation, reducing s for both alleles, potentially to near neutrality.

Allan Miller wrote:What recombination enables (among other things) is the engagement of the whole population in the (passive) search for novelty. Therefore, in my 'spreadsheet' model, a mutation in any row can progress along its column by insertion into the future population within the same sheet.

It´s something I´d like to see made more explicit. In particular you have to note that this expands the original models in a non-trivial way - you are now looking at multiple sites, which means you are using more than one moran model (or fisher wright model) and you now have s depend on the frequencies of other alleles.

Allan Miller wrote:The sexual population is a particular evolutionary unit, and this is thanks to both recombination and the constraint of mating. The asexual 'population' is a rather repetitive bunch of individuals, out of which evolution can emerge, but with significant differences in dynamic that are not always reflected in the models.

Again, the difference does not come in in the basic "building block" models we´ve been discussing here. If you take multiple of these and model their interaction, then you get these different dynamics. Both a ball falling to the ground and a pendulum swinging can be modeled with classical mechanics. Both show very different dynamics, build by taking some basic equations and adding boundary conditions.

susu.exp wrote:

Allan Miller wrote:Recombination is a yin-yang process, with multi-level effects. Genomically, it simultaneously sunders linkages and creates them (rendering the other old saw about recombination load something of an oddity - to offer as detrimental the very process that enables creation of co-adapted gene complexes in the first place.).

Well, there´s something of a smearing out of selection coefficients if you have recombination. Assume two advantageous alleles A and B arise in one asexual organism. Then the linkage means that the benefits do compound. In a sexual population with recombination even with A and B arising in one individual you will more likely see Ab and Ba type organisms in the next generation, reducing s for both alleles, potentially to near neutrality.

Well, this is where I get confused! Alleles A and B? They don't 'recombine with appreciable frequency, so they aren't alleles!(?). Say we have the following 'alleles' in the population: ---A---, ---A-B--, -----B-- and --------. Now, you are saying that ---A-B-- is the fittest genotype, and, lacking recombination, additive fitness effects can be reaped in every instance. Now, if we imagine these alleles as haploid gametes instead, it is true that some recombinant gametes - (---A-B-- x ????????) will not be ---A-B--. Either there will be segregation (in which case ???????? may be passed on, 50% of the time) or recombination may sunder the A-B link (giving ????-B-- or ---A????). So this is the cost of recombination/segregation. But this is incomplete accounting. Suppose we only got a ---A-B-- combination in the first place because of recombination. An asexual mutant may choose to say "stick" at this point - it has the advantageous genome. But ---A-B-- is kept afloat in the sexual population by a number of factors. Recombination destroys it only a proportion of the time. In destroying it, it may replace B with something even better. Or it may create a new combination, ---A-BC- that is better yet. And if those dashes are detrimental, replacing them with something better helps again.

The net result of recombination is not solely "co-adapted complexes broken", but a four-way sum:

Useful linkages broken
Useful linkages forged
Detrimental linkages broken
Detrimental linkages forged

Only if the net result of that sum over many generations is negative would we find recombination selected against. But genes for recombination find themselves attached to winners, because many of the genes they bring in have already proved their worth, by being selected in the first place.

susu.exp wrote:

Allan Miller wrote:What recombination enables (among other things) is the engagement of the whole population in the (passive) search for novelty. Therefore, in my 'spreadsheet' model, a mutation in any row can progress along its column by insertion into the future population within the same sheet.

It´s something I´d like to see made more explicit. In particular you have to note that this expands the original models in a non-trivial way - you are now looking at multiple sites, which means you are using more than one moran model (or fisher wright model) and you now have s depend on the frequencies of other alleles.

Putting it firmly beyond my grasp! But it adds to my conviction that, the simpler (and less realistic) you make the models, the more of a mystery sex is. All of the things that sex gives to a population - resident variation, the ability to incubate and wither multiple solutions independently, an ability to deal with the rest of the (mostly sexual) biosphere - become more clear in proportion to their decreasing mathematical tractability. I realise this is all known stuff, but it puzzles me why people still make the demand (repay the twofold cost, and the recombination load while you're at it) in terms of unrealistic models. I think we know all we are ever going to know about sex from an explanatory point of view - there is no hidden twofold benefit.

