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Segregation Maintains Genetic Variance
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Siblings vary One of the most curious things to people is that siblings can vary a great deal in their traits. Sometimes, this is not simply due to environment. Height is a predominantly genetic characteristic in terms of its heritability within the population, but the correlation between siblings is only 0.50 in terms of the trait value. The standard deviation in IQ among siblings is only a bit less than the standard deviation among the general population.

And yet with a quantitative trait where most of the variation is due to genes of small effect this seems peculiar. Though genetics is not “blending,” it seems that inheritance should be closer to blending when it comes to thousands of genes combining to account for the variation on one trait.

Andrew Oh-Wilke brings up the objection below:

Because if there are really 5,000-10,000 loci, the law of averages is going to kick in with a vengeance and similarly regression to the mean should be huge, but while IQ breeds fairly true, IQ variation between fairly closely related individuals is often quite significant. If children inherit randomly from both parents and there are really 5,000-10,000 loci that matter, all of which have very small effects, IQ differences between siblings ought to be really, really slight and rare, because the 5,000-10,000 random trials for the large number of low effect SNPs should average out between full siblings almost completely. But, while full siblings are definitely correlated, there are routinely meaningful magnitude sibling IQ differences. When no one inherited factor has an impact of more than say 0.02%, that shouldn’t happen.

Siblings vary

Siblings vary

The short answer is that segregation maintains variance. I allude to this in my Slate piece on grandparents. Siblings may be expected to be 50% identical in terms of their genetic state due to parental contribution, but in reality there is variation around this value. I have two siblings who are 41% identical. The standard deviation around 50% is about 3%.

For the deeper and more explicit formalism in relation to quantitative traits and polygenetic inheritance, you could get a copy of Introduction to Quantitative Genetics (I do recommend this of course). But Alan Rogers published a paper from 1983 which touches upon most of the major issues in a clear manner, Assortative mating and the segregation variance:

Feldman and Cavalli-Sforza (Theoret. Pop. Biol. (1979), 15, 276-307; (1981), 19, 370-377) have emphasized the role of the segregation variance in models of assortative mating for continuous characters. This note examines its behavior in the context of a general additive model. Using known results concerning the effects of assortative mating and selection on genic variance and correlations among uniting gametes it is shown that the effects of these processes on segregation variance will be small if the effective number of loci is large. Thus models in which the segregation variance remains constant are approximate descriptions of the behavior of characters determined by many loci.

Basically he’s saying that contra what some had modeled, segregation variance is rather constant across generations if the genetic variance is on a highly polygenic trait. Naturally this means polygenic traits exhibit segregation variance.

Screenshot 2016-05-15 10.39.25 Rogers shows through some algebra that the segregation variance is a function of the additive genetic variance (the first term after 1/2), and, (1 – f). Therefore if f ~0, the segregation variance is about the same as the additive genetic variance, which to me aligns intuitively with why there is roughly the same standard deviation across groups of siblings and the general population in IQ (though the former is smaller than the latter).

Screenshot 2016-05-15 10.45.41 Rogers shows that f is a function of variance at the locus (weighted across all the loci) and f i, which is the correlation between uniting gametes. If the correlation between gametes is very high (in the context of this paper he is focused on phenotypes and assortative mating), then variance will naturally be low, as there is not going to be genetic variation at that locus in that individual. Basically, f measures deviation from Hardy-Weinberg equilibrium. In a random mating population then f is small, so the segregation variance and additive genetic variance will be of similar magnitude.

 
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  1. Sean says:

    If the correlation between gametes is very high (in the context of this paper he is focused on phenotypes and assortative mating), then variance will naturally be low, as there is not going to be genetic variation at that locus in that individual.

    Isn’t the myopia gene supposed to have the biggest known effect on IQ. Negative assortative mating seems plausible http://www.ncbi.nlm.nih.gov/pubmed/12629855

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    • Replies: @Razib Khan
    please don't cite papers from 2002 in this field. it makes you look like an ignorant dumbass. or, step away from PUBMED if you don't know how to filter its usage.
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  2. djw says:

    I am quite lost in the terminology here, but I wonder if the following colloquial explanation is accurate.

    When a gamete is formed you do not “flip a coin” for every single locus. Rather, several long stretches of a parents chromosome are copied. So, when comparing siblings on a trait you do not really compare the result of 10,000 coin flips, you compare instead the result of fewer (not sure how many, maybe on order of 100?) that occur because the siblings may inherit different blocks from their parents.

    Is the math that you quoted related to this? Or am I completely missing something?

    Read More
    • Replies: @Razib Khan
    basically right direction.
    , @RCB
    It works even for 10,000 coin flips. See the math I did below, which assumes independent segregation of alleles at all loci.
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  3. Twinkie says:

    Siblings vary

    Did you see “Martha Marcy May Marlene” (https://youtu.be/0_k3wCsOgqk)? Wow, Elizabeth Olsen, whose image you insert in your post, can act… unlike her siblings!

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  4. aeolius says:

    Rahib said:
    “And yet with a quantitative trait where most of the variation is due to genes of small effect this seems peculiar. Though genetics is not “blending,” it seems that inheritance should be closer to blending when it comes to thousands of genes combining to account for the variation on one trait.’
    I believe that this is error.
    IQ is not a trait, like say blue eyes. In solving a problem,where there are so many genes involved, one needs to wonder if there are several successful combinations If you examine in depth the way a problem is solved by several individuals, you get a variety of processes that are successful. Assuming a relationship between process and some combination of genes, then perhaps we have a number of successful combinations. An analog of convergent evolution.
    Also when one is dealing with cognitive IQ (versus say Social IQ or Body IQ) then a theory of cognition seems to be necessary. Is there yet an accepted “Standard Model” of Cognition?
    I am certainly no expert in quantum physics. But there, there is not a single answer but all possible answers existing at once. I have a hunch that we will need that kind of theorizing to understand cognition and then to rank cognitive successes.

    Read More
    • Replies: @Razib Khan
    i have no fucking idea what you are trying to say.
    , @Karl Zimmerman
    The idea that genes controlling for intelligence in humans are massively redundant is quite intriguing. If your father has gene X and your mother gene Y, both of which control for intelligence, it may be that they functionally cause an IQ boost through the same pathway, and thus getting copies of both isn't advantageous.

    The problem is, I don't think you can make a claim that human evolution has worked this way. I mean yes, we have examples like multiple genetic pathways for lactase persistance. But these are historically recent, along with being controlled by single mutations. For the genetic architecture of intelligence to be massively redundant, you'd need to presume the reproductive isolation of lots of human populations, most of which then underwent selection for higher IQ. New alleles would have to develop quickly enough that simple introgression from neighboring populations wouldn't become the favored method of enhancing the trait. Given how much admixture there has been through various periods of human history, this seems rather unlikely. More limited versions of this (like different genes controlling higher IQ in Eastern Asia and Europe, but those genes for the most part expressing through parallel pathways) do seem plausible however.
    ReplyAgree/Disagree/Etc. More... This Commenter This Thread Hide Thread Display All Comments
  5. @Sean

    If the correlation between gametes is very high (in the context of this paper he is focused on phenotypes and assortative mating), then variance will naturally be low, as there is not going to be genetic variation at that locus in that individual.
     
    Isn't the myopia gene supposed to have the biggest known effect on IQ. Negative assortative mating seems plausible http://www.ncbi.nlm.nih.gov/pubmed/12629855

    please don’t cite papers from 2002 in this field. it makes you look like an ignorant dumbass. or, step away from PUBMED if you don’t know how to filter its usage.

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  6. @aeolius
    Rahib said:
    "And yet with a quantitative trait where most of the variation is due to genes of small effect this seems peculiar. Though genetics is not “blending,” it seems that inheritance should be closer to blending when it comes to thousands of genes combining to account for the variation on one trait.'
    I believe that this is error.
    IQ is not a trait, like say blue eyes. In solving a problem,where there are so many genes involved, one needs to wonder if there are several successful combinations If you examine in depth the way a problem is solved by several individuals, you get a variety of processes that are successful. Assuming a relationship between process and some combination of genes, then perhaps we have a number of successful combinations. An analog of convergent evolution.
    Also when one is dealing with cognitive IQ (versus say Social IQ or Body IQ) then a theory of cognition seems to be necessary. Is there yet an accepted "Standard Model" of Cognition?
    I am certainly no expert in quantum physics. But there, there is not a single answer but all possible answers existing at once. I have a hunch that we will need that kind of theorizing to understand cognition and then to rank cognitive successes.

    i have no fucking idea what you are trying to say.

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  7. Razib,

    As you know well, the motivational belief of the social conservative faction is this country is the notion that society is somehow decaying or declining. Yet, objective metrics of such decay – crime, teen pregnancy, drug abuse – have either improved dramatically or at least remained flat over the past 20-30 years. This suggests that, far from decaying, society is actually improving.

    Some years ago you did a series titled “previous generations were more depraved”. Perhaps its time for a encore.

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  8. @djw
    I am quite lost in the terminology here, but I wonder if the following colloquial explanation is accurate.

    When a gamete is formed you do not "flip a coin" for every single locus. Rather, several long stretches of a parents chromosome are copied. So, when comparing siblings on a trait you do not really compare the result of 10,000 coin flips, you compare instead the result of fewer (not sure how many, maybe on order of 100?) that occur because the siblings may inherit different blocks from their parents.

    Is the math that you quoted related to this? Or am I completely missing something?

    basically right direction.

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  9. RCB says:

    Basic additive model:

    Your genetic (breeding) value is the sum of the values from the gametes that your father and mother produce. Call these random variables X_f and X_m, so your phenotype X = X_f and X_m. In particular, assume that your phenotype is alpha * Sum_i n_i, where n_i is the number of “good” alleles (that add to the breeding value) you have at that locus. Alpha is just the effect of a single allele; it’s the same across all loci, here.

    The variance in your father’s gametes can only be due to the loci at which he is heterozygous. Each such locus will yield one allele during meiosis; this is a bernoulli trial with p=0.5. So

    X_f = C_f + alpha * Sum_i B_i

    where C_f is the constant value he must give you based on the loci at which he is homozygous, and B_i is a Bernoulli random variable. The variance is (assuming independent segregation… no linkage)

    var(X_f) = alpha^2 * N_Hf * 1/4

    Where N_Hf is the number of loci at which the father is heterozygous and 1/4 is the variance of a bernoulli trial with p=0.5. Then, including the mother, we have

    var(X) = var(X_f + X_m) = alpha^2 * (N_Hf + N_Hm) * 1/4

    The expected number of loci at which an individual is heterozygous is actually 2*Sum_i p_i*(1-p_i), where p_i is allele frequency at locus i. So on average this quantity is going to be

    var(X) = 1/2 * alpha^2 * 2 * Sum_i p_i(1-p_i) = 1/2 * V_A

    I.e. the latter part is the total (additive) variance in the population. I assumed many loci and random mating here.

    This is true for arbitrarily large N. So clearly the “law of large numbers” argument that siblings can’t vary genetically must be wrong. Segregation variance scales with total population variance.