Allan Miller wrote:Well, this is where I get confused! Alleles A and B? They don't 'recombine with appreciable frequency, so they aren't alleles!(?).

That´s the problem with the formulation of the allele definition as you give it here. The definition is:
A discrete trait, with variation that is inherited with an expected number of changes <1.
For sexual diploids this is equivalent to the recombination formulation and in a lot of texts which focus on sexual diploids use it because it´s simpler than the other one. In the same way that species are often defined through reproduction, when they are defined in a more general way through gene flow (but for sexual diploids this is equivalent to the reproduction definition).
This does mean that given a mutation rate of µ (in BP per generation), a string of bases of lenght 1/µ per generation is a gene (longer strings are not genes because the expected number of changes is >1). This means that in a haploid genome we can find a lot of alleles.

Allan Miller wrote:Only if the net result of that sum over many generations is negative would we find recombination selected against. But genes for recombination find themselves attached to winners, because many of the genes they bring in have already proved their worth, by being selected in the first place.

Just because there´s a cost, that doesn´t mean there isn´t also a benefit. Size growth in metazoans comes at an energetic cost. Still there are big metazoans, because size does also confer benefits.

Allan Miller wrote:Putting it firmly beyond my grasp! But it adds to my conviction that, the simpler (and less realistic) you make the models, the more of a mystery sex is.

But that´s the thing. The simple model is very realistic (because so far it hasn´t made false predictions). It´s just not everything. It´s a building block for more complicated models.

susu.exp wrote:

Allan Miller wrote:Only if the net result of that sum over many generations is negative would we find recombination selected against. But genes for recombination find themselves attached to winners, because many of the genes they bring in have already proved their worth, by being selected in the first place.

Just because there´s a cost, that doesn´t mean there isn´t also a benefit. Size growth in metazoans comes at an energetic cost. Still there are big metazoans, because size does also confer benefits.

Yes, but recombination load is not presented in terms of a net effect, but simply an additional burden that the sexual population must bear. You don't get one bit of recombination without getting all the rest, whereas recombination load tends to be presented specifically as the breakup of adaptive combinations (magically created out of thin air?) .

We should also bear in mind that sex/no-sex is a species boundary. To take your example of size: the size of a given metazoan species is tuned by cost/benefit considerations favouring certain genes over others. The size of a different metazoan species is also tuned by its own, possibly different, cost/benefit considerations, in both cases preventing 'too-large' and 'too-small' genes from proliferating. The population weighs the options, in a sense. But the cost/benefit of being species A's size cannot be addressed by reference to anything species B's gene pool has on offer. Which is how sex's costs are often treated, without realising - "the cost to individuals of species A of not doing what species B can do". That is an ecological matter, as Father Jack would say. You either stay in the sexual 'gene-of-the-month club', and pay the fees, or you found your own club outside. You can't reduce the 'fees' from within, because there is no opportunity for a gene to do so.

susu.exp wrote:

Allan Miller wrote:Putting it firmly beyond my grasp! But it adds to my conviction that, the simpler (and less realistic) you make the models, the more of a mystery sex is.

But that´s the thing. The simple model is very realistic (because so far it hasn´t made false predictions).

It makes the prediction that sex should be a minority interest because it is twice as costly as asexuality, for both organism and gene. I'd say that's wide of the mark. It is used to make the prediction that there has to be a hidden twofold benefit that will explain it all away. We are still waiting.

Allan Miller wrote:It makes the prediction that sex should be a minority interest because it is twice as costly as asexuality, for both organism and gene. I'd say that's wide of the mark. It is used to make the prediction that there has to be a hidden twofold benefit that will explain it all away. We are still waiting.

A quick note here: How do you derive that from either the Moran or the Fisher-Wright model? Both require as input the population size and the selection coefficient s. The prediction that sex is twice as costly as asexuality does not follow from that (after all it is a hypothesis about the value s takes for particular alleles). You seem to be so engulfed in the whole sex thing (something I´m not well read up in and which isn´t a research interest of mine, so I can´t comment that much) that you are willing to throw out the child with the bathwater. Neither the FW nor the Moran model tells you aynthing about the cost of any allele. They do tell you how allele frequencies are going to change if an allele has a particular selection coefficient, i.e. if the mean fitness of carriers differs from that of non-carriers. But in itself they don´t allow the calculation of fitness values.

susu.exp:

throw out the child with the bathwater]

That was kind of a smooth bit of non-sexism, for one for whom

whole sex thing

is not that much of a research interest...

susu.exp wrote:

Allan Miller wrote:It makes the prediction that sex should be a minority interest because it is twice as costly as asexuality, for both organism and gene. I'd say that's wide of the mark. It is used to make the prediction that there has to be a hidden twofold benefit that will explain it all away. We are still waiting.