    Read More
    • Replies: @RCB
    Put another way:
    As the number of loci grows, the expected number of loci for which parents are heterozygous also grows. This means that both the total additive variance in the population *and* the within-family segregation variance scale linearly with number of loci. Hence their ratio remains the same.
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  10. RCB says:
    @RCB
    Basic additive model:

    Your genetic (breeding) value is the sum of the values from the gametes that your father and mother produce. Call these random variables X_f and X_m, so your phenotype X = X_f and X_m. In particular, assume that your phenotype is alpha * Sum_i n_i, where n_i is the number of "good" alleles (that add to the breeding value) you have at that locus. Alpha is just the effect of a single allele; it's the same across all loci, here.

    The variance in your father's gametes can only be due to the loci at which he is heterozygous. Each such locus will yield one allele during meiosis; this is a bernoulli trial with p=0.5. So

    X_f = C_f + alpha * Sum_i B_i

    where C_f is the constant value he must give you based on the loci at which he is homozygous, and B_i is a Bernoulli random variable. The variance is (assuming independent segregation... no linkage)

    var(X_f) = alpha^2 * N_Hf * 1/4

    Where N_Hf is the number of loci at which the father is heterozygous and 1/4 is the variance of a bernoulli trial with p=0.5. Then, including the mother, we have

    var(X) = var(X_f + X_m) = alpha^2 * (N_Hf + N_Hm) * 1/4

    The expected number of loci at which an individual is heterozygous is actually 2*Sum_i p_i*(1-p_i), where p_i is allele frequency at locus i. So on average this quantity is going to be

    var(X) = 1/2 * alpha^2 * 2 * Sum_i p_i(1-p_i) = 1/2 * V_A

    I.e. the latter part is the total (additive) variance in the population. I assumed many loci and random mating here.

    This is true for arbitrarily large N. So clearly the "law of large numbers" argument that siblings can't vary genetically must be wrong. Segregation variance scales with total population variance.

    Put another way:
    As the number of loci grows, the expected number of loci for which parents are heterozygous also grows. This means that both the total additive variance in the population *and* the within-family segregation variance scale linearly with number of loci. Hence their ratio remains the same.

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  11. RCB says:
    @djw
    I am quite lost in the terminology here, but I wonder if the following colloquial explanation is accurate.

    When a gamete is formed you do not "flip a coin" for every single locus. Rather, several long stretches of a parents chromosome are copied. So, when comparing siblings on a trait you do not really compare the result of 10,000 coin flips, you compare instead the result of fewer (not sure how many, maybe on order of 100?) that occur because the siblings may inherit different blocks from their parents.

    Is the math that you quoted related to this? Or am I completely missing something?

    It works even for 10,000 coin flips. See the math I did below, which assumes independent segregation of alleles at all loci.

    Read More
    • Replies: @djw
    Thanks, that made sense. Let me see if I can successfully paraphrase it once again:

    For large N, the heterozygosity of an individual will be very close to that of the population at large.

    The variance of the population on a trait is determined by the heterozygosity of the population on that trait.

    Since parents have roughly the same heterozygosity as the population at large, there children will be drawn from a set of alleles with the same variance as the population at large, and will therefor have the same variance on that trait as the general population.

    It seems like this should increase, not decrease, as N gets larger.

    Apologies if this is too spammy.
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  12. djw says:
    @RCB
    It works even for 10,000 coin flips. See the math I did below, which assumes independent segregation of alleles at all loci.

    Thanks, that made sense. Let me see if I can successfully paraphrase it once again:

    For large N, the heterozygosity of an individual will be very close to that of the population at large.

    The variance of the population on a trait is determined by the heterozygosity of the population on that trait.

    Since parents have roughly the same heterozygosity as the population at large, there children will be drawn from a set of alleles with the same variance as the population at large, and will therefor have the same variance on that trait as the general population.

    It seems like this should increase, not decrease, as N gets larger.

    Apologies if this is too spammy.

    Read More
    • Replies: @RCB
    I think that's all correct, except that *within* a family the offspring's variance will only be 1/2 of the total variance, not equal.
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  13. RCB says:
    @djw
    Thanks, that made sense. Let me see if I can successfully paraphrase it once again:

    For large N, the heterozygosity of an individual will be very close to that of the population at large.

    The variance of the population on a trait is determined by the heterozygosity of the population on that trait.

    Since parents have roughly the same heterozygosity as the population at large, there children will be drawn from a set of alleles with the same variance as the population at large, and will therefor have the same variance on that trait as the general population.

    It seems like this should increase, not decrease, as N gets larger.

    Apologies if this is too spammy.

    I think that’s all correct, except that *within* a family the offspring’s variance will only be 1/2 of the total variance, not equal.

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  14. @aeolius
    Rahib said:
    "And yet with a quantitative trait where most of the variation is due to genes of small effect this seems peculiar. Though genetics is not “blending,” it seems that inheritance should be closer to blending when it comes to thousands of genes combining to account for the variation on one trait.'
    I believe that this is error.
    IQ is not a trait, like say blue eyes. In solving a problem,where there are so many genes involved, one needs to wonder if there are several successful combinations If you examine in depth the way a problem is solved by several individuals, you get a variety of processes that are successful. Assuming a relationship between process and some combination of genes, then perhaps we have a number of successful combinations. An analog of convergent evolution.
    Also when one is dealing with cognitive IQ (versus say Social IQ or Body IQ) then a theory of cognition seems to be necessary. Is there yet an accepted "Standard Model" of Cognition?
    I am certainly no expert in quantum physics. But there, there is not a single answer but all possible answers existing at once. I have a hunch that we will need that kind of theorizing to understand cognition and then to rank cognitive successes.

    The idea that genes controlling for intelligence in humans are massively redundant is quite intriguing. If your father has gene X and your mother gene Y, both of which control for intelligence, it may be that they functionally cause an IQ boost through the same pathway, and thus getting copies of both isn’t advantageous.

    The problem is, I don’t think you can make a claim that human evolution has worked this way. I mean yes, we have examples like multiple genetic pathways for lactase persistance. But these are historically recent, along with being controlled by single mutations. For the genetic architecture of intelligence to be massively redundant, you’d need to presume the reproductive isolation of lots of human populations, most of which then underwent selection for higher IQ. New alleles would have to develop quickly enough that simple introgression from neighboring populations wouldn’t become the favored method of enhancing the trait. Given how much admixture there has been through various periods of human history, this seems rather unlikely. More limited versions of this (like different genes controlling higher IQ in Eastern Asia and Europe, but those genes for the most part expressing through parallel pathways) do seem plausible however.

    Read More
    • Replies: @Razib Khan
    If your father has gene X and your mother gene Y, both of which control for intelligence, it may be that they functionally cause an IQ boost through the same pathway, and thus getting copies of both isn’t advantageous.

    an additive model for intelligence works quite well. so there is no evidence of the model outlined above that you are responding to. (you made more sense of it than i did)
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  15. @Karl Zimmerman
    The idea that genes controlling for intelligence in humans are massively redundant is quite intriguing. If your father has gene X and your mother gene Y, both of which control for intelligence, it may be that they functionally cause an IQ boost through the same pathway, and thus getting copies of both isn't advantageous.

    The problem is, I don't think you can make a claim that human evolution has worked this way. I mean yes, we have examples like multiple genetic pathways for lactase persistance. But these are historically recent, along with being controlled by single mutations. For the genetic architecture of intelligence to be massively redundant, you'd need to presume the reproductive isolation of lots of human populations, most of which then underwent selection for higher IQ. New alleles would have to develop quickly enough that simple introgression from neighboring populations wouldn't become the favored method of enhancing the trait. Given how much admixture there has been through various periods of human history, this seems rather unlikely. More limited versions of this (like different genes controlling higher IQ in Eastern Asia and Europe, but those genes for the most part expressing through parallel pathways) do seem plausible however.

    If your father has gene X and your mother gene Y, both of which control for intelligence, it may be that they functionally cause an IQ boost through the same pathway, and thus getting copies of both isn’t advantageous.

    an additive model for intelligence works quite well. so there is no evidence of the model outlined above that you are responding to. (you made more sense of it than i did)

    Read More
    • Replies: @Carl Churchill
    Only in theory, however. I don't think we have found common variants for cognitive ability which have been shown to be perfectly additive (zero interaction terms), or more importantly, additive biochemically. I think some people, like Kevin Mitchell, are right when they criticize assumptions of additive model.
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  16. AG says:

    Even for single gene location, you have potentially 4 alleles to draw from and end up with 4 possible combinations. There are numerous more alleles for cognition ability. The lottery odds are numerous.

    when a trait involving numerous alleles, a single pair of parents can produce numerous possibility or odds.

    In domesticated animals, breeding is really reduced to genetic variance to increase the odd of specific trait.

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  17. ohwilleke says: • Website

    Thanks for the analysis in the post.

    I’ve read the paper cited in the OP a few times, and it basically addresses a different problem than the one that I was suggesting although it does go to regression to the mean a little.

    The paper examines the soundness of the assumption that in a continuously variable trait like IQ or height, where the genetic effects are assumed to be largely additive, the variance will be the same at almost all values of the trait. Hence, the variance of IQ at 100 and IQ at 135 will be about the same, and the variance of height at 5’7″ and at 6’3″ will be about the same. It also concludes that the physical location of one loci relative to another on the genome is largely irrelevant to this effect. But, the paper does not itself address the relationship between the number of loci N and the expected variance.

    But, RCB in the comments did capture the reasons that my intuition was wrong, so its all good.

    RCB also clarified how variance could be high within the whole population which seemingly faces the same law of large numbers issue. The law of averages is applicable only when every Bernouli trial has the same probability. But, at the population level, the probability associated with each, say IQ enhancing configuration at a particular loci will be different (and in the limit of larger N for loci, the mix of probabilities in an individual will mirror the mix of probabilities for the population at large), and the law of averages does not hold when the probabilities associated with each trial range roughly randomly from 0 to 1 on a trial by trial basis (as it roughly is in the real world for a complex trait).

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    • Replies: @Razib Khan
    But, the paper does not itself address the relationship between the number of loci N and the expected variance.

    it does, but i didn't want to put up too many equations. i should have just uploaded the paper....
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  18. @Razib Khan
    If your father has gene X and your mother gene Y, both of which control for intelligence, it may be that they functionally cause an IQ boost through the same pathway, and thus getting copies of both isn’t advantageous.

    an additive model for intelligence works quite well. so there is no evidence of the model outlined above that you are responding to. (you made more sense of it than i did)

    Only in theory, however. I don’t think we have found common variants for cognitive ability which have been shown to be perfectly additive (zero interaction terms), or more importantly, additive biochemically. I think some people, like Kevin Mitchell, are right when they criticize assumptions of additive model.

    Read More
    • Replies: @Razib Khan
    I don’t think we have found common variants for cognitive ability which have been shown to be perfectly additive (zero interaction terms), or more importantly, additive biochemically.

    why is it more important biochemically? i'm assuming you actually understand that the statistical genetic and molecular genetic frameworks are orthogonal; usually it doesn't make sense to talk about 'additivity' in a biochemical sense. there are some dosage affects, especially cnvs, but really in molecular genetics everything is in a pathway.

    i have no idea what you are getting at, so either say nothing or say more.


    . I think some people, like Kevin Mitchell, are right when they criticize assumptions of additive model.

    kevin mitchell doesn't criticize the additive model, he criticizes the common variants of small effects model. his model is just as additive, it just relies on many alleles of very lower frequency and larger effect. that is why quantitative genetic models of intelligence always yield a mostly additive genetic variance; that's not conditional on a particular architecture.
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  19. @Carl Churchill
    Only in theory, however. I don't think we have found common variants for cognitive ability which have been shown to be perfectly additive (zero interaction terms), or more importantly, additive biochemically. I think some people, like Kevin Mitchell, are right when they criticize assumptions of additive model.