A quick note here: How do you derive that from either the Moran or the Fisher-Wright model? Both require as input the population size and the selection coefficient s. The prediction that sex is twice as costly as asexuality does not follow from that (after all it is a hypothesis about the value s takes for particular alleles). You seem to be so engulfed in the whole sex thing (something I´m not well read up in and which isn´t a research interest of mine, so I can´t comment that much) that you are willing to throw out the child with the bathwater. Neither the FW nor the Moran model tells you aynthing about the cost of any allele. They do tell you how allele frequencies are going to change if an allele has a particular selection coefficient, i.e. if the mean fitness of carriers differs from that of non-carriers. But in itself they don´t allow the calculation of fitness values.

Yes, I am a bit sex-obsessed, you are right. It is one issue where I find myself at odds with conventional wisdom, and I frequently attempt to stir up a bit of debate on the topic for that very reason. I don't derive those comments from the models; I am reporting that many do. Sex is commonly regarded as a straight halving of fitness for the sexual female, pure and simple. Fitness is typically defined as the per capita lifetime contribution of individuals of a given genotype to the population after (x) generations. Generally, x is 1, but for gendered sex, we choose 2 (since after 1, the offspring count is the same - it is the non-production of males that renders asexuality a way of producing more grandchildren, which can be mathematically equated to a single-generation measure). This goes right back to Fisher.

This is without even looking at anything else - it purely falls out mathematically from the use of that kind of model. This is the "Twofold Cost of Sex" in a nutshell. Classically, in order to survive, there is expected to be something about sex that causes s values to average out in a way that redresses the balance in sex's favour. That would certainly be the situation if an allele within a sexual population doubled fitness - its opponent would rapidly expire, because the two alleles are competing in the same closed system.

But my argument is that this is a misapplication of the model. If one is determined to reduce all of evolution to this 'container-based' comparison of alleles via averages, then sex will forever be a mystery, because when you perform, mathematically or computationally, an analysis that shakes all 'alleles' up in the one container, you return the twofold cost, and need a twofold benefit. This is why I keep banging on about ecology. Models frequently ignore ecology, heterogeneity and mechanistic effects of alleles upon the population's behaviour. You posit a panmictic group and look at the way in which alleles in this well-shaken group progress on the basis of their relative average effect on fitness. But if every instance of a particular mutation involves leaving this well-shaken group, you don't get an accurate picture by pretending that it is still part of it.

Part of the mixing that enables population-level mathematical analysis at all is sex/recombination itself. If there were no such thing as sex, we would have collections of haploid cells with no relation beyond the fact that each is surrounded by the others. The competition between these cell types is, to some degree, amenable to modelling as alleles with selection coefficients, but how is a particular 'population' of these bounded and composed? There is no motor mixing the cells and ensuring that generalised probabilities are shared equally among all the members of this population. I see haploid population dynamics as a bit of retrospective fiddling - the maths, from Hardy-Weinberg onwards, was devised for ideal panmictic populations of sexual diploid organisms, and departures therefrom. It turns out that it works OK for asexual collections too up to a point - provided that something other than sex does the mixing.

Essentially, a sexual diploid population is a population of paired haploids, the cyclic re-pairing of which is part of the dynamic. If you could follow haploid alleles on a 'Marauder's Map', or one of those air-traffic control displays, they would wander about in double harness, but every spring, it would look as if someone had flicked a switch on an electro-magnet - suddenly, the pairs reveal their 'true' haploid natures and part before coming together in new pairings. From the perspective of the haploid genomes, this process is essentially free of intrinsic cost - and the haploid genome is the basic unit of sex, not the diploid.

We are not so far from the OP here either - the genome assembled in each new haploid is stochastic, as is subsequent pairing, and hence diploid genotype reconstitution. In fact the initial haploid pairing itself is likely a single, chance event, much as mitochondrial endosymbiosis was before it. It founded a dynasty of sexual diploids.

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