    I don’t think we have found common variants for cognitive ability which have been shown to be perfectly additive (zero interaction terms), or more importantly, additive biochemically.

    why is it more important biochemically? i’m assuming you actually understand that the statistical genetic and molecular genetic frameworks are orthogonal; usually it doesn’t make sense to talk about ‘additivity’ in a biochemical sense. there are some dosage affects, especially cnvs, but really in molecular genetics everything is in a pathway.

    i have no idea what you are getting at, so either say nothing or say more.

    . I think some people, like Kevin Mitchell, are right when they criticize assumptions of additive model.

    kevin mitchell doesn’t criticize the additive model, he criticizes the common variants of small effects model. his model is just as additive, it just relies on many alleles of very lower frequency and larger effect. that is why quantitative genetic models of intelligence always yield a mostly additive genetic variance; that’s not conditional on a particular architecture.

    Read More
    • Replies: @Carl Churchill
    And why not consider additivity in the molecular genetic sense? It's all well and good to talk about additive models in quantitative genetics sense but on the molecular genetic level there's no evidence for such a thing when it comes to complex cognitive traits.

    I'm not in disagreement with the common variant additive model for IQ and such personally, but so far not really found any additive independent effect common variant. So maybe rare variant hypothesis is true
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  20. @ohwilleke
    Thanks for the analysis in the post.

    I've read the paper cited in the OP a few times, and it basically addresses a different problem than the one that I was suggesting although it does go to regression to the mean a little.

    The paper examines the soundness of the assumption that in a continuously variable trait like IQ or height, where the genetic effects are assumed to be largely additive, the variance will be the same at almost all values of the trait. Hence, the variance of IQ at 100 and IQ at 135 will be about the same, and the variance of height at 5'7" and at 6'3" will be about the same. It also concludes that the physical location of one loci relative to another on the genome is largely irrelevant to this effect. But, the paper does not itself address the relationship between the number of loci N and the expected variance.

    But, RCB in the comments did capture the reasons that my intuition was wrong, so its all good.

    RCB also clarified how variance could be high within the whole population which seemingly faces the same law of large numbers issue. The law of averages is applicable only when every Bernouli trial has the same probability. But, at the population level, the probability associated with each, say IQ enhancing configuration at a particular loci will be different (and in the limit of larger N for loci, the mix of probabilities in an individual will mirror the mix of probabilities for the population at large), and the law of averages does not hold when the probabilities associated with each trial range roughly randomly from 0 to 1 on a trial by trial basis (as it roughly is in the real world for a complex trait).

    But, the paper does not itself address the relationship between the number of loci N and the expected variance.

    it does, but i didn’t want to put up too many equations. i should have just uploaded the paper….

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  21. Surely the term intelligence is much more interesting and correct than ” iq ”. However, a lot of psychometricians decided to just throw away the theory of multiple (phenotypic combinations of) intelligence.

    The iq tests, always worth mentioning to the most unsuspecting, is a means to reach a purpose, understand, comprehend, reflect the complex and diverse phenomenon that we understand as intelligence. Iq is not an end. It is useful but its validity is limited, and I think most psychometricians know that, at least in its intimacy.

    Understanding the genetics of intelligence, you must first think of a number of ad hoc and highly influential factors. What kind of intelligence that is being emphasized *

    We are dealing with a pollution of the complex factors, we need to organize them and put on the head that intelligence is like a tree, has a main trunk, but many branches of specialization.

    Cognitive tests analyze our decontextualized cognitive abilities. That is, in a culturally neutral scenario, we analyze the reasoning of people to answer (predominant) neutral questions. Some might think it in ” pure reasoning ‘, but because it is acultural or decontextualized, does not mean that will be the most essential meaning of the word’ pure ‘. The being does not work without their scenario where he live.

    iq tests simulate a situation in which human beings are treated like machines that respond operationally to the world, without taking into account many factors that prevent this ‘operationally direct reciprocity’ be constant and ideally predictable.

    Cognitive tests simulate human behavior and has striked in a Considerable way, but why **

    Basically because there are different types of psycho-cognitive profiles, a qualitative and quantitative variety of types, some of which are more selected than others in the workplace.

    The most competent / efficient WORKER will be the most likely to score higher on cognitive tests. But that does not mean it will be the most intelligent, because the human being is not a being who are atomized and alienated to their cultural reality. And a significant incidence of people ” with ” high iq embrace silly ” ideologies ” and / or misunderstand the reality in which they live (in the non-human biological kingdom is fatal) shows that the relationship between intelligence and especially its more vitally decisive expressions and iq, will not be as extremely high as most psychometricians believe.

    We live in illusion where mistakes are always excusable and even embraced. This explain the main fails of human civilizations.

    We are seeing a large proportion of people ” from ” iq high committing significant errors of perception and logically subsequent action.

    Because most people in general are good at work, but not in pure reasoning or thinking directly directed to the lived reality.

    One of the main causes of the fall of civilization are not the partially anencephalic masses, but the cognitive elite, because most of those who belong to the elite, are nothing more than workers trying to think as thinkers who or that was born skilled for simple and critical thinking.

    The humanities are crowded by these hybrid types of workers trying to think as thinkers.

    Cognitive elites It has shown fatal weaknesses of perception or pure reasoning .

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    • Replies: @Razib Khan
    be more concise if you decide to ramble on about a bunch of incoherent and/or obvious things in the future. otherwise i won't publish it.
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  22. @Santoculto
    Surely the term intelligence is much more interesting and correct than '' iq ''. However, a lot of psychometricians decided to just throw away the theory of multiple (phenotypic combinations of) intelligence.

    The iq tests, always worth mentioning to the most unsuspecting, is a means to reach a purpose, understand, comprehend, reflect the complex and diverse phenomenon that we understand as intelligence. Iq is not an end. It is useful but its validity is limited, and I think most psychometricians know that, at least in its intimacy.

    Understanding the genetics of intelligence, you must first think of a number of ad hoc and highly influential factors. What kind of intelligence that is being emphasized *

    We are dealing with a pollution of the complex factors, we need to organize them and put on the head that intelligence is like a tree, has a main trunk, but many branches of specialization.

    Cognitive tests analyze our decontextualized cognitive abilities. That is, in a culturally neutral scenario, we analyze the reasoning of people to answer (predominant) neutral questions. Some might think it in '' pure reasoning ', but because it is acultural or decontextualized, does not mean that will be the most essential meaning of the word' pure '. The being does not work without their scenario where he live.

    iq tests simulate a situation in which human beings are treated like machines that respond operationally to the world, without taking into account many factors that prevent this 'operationally direct reciprocity' be constant and ideally predictable.

    Cognitive tests simulate human behavior and has striked in a Considerable way, but why **

    Basically because there are different types of psycho-cognitive profiles, a qualitative and quantitative variety of types, some of which are more selected than others in the workplace.

    The most competent / efficient WORKER will be the most likely to score higher on cognitive tests. But that does not mean it will be the most intelligent, because the human being is not a being who are atomized and alienated to their cultural reality. And a significant incidence of people '' with '' high iq embrace silly '' ideologies '' and / or misunderstand the reality in which they live (in the non-human biological kingdom is fatal) shows that the relationship between intelligence and especially its more vitally decisive expressions and iq, will not be as extremely high as most psychometricians believe.

    We live in illusion where mistakes are always excusable and even embraced. This explain the main fails of human civilizations.

    We are seeing a large proportion of people '' from '' iq high committing significant errors of perception and logically subsequent action.

    Because most people in general are good at work, but not in pure reasoning or thinking directly directed to the lived reality.

    One of the main causes of the fall of civilization are not the partially anencephalic masses, but the cognitive elite, because most of those who belong to the elite, are nothing more than workers trying to think as thinkers who or that was born skilled for simple and critical thinking.

    The humanities are crowded by these hybrid types of workers trying to think as thinkers.

    Cognitive elites It has shown fatal weaknesses of perception or pure reasoning .

    be more concise if you decide to ramble on about a bunch of incoherent and/or obvious things in the future. otherwise i won’t publish it.

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  23. [deleted]

    The vast majority of people, myself included, are illiterate with complex genetics (even with simple). You should teach what you know to us, but his blog has been done only for those who deal with it on a daily basis. Then it should be a separate blog or only for connoisseurs (atomized).

    [deleted]

    People who comment on your blog first, like to read it, I think, second, can not be experts on the subject, but that does not mean you should be arrogant and stupid with them.

    Are comments that add, not add, BUT sane people do not respond in this aggressive tone as you are doing. Do not discount their frustrations on other dumbass.

    Iq is to the man, that is not an end but a means, a channel, as prophesied the ‘philosopher’ Nietzche. Where is the obvious or incoherence here **
    [deleted]

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  24. 1) if you have something simple to say, say it simply. e.g., “some psychometricians believe in multiple intelligences.” don’t go on for paragraphs.

    2) if you don’t know much about something, do not comment on it.

    3) this is not a SAFE SPACE.

    it’s really fucking hilarious when the sort of people who enjoy reading blogs that will take on taboos are shocked and offended when you tell them to shut up when they talk about what they don’t know about. sorry if i triggered you, but my job isn’t to validate your own identity as a smart person. smartness is made, not identified, so read some of the books i recommend. hartl & clark. if too expensive, read graham coop’s free popgen notes or felsenstein’s free textbook online. talk about at length on what you know about. ask short quick concise questions on what you don’t know about it. pretty simple.

    no more comments on this thread about this. there are plenty of blogs on this website with liberal comment policies. go comment on them.

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  25. Lucho says:

    So, Am I understanding the formula correctly?

    1) the larger the population, the more the variance, and so more possible (probable?) variation between siblings compared to smaller populations.

    2) Taking this further, if hypothetical Jack from anywhere, USA (american , european ancestry) had children with hypothetical Keiko from Japan, their offspring would show more variation than if Jack had children with his high school sweetheart. Correct?
    (just a hypothetical example to illustrate the point)

    Or did I miss the point?

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    • Replies: @Razib Khan
    the larger the population, the more the variance, and so more possible (probable?) variation between siblings compared to smaller populations.


    no, not pop size such much as pop variation. the pop size though often correlates with variation (positively).

    2) Taking this further, if hypothetical Jack from anywhere, USA (american , european ancestry) had children with hypothetical Keiko from Japan, their offspring would show more variation than if Jack had children with his high school sweetheart. Correct?

    only because of the more genetic variation. in practice this does not apply in all cases as genes don't always vary in direction proportion to genome-wide variation. this is more apposite when you have populations which are fixed for alternative alleles, so you see combinations in offspring you'd never see in parents (this is not usually the case for highly polygenic traits....)
    , @RCB
    1)
    My formula wasn't very clear. "N" was the number of loci that additively affect the trait in question. The variance depends on N but also on alpha, the effect of those loci on the trait (which needn't and in general shouldn't be fixed across loci, but I simplified). So in general there needn't be a relationship between N and trait variance.

    On the other hand, larger N ought to imply a more normally-distributed phenotype, unless the effects happen to be dominated by just a few of those many alleles.

    2)
    The offspring's trait variance is the sum of the variances of the parent's gametic values, which depends on how heterozygous they are at the alleles that affect the trait. If lots of loci affect a trait, then most people will (by law of large numbers) have the same amount of heterozygosity for a trait - i.e. the average amount (inbreds will consistently have less). This means that the expected variance among the children of an American - Japan pair is approximately 1/4(V_Amer + V_Japa). If the Japanese happen to have greater variation in the trait than Americans, then you'd see more.

    Note that this is true even if Japanese and Americans were fixed for opposite alleles. Then V=0 for both, and their kids will show no genetic variation: all will be heterozygous at every relevant locus.

    But watch out with *their* kids start reproducing. Those heterozygotes will produce a lot of variation during meiosis. In other words, Jack and Keiko's grandkids would show a lot of variation, in that case. Same story if Americans and Japanese are also segregating at different loci.
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  26. @Lucho
    So, Am I understanding the formula correctly?

    1) the larger the population, the more the variance, and so more possible (probable?) variation between siblings compared to smaller populations.

    2) Taking this further, if hypothetical Jack from anywhere, USA (american , european ancestry) had children with hypothetical Keiko from Japan, their offspring would show more variation than if Jack had children with his high school sweetheart. Correct?
    (just a hypothetical example to illustrate the point)

    Or did I miss the point?

    the larger the population, the more the variance, and so more possible (probable?) variation between siblings compared to smaller populations.

    no, not pop size such much as pop variation. the pop size though often correlates with variation (positively).

    2) Taking this further, if hypothetical Jack from anywhere, USA (american , european ancestry) had children with hypothetical Keiko from Japan, their offspring would show more variation than if Jack had children with his high school sweetheart. Correct?

    only because of the more genetic variation. in practice this does not apply in all cases as genes don’t always vary in direction proportion to genome-wide variation. this is more apposite when you have populations which are fixed for alternative alleles, so you see combinations in offspring you’d never see in parents (this is not usually the case for highly polygenic traits….)

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  27. RCB says:
    @Lucho
    So, Am I understanding the formula correctly?

    1) the larger the population, the more the variance, and so more possible (probable?) variation between siblings compared to smaller populations.

    2) Taking this further, if hypothetical Jack from anywhere, USA (american , european ancestry) had children with hypothetical Keiko from Japan, their offspring would show more variation than if Jack had children with his high school sweetheart. Correct?
    (just a hypothetical example to illustrate the point)

    Or did I miss the point?

    1)
    My formula wasn’t very clear. “N” was the number of loci that additively affect the trait in question. The variance depends on N but also on alpha, the effect of those loci on the trait (which needn’t and in general shouldn’t be fixed across loci, but I simplified). So in general there needn’t be a relationship between N and trait variance.

    On the other hand, larger N ought to imply a more normally-distributed phenotype, unless the effects happen to be dominated by just a few of those many alleles.

    2)
    The offspring’s trait variance is the sum of the variances of the parent’s gametic values, which depends on how heterozygous they are at the alleles that affect the trait. If lots of loci affect a trait, then most people will (by law of large numbers) have the same amount of heterozygosity for a trait – i.e. the average amount (inbreds will consistently have less). This means that the expected variance among the children of an American – Japan pair is approximately 1/4(V_Amer + V_Japa). If the Japanese happen to have greater variation in the trait than Americans, then you’d see more.

    Note that this is true even if Japanese and Americans were fixed for opposite alleles. Then V=0 for both, and their kids will show no genetic variation: all will be heterozygous at every relevant locus.

    But watch out with *their* kids start reproducing. Those heterozygotes will produce a lot of variation during meiosis. In other words, Jack and Keiko’s grandkids would show a lot of variation, in that case. Same story if Americans and Japanese are also segregating at different loci.

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  28. @Razib Khan
    I don’t think we have found common variants for cognitive ability which have been shown to be perfectly additive (zero interaction terms), or more importantly, additive biochemically.

    why is it more important biochemically? i'm assuming you actually understand that the statistical genetic and molecular genetic frameworks are orthogonal; usually it doesn't make sense to talk about 'additivity' in a biochemical sense. there are some dosage affects, especially cnvs, but really in molecular genetics everything is in a pathway.

    i have no idea what you are getting at, so either say nothing or say more.


    . I think some people, like Kevin Mitchell, are right when they criticize assumptions of additive model.

    kevin mitchell doesn't criticize the additive model, he criticizes the common variants of small effects model. his model is just as additive, it just relies on many alleles of very lower frequency and larger effect. that is why quantitative genetic models of intelligence always yield a mostly additive genetic variance; that's not conditional on a particular architecture.

    And why not consider additivity in the molecular genetic sense? It’s all well and good to talk about additive models in quantitative genetics sense but on the molecular genetic level there’s no evidence for such a thing when it comes to complex cognitive traits.

    I’m not in disagreement with the common variant additive model for IQ and such personally, but so far not really found any additive independent effect common variant. So maybe rare variant hypothesis is true

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    • Replies: @Razib Khan
    And why not consider additivity in the molecular genetic sense?

    i don't really have an idea what you are talking about here. molecular genetics deploys some of the same terminology as statistical genetics, but in different ways (e.g., epistasis). but additivity really doesn't transpose very well at all, unless you mean direct dosage dependence based on allele state counts. anyway, you can say more. i don't know what you're really getting at.
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  29. @Carl Churchill
    And why not consider additivity in the molecular genetic sense? It's all well and good to talk about additive models in quantitative genetics sense but on the molecular genetic level there's no evidence for such a thing when it comes to complex cognitive traits.

    I'm not in disagreement with the common variant additive model for IQ and such personally, but so far not really found any additive independent effect common variant. So maybe rare variant hypothesis is true

    And why not consider additivity in the molecular genetic sense?

    i don’t really have an idea what you are talking about here. molecular genetics deploys some of the same terminology as statistical genetics, but in different ways (e.g., epistasis). but additivity really doesn’t transpose very well at all, unless you mean direct dosage dependence based on allele state counts. anyway, you can say more. i don’t know what you’re really getting at.

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    • Replies: @Carl Churchill
    Well, OK. Would you say that the assumption of additivity and independent effect for genes molecular level is warranted? I ask because I agree with Hsu's argument that any variants for IQ (or such) that we find can be used to genetically engineer a phenotype of extremely high IQ. So I'm assuming that there's no problem with that molecular genetic wise, not with things like copy-number variation, epistasis, dosage dependence etc.

    So far I haven't thrown in my towel with the rare variant hypothesis, because Hsu's argument needs additive common variants with independent effect and he has cogently defended that model. So ultimately, I'm wondering why shouldn't we assume that these variants are additive on the molecular genetic level? This is not so much about explaining missing heritability, but more asking whether or not genetic engineering is possible if that weren't true.
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  30. @Razib Khan
    And why not consider additivity in the molecular genetic sense?

    i don't really have an idea what you are talking about here. molecular genetics deploys some of the same terminology as statistical genetics, but in different ways (e.g., epistasis). but additivity really doesn't transpose very well at all, unless you mean direct dosage dependence based on allele state counts. anyway, you can say more. i don't know what you're really getting at.

    Well, OK. Would you say that the assumption of additivity and independent effect for genes molecular level is warranted? I ask because I agree with Hsu’s argument that any variants for IQ (or such) that we find can be used to genetically engineer a phenotype of extremely high IQ. So I’m assuming that there’s no problem with that molecular genetic wise, not with things like copy-number variation, epistasis, dosage dependence etc.

    So far I haven’t thrown in my towel with the rare variant hypothesis, because Hsu’s argument needs additive common variants with independent effect and he has cogently defended that model. So ultimately, I’m wondering why shouldn’t we assume that these variants are additive on the molecular genetic level? This is not so much about explaining missing heritability, but more asking whether or not genetic engineering is possible if that weren’t true.

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    • Replies: @Razib Khan
    So I’m assuming that there’s no problem with that molecular genetic wise

    small effects can result in big differences when targeted. statins http://www.gnxp.com/blog/2010/02/small-genetic-effects-do-not-preclude.php

    I’m wondering why shouldn’t we assume that these variants are additive on the molecular genetic level

    i'm asking what you mean by 'additive on the molecular genetic level.' the molecular geneticists i know don't talk about additivity. so what are you talking about? it's not a rhetorical question. if i don't know what you mean i can't respond.
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  31. @Carl Churchill
    Well, OK. Would you say that the assumption of additivity and independent effect for genes molecular level is warranted? I ask because I agree with Hsu's argument that any variants for IQ (or such) that we find can be used to genetically engineer a phenotype of extremely high IQ. So I'm assuming that there's no problem with that molecular genetic wise, not with things like copy-number variation, epistasis, dosage dependence etc.

    So far I haven't thrown in my towel with the rare variant hypothesis, because Hsu's argument needs additive common variants with independent effect and he has cogently defended that model. So ultimately, I'm wondering why shouldn't we assume that these variants are additive on the molecular genetic level? This is not so much about explaining missing heritability, but more asking whether or not genetic engineering is possible if that weren't true.

    So I’m assuming that there’s no problem with that molecular genetic wise

    small effects can result in big differences when targeted. statins http://www.gnxp.com/blog/2010/02/small-genetic-effects-do-not-preclude.php

    I’m wondering why shouldn’t we assume that these variants are additive on the molecular genetic level

    i’m asking what you mean by ‘additive on the molecular genetic level.’ the molecular geneticists i know don’t talk about additivity. so what are you talking about? it’s not a rhetorical question. if i don’t know what you mean i can’t respond.

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  32. Within the context of the US segregation/apartheid system, based on its legal manipulation and ability to maintain a status quo that choose winner and losers, it is obvious if you prevent the ‘losers” from education, its access, social integration with the winners (by priviledge) will objectively lead to the winner having the tools of social adjustment as shown by IQ, employment, etc so why are IQ enthusiasts dumbfounded by the statistical outcomes. They pretend we all started at the same gate, had the same continuance/legacy of access when this was not only false but a lie. They still pretend it was fair and that is my amusement!

    No doubt that the “losers” were able to find alternative ways of success through sports, games, etc but in essence when you have men vying for sport, it is more difficult to cheat so all eyes are on the contest at hand. In the boardroom,it is easier to pretend and pull off the con despite the changes in the present societal direction.

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    • Replies: @Razib Khan
    be clearer in the future. i have a hard time understanding what you're trying to say (or, more precisely, if what you are trying to say is as simple as it seems to me, say it more concisely; if it's more subtle, then be clearer).
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  33. @jack shindo
    Within the context of the US segregation/apartheid system, based on its legal manipulation and ability to maintain a status quo that choose winner and losers, it is obvious if you prevent the 'losers" from education, its access, social integration with the winners (by priviledge) will objectively lead to the winner having the tools of social adjustment as shown by IQ, employment, etc so why are IQ enthusiasts dumbfounded by the statistical outcomes. They pretend we all started at the same gate, had the same continuance/legacy of access when this was not only false but a lie. They still pretend it was fair and that is my amusement!

    No doubt that the "losers" were able to find alternative ways of success through sports, games, etc but in essence when you have men vying for sport, it is more difficult to cheat so all eyes are on the contest at hand. In the boardroom,it is easier to pretend and pull off the con despite the changes in the present societal direction.

    be clearer in the future. i have a hard time understanding what you’re trying to say (or, more precisely, if what you are trying to say is as simple as it seems to me, say it more concisely; if it’s more subtle, then be clearer).

    Read More
